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POSTER PAPERS

International Conference on Atomic and Molecular

Data and Their Applications (ICAMDATA 97)

Wolfgang L. Wiese and Peter J. Mohr, Editors
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NIST Special Publication 926

POSTER PAPERS

International Conference on Atomic and Molecular

Data and Their Applications (ICAMDATA 97)

at the National Institute of Standards and Technology

Gaithersburg, Maryland, USA

September 29 - October 2, 1997

Wolfgang L. Wiese and Peter J. Mohr, Editors

Atomic Physics Division

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

August 1998

U.S. Department of Commerce

William M. Daley, Secretary

Technology Administration

Gary R. Bachula, Acting Under Secretary for Technology

National Institute of Standards and Technology

Raymond G. Kammer, Director
National Institute of Standards

and Technology

Special Publication 926

Natl. Inst. Stand. Technol.

Spec. Publ. 926

277 pages (Aug. 1998)

CODEN: NSPUE2

U.S. Government Printing Office

Washington: 1998

For sale by the Superintendent

of Documents

U.S. Government Printing Office

Washington, DC 20402
Sponsor

National Institute of

Standards and Technology:

Physics Laboratory

Atomic Physics Division

Standard Reference Data Program

Co-Sponsors

Electric Power Research Institute

Office of Fusion Energy Science,

Department of Energy

Institute of Theoretical Atomic and

Molecular Physics at the Harvard-Smithsonian

Center for Astrophysics

Lawrence Livermore National Laboratory

U.S. Naval Research Laboratory

SEMATECH

Office of Space Sciences,

National Aeronautics and Space Administration
Conference Committee

Dr. Wolfgang Wiese, NIST-Atomic Physics

Division, Conference Chair

Dr. Peter Mohr, NIST-Atomic Physics

Division, Conference Secretary

Dr. James Babb, Harvard- Smithsonian

Center for Astrophysics

Prof. Kurt Becker, Stevens Institute of

Technology

Dr. George Doschek, Naval Research

Laboratory

Prof. James Lawler, University of

Wisconsin

Dr. David Leckrone, NASA Goddard Space

Flight Center

Prof. Michael Pindzola, Auburn Unicersity

Prof. Anil Pradhan, Ohio State University

Dr. John Rumble, NIST-Standard

Reference Data Program

Dr. David Schultz, Oak Ridge National

Laboratory

Dr. Peter Smith, Harvard-Smithsonian

Center for Astrophysics

International Program

Committee

A. Dalgarno (USA), Chair

R. Janev (Austria), Vice-Chair

D. Schultz (USA), Treasurer

K. Berrington (N. Ireland), Secretary

L. Brown (USA)

M. Capitelli (Italy)

G. Lister (USA)

H. Mason (United Kingdom)

K. Niemax (Germany)

L. Presnyakov (Russia)

E. Roueff (France)

H. Tawara (Japan)

W. Wiese (USA)

International Advisory Board

N. Bardsley (USA)

P. Burke (N. Ireland)

R. Crompton (Australia)

J. Delcroix (France)

G. Dunn (USA)

F. Gianturco (Italy)

R. Hulse (USA)

J. Li (P.R. China)

I. Martinson (Venuzuela)

J. Rumble (USA)

E. Salzborn (Germany)

M. Seaton (United Kingdom)

I. Sobelman (Russia)

K. Takayanagi (Japan)
Foreword This Special Publication contains the poster papers presented at the first

International Conference on Atomic and Molecular Data and Their

Applications (ICAMDATA), which was convened at the National Institute

of Standards and Technology (NIST), Gaithersburg, MD from September

29 through October 2, 1997. One hundred seventy-one registered

participants from 20 countries attended the conference. In addition to the

poster papers recorded here, twenty-seven invited talks were given,

which are collected in a separate volume of proceedings [1]. Atomic and molecular (A+M) data are essential for the solution of a wide

range of problems in diverse fields of science and technology. Major

current areas of science requiring large amounts of A+M data are

astrophysics, plasma physics, atmospheric physics, and basic atomic

physics. Major current technology areas in which A+M data are an

essential input are the plasma processing of materials, the development

of lighting sources, and spectrochemistry.

The enormous variety of A+M data and the diverse data needs have

led to quite a fragmentation of this field, and a focal point has been

missing. This conference, as well as a planned future conference series, is therefore intended to serve as such a focal point, with one of its main

purposes to bring together data producers, compilers, and users in an

open forum and provide close interactions and intensive exchanges of

ideas.

The principal topics of the poster presentations were (a) the

production of collision and radiation data, both atomic and molecular,

including benchmark data; (b) the presentation and detailed description

of available atomic and molecular databases, their management and data

assessment, and (c) reviews of data needs in various user communities.

It is a pleasure to acknowledge the competent editorial assistance of

C. Marlow and R. Jocson.

Reference

[1] P. J. Mohr and W. L. Wiese, Eds. Atomic and Molecular Data and

Their Applications, AIP Conf. Proceed., 434, New York 1998

v

Contents

Databases

A Compilation of Electron-Molecule Scattering Cross Sections

M. Brunger and S. Buckman 3

Electron Interactions with Plasma Processing Gases

L. Christophorou and J. Olthoff 8

NIST Atomic Spectra Database

G. R. Dalton, R. A. Dragoset, J. R. Fuhr, D. E. Kelleher, S. A. Kotochigova,

W. C. Martin, P. J. Mohr, A. Musgrove, K. Olsen, L. Podobedova, E. B. Saloman,

J. Sugar, W. L. Wiese, C. Stern Grant, G. Eichhorn, R. L. Kelly, T. Shirai,

V. I. Azarov, A. E. Kramida, A. N. Ryabtsev, J. Blaise, J. F. Wyart 12

Atomic Database Development of Mid-to-High-Z Elements

A. Dasgupta and P. Kepple 16

GAPHYOR Data Center http://gaphyor.lpgp.u-psud.fr

J. L. Delcroix, D. Humber, and C. Leprince ....20 NIST Atomic and Molecular Databases on the World Wide Web

R. Dragoset, P. Mohr, K. Olsen, E. Saloman, G. Wiersma, and D. Zucker 24

Vibrational and Electronic Energy Levels of Polyatomic Transient Molecules

M. Jacox 28

Database for Dielectronic Recombination Rate Coefficients to the Excited

States of the Carbon Atom and Ions

T. Kato, U. Safronova, and J. Dubau 30

Critical Evaluation of Transition Probabilities of Na-Ca (Z=ll-20)

D. Kelleher and L. Podobedova 34

Database for Electron-Impact Total Ionization Cross Sections of Atoms and

Molecules

Y. K. Kim, D. Zucker, M. Ali, and M. Rudd 38

The Atomic Spectroscopy Bibliography Database of the Institute for

Spectroscopy, Troitsk

A. Kramida, A. Ryabtsev, and G. Vedeneeva 43

Atomic Data Center on PC

K. Lu, D. Baba, and R. Engleman 44

Los Alamos Opacity Web Ring

N. Magee, Jr. and R. Clark 49
TOPbase/TIPbase

C. Mendoza and C. Zeippen 53

NIFS Retrieval Display System for Atomic Data Through the WWW

I. Murakami, M. Kato, T. Kato, and NEC nifs team 57

Wavelengths of Six Times Ionized Germanium, Ge VII

L. I. Podobedova and A. N. Ryabtsev 61

The ORNL Controlled Fusion Atomic Data Center

D. Schultz, P. Kristic, F. Ownby, F. Meyer, C. Havener, M. Bannister, W. Liu,

D. Jeffery, and P. Stancil 65

The Database «SPECTR» on Spectral Projects of Atoms and Ions

I. Skobelev, A. Faenov, A. Magunov 69

The Plasma Chemistry Database

W. Trail, C. Davis, and W. Morgan 73

Development of an Atomic Spectroscopy Reference Implemented on a PC

Platform Under Windows 95

K. Visser and G. Hattingh 76

Data Needs

Absolute Infrared Intensities for: Standards and Reactive Molecules

C. Chackerian, Jr 83

NASA's Laboratory Astrophysics Program

H. Hasan and H. Thronson 88

Atomic Inputs to Calculate Radiative Forces in Stellar Models

G. Massacrier, J. F. Gonzalez, M. C. Artru, G. Michaud, J. Richer, and F. LeBlanc 92

New Electron Temperature and Density Diagnostics for Photoionized Gas

D. Savin, T. Bartsch, M. Chen, S. Kahn, D. Liedahl, J. Linkemann, A. Miiller,

S. Schippers, M. Schmitt, D. Schwalm, and A. Wolf , 96

Data Production

1 Atomic Structure and Spectroscopy

The Platinum Group Ion Project

V. Azarov, S. Churilov, R. Kildiyarova, A. Ryabtsev, A. Raassen, P. Uylings,

Y. Joshi, L. Tchang-Brillet, and J. F. Wyart 103

An Integrated Approach to Bound and Continuum States: Application to

Beryllium-like Ions

K. Berrington and J. Pelan 106

Contents
Efficient Method to Account for Correlation Effects when Generating Atomic

Parameters for Complex Atoms

P. Bogdanovich, G. Gaigalas, and Z. Rudzikas 109

Relativistic Calculations in the Arsenic Sequence: Fine-Structure Transitions

E. Charro and I. Martin 113

Atomic Database for C I from C II

J. Dubau, T. Kato, and U. I. Safronova 117

A Project for Large-Scale Stark Broadening Data Production: Ca DX and CaX T Spectral Lines

M. Dimitrijevic and S. Sahal-Brechot 121

Accurate MCHF/MCDF Transition Rates

C. Fischer, P. Jonsson, and S. Fritzsche 124

Secondly Quantized Multi-Configurational Approach for Atomic Databases

G. Gaigalas and Z. Rudzikas 128

Polarization Profile Calculations for Plasma Diagnostics

M. A. Gonzalez and M. A. Gigosos 132

Laboratory Measurements of Resonant Contributions to Fe XXIV

Line Emission

M. Gu, P. Beiersdorfer, G. Brown, S. Kahn, D. Liedahl, K. Reed, and D. Savin 137

Modeling Electromagnetic Interactions in Quantized Electronic Systems

V. L. Jacobs 141

Relativistic Oscillator Strengths in Chlorine

I. Martin, C. Lavin, and A. Velasco 145

Oscillator Strengths of Rydberg Transitions

W. Mende and M. Kock 149

Atomic Data for Lighting Applications

G. Nave, C. Sansonetti, and J. Reader 153

Investigation of the Autoionization Spectra of Samarium from

48,800 cm-1 to 51,200 cm 1 H. Park, H. C. Kim, Y. J. Rhee, and J. Lee 156

Upgrading the Atomic and Molecular Database for Astrophysics and

Atmospheric Physics by Fourier Transform Spectroscopy

J. C. Pickering, R. Schermaul, G. Cox, J. Rufus, A. P. Thorne, and R. C. M. Learner 159

Calculations of Oscillator Strengths for Singly Ionized Iron Group Elements

by Means of the Orthogonal Operator Approach

A. Raassen and P. Uylings 164

Autoionizing Rates for Excited States of Many-Electron Ions

U. I. Safranova and W. R. Johnson 167

Complete Atomic Database for Autoionizing Levels of B-like Ions with Z = 6-54

U. I. Safronova, A. S. Shlyaptseva, M. Cornille, and J. Dubau 171

Inner-shell Excitation Energies for C-, N-, 0-, and F-like Ions with Z = 6-54

U. I. Safronova and A. S. Shlyaptseva 175

Contents ix
Accurate Lifetime Measurements of Fine-Structure States of Neutral Lithium

by Beam-Gas-Laser-Spectroscopy

A. Schmitt, U. Volz, and H. Schmoranzer 179

Accurate Atomic Data for S I, S II, S III

S. Tayal 183

Precise Atomic Lifetimes Measured at a Heavy-Ion Storage Ring

E. Trabert 186

Light Ion Absorption, Probed with High Spatial, Temporal, and Spectral

Resolution: The Spectrum of C II

P. Villoresi and P. Nicolosi 190

Systematic Studies of the n=2 to n=3,4 Transitions in the Ions of Elements Cu

through As Isoelectronic with Li I through Na I Produced by Laser

Irradiation

J. F. Wyart, T. Missalla, J. C. Gauthier, and C. Chenais-Popovics 194

Self-Consistent Sets of Oscillator Strength for Ultraviolet Lines in C I, S I, and

Ni II

J. Zsargo, S. Federman, and J. Cardelli 198

2 Collisions

Electron Impact Ionization and Surface Induced Reactions of Fusion Plasma

Edge Constituents

K. Becker, F. Biasioli, G. Denifl, H. Deutsch, T. Fiegele, V. Grill, T. Mark, C. Mair,

S. Matt, D. Muigg, P. Scheier, M. Sonderegger, A. Stamatovic, and R. Worgotter 205

The Role of Electron Impact Ionization Cross Sections in

Low-Temperature Plasmas

K. Becker, V. Tarnovsky, H. Deutsch, and T. Mark 210

Atomic Data: Energy Levels, Transition Rates, and Collision Strengths;

An Example of Mg VIII

A. Bhatia 214

Collisional and Spectroscopic Data Relevant to the Fundamental Processes in

Plasmas Containing Si-Organic Admixtures

R. Foest, R. Basner, M. Schmidt, P. Kurunczi, and K. Becker 217

Measurements of the Absolute Cross Sections of Inelastic Processes for Slow

Atomic Collisions

M. Gochitashvili, B. Kikiani, and R. Lomsadze 221

Ionization, Charge Transfer, and Stripping Cross Sections for Alkali Metal Ion

Collisions with Inert Gas Atoms and H2 and N2 Molecules in the 0.5 - 7.0 keV

Energy Range

B. I. Kikiani, R. A. Lomsadze 224

Atomic Data for Recombination Calculations

R. Kisielius, P. Storey, and A. Davey 227

Contents
Unified Electron-Ion Recombination Cross Sections and Rates

S. Nahar, H. Zhang, and A. Pradhan 231

K-Matrix Correction of B, CB Cross-Sections

L. Vainshtein 235

The Iron Project (OSU): Large-Scale Computations of Atomic Data

H. Zhang, M. Bautista, S. Nahar, P. Romano, and A. Pradhan 239

3.3 Molecules

Ultraviolet Emission in the Dissociation of N2 and O2 by K

+ Impact

M. Gochitashvili, B. Kikiani, R. Kvizhinadze, and N. Jaliashvili 245

Electron Collision Cross Sections for the CF4 Molecule by

Electron Swarm Study

Y. Hayashi and Y. Nakamura 248

Inelastic Cross Sections for the C3F8 Molecule from Electron Transport

Coefficients in C3Fs-Ar Mixtures

B. H. Jeon and Y. Nakamura 252

Accurate ab initio Calculation of Molecular Constants

S. Kotochigova and I. Tupitsyn 256

Electron Collisions with Small Molecules

B. McLaughlin, C. Ballance, D. Thompson, K. Berrington, and P. Burke 260

Electron Transport Coefficients in C2F6-Ar Mixtures and Inelastic Cross

Sections for the C2F6 Molecule

H. Okumo and Y. Nakamura 265

Validation of Ozone Infrared Line Intensities

M. Smith 269

Hyperfine Structure Constants for Diatomic Molecules

I. Tupitsyn and S. Kotochigova 272

Contents xi

Databases

A Compilation of Electron-Molecule Scattering

Cross Sections

M.J. Brunger+ and S.J. Buckman*

^Department of Physics, Flinders University of South Australia

*AMPL, Australian National University, Canberra

1 Introduction

The intention of this project-is to attempt to update the critical review and cross section data

compilation of Trajmar et al. [1] to account for measurements over the past 15 years. As in the

original review the emphasis will be on both differential and integral cross section measurements

at low to intermediate energies (meV- 1000 eV) for elastic scattering, rotational, vibrational and

electronic excitation. These cross sections are of relevance in applied areas as divergent as plasma

deposition and etching of semiconductors, gaseous high voltage switches and electrostatic

precipitators for the processing of atmospheric pollutants. The active constituents in each of these

devices are typically polyatomic molecules and as such there has been a marked increase in both

experimental and theoretical studies for these complicated targets.

We will also attempt to discuss in a critical fashion the comparison between the various

experimental results and between the experimental and theoretical cross sections. However it is beyond the extent of this article, and the expertise of the authors, to offer a detailed critique of the

many theoretical approaches. We shall give a brief discussion of experimental techniques with

particular emphasis on new developments in the measurement of absolute scattering cross sections since Trajmar et al. [1] Finally we note that whilst temporary negative ion resonances

are often of great importance in low energy electron- molecule scattering the treatment of resonance dynamics is beyond the scope of this project and we will only discuss them in the

context of cross section enhancement.

2 Scope

The extent of the review article is perhaps best illustrated by its table of contents, as given below:

1. Introduction

2. Experimental Techniques - Recent Developments

2.1 High resolution sources

2.2 Single collision experiments

2.3 Swarm experiments

2.4 Parallel detection techniques

2.5 Sources of excited species

2.6 Normalisation techniques

2.7 Techniques for the generation

of integral cross sections

3. Experimental Data - Diatomic

Molecules

3.1 H2 3.2 N2 3.3 02

3.4 Halogens

3.5 CO

3.6 NO

3.7 Hydrogen Halides

3.8 Alkali Halides

1 Databases 3
4.

3.9 Cross section trends amongst

diatomic molecules.

Experimental Data - Polyatomic Molecules

4.11

4.12

4.13

4.14

4.15

4.16

Hydrocarbons and derivatives

Silane and derivitives

Germane and derivitives

Halocarbons and derivitives

SF6 Cross section trends amongst

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

H2 0

H2S

HCN

O3

OCS

CO2

N2O

NH3

SO2

CH4

7.

8.8.1

5.

6.

polyatomic molecules

Epilogue

Summary and Suggested

Measurements

References

Appendix

Tables of cross section data

It is our intention that, subject to satisfying copyright requirements, all the cross section data

tables will be placed on the Web for viewing and downloading.

3 Status of Project

At this time we have covered about 80-85% of the topic and hope that the final sections and

editing can be completed in the next 6-9 months. The article will contain in excess of 260 tables of cross section data and over 200 figures, as well as a (hopefully) critical assessment of the cross sections for each gas. The reference list currently stands at 750, most of which is due to work that

has been generated since the original review of Trajmar et al. [1]

One of the nice things about a review such as this is that, in having an extensive database

available at your fingertips, you can start to get a picture for any trends in the cross sections for a given molecule, or across different molecular species, and for any gaps (either experimental or

theoretical) in the literature. This in turn allows one to form an opinion as to where it might be

profitable to conduct new experiments or perform new calculations in the future.

We now examine just two of these areas, both of which we believe are illustrative of some very

interesting physics.

5 Cross Section Trends Across Molecules

In the graphs in Fig. 1, we show the results of some elastic differential cross section (DCS)

measurements for electron scattering from N2, CO, O2, NO, and CO2. All the illustrated data were measured at the Australian National University (ANU) with a crossed beam apparatus and

employed the relative flow technique [2] to set the absolute scale.

4 Highlights

4 ICAMDATA 97 Proceedings
Figure 1: Elastic differential cross section (DCS) measurements for electron scattering from N2,

CO, O2, NO and CO2. See text for explanation.

For each of these molecules we observe an interesting behavior in the elastic DCS at forward

angles. This occurs at energies above the shape resonance in each molecule but below about 10

eV. This behavior appears to be associated with those systems that possess a strong, low energy

shape resonance. Where the resonances are at relatively low energy and are "sharp", e.g. O2 and

NO, the DCS at low energy (~ 1 eV) dips strongly at forward scattering angles. It then passes

through a transition from weak forward scattering to a forward-peaked DCS in the energy region

4-7 eV. In the other systems (N2, CO, CO2), which all have a broad shape resonance that peaks

between 2-4 eV, the DCS in the resonance region are strongly forward peaked but then decrease

in magnitude at forward angles as the energy increases just above the resonance. Sun et al. [3] noted, in their calculations of N2 elastic DCS, that above the resonance, where

the rig symmetry is no longer dominant, it is essential to include higher order partial waves and

additional symmetries to reproduce the observed behavior. In the case of diatomic systems it is interesting to note that each of the above molecules possess similar dipole polarisabilities and so

it is tempting to speculate that it is this which may be responsible for the angular behavior of the

DCS. However, as it also appears that this effect is present in a class of polyatomic molecule

systems the problem is deserving of some careful theoretical attention.

1 Databases 5
6 Polyatomic Molecule Scattering Theory

Most polyatomic molecule scattering calculations have concentrated on DCS and integral cross sections (ICS) for the elastic scattering process, although some calculations for excitation of the

vibrational modes of molecules are available in the literature. In this latter case both DCS and

ICS are also typically reported. An extensive series of calculations have been performed for elastic

scattering from methane which, because of its near-spherical symmetry, has become something of a prototypical system for low energy electron-polyatomic molecule scattering calculations. A

summary of the available experimental and theoretical data for this molecule can be found in the

recent publication of Bundschu et al. [4] In Fig. 2, we show the level of agreement that has been obtained amongst experimental

groups and between theory and experiment for CH4. While we only show DCS at 1 eV and 3 eV,

the level of accord in these figures is indicative of that found up to about 5.5 eV. Note the very

good agreement between the two most recent experimental measurements [4] [5] , both of which

independently applied the relative flow technique, and between these measurements and the

calculation of Gianturco and Sanna [4].

Figure 2: Comparison of theory and experiment, for CHU at 1 eV and 3 eV. See text for explanation.

Unfortunately, this level of agreement between theory and experiment for low energy elastic

polyatomic molecule scattering is quite unique. In general, for energies less than 10 eV, one

usually finds quite poor agreement between the calculations and measurements, as we now

specifically illustrate for e' + CO2 scattering.

In the next figure, we show the situation in CO2 at energies of 1 and 5 eV. Whilst it is clear

that the level of agreement between the various experiments is only fair, the major point that we

wish to make here is the serious discrepancies between experiment and theory. Neither the

model of Takekawa and Itikawa or that of Gianturco and Stoecklin adequately reproduces the

shape or magnitude of these low energy DCS, even when additional symmetries were employed in

the latter case.

6 ICAMDATA 97 Proceedings
f t N

* // V

A.

Figure 3: Comparison of theory and experiment for CO2 at 1 eV and 5 eV. See text for explanation.

References

[1] S. Trajmar, D. F. Register, and A. Chutjian, Phys. Rep. 97, 219 (1983)

[2] J. C. Nickel, P. W. Zetner, G. Shen, and S. Trajmar, J. Phys. E 22, 730 (1989)

[3] W. Sun, M. A. Morrison, W. A. Isaacs, W. K. Trail, D. T. Alle, R. J. Gulley, M. J. Brennan, and

S. J. Buckman, Phys. Rev. A 52, 1229 (1995)

[4] C. T. Bundschu, J. C. Gibson, R. J. Gulley, M. J. Brunger, S. J. Buckman, N. Sanna, and F.

A. Gianturco, J. Phys. B 30, 2239 (1997)

[5] L. Boesten and H. Tanaka, J. Phys. B 24, 821 (1991)

[6] H. Tanaka, T. Ishikawa, T. Masai, T. Sagara, L. Boesten, M. Takekawa, Y. Itikawa, and

M. Kimura, private communication (1997)

[7] F. A. Gianturco and T. Stoecklin, J. Phys. B 29, 3933 (1996)

[8] M. Takekawa and Y. Itikawa, J. Phys. B 29, 4222 (1996)

1 Databases 7
Electron Interactions with Plasma Processing Gases

L. G. Christophorou and J. K. Olthoff

National Institute of Standards and Technology

Gaithersburg, MB 20899

1 Introduction

To assess the behavior of gases in their uses in manufacturing semiconductor devices and other

applications and to promote the modeling of these processes, it is necessary to have accurate

information on the fundamental interactions of low energy (< 100 eV) electrons with process

gases. NIST has begun the formation of a database containing fundamental electron-interaction

data for gases of interest to the plasma community. In support of this effort, we have undertaken

the assessment and evaluation of the available information on cross sections and rate coefficients

for collisional interactions of electrons with three groups of gases: those used in etching,

deposition, or cleaning (e.g., CF4, CHF3, C2F6, C3F8 CI2, and HBr), those used as buffer gases

(e.g., Ar, He), and those that are present in practical systems as impurities (e.g., O2, N2, H2O). In

this paper, we summarize our recommended data on cross sections and rate coefficients for the

gases CF4, CHF3, C2F6 and CCI2F2, based upon our assessment of available data, and indicate

specific electron-interaction data needs for these gases. The assessed data for the four gases are

available via the World Wide Web at http:/ / www.eeel.nist.gov/ 81 1 /refdata.

2 Reference Data Sets

Carbon Tetrafluoride (CF4) - Figures 1 and 2 show the assessed electron scattering cross section

data [1] and the assessed electron attachment, ionization, and effective ionization coefficients for

CF4, respectively. The data on electron scattering cross sections for CF4 are reasonably complete,

as indicated by the good agreement between the total scattering cross section and the sum of the

individual cross sections shown by the dotted line in Figure 1. The coefficient data are also of good

quality. The few data needs include the experimental determination of direct and indirect

vibrational excitation, and investigation of the apparent discrepancy between the measured cross section for dissociation into neutrals and other related cross sections (recent unpublished

measurements indicate that the experimental cross section values shown here for dissociation

into neutrals are much smaller than the true values).

Trifluoromethane (CHF3) - Figure 3 shows the meager electron scattering-cross section data [2] for this important plasma processing gas. With the possible exception of the data for total

dissociation and total ionization, the rest of the data in Figure 3 are approximate. Basic

measurements and calculations are needed for virtually all elastic and inelastic electron

scattering processes, including momentum transfer, vibrational excitation, elastic scattering,

differential scattering, and electron transport, attachment and ionization coefficients.

Confirmation is needed of the cross section for total electron scattering and total ionization

measurements. Resolution is also needed of the discrepancy between the measured cross section

for dissociation into neutrals and other related cross section data.

8 ICAMDATA 97 Proceedings
Perfluoroethane (C2F6) - Figure 4 shows the electron-interaction cross sections for this molecule

[3], although many of these are still preliminary (e.g., the cross section for momentum transfer at low energies). Only the cross sections for dissociative attachment and total dissociation are recommended, nonetheless, the cross sections in Figure 4 are the most reasonable values

presently available. Figure 5 shows our recommended data for attachment, ionization and

effective ionization coefficients for this molecule. Cross section data are needed especially for

dissociation into neutrals and vibrational and electronic excitation. Additional data are needed

for the momentum transfer, elastic integral, total ionization, and total scattering cross sections.

Dichlorodifluoromethane (Freon-12, CCI2F2) - The available cross section data [4] for the CCI2F2

molecule are shown in Figure 6. They are reasonably complete but still limited. No cross section

data exist on momentum transfer and dissociation into neutrals. Further measurements are needed of the total ionization cross section, and measurements of the elastic integral cross section over a broader energy range are indicated. The attachment, ionization and effective ionization

coefficients are satisfactory (Fig. 7).

References

[1] L. G. Christophorou, J. K. Olthoff, and M. V. V. S. Rao, J. Phys. Chem. Ref. Data 25, 1341

(1996)

[2] L. G. Christophorou, J. K. Olthoff, and M. V. V. S. Rao, J. Phys. Chem. Ref. Data 26, 1 (1997)

[3] L. G. Christophorou and J. K. Olthoff, J. Phys. Chem. Ref. Data (in press)

[4] L. G. Christophorou, J. K. Olthoff, and Y. Wang, J. Phys. Chem. Ref. Data 26, 1205 (1997)

0.01 0.1 1 10 100 1000

Electron Energy (eV)

Figure 1: Electron-interaction cross sections for CF4 [1].

1 Databases 9

4
E

o

CMb

Z

~P

i_o

40

600

80 120 160 200

E/N (10-21 Vm2

) Figure 2: Electron-interaction coefficients for CF4 [1].

E

oCVJb

c

o

o

CD

to

cooO

103

102

10 1 r

10°

10- 1

1 CHF3 10-2

1 0.01

Total Scattering

Total Dissociation -

Total Ionization ^.

Dissociation into Neutrals

0.1 10 100

Electron Energy (eV)

Figure 3: Electron-interaction cross sections for CHF3 [2].

o

CDw

COo

10'

"

E

101 o

CVJE ,0'

C

o

10- 1

O 10";

10"'

:

1 1 ""'I 1

1 1 1 '""1 '

1 " 1

1 1 1 ""!

Elastic Integral . . / Total Scattering

V\N. y Total Dissociation AT

Momentum's^ /

J Ionization

Attachment \\ !

1 '

'

0.01 0.1 1 10 100 1000

Electron Energy (eV)

Figure 4: Electron-interaction cross sections for C2F6 [3].

ICAMDATA 97 Proceedings
10c

ioCME

ob 10,-2

> 10"3 O

i io-4 ^-

10'5

:

: n/N

^

a/N

I -.80

1 ^

r 1 ^60

: i Si

: i o 40

rj |

20

: | C2F6 F o

'

1 »

rl -20

- i i

• •

•

•

•

• •

•

• •

»•

1 200 400

v21 v/^2x

200 400 600 E/N (10"21 Vm2

) E/N (10^n Vm')

Figure 5: Electron-interaction coefficients for C2F6 [3].

c

oo

CD in

inoo

10'

101

10c

10"

10-2

Total Scattering V^^^

""1 1

1 1 1 ""M !

\ "—

N Elastic Integral

t1 •-^ '

r \ // Total Ionization

/

'-

Direct Vibrational

CCI2 F2

, ..1 , . .

\J \ Total Attachment

••1 1 1

' li.nl . . . . mil , 1 1 1 mh

0.01 0.1 10 100 1000

Electron Energy (eV)

Figure 6: Electron-interaction cross sections for CCI2F2 [4].

CCI2F2 200 400 600 800 E/N (10"21 Vm2

)

200 1000 4000

E/N (IO-21 Vm2

) Figure 7: Electron-interaction coefficients for CCI2F2 [4].

1 Databases 11
NIST Atomic Spectra Database

G. R. Dalton, R. A. Dragoset, J. R. Fuhr, D. E. Kelleher, S. A. Kotochigova,

W. C. Martin, P. J. Mohr, A. Musgrove, K. Olsen, L. Podobedova,

E. B. Saloman, J. Sugar, W. L. Wiese

NIST, Gaithersburg, MD

C. Stern Grant, G. Eichhorn

Center for Astrophysics, Cambridge, MA

R. L. Kelly

Naval Postgraduate School, Monterey, CA

T. Shirai

JAERI, Tokai-mura, Japan

V. I. Azarov, A. E. Kramida, A. N. Ryabtsev

Institute for Spectroscopy, Troitsk, Russia

J. Blaise, J. F. Wyart

CNRS, Orsay, France

Version 1 of the NIST Atomic Spectra Database became available online as an interactive

Web server in 1995. It is accessible at the NIST Physics Laboratory Web site (physics.nist.gov,

select Physical Reference Data). Version 1 has data on atomic energy levels for some 500 spectra,

transition probability data for spectra of the iron-group elements, and comprehensive wavelength

data for spectra of several elements. It includes no data for one or more of these three types of

data for many important spectra, however.

Pending new critical compilations of the most needed data, we are extending the database

by editing and adding data from earlier NIST compilations, selected non-NIST compilations, and

selected recent publications or unpublished material. The new Version 2 (hereafter referred to as "ASD") contains significantly more data on atomic and ionic transitions and energy levels. It should be available on the Web within a few months. ASD has data for about 950 spectra, with

about 70,000 energy levels and 90,000 lines, 40,000 of which have transition probabilities.

The data available in both Versions 1 and 2 are indicated according to spectrum in Figures 1,

2, and 3. The additional energy level data in Version 2 (Fig. 1) are largely taken from material

compiled by R. L. Kelly in connection with his wavelength tables [1]. The additional transition

probability data (Fig. 2) include new NIST compilations for the C, N, and O spectra [2], and data

from other, mostly earlier, NIST compilations [3, 4, 5, 6]. In addition to wavelengths compiled in

connection with transition probability data, extensive wavelength data for the first five spectra of

many elements are included from the tables of Reader et al. [7] (Fig. 3). Version 2 thus has energy level data for most spectra of H through Kr (Z=l-36), Mo (Z=42),

and for 65 spectra of the rare-earth elements La through Lu (Z=57—71). Wavelengths of observed

12 ICAMDATA 97 Proceedings
z

Ha

Be

5 Co

10 NoMg

Sis

Ar 20 Cb

TlCr

Energy Levels

15

iWSSSSSSSSSSSSSSSS nsKosnsnsii

'//////////////////i

SSSSS5SSSS >. . s -\.~

HI Version 2

Charge Figure 1: Holdings of energy-level data in Versions 1 and 2 of the NIST Atomic Spectra Database.

Transition Probabilities z

He HU

Be 5 B

C

N O

F

10 Ne

Na Mg

Si

Al

15 P S

CI Ar K

20 Ca

Sc

Ti V

Cr 25 Mn

Fe Co

Ni 29 Cu 1

92 u

Y////////////777Z\

0

}

~V7A 0

X I

fe

A

I for Cu (Z=29) through U (2=92), some neutral

' and singly Ionized atoms are Included.

10 15 Charge

20

I 25

Figure 2: Holdings of transition-probability data in Versions 1 and 2 of the NIST Atomic Spectra Database.

1 Databases 13
Wavelengths

z

*» co

10 NeMg

SiS

Ar 20 Co

TlCr

Fa

Nl 30 2nGe

So

Kr

Sr 40 *

Mo

43%

15

25

35

Version 1

Version 2

mm

//////////////<»

///// ^"mmws^wmsssss^^ wszxnmmmmmmmmmmmmrnrnm

mwsMWAmmmmmmmmmmmmmmmm

'/////.

99 Es

, for Tc (Z=43) through Es (Z=9S), neutral through

J quadruply ionized atoms are mostly included.

1 1 1———i r

- 1

10 15 20 25 35 40 Charge

Figure 3: Holdings of wavelength data in Versions 1 and 2 of the NIST Atomic Spectra Database.

transitions are included for 99 elements. Energy-level classifications and transition probabilities are included for the lines of most spectra of H through Ni (Z=l—28). Comprehensive lists of

observed wavelengths with classifications based on critically compiled level data are available for some elements, including all spectra of Mg, Al, S, and Sc. Wavelengths without level classifications are included for prominent lines of up to the first five spectra of Cu through Es (Z=29—99), with

selected transition probabilities for the first two spectra. Several extensive data sets from recent NIST compilations are being prepared for inclusion in the database during the next year. The two broad categories of queries handled by ASD are for data on energy levels and for data on spectral lines. The data are displayed in formats similar to those in NIST print publications

of atomic spectroscopic data. In addition to graphical user interface format, users can choose

output in an ASCII form easily read by spread-sheet software. ASD offers a range of user-specified

options and selection criteria, each with its own default. For example, for transition strengths one may choose to search or display any combination of transition probability, oscillator strength, line

strength, \og(gf), and relative intensity. One may also choose from a variety of units and selection

criteria on transition-strength accuracy and properties of energy levels. Outputs for transitions

may be ordered by wavelength or by multiplets for a particular spectrum.

The database search programs for ASD are written in ANSI C and are thus portable to any

environment, including PC's and UNIX-based machines. Only the graphical user interface for input/output is platform-specific. ASD comes with a built-in character-based interface, which itself

is platform independent, and thus facilitates its inclusion in other character-based environments

such as ALADDIN. In addition to the Web version, a PC version with a Windows interface will be

made available on diskettes for purchase. This will replace the currently available DOS version.

14 ICAMDATA 97 Proceedings
Acknowledgements

We gratefully acknowledge partial funding of work on this database by the U.S. Department of

Energy, Office of Fusion Energy Sciences, and by the UV, Visible and Gravitational Astrophysics

Division of NASA. We also appreciate support under a Collaborative Research Grant, CRG 930793,

from NATO.

References

[1] R. L. Kelly, "Atomic and Ionic Spectrum Lines Below 2000 A: Hydrogen through Krypton,"

J. Phys. Chem. Ref. Data 16, Supplement 1 (1987)

[2] W. L. Wiese, J. R. Fuhr, and T. M. Deters, "Atomic Transition Probabilities of Carbon,

Nitrogen, and Oxygen," J. Phys. Chem. Ref. Data Monograph 7 (1996)

[3] W. L. Wiese, M. W. Smith, and B. M. Glennon, "Atomic Transition Probabilities (H through

Ne-A Critical Data Compilation," Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. (U.S.) 4, Vol. I (1966)

[4] W. L. Wiese, M. W. Smith, and B. M. Miles, "Atomic Transition Probabilities (Na through

Ca-A Critical Data Compilation," Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. (U.S.) 22,

Vol. II (1969)

[5] NIST Atomic Transition Probability Tables, J. R. Fuhr and W. L. Wiese, in "CRC Handbook

of Chemistry and Physics," 77th Edition, D. R. Lide, ed., p. 10-128 - 10-186, CRC Press, Boca

Raton, FL 1996

[6] Atomic Spectroscopy, W. C. Martin and W. L. Wiese, in "Atomic, Molecular, and Optical

Physics Handbook," G. W. F. Drake, ed., Ch. 10, p. 135-153, AIP Press, New York 1996

[7] J. Reader, C. H. Corliss, W. L. Wiese, and G. A. Martin, "Wavelengths and Transition Probabilities for Atoms and Atomic Ions, Part I. Wavelengths, Part II. Transition Probabilities,"

Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. (U.S.) 68 (1980)

1 Databases 15
Atomic Database Development of

Mid-to-High-Z Elements

Arati Dasgupta and Paul C. Kepple

Radiation Hydrodynamics Branch, Plasma Physics Division,

Naval Research Laboratory, Washington, DC 20375

1 Introduction

Detailed atomic databases are needed for some applications, such as in hydrodynamics codes for

plasma diagnostics and analysis of x-ray spectra. For plasma diagnostics requiring data for many

ionization stages with many fine-structure levels, atomic models developed using very complex

calculations have limitations. Again, for accurate diagnostics, a detailed level accounting cannot

be simplified by an averaging process such as used in the average atom model, which will inhibit

all the important and relevant radiation dynamics. To include a large number of states with a minimum of computational effort, we have developed atomic models where many of the multiplet

levels are lumped into the configuration states, but the important low-lying states are kept at fine

structure levels and they are connected by the relevant atomic processes to allow detailed analysis

of diagnostically important emission processes.

This model for F-like and Ne-like stages has already been used for diagnosing[l] selenium plas- mas. In the present work we use this model to calculate databases for all L- and M-shell ionization

stages of titanium. Currently, z-pinch experiments are being performed using titanium wires producing x-ray emission with very high yields. Titanium is also an important element in tokamak

discharges for fusion research. Our complete database will include both radiative and collisional

data, including dielectronic recombination (DR) connecting all the levels for all the ion stages.

However, we will present here only partial data for Ti XIX and Ti XX.

Effectiveness of this method will be evaluated by comparing our results with other published

calculations, and these theoretical methods used to calculate the data for all important processes

when properly benchmarked by measurements can provide adequate data.

2 Atomic Model

For the Ti XIX and TI XX ion stages we have kept all the n=2 and 3 fine structure levels while

the higher lying excited levels are lumped in our model. The Ti XX model consists of 10 levels including the ground level, two An=0 2p excited state, 5 fine structure levels of the n—3 manifold, one lumped n=4 level and one lumped level of n—5, 6, and 7 excited states. The Ti XIX model

contains 25 levels including the ground state, fine structure levels of 9 n=2 and 10 n=3 excited

states, 3 lumped inner-shell excited configurations of 2p3Z, one lumped n=4 level and one lumped

level of n=5,6, and 7 states. All the excited levels are fully coupled to the ground states and among

themselves for each ion. Table 1 lists the energy level designations and energies of these levels. The atomic structure data such as the energies and radiative transition probabilities for the fine- structure levels are calculated using the DFW atomic code of Sampson et al.[2]. For the lumped n=3

states, these structure data are obtained using the HFR (Hartree-Fock with Relativistic corrections)

method of Cowan[3]. These radiative transition rates from the excited levels to the ground states

16 1CAMDATA 97 Proceedings
for Ti XX and XIX are also included in Table 1. Our level energies and transition probabilities

agree very well with other state-of-the-art calculations.

For dipole allowed transitions, collisional data are obtained using the Semiclassical Impact

Parameter (SCIP) method[4] and for other transitions, the Coulomb Born Distorted Wave (CBDW)

method[5] is used to calculate collisional data coupling the levels in our model. For diagnostically

important transitions when either the SCIP or the CBDW methods are inadequate, collisional data

are obtained using a suite of more sophisticated fully relativistic atomic structure and distorted wave (RDW) codes [2, 6]. Collision strengths for some of the transitions for Ti XX and Ti XIX are shown

in Tables 2 and 3 and they are compared to those obtained using another DW calculation[7] . Our

collisional excitation data will be updated by including resonance excitation in the future. Electronimpact ionization cross sections are calculated by the exchange classical impact-parameter method.

Again, for important transitions the ionization cross sections are replaced by those calculated using

the RDW ionization codes of Ref. [8]. The ground to ground DR rates can be approximated by the semi-empirical formulas derived

by Burgess and modified by Merts, Cowan, and Magee (BM)[9]. However for ions of interest, more

accurate and detailed state-specific DR data are obtained using the HFR method of Cowan[3]. DR

data such as autoionization rates and DR branching ratios from the ground and An = 0 states of the recombining ion to each specific fine structure level of the recombined ions are calculated.

For low lying doubly-excited states, DR branching ratios are explicitly calculated, while for higher

Rydberg states, we used a 1/n3 falloff extrapolation of the DR branching ratios. The DR rates for

Ti XX and TI XIX are shown in Table 4. Our total ground-to-ground DR rates for Ti XX agree

very well with those obtained by Chen using a multi-configuration Dirac-Fock calculation[10].

References

[1] A. Dasgupta, K. G. Whitney, H. L. Zhang, and D. H. Sampson, Phys. Rev. £55, 3460 (1997)

[2] D. H. Sampson, H. L. Zhang, A. K. Mohanty, and R. E. H. Clark, Phys. Rev. A 40, 604 (1989)

[3] Atomic Structure Code of R. D. Cowan, "The Theory of Atomic Structure and Spectra",

University of California Press, Berkeley, CA 1981

[4] E. Oran and J. Davis, J. Appl. Phys. 45, 2480 (1974)

[5] J. Davis, P. C. Kepple, and M. Blaha, J. Quant. Spectrosc. Radiat. Transfer 16, 1043 (1977)

[6] H. L. Zhang, D. H. Sampson, and A. K. Mohanty, Phys. Rev. A 40, 616 (1989); D. H. Sampson,

H. L. Zhang, and C. J. Fontes, At. Data Nucl. Data Tables 48, 25 (1991); H. L. Zhang and D.

H. Sampson, Phys. Rev. A 47, 208 (1993)

[7] R. E. H. Clark, J. Abdallah, Jr., G. Csanak, J. B. Mann, and R. D. Cowan, Theoretical Atomic

Physics Code Development I. ACE: Another Collisional Excitation Code, Los Alamos National

Laboratory manual (December 1988)

[8] H. L. Zhang and D. H. Sampson, Phys. Rev. A 42, 5378 (1990); D. H. Sampson and H. L. Zhang, Phys. Rev. A 45, 1657 (1992)

[9] A. Burgess, Astrophys. J. 141, 1589 (1965); A. L. Merts, R. D. Cowan, and N. M. Magee, Jr., Los Alamos Scientific Laboratory Report No. LA-6220-MS, 1976 (unpublished)

[10] M. H. Chen, Phys. Rev. A 33, 994 (1986)

1 Databases 17
Table 1: Level identifications, state designations, energies and radiative decay rates to the ground

levels for Ti XX and Ti XIX.

Ti XX Ti XIX

level state Eng (eV) A

r (s- 1 ) level state Eng (eV) Ar (s" 1

) 1 ls'

2 2s 2Sl/2 0.0 1 U'2s' % 0.0

2 ls2 2p 2P°

/2 4.0287[1] 1.466[9] 2 ls2 2s2p 3P0

° 3.5842(1]

3 l*2 2p

2i£

/2 4.7966[1] 2.504[9] 3 ls2 2s2p 3Pf 3.7888[1] 1.274(7]

4 ls2 3s 2Sl/2 8.0163(2] 4 ls2 2s2p 3P2

°

ls2 2s2p ^Pf

4.3145(1]

5 ls2 3p

2 y P°

1/2/9 8.1276 2L J 3.558T12] L J 5 7.4791 1

L J 1.408(10] L J 6 ls2 3» 2PS,n 8.1504[2] 3.473[12] 6 ls2 2p2 3P0 9.6645[1]

7 IS OU U%/2 8 1Q2fU2l 71 ls2 2p2 3PX

1 0018T21

0o is oa i/5/2 0. iyyo [zj Q0 16 Zp ^2 l.UO 1 UIZJ 0y

1 o2/|7 IS 4t 1.U001 [oj z.yzo[iij Qy

1 c29„2 lo IS zp X/2 i.iouy[zj

1U is 01 — (I l.Z00o[0j 1 n1U

1

1

1

1

11 9L

is zp 00

IS ZSOS u\

1

c

2 9„q„ lc

1 QftQ4T9l i.«3oy^t[zj

1 .OOUU[ZJ

7 7404 T91

1 3 1 <? 2 9 t? Q„ 3po

1 q2 9 c 3ti 3P°

1 « 2 9 C! Q r) 3po

1 ^290^ 3po

7 8239 T21

1 4 7 897QI91 4 n?3fi 11 10 7 8447 [91

11 fiu 7/ .OUOO RfiR<ir9l 1 ZfJ

1 7 1 <? 2 2s3rf 3Di 7 9349 T21 18 ls2 2s3d 3L>2 7.9369(2]

19 ls2 2s3d 3D3 7.9407(2]

20 ls2 2s3d 3£>2 8.0075 [2] 21 ls2 2p3s 8.0981 [2] 1.421(10]

22 ls2 2p3p 8.2513(2]

23 ls2 2p3d 8.3612(2] 2.604(10]

24 ls2 2s4/ 1.0312(3] 1.261(11]

25 ls2 2s5Z - 71 1.1967(3] 1.807(10]

Table 2: Collision strengths for some of the n=2-2 transitions in Ti XIX.

Transition Transition Energy(eV) E/Eth This Work Ref. [7] 2s2 ^ - 2s2p lP 6.793(2] 1.05 4.27[-l] 4.28 [-1] 3.47 4.84(-l] 4.82[-l]

6.38 5.46[-l] 5.22[-l]

9.85 6.04[-l] 5.62(-l]

14.0 6.55[-l] 6.06[-l]

2s2p lP - 2p2 lD 4.413(2] 1.05 8.47[-l] 9.55[-l]

3.47 9.58[-l] 1.04

6.38 1.08 1.10

9.85 1.19 1.18

14.0 1.29 1.27

2s'

1 lS - 2s2p 3P0 3.548(2] 1.04 1.831-3] 2.07[-3]

1.64 1.76[-3] 2.03(-3]

4.04 1.63[-3] 1.88(-3]

9.04 1.39[-3] 1.60[-3]

18 ICAMDATA 97 Proceedings
Table 3: Collision strengths for some of the n=2-2,3 transitions in Ti XX.

Transition Transition Energy(eV) E/Eth This Work Ref. [7] 2s 2S - 2p

2P1/2 4.036[2] 1.05 1.93 [-1] 2.16[-1]

3.47 2.17[-1] 2.34[-l]

6.38 2.42[-l] 2.46[-l]

14.0 2.92 [-1] 2.79[-l]

2s 2S - 2p

2P3/2 4.793[2] 1.05 3.80[-l] 4.20[-l]

3.47 4.28 [-1] 4.57[-l]

6.38 4.79 [-1] 4.82[-l]

14.0 5.76[-l] 5.50[-l]

2s 2S - 3d 2D3/2 8.201 [3] 1.30 1.98[-2] 2.43 [-2] 2.20 2.28 [-2] 2.84[-2]

4.00 2.59 [-2] 3.37[-2]

9.00 2. 84 [-2] 3.91[-2]

Table 4: Dielectronic recombination rate coefficients (in 10 11 cm3 /sec) from the ground state of

Ti XXI and the ground and An = 0 levels of Ti XX.

Ti XXI Ti XX

T This calc. Ref. [10] ls2 2s 2S ls2 2p

'lP

(keV) An = 0 An = 1 0.02 14.9 1.44(-4) 9.91(-4)

0.04 8.26 1.72(-2) 5.00(-2)

0.06 5.33 6.79(-2) 1.49(-1)

0.08 3.79 1.28(-1) 2.47(-l)

0.10 2.87 1.92(-1) 3.42(-l)

0.20 3.79(-7) 3.57(-7) 1.14 5.22(-l) 7.91(-1)

0.30 5.50(-5) 5.25(-5) 6.43(-l) 7.11(-1) 1.01

0.50 2.50(-3) 2.41(-3) 3.08(-l) 7.43(-l) 9.95(-l)

1.00 3.26(-2) 3.20(-2) 1.12(-1) 4.99(-l) 6.41(-1)

2.00 7.61 (-2) 7.40(-2) 3.99(-2) 2.46(-l) 3.09(-l)

3.00 7.88(-2) 7.71(-2)

4.00 7.08(-2) 6.91(-2) 1.42(-2) 1.03(-1) 1.28(-1)

5.00 6.16(-2) 6.07(-2)

6.00 5.34(-2) 5.15(-2)

8.00 4.09(-2) 3.93(-2)

10.00 3.22(-2) 3.11(-2) 3.61(-3) 2.88(-2) 3.55(-2)

1 Databases 19
GAPHYOR Data Center

http://gaphyor.lpgp.u-psud.fr

Jean-Loup Delcroix, Denis Humbert, Claudette Leprince

delcroix@supelec.fr, gaphyor@lpgp.u-psud.fr

Universite Paris-Sud, Orsay

The GAPHYOR Data Center produces a Database on the properties of atoms, molecules and

neutral or ionized gases, including Chemical Reactions, with about 500,000 entries.

1 Structure of a GAPHYOR record

The structure of a GAPHYOR entry was originally conceived to describe collisions/reactions in

gases. It now describes also simpler (energy levels, ...) or more complex (gas-surface interactions,

clusters, ...) phenomena. Every GAPHYOR entry includes the following fields: /se/Ml,M2,M3/pr/M4,M5,M6/

/info/enva/val/rem/

/an/jo,vo,page/aul,au2,...aul0/nastci/

2 Initial and Final state: Ml M2 M3 - M5 M6 M7

Atomic and molecular reactants: /n form ix/s/

• form Chemical formula: Example /H1C3N102/

.

1 to 4 elements, no more than 8 atoms in the molecule.

• i Index of ionization, x Index of excitation, s Index of internal structure.

• n Multiplicity of the Reactant (e.g. 2 H atoms in initial state).

Electrons, photons, fields, particles.

Special Reactants:

• Iso-electronic series. Example: Aa(He)Z(02 — 12)

• Clusters. Examples: He(H20)3/+, (C)60

• Surface reactants (solid/liquid wails, adsorbed atoms/molecules).

20 ICAMDATA 97 Proceedings
3 Sections SE and Processes PR

GAPHYOR is a "broad band" Database organized into 5 Sections:

• 1 Properties of isolated atoms and molecules

• 2 Photonic Collisions

• 3 Electronic Collisions

• 4 Collisions between atoms or molecules

• 5 Macroscopic properties of Gases

Struct. hv coll. e coll. At.mol.coll. Mac.prop. E

Fact.Data 267178 26941 29743 124753 32006 480621

Num.Data 6642 347 1650 9010 734 18383

E 272730 27244 30810 132107 32642 495533

Table 1: Statistics of Data (June 15th, 1997)

The list of Processes (PR) included in every Section (SE) is given in Appendix 1.

4 Additional information INFO

• Type of Data: S Total and transport cross sections, R Reaction rate constants, ...

• Nature of Data: T Theoretical data, E Experimental data, ...

• Energy domains: L Thermal, J Medium, H High energies

• Special information: 8 Clusters, / Gas-surface interactions, ...

5 Numerical Data

• ENVA gives the energy, or energy range covered by the Data. Example: 10 - 50 - 100 eV

• VAL gives the values them-selves (cross-sections, . .

. ). Example: 3.5 - 12.2 - 6.4 E-16 cm2

• REM gives additional information (e.g. spectroscopic notations).

Note that the general idea is to give simple information (eg. lifetimes, reaction rates), or some

orders of magnitude.

6 Internet server

GAPHYOR WWW server is now well developed and user-friendly. Its main features are:

• Query forms. Two query forms (simple and advanced search) are offered.

• Intermediate report. This gives a sketch of the first results of a search and offers some

specific additional choices to the user.

1 Databases 21
• Data displays. Two displays are offered: a full display of all the found entries (possibly

selecting the most recent ones), or, for large Data sets, a tabular display obtained by downloading a postscript file, which can then be printed locally.

Simplified statistics on User Locations are shown below.

na data sets org.na data sets

fr 6098 u-psud.fr 1099

?? 2293 uni-heidelberg.de 857

de 1194 cnrs-imn.fr 597

ru 1151 univ-lillel.fr 580

us 993 cea.fr 535

JP 530 onera.fr 337

S 14 885 14 885

Table 2: Nations and Organizations using GAPHYOR

7 GAPHYOR Handbook

GAPHYOR is going to publish a new (fully redesigned) version of the HANDBOOK. The Volumes

will be grouped in two Series:

• Chemical Volumes (17) describing the properties of a given group of Chemical systems.

• Thematic Volumes (9) describing a given group of Processes for ail Chemical Systems.

The publication timing will be a function of the various orders from users for one or several specific

Volumes. The sizes are small, so as to make it easy for every user to order only the Volumes

covering their own field of interest.

The orders (see form in the Web) will be satisfied within a period of one month after receipt of

payment.

Chemical Volumes Selection Pages Price $

C01 Hydrogen,Deuterium,Tritium

C02 H + Noble Gases (He,Ne,Ar,Kr,Xe,Rn) + .. COS H + Mono-,bi- and trivalent elements + .. C04 H + Carbon/Titanium Groups + .. see List in the Web

C17 Surfaces/Clusters

62% 130 12

72% 130 12

60% 130 12

48% 410 30

52% 130 12

Thematic Volumes

TOO Cross Sections/Reaction Rates (Numerical values) see List in the Web

T30 Electronic Collisions (Section 3)

T50 Macro.Prop. of Gases (Section 5: Transport coefficients,..)

100% 110 10

62% 210 18

58% 210 15

E 4640 321

Table 3: Handbook Volumes

22 1CAMDATA 97 Proceedings
8 Appendix 1

Section 1. Structure

EN Energy levels , wave functions

EA Unstable energy levels EI Energy of isomerization

VR Potentiel curves, structure of molecules

DP Dipolar moments

PE Electric (or magnetic) polarizability

TR Radiative transition (probability,. .

.

)

IN Autoionization

DT Autodetachment

Section 2. Photonic collisions

SN Effective absorption, total diffusion

AN True absorption

SC Angular diffusion (scattering)

EL Elastic diffusion (Thomson, Rayleigh)

DO Depolarization, Change of polarization

EX Photoexcitation

ER Emission of line DX Photodeexcitation (stimulated emission)

FF Free-free absorption(inv. bremsstrahlung)

IN Photoionization

IM Creation of an ion pair (positive-negative)

DT Photodetachment

DS Photodissociation

EE Photoemission of electrons (ions) by solids

Section 3. Electronic Collisions

SN Total cross sections

SM Transport cross sections (momentum, ...) EL Elastic collision DO Depolarization, Change of polarization

EX Excitation

DX Deexcitation

BS Bremsstrahlung

IN Ionization

IM Creation of an ion pair (positive-negative)

DT Detachment

AT Attachment

RR Radiative recombination

RD Dielectronic recombination

RE e-e-i recombination

RO e-i-o recombination

RS Dissociative recombination

DS Dissociation DG Desorption

EE Emission of electrons by a solid PU Emission of neutrals or ions by solids (sputtering)

Section 4. Atom./mol. Coll. (and Reactions)

EN Energy or enthalpy of reaction

KE Constant of chemical equilibrium

SN Total cross sections

SM Transport cross sections (momentum, ...) SC Angular diffusion (scattering)

SP Stopping power

EL Elastic collision DO Depolarization, change of polarization

EX Excitation

DX Deexcitation (quenching)

TE Excitation transfer IN Ionization

IM Creation of an ion pair (positive-negative)

DT Detachment

TI Ionizing charge transfer PJ Recombination ion-ion CX Charge transfer XD Dissociative charge transfer CA Capture of electrons SR Loss of electrons (stripping)

DS Dissociation

IR Interchange reaction (of one or several atoms) IA Associative interchange reaction ID Dissociative interchange reaction AS Association

DG Desorption

AD Adsorption

EE Emission of electrons by a solid PU Emission of neutrals or ions by solids (sputtering)

Section 5. Macroscopic properties

ST Statistics of levels FT Thermodynamic functions

PV Compressibility, equation of state PE Dielectric and magnetic constants DN Diffusion

VI Viscosity

CT Thermal conductivity

LW Line broadening and shift (collisional effects) PI First coefficient of Townsend

DT Detachment

AT Attachment

FE Distribution function of electrons ME Mobility of electrons CE Electrical conductivity

DE Diffusion of electrons MD Characteristic temperature of electrons (D//z)

PC Power delivered by electron-neutral collisions FI Distribution function of ions

MI Mobility of ions DI Diffusion of ions DA Ambipolar diffusion

Remark This list is slightly simplified (see the Web)

1 Databases 23
NIST Atomic and Molecular Databases

on the World Wide Web

R. A. Dragoset, P. J. Mohr, K. J. Olsen, E. B. Saloman, G. Wiersma, D. S. Zucker

National Institute of Standards and Technology

Office of Electronic Commerce in Scientific and Engineering Data

Gaithersburg, MD 20899

The Physics Laboratory of the National Institute of Standards and Technology is using the World

Wide Web to disseminate the physical reference data it has been producing and/or evaluating.

Each Web database developed has an interface specially designed for its user community. The

databases currently available are: 1) CODATA Recommended Values of the Fundamental

Physical Constants; 2) Fundamental Constants Bibliographic Database; 3) Atomic Spectroscopic

Database; 4) Platinum Lamp Spectrum, 113 nm to 443 nm; 5) Bibliographic Database of Atomic

Transition Probabilities; 6) Infrared Spectrometer Calibration Tables; 7) Rest Frequencies for

Observed Interstellar Microwave Transitions; 8) Electron-Impact Ionization Cross Section

Database; 9) Tables of X-ray Mass Attenuation Coefficients; 10) Bibliographic Database of X-ray

Attenuation Coefficient Measurements; 11) X-Ray Form Factor, Attenuation, and Scattering

Tabulation; 12) Radionuclide Half-Life Measurements Made at NIST; and 13) Atomic Model Data

for Electronic Structure Calculations. The Web versions of these databases represent the work of

many people —from the compilers and evaluators of the data to the designers and programmers

of the web interfaces. Work continues to add new databases and to improve those currently

provided. The databases may be obtained from the Web at the URL http://physics.nist.gov/ by

selecting the link Physical Reference Data.

The 13 databases currently on the Web are divided into seven categories:

1 Physical Constants, Units, and Measurement Uncertainty

Fundamental Physical Constants

by E. Richard Cohen and Barry N. Taylor

This database gives values of the basic constants and conversion factors of physics and chemistry

resulting from the 1986 least-squares adjustment of the fundamental physical constants as published by the CODATA Task Group on Fundamental Constants and recommended for

international use by CODATA.

Fundamental Constants Bibliographic Database

by Peter J. Mohr and Barry N. Taylor

This searchable database gives the citations for the most important theoretical and experimental

publications relevant to the fundamental physical constants and closely related precision

measurements published since the mid 1980s. Earlier papers of particular interest are also

included. The database is regularly updated through the addition of papers from the current

literature and made more comprehensive through the addition of earlier papers.

24 ICAMDATA 97 Proceedings
2 Atomic Spectroscopic Data

Atomic Spectroscopic Database

by J. R. Fuhr, W. C. Martin, A. Musgrove, J. Sugar, and W. L. Wiese

This database includes most of the existing critically evaluated NIST data on atomic energy

levels, transition probabilities, and wavelengths that are reasonably up-to-date. This interactive

database has energy level data for over 500 spectra, transition probabilities for Sc through Ni, and

wavelength data for spectra of several elements.

Spectrum of Platinum Lamp for Ultraviolet Spectrograph Calibration

by J. E. Sansonetti, J. Reader, C. J. Sansonetti, and N. Acquista

An atlas of the spectrum of a platinum/neon hollow-cathode reference lamp in the region 1130 A

to 4330 A is given, with the spectral lines marked and their intensities, wavelengths, and

classifications listed. Graphical figures of the spectrum are included.

Bibliographic Database on Atomic Transition Probabilities

by J. R. Fuhr and H. R. Felrice

This interactive database contains references on atomic transition probabilities (oscillator

strengths, line strengths, and radiative lifetimes). Both theoretical and experimental papers are

listed.

3 Molecular Spectroscopic Data

Wavenumber Tables for Calibration of Infrared Spectrometers

by Arthur G. Maki and Joseph S. Wells

This database is an atlas of molecular spectra and associated tables of wavenumbers from

heterodyne frequency measurements for the calibration of infrared spectrometers. Five molecules

are included in the atlas: CO, OCS, N2 0, NO, and CS2. The spectra cover the 488 cm 1 to 3120 cm 1 and 4000 cm 1 to 4400 cm1 regions.

Frequencies for Interstellar Molecular Microwave Transitions

by Frank J. Lovas

This database contains critically evaluated transition frequencies for molecular transitions

detected in interstellar and circumstellar clouds recommended by NIST for reference in future

astronomical observations in the microwave and millimeter wavelength regions.

1 Databases 25
4 Ionization Data

Electron-Impact Ionization Cross Section Database

by Y.-K. Kim and M. E. Rudd

This is a database of total ionization cross sections of various molecules by electron impact. The

cross sections were calculated using the Binary- Encounter-Bethe (BEB) model, which combines

the Mott cross section with the high- T behavior of the Bethe cross section. Selected experimental

data are included.

5 X-Ray and Gamma-Ray Data

X-Ray Attenuation and Absorption for Materials of Dosimetric Interest

by J. H. Hubbell and S. M. Seltzer

Tables and graphs of computed photon mass attenuation coefficients and mass energy-absorption

coefficients from 1 keV to 20 MeV are presented for all of the elements (Z = 1 to 92) and for 48

compounds and mixtures of radiological interest. These coefficients are basic quantities used in

calculations of the penetration and the energy deposition by photons (x-ray, gamma-ray,

bremsstrahlung) in biological, shielding, and other materials.

Bbibliography of Photon Attenuation Measurements

by J. H. Hubbell

This bibliography contains papers (1907-1995) reporting absolute measurements of photon (XUV,

x-ray, gamma-ray, bremsstrahlung) total interaction cross sections or attenuation coefficients for the elements and some compounds used in a variety of medical, industrial, defense, and scientific

applications. The energy range covered is from 10 eV to 13.5 GeV.

X-Ray Form Factor, Attenuation and Scattering Tabulation

by C. T. Chantler

The primary interactions of x rays with isolated atoms from Z = 1 (hydrogen) to Z = 92 (uranium)

are described and computed within a self-consistent Dirac-Hartree-Fock framework. The results are provided over the energy range from either 1 eV or 10 eV to 433 keV, depending on the atom.

Self-consistent values of the f\ and fi components of the atomic scattering factors are tabulated,

together with the photoelectric attenuation coefficient for the atom, /u, and the value for the Kshell, juk, as functions of energy and wavelength.

26 ICAMDATA 97 Proceedings
6 Nuclear Physics Data

Radionuclide Half-Life Measurements Made at NIST

by M. P. Unterweger, D. D. Hoppes, and F. J. Schima

This database is a table of the half lives of 56 important radionuclides measured with ionization

chambers by the Radioactivity Group of NIST. The included half lives range from 1.8 hours to 31.5 years.

7 Condensed Matter Physics Data

Atomic Model Data for Electronic Structure Calculations

by Svetlana Kotochigova, Zachary Levine, Eric Shirley, Mark Stiles, and Charles Clark

This database consists of evaluated data for use in total-energy calculations of electronic structure

by density-functional theory. It contains total energies and orbital energy eigenvalues for all atoms from hydrogen to uranium, with micro-Hartree uncertainty in the total energy, as computed in the local-density approximation (LDA), the local-spin-density approximation (LSD),

the relativistic local-density approximation (RLDA), and the scalar-relativistic local-density

approximation (ScRLDA).

Conclusion

There are several new or improved databases currently being prepared for dissemination on the

Web to meet the needs of the atomic and molecular data community. In particular, a description

of the extended version of the Atomic Spectroscopic Database under development is included in

this NIST Special Publication in the paper "NIST Atomic Spectroscopic Database," by G. R. Dalton, et al. All Physics Laboratory databases can be accessed from the Web at

http://physics.nist.gov/ by selecting the link Physical Reference Data.

1 Databases 27
Vibrational and Electronic Energy Levels of

Polyatomic Transient Molecules

Marilyn E. Jacox

National Institute of Standards and Technology

Gaithersburg, MB 20899

Abstract

The database concerned with the vibrational and electronic energy of polyatomic transient

molecules with from 3 to 16 atoms now contains the experimentally determined vibrational

fundamentals and electronic band origins of approximately 2,140 neutral and ionic transient

molecules. This database is distributed in both published and computer-searchable forms. Emphasis is placed on species with lifetimes too short for study using conventional sampling

techniques. The compilation also includes many high temperature molecules and several less reactive species which have presented spectral evaluation problems and which are important in a wide variety of environmental and industrial chemical systems. Radiative lifetimes and the

principal rotational constants are given. Observations in the gas phase, in molecular beams, and

in rare-gas and diatomic molecule matrices are evaluated. The types of measurement surveyed

include conventional and laser-based absorption and emission techniques, laser absorption with mass analysis, and photoelectron spectroscopy.

Discussion

Transient molecules are important in a wide variety of chemical reaction systems, including those

typical of combustion, plasma processing, chemical vapor deposition, decomposition of energetic

materials, and environmental research and monitoring. A database concerned with critically

evaluated vibrational and electronic energy levels of polyatomic transient molecules with from 3

to 16 atoms now contains the experimentally determined vibrational fundamentals and electronic

band origins of approximately 2,140 neutral and ionic species. Emphasis is placed on molecules

with lifetimes too short for study using conventional sampling techniques. These molecules

include free radicals, molecular ions, and other short-lived reaction intermediates. The database

is gradually being extended to include small high-temperature molecules. At this time, it contains

spectroscopic information on many polyatomic oxides. Certain other especially important species

that are difficult to isolate in pure form and have presented spectral evaluation problems,

including OCIO, HNCO, H2O2, cis- and trans- HONO, and HONO2, are also included.

The focus of this database is on the spectroscopic properties of the species of interest under

conditions of minimal interaction with other species. Thus, the most definitive data are those

obtained in low-pressure gas-phase measurements, including studies of molecular beams. Also

included are data for the molecule trapped in rare-gas matrices and/or in small molecule matrices

such as H2, N2, O2, CO, or CO2. Matrix shifts for uncharged molecules and ionic species trapped in

Ne are generally less than 1%, as are those of uncharged molecules trapped in Ar. H2 is also a promising matrix material, but there are insufficient data for a satisfactory estimate of matrix

shifts characteristic of molecules trapped in solid H2. More polar matrix materials such as H2O

28 1CAMDATA 97 Proceedings
and the Freons are not included, nor are data for high-temperature molecules in the solid state,

which generally have very broad absorptions.

Many types of measurement are included in the database. Among these are conventional and

laser-based absorption and emission techniques, laser absorption with mass analysis, and

photoelectron spectroscopy.

As of 1 October 1997, earlier versions of the database were available both as a monograph [1] and as a computer-searchable database, VEEL 4.0 [2]. Spectroscopic data for 1,582 molecules are included in the monograph, and data for 1,796 molecules are included in VEEL 4.0. Both forms

include excited-state band origins, ground- and excited-state vibrational fundamentals, and a full bibliography. The monograph also includes radiatiye lifetimes and principal rotational constants,

cited to 0.001 cm-1. The system requirements for VEEL 4.0 are an IBM3 AT class or PS/2 personal

computer (80286, 80386, 80486, or Pentium processor) with PC- or MS-DOS 2.1 or greater or with

Windows 95, as well as 512 kilobytes of RAM and at least 4.0 megabytes of hard disk storage.

VEEL 4.0 can also be used with Macintosh computers that have PC emulation software, and

instructions for installing it on systems which use Windows NT are available.

Three new outputs which revise and extend the coverage of the database will soon become

available. A supplement to the monograph [1] is to be published early in 1998 in the Journal of

Physical and Chemical Reference Data. Version 5.0 of VEEL is to be released in late 1997. The

December 1997 version of NIST Standard Reference Database 69 (http://WebBook.NlST.gov) is also scheduled to include the data contained in VEEL 5.0, searchable by vibrational and

electronic energy levels, together with other molecular properties.

Acknowledgments

This work was supported by the Standard Reference Data Program of the National Institute of

Standards and Technology.

Footnotes and References

[1] M. E. Jacox, "Vibrational and Electronic Energy Levels of Polyatomic Transient Molecules,"

Monograph No. 3, J. Phys. Chem. Ref. Data, 461 pages (1994)

[2] NIST Standard Reference Database 26, NIST Vibrational and Electronic Energy Levels of

Small Polyatomic Transient Molecules (VEEL), Version 4.0

a Certain commercial instruments and software are identified in this paper in order to specify adequately the range

of utility of the VEEL data package. In no case does such identification imply recommendation or endorsement by

the National Institute of Standards and Technology, nor does it imply that the items identified are necessarily the best available for the purpose.

1 Databases 29
Database for Dielectronic Recombination Rate

Coefficients to the Excited States of

the Carbon Atom and Ions

T. Kato, U. Safronova, and J. Dubau*

National Institute for Fusion Science, Nagoya, 464-01, Japan

'Observatory of Paris, Meudon, F-92195 MEUDON Cedex, France

1 Introduction

Dielectronic recombination processes for L-shell ions are important in plasmas such as the solar corona and divertor plasma for plasma diagnostics. We have calculated the dielectronic

recombination rate coefficients to the excited states (n = 2 - 6) of L-shell carbon atom and ions (C I

- C IV). These data are necessary to calculate the population density of excited states of each ion as well as for total recombination rate coefficients. Atomic data (energy levels, transition

probabilities, autoionization rates) are calculated by the Cowan code and AUTOLSJ methods [1]. Scaling methods are used for highly excited states because the contribution of the highly

excited states up to more than n = 100 is not negligible. We present the dielectronic recombination

rate coefficients to the excited states by a parameter fit to an analytical formula. Density effects on the effective recombination rate coefficients are discussed.

2 Method

Dielectronic recombination rate coefficients oca to the excited states nl [LS] of an ion X(z_1)+ from an

initial state a0 of a recombining ion X

z+are calculated by

ad(nl[LS] la0) = (h2/ 2% mkTeP Iy Zj ( gz -i (y [L'S'J']) / 2gz (l)

)

x (Aa (y [L'S'J'], a0) Ar (y [L'S'J'], nl[LSJ]) / £Aa + £Ar) exp(-Es / kTe) (1)

for the process as follows,

Xz+(a0) + e -» X^-D + **(y) -> X^>+ (nl [LS] )+ hv (2)

where y is the autoionizing state, nl the bound states, Aa the autoionization rate, Ar radiative

transition probability, Es the energy of the state y relative to the initial state a0 which we

assumed to be the ground state of a recombining ion. The values for Aa, Ar, and Es are calculated

for fine structure levels with n = 1 - 6 [1-4] and the rate coefficients are summed into LS levels by

Eq. (!)•

30 ICAMDATA 97 Proceedings
3 Fit Parameters for the Rate Coefficients ad(nl [LS])

We have fitted the rate coefficients to each excited state by a fitting formula as follows,

ad (nl [LS] I a0) = IiAi exp{-(E, I Te)} Te

- 3/2 cnrV1 (3)

where Ei and Te are in eV. An example of these parameters is given in Table 1. The data for C I - C III are available upon request (takako@nifs.acjp).

* 4 nl-Dependence of ad

The rate coefficients have large values even if the principal quantum number is above n = 100,

and their contribution is not negligible for the total recombination rate and for the population

density in a recombining plasma. We obtained the values for n > 6 by using scaling formulae [1] of

Ar (2pnl, 2snl) = Ar (2p61, 2s61) and Aa (2pnl) = (6/n) 3 Aa(2p61) for each LSJ level and summed up

with LSJ after scaling. In Fig.l, we show the distribution of ad(nl) of C I as an example.

5 Total Recombination Rate Coefficients and the Density Effect

In order to obtain the total recombination rate coefficients we summed the rates up to n = 500.

However, a real plasma has a finite electron density, and the collisional effects for such high n

cannot be neglected. For example, the thermal limit is estimated to be n ~ 15 for a plasma of

Te = 30 eV and ne = 108 cm"3

. Therefore, it is necessary to include the density effect when the

recombination rate coefficients are used to obtain the ion abundances in plasmas. We define the

effective recombination rate coefficient as follows,

aeff = I. (Aii / ne + Cii) n(i) + at(l) ne + ar (l) + otd(l) (4)

where at(l) and ar (l) indicate the three body and radiative recombination rate coefficients to the

ground state, respectively and Cu is the collisional de-excitation rate coefficient from the level i to the ground state. The oceff for the various electron densities as a function of electron temperature

are shown in Fig. 2. However, in order to obtain aeff, we should consider collisional and microfield

1-mixing in autoionizing levels which are not included in our calculation. Further investigations are required for these processes.

References

[1] J. Dubau, T. Kato, U. I. Safronova, these proceedings (1997)

[2] U. I. Safronova and T. Kato, Physica Scripta 53, 461-472 (1996)

[3] T. Kato, U. I. Safronova and M. Ohira, Physica Scripta 55, 185 -199 (1997)

[4] U. Safronova, T. Kato and M. Ohira, NIFS-DATA-37 (1996), J. Quant. Spectrosc. Radiat.

Transfer 58, 193 (1997)

1 Databases 31
Table 1: Fitting parameters by formula Eq. (3) for ad(k) of C I.

Excited state Ai(cm3s

:) Ei(eV) A2(cm3 s *) E2 (eV)

2s2 2p2 3P 1.051E-13 1.723E+00 1.088E-12 3.887E+00

2s2 2r>2 IDJ. J—

/

6W.T:WiJXJ 402E-13XW 2 310E+00 5W . 551E-13 W W X XJ X W 4 706E+00

2s22o2 1 S 1X • 276E-13 t-i 1 W 1 i X W 3 522E+00 1 263E-14 1X . 247E+01 Aj x 1 XJ ' W X

2s2p3 5 S 1.177E-13 3 664E+00 3' ' • 820E-14 1 -' —J W * * X I 1 017E+00

2s2p3 3D 5 296E-13 4.615E+00 3 368E-14 1 588E+00

2s2p3 3P 7 903E-13 7 606E+00 4 663E-14 2 488E+00

2s2 2d3s 3p 4.716E-13 6.671 E+00 4.671E-15 1 584E+00

2s2 2d3s *P 4.263E-13 9.887E+00 2.828E-14 5 982E+00

2s2 2p3p *P 4.525E-16 2.323E+00 5.378E-14 8.250E+00

2s2 2d3d 3 D 3.551E-16 2.820E+00 5.530E-13 1 015E+01

2s2 2p3p 3S 8.293E-17 2.835E+00 1.130E-13 9.877E+00

2s2 2p3p 3p 2.585E-13 9.126E+00 2.995E-14 3 057E+00

2s2 2p3p lD 1.394E-13 7.211E+00 7.422E-17 2.311E+00

2s2 2p3p MS 1.917E-14 9.648E+00 3.491E-17 3.532E+00

2s2 2o3d 3P 71 . 198E-13 X \J KJ XJ X KJ 71 • 971E+00 \J I X XJ 1 v_/ W 2 832E-14 2^J.UUCJJ 385E+00 1 \J\J 2s2 2o3d : D 2 822E-13 1X • 195E+01 X \J W XJ ' W X W3 • 188E-14 X (_/ WXJ X JT 7f .UvUXJ 500 E+00 1 \J\J 2s2 2o3d 3 F 3.012E-12 1X • 177E+01 X 1 1 -I J 1 W X 3 278E-13 7 593E+00

2s2 2p3d 3D 1.420E-12 1.016E+01 9 464E-15 2 468E+00

2s2 2o3d J P 2 759E-13 1X • 118E+01 X X 11 I -i W X 2 014E-15 4 325E+00

2s2 2p3d lF 8.183E-13 1.135E+01 2.966E-14 6 126E+00

2s2 2p4s 3P 6.280E-13 9 549E+00 9 864E-16 11 . 608E+00 VUWXi 1 WW

2s2 2p4s *D 3 266E-13 1X * 189E+01 X V i * J J

1 W X 1.628E-14 71 139E+00 X W W XJ 1 ww 2s2 2p4p iP 5.684E-14 9.861 E+00 2.220E-16 2.426E+00

2s2 2p4p 3D 7.955E-13 1.180E+01 7.628E-16 2.862E+00

2s2 2d4d 3 S 1x.wwljxj 508E-13xw 1 142E+01 2 162E-16 Lj2 . 875E+00 kJ 1 UD 1 WW

2s2 2p4p 3P 3.271E-13 1.140E+01 1.060E-14 3.154E+00

2s2 2p4p *D 1.826E-13 8.673E+00 4.409E-16 2.944E+00

2s2 2p4p 2.975E-14 1.080E+01 2.291E-16 3.524E+00

2s2 2p4d lD 4.912E-13 1.241E+01 1.285E-14 7.266E+00

2s2 2p4d 3F 3.024E-12 1.123E+01 2.781E-15 3.138E+00

Sum (n=7-500) 1.006E-09 1.189E+01 1.378E-11 6.406E+00

32 ICAMDATA 97 Proceedings
Principal quantum number n Figure 1: The dielectronic recombination rate coefficients to n-1 states from C II to C I.

1 10 100

Te (eV)

Figure 2: The effective recombination rate coefficients from C II to C I.

1 Databases
Critical Evaluation of Transition Probabilities

ofNa-Ca (Z=ll - 20)

D. E. Kelleher and L. I. Podobedova

NIST, Gaithersburg, MB 20899

NIST is in the process of critically evaluating and compiling transition probabilities of H-Ca

(Z=l-20). These elements were covered about 30 years ago in Vols. I and II of "Atomic Transition

Probabilities" by W. L. Wiese et al. Much work has been done since then, mostly theoretical, with

by far the most extensive results being provided by members of the "Opacity Project" (OP). In

1996, "Atomic Transition Probabilities of Carbon, Nitrogen, and Oxygen" was published by W. L. Wiese, J. R. Fuhr, and T. M. Deters [1]. Work on updating the other elements is continuing, and

revision of Vol. II is currently focused on Na, Mg, Al, and Si (Z=ll-14). For many spectra, our new

compilations contain about an order of magnitude more transitions than the earlier ones. Our new compilations rely heavily on OP results because they are so extensive and because

they appear to be reasonably accurate in many cases. Accurate experiments (and high precision

computational results) are also essential, primarily for reference values in critical evaluation and

for benchmark values in their own right. OP calculations cover an extensive range of allowed

transitions, essentially comprehensive up to n=10 and .£=3,4. OP values have been made

electronically available for all stages of H-Ca, except P, CI, and K, which are planned for future

work. Currently available OP calculations do not, however, include the effects of the spin-orbit

interaction, and only average-multiplet values are reported. We decompose the LS multiplet

averages into their LSJ fine structure components using the following LS coupling rule:

where S is the line strength, and the curly brackets indicate a 6-J symbol. We consider only those

transitions for which experimental energies are tabulated in NIST energy level tables for both the

lower and upper level. We take only the line strengths from the Opacity Project, using

experimental energies to derive wavelengths and to convert line strengths to oscillator strengths

and transition probabilities.

For the stronger transitions of most spectra, reasonably good agreement is found between the

Opacity Project on the one hand, and experiments and accurate calculations which include

spin-orbit effects on the other. Large spin-orbit effects such as those in noble-gas-like spectra can

probably account for large differences observed in such spectra. However, the origin of large

discrepancies in all but the strongest transitions in some other spectra is not yet understood.

Note, for example, the comparison of line strengths for OP [2] and CIV-3 [3] in fluorine-like

spectra of Na III and Si VI in Figures 1 and 2. Comparisons in the figures only include transitions

for which the outermost electron of the upper level is in an n=3 principal quantum number,

because only these are listed in [3].

Slsj-l'S'J' = Sls-l'S-(2J+1)(2J'+1)

34 ICAMDATA 97 Proceedings
-3 -1

log S (OP)

Figure 1: Logarithms of the ratios of line strengths S(CIV-3)/S(OP) are plotted vs. log S(OP) for fluorine-like Na III. All transitions involve 2s2 2p43^ upper levels.

Si VI

a.O

V)fI |

o

0)a>o

log S (OP)

Figure 2: Logarithms of the ratios of line strengths S(CIV-3)/S(OP) are plotted vs. log S(OP) for

fluorine-like Si VI. All transitions involve 2s22p4 3^ upper levels.

1 Databases 35
The discrepancy in line-strengths for fluorine-like spectra between OP and CIV- 3 results deserves

special attention. These methods represent two of the most important methods to-date for large

scale line strength calculations. The OP method relies on CrV-3 (or the similar "Superstructure"

approach) for its core state correlations, as discussed below. All but the lowest three bound levels

of Na III have configurations of the type 2s2 2p4

( )n£, where the parentheses indicate a parent term

of either X S, 3P, or X D. Bound interloper levels, such as the 2s5pn^ levels, exist only for the more

highly ionized members of the isoelectronic series. The three parent configurations cited above lie sufficiently close in energy that both intermediate coupling and configuration interaction occur at noticeable and frequently comparable levels throughout the bound spectrum. Relative Lande

intervals of the quartet states (relative intervals for doublets cannot be derived from level

energies) are typically far from those expected for LS coupling.

The OP uses a close-coupling expansion (CC) approximation that represents the total

wavefunction as a superposition of ionic core and valence- electron wavefunctions. The ionic core (without the valence electron) is described by a configuration-interaction method, using either

CIV-3 (Slater-type Orbitals) or superstructure (effective-charge statistical-model potentials). The

R- matrix method is used to solve the core plus valence electron problem in the inner region. It divides the problem into two regions of space: the "inner" and "outer" regions, and requires that

the wavefunctions in these two regions and their radial derivatives match at an intermediate

boundary. The outer-region wavefunction approaches a "Coulomb" solution asymptotically. It is usually evaluated by integrating the asymptotic solutions inward. The ab initio CC expansion

method is similar in spirit to, but considerably more sophisticated than, such semi-empirical

methods as the Coulomb approximation, quantum defect theory, or core polarization models.

Even the latter, for example, must use a short-range cut-off of the potential to simulate the effect of exchange between the excited and core electrons. The CC approach is generally more efficient

than variational methods for large-sweep calculations of transitions involving more highly excited

levels. In principle at least, the assumptions of the CC model become increasingly valid for more

highly excited states. (One caveat is that the CC model must be built on an intermediate-coupled

core, if intermediate coupling is significant.) This advantage tends to offset the intrinsic fact that

binding energies are smaller for more highly excited states. Thus, a fixed absolute error yields a

larger relative error, as well as the fact that more basis states often need to be included to obtain

the same level of absolute accuracy. Some authors argue that the CC method becomes more

accurate than variational methods for more highly excited states because it builds in the effect of

highly excited states and the continuum; as a practical matter, it may prove difficult to expand

the basis set sufficiently as n and t increase. The CC method, however, usually cannot practically

build-in as much correlation between the core and low-excited electron as can full-blown

multi-configurational variational methods. Thus the latter can be superior for calculating

transitions involving the lowest-excited levels, for transitions whose strengths are sensitive to cancellations in the dipole matrix elements, and, of course, for calculating wavefunctions for the

ion core used in CC calculations.

Recently, the Opacity Project group in Belfast has gained the capability to include

intermediate coupling via inclusion of the Breit Pauli (BP) interaction in their CC calculations.

This is an important new development. NIST has received the Na III (F-like) energy levels of and

the transition strengths between the odd J=l/2, J=3/2, and even J=l/2 states [4]. The energies

agree with experimental values to within 0.8% or better, and the agreement between the length

and velocity values for the electric dipole matrix element is encouraging. The agreement between

the CIV-3 and CC with BP, however, is not much improved compared to CIV-3 vs. OP results. The

origin of these discrepancies is not understood and is presently under study. It will thus be

36 ICAMDATA 97 Proceedings
interesting to compare CIV-3 and forthcoming CC/BP calculations of transition strengths with

experimental results available for other spectra, particularly for weaker transitions.

Because it overcomes the primary limitation of OP calculations, this extended CC/BP version

may offer the potential for mass production of accurate transition probabilities of all spectra, at

least for Z<~36 and for transition strengths whose values are not dominated by cancellation

effects. Only time will tell, however, if the extended method is capable of generating reasonably

accurate line strengths for values significantly less than one.

References

[1] W. L. Wiese, J. R. Fuhr, and T. M. Deters, "Atomic Transition Probabilities of Carbon,

Nitrogen, and Oxygen" J. Phys. Chem. Ref. Data, Monograph 7 (1996)

[2] K. Butler and C. J. Zeippen, Opacity Project, to be published (data is available on the internet

via "topbase")

[3] H. M. S. Blackford and A. Hibbert, At. Data Nucl. Data Tables 58, 101 (1994)

[4] K. Berrington, private communication

1 Databases 37
Database for Electron-Impact Total Ionization Cross

Sections of Atoms and Molecules*

Y.-K. Kim and D. S. Zucker

National Institute of Standards and Technology,

Gaithersburg, MD 20899-0001

M. A. Ali

Chemistry Department, Howard University,

Washington, DC 20059

M. E. Rudd

Department of Physics and Astronomy,

University of Nebraska-Lincoln, Lincoln, NE 68588-0111

1 Introduction

A database for electron-impact total ionization cross sections of 43 atoms and molecules is available as part of the NIST Physics Laboratory web presentation:

http://physics.nist.gov/PhysRefData/Ionization/Xsection.html

This database presents theoretical cross sections based on the Binary-Encounter-Bethe (BEB)

model for a large number of atoms, molecules, and radicals of interest in modeling

low-temperature plasmas in magnetic fusion devices, plasma processing of semiconductors,

radiation damages to materials, and cleaning of air pollutants by corona discharge. The database

includes molecules such as H2, H2O, NO2, 03, SiBU, and SF6. For each target, the database

compares the BEB cross section to available theoretical and experimental data.

2 Theory

The BEB model [l]-[4] combines a modified form of the Mott cross section with the Bethe cross section for high incident energy, T. The BEB model requires three constants per orbital, viz., the

binding energy B, the average kinetic energy U, and the electron occupation number N. Then, the

ionization cross section per orbital is given by:

a BEB ~

t+ u+ 1 Q Int

1 - ±\U2 - Q) 1 2 t t t+ 1 (1)

where t=T/B, u=U/B, S=47tao2 N(R/B)2

, ao=0.529 A, R=13.61 eV and Q is a weighted integral of the

target=s continuum oscillator strength [1]. For most targets, Q=l is an excellent approximation.

The total ionization cross section, m, is obtained by summing ctbeb over occupied orbitals.

The first logarithmic term in eq (1) is associated with the dipole interaction term from the

Work at NIST was supported in part by the Office of Fusion Sciences, USDOE.

38 ICAMDATA 97 Proceedings
Bethe theory, 1 - 1/t comes from the direct and exchange Coulomb interaction in the Mott cross

section, and the last logarithmic term results from the interference between the direct and

exchange terms of the Coulomb interaction.

Equation (1) is not a fitting formula, nor does it contain any adjustable or empirical

parameters. Instead, the model uses ab initio constants obtained from the ground-state wave

function of the target (with Q = 1). To match the experimental threshold, however, we

recommend using the experimental vertical ionization potential for the outermost valence orbital,

if available. Experimental ionization potentials (mostly adiabatic) of many molecules and radicals are available from another NIST database [5]

.

3 Results

The BEB model was found to be very effective in reproducing known ionization cross sections

from threshold to several keV (within ±10% of reliable experimental data at the peak) for most of more than 50 atoms, molecules, and radicals we have tested so far. As an example, the BEB cross sections for CH and CF4 are compared to available experimental data in Figures 1 and 2. Using this database, a user can (a) calculate the BEB cross section on-line by typing in the

desired incident energy; (b) look at graphical comparison of the BEB cross section to other theory

and experiment with full references; and (c) download orbital constants and BEB cross sections in

ASCII form. We found so far that the BEB model works extremely well for hydrocarbons, both

stable molecules and radicals. The BEB model works better for closed-shell molecules than open

shell molecules, and better for molecules than atoms.

4 Outlook

Ionization cross sections for more atoms and molecules will be added to the database as they

become available. For instance, preliminary studies indicate that the BEB model produces

reliable cross sections for closed-shell compounds of fluorine, such as CF4, CHF3, and C4F8, while

substantial disagreement with experiments (sometimes a factor of 2) is found for radicals of

fluorine compounds, such as CF and NF.

References

[1] Y.-K. Kim and M. E. Rudd, Phys. Rev. A 50, 3954 (1994)

[2] W. Hwang, Y.-K. Kim, and M. E. Rudd, J. Chem. Phys. 104, 2956 (1996)

[3] Y.-K. Kim, W. Hwang, N. M. Weinberger, M. A. Ali, and M. E. Rudd, J. Chem. Phys. 106,

1026 (1997)

[4] M. A. Ali, Y.-K. Kim, W. Hwang, N. M. Weinberger, and M. E. Rudd, J. Chem. Phys. 106,

9602 (1997)

[5] S. G. Lias, J. F. Liebman, R. D. Levin, and S. A. Kafafi, "NIST Positive Ion Energetics

Database"

1 Databases 39
[6] V. Tarnovsky, A. Levin, H. Deutsch, and K. Becker, J. Phys. B 29, 139 (1996)

[7] H. U. Poll, C. Winkler, D. Margreiter, V. Grill and T. D. Mark, Int. J. Mass Spectrom. Ion

Processes 112, 1 (1992)

[8] R. A. Bonham, private communication (1997)

[9] M. V. V. S. Rao and S. K. Srivastava, Abstracts of the XXth International Conference on the

Physics of Electronic and Atomic Collisions, 23-24 July 1997, Vienna, Austria, p. MO150

[10] J. A. Beran and L. Kevan, J. Phys. Chem. 73, 3866 (1969)

40 ICAMDATA 97 Proceedings
T(eV)

Figure 1: Comparison of ionization cross sections for CH. ai, total ionization cross section; T,

incident energy; solid curve, BEB cross section; circles, experimental data by Tarnovsky et al. [6].

1 Databases 41
I I I I I I I I

I 1 I I I I III

T(eV)

Figure 2: Comparison of ionizations cross sections for CF4. m, total ionization cross section; T,

incident energy; solid curve, BEB cross section; upright triangle, experimental data by Poll et al.

[7]; squares, data by Bonham [8j; inverted triangles, data by Rao and Srivastava [9]; circles, data

by Beran and Kevan [10].

42 ICAMDATA 97 Proceedings
The Atomic Spectroscopy Bibliography Database

of the Institute for Spectroscopy, Troitsk

A. E. Kramida*, A. N. Ryabtsev, and G. V. Vedeneeva

Institute for Spectroscopy of the Russian Academy of Sciences,

Troitsk, 142092, Russia.

A data bank BIBL containing bibliography on atomic data for plasma physics, atomic physics,

astrophysics etc. is being developed at the Institute for Spectroscopy since 1987. The bibliographic

information is supplemented by abstracts of papers and search keywords. A special system of

spectroscopic keywords has been designed for the BIBL database. It allows very easy retrieval of

information on search requests commonly required by spectroscopists, such as papers containing

some specific kind of data concerning some specific ion or isoelectronic sequence. These kinds of

search requests can not be executed in any other available bibliographic system. The data

retrieval system is very simple and easy to use. It is self-documented and utilizes a menu system

supplied with a context-sensitive help. The database works on IBM PC compatible computers

with the MS DOS operating system or those that can emulate the MS DOS system.

The topics covered by BIBL are:

1. Spectra of atoms and positive ions:

ionization potentials, line classification, energy levels, wavelengths, hyperfine

structure, isotopic effects, broadening and shifts of spectral lines, the Stark and

Zeeman effects, plasma diagnostics, astrophysical spectra, theory of atomic spectra,

radiation and autoionization rates, oscillator strengths, QED and relativistic effects in

atoms and ions, atomic-spectroscopy tests of the fundamental principles, spectral sources, techniques of spectral measurements.

2. Cross sections of the collision processes:

excitation and ionization by electrons and photons, multiphoton processes, Auger

decay, ion-electron recombination. To a lesser extent - charge exchange, excitation and

ionization in collisions with heavy particles - if any new data related to atomic

structure are obtained in these publications.

The bibliography related to experimental and theoretical papers on identification and prediction

of atomic and ionic structure should be complete from 1983, the year of the last issue of NBS

Special Publication "Bibliography on Atomic Energy Levels and Spectra", but the experimental

spectral analysis can be traced back to about 1970. On the other topics, it is systematically

maintained since 1989. For the last three years, the commercial database "Current Contents on

Diskettes" has been used for this purpose, with corresponding software for transforming the

articles found into the BIBL format. Presently, there are about 6000 bibliographic records stored

in the BIBL system.

The BIBL database is available free of charge and can be received on the Internet via the ftp

service. The link to its location can be found on ISAN home page at address

http://lls.isan.troitsk.ru/. The files are supplied in compressed form and occupy about 2 Mbytes,

while the size of the uncompressed database is about 10 Mbytes.

An on-line network access to the database is under development and is planned to be ready

within a year. The information will appear on ISAN Internet home page.

* e-mail kramida@isan.troitsk.ru

1 Databases 43
Atomic Data Center on PC

K. T. Lu, Dennis Baba, and Rolf Engleman

Atomic Engineering Corp.

1 Introduction

"Atomic Data Center on PC" is a long range and large scale program of Atomic Engineering Corp.

This data center provides a generic format which makes spectroscopic data uniform and usable in a PC-based format. This program consists of three functions:

(1) data collection and production,

(2) database development and

(3) evaluation and analysis.

The data center consists of two types of data:

(A) Reference laboratory data of atomic and ionic data specialized on heavy elements with Z>26.

AEDB consists of data of energy levels and lifetimes and is capable of "multi-photon Grotrian

Diagram". ASDB consists of data of wavelengths, transition probabilities and intensities. The

source of data are from open literatures and data archive at National Solar Observatory in

Tucson, AZ.

(B) Knowledge database for laser remote sensing.

This database is designed for "new fingerprints" and related parameters for laser remote

sensing. This program is in collaboration with "Laser Induced Breakdown Spectroscopic

(LIBS) User Facility" at Los Alamos National Lab.

2 Database Management

Multichannel Quantum Defect Theory (MQDT) [1,2,3] is used to organize, manage and evaluate

the data in the Atomic Engineering System (AES) [4] . MQDT is an unified theory comprising the

Rydberg states of spectroscopy and the autoionizing states of collisional processes in atoms and

small molecules [2]. It organizes atomic structures in terms of channel sets and structural

parameters. A "channel set" is defined as a set of discrete and continuum states of an electron

plus ion core. Each state differs in the energy of the excited electron. Subsequently, an atomic

structure is characterized by three sets of quantum defect parameters:

(1) eigen- quantum defect Ma, (2) channel mixing angle 0a, and

(3) dipole transition matrix element da .

These parameters can be obtained by fitting the analytic relations to the discrete energy levels,

oscillator strengths and photoionization cross sections. These parameters may also be calculated

[5]. Relativistic MQDT is used to characterize high Z ions [6].

44 ICAMDATA 97 Proceedings
Highly efficient and powerful algorithms based on the structure parameters has been

developed to organize and evaluate the data : energy levels, oscillator

strengths/intensities/transition probabilities, lifetimes, photoionization cross sections and

quantum defect of isoelectronic sequencies [4]. For example the whole Rydberg series and

autoionizing structures as well as photoelectron angular distribution of noble gases Ne, Ar, Kr, Xe

and Rn are characterized by 5 interaction channels with 5 eigen-quantum defect parameters, 5

dipole matrix elements and 10 channel mixing angle parameters [1].

« 3 Data Evaluation Procedures

We developed the following procedures to evaluate transition probability, intensity and lifetime.

The transition probability Aui, intensity Iui and lifetime tu of upper energy level Eu are related by

the following expression:

Aui = (WErluiO/tu (1)

where 1' refers to all the lower energy levels to which the upper level u decays.

The intensity data are taken using a hollow cathode discharge and measured by high

resolution Fourier Transform Spectrometer at National Solar Observatory at Kitt Peak, AZ,

U.S.A. The intensity is measured by an automated AEC software MCCS system [7] that fits a line

profile and the integrated area. The analysis of the spectral lines in terms of energy levels, J

values and assignments is also carried out using MCCS software.

The lifetime is obtained using published data by laser-induced fluorescence from atoms and

ions in a beam. We have developed an evaluation procedure for lifetime measurements based on

the threshold laser induced fluorescence measurement as function of beam density and laser

intensity (see the following) [8]

.

The transition probability is obtained from equation (1). Most of the up-to-date data on

transition probabilities are obtained by this method [9]. In the absence of lifetime data, we obtain the reliable intensity by normalizing the intensity to the known data of transition probability. The normalized intensity carries the similar weight of

reliability as the transition probability in terms of concentration measurement. For example,

there is no reliable transition probability available for 257.601 nm line of Mn-II however it was

seen in the LIBS spectrum. Following the above procedure, we determined that the normalized

intensity of 257.601 nm line to be 35.

4 Knowledge Database for Laser Remote Sensing

The formation of a plasma plume and generation of emission induced by a high-power laser beam

in solid material has led to the development of elemental composition analytic tools of condensedphase specimens [10]. One high power laser beam vaporizes the sample and generates a plasma

plume. Emission from the plasma is collected by a detector, e.g., a laser induced breakdown

spectrometer (LIBS). This method has the advantage of being developed as a powerful in-situ and

remote sensing tool which requires minimally invasive sample preparation and separation.

However, there are several challenging problems of a in-situ laser induced breakdown

spectroscopy. The calibration problem is more serious because of the lack of reliable library

1 Databases 45
database for environmental matrix effects, such as soil matrix, moisture and laser induced

plasma. The spectral shifts, broadening and "quenching" effects generated by environmental

effects make quantitative characterization difficult. Lack of computational techniques to apply the

knowledge base to the correction of in-situ measurements in real-time for quantitative

characterization contributes to the challenging problems.

An intelligent software system, the Multi- spectral Chemical Characterization System

(MCCS), was used to analyze the matrix effects of two of the toxic metals, Be and Pb, in soil samples measured by a LIB spectrometer [11]. MCCS can convert ASCII, binary, tape and

Flexible Image Transport System (FITS) which is a standard data format for Astrophysics and

Astronomy into AEC's data format. The raw data collected from LIBS are downloaded into the

MCCS. The spectra are measured by the powerful and efficient algorithm which is capable of

measuring 100 integrated spectra in terms of width, peak height and position in less than 15 sec. The spectra are then searched, calibrated and identified in reference to the knowledge database.

The search algorithm includes a "tolerance" parameter to account for the spectral shift and

broadening caused by the matrix effects. The algorithm also includes "filters" in disentangling

"spectral interference". These unique softwares allow user to identify quantitatively the relative

concentration ratio (ppm) of the analyte in a sample. The final decision making can be displayed

in terms of tables and graphics. The results indicate that the selected fingerprints used to measure Be at 313 nm survive the matrix effects. The fingerprint of Pb, 405.9 nm, used in the

calibration is quenched by the laser induced plasma. The following reports an investigation of the

calibration procedure for laser induced effects. Then we use these results as guidance to search for

"new fingerprints" under various environmental matrix effects.

5 The Calibration Procedure for Laser Induced Effects

We have developed a calibration procedure for non-LTE laser induced effects. The calibration

procedure combines modeling with experimental measurement.

In a laser induced plasma the discrete line emission develops in the fringes (optical thin

region) of the expanding plasma core where local thermodynamic equilibrium may not exist. The

usual method based on local thermal dynamic equilibrium in measuring the intensities relatively

and calibrating their relationship to the respective elemental composition, which has been

analyzed by calibration standards, may not be sufficient.

This non-LTE model is based on the assumption that the quenching of the emission process of an element is caused by the competing ionization process of the same element. The emission rate can be derived from a rate equation analysis, which includes as many as four processes:

ionization process, emission process, excitation process and stimulated process.

In order to test the model, we compare the results with a laboratory experimental

investigation [8]. The experimental measurements were carried out at JilinUniversity, in a Pb

atomic beam excited by a Quanta-Ray Nd:YAG dye laser system. The state 6p7s 3P°i at 283.3 nm

is excited by a uv photon (w~ 283.3 nm). The 405.9 nm radiates to level 3, 6p2 3P2 . The ionization

process from level 2 can be produced by a two photon process since the two photon energy is greater than the ionization energy of Pb (=7.415 ev). The photoelectrons were collected by a channeltron. The ionization signal is processed by a boxcar and displaced on a chart recorder. The

fluorescence signal was simultaneously measured by a PMT with a filter. The data shows that the

fluorescence process is simultaneously present and in competition with the ionization process [8]. The result of a model calculation compared with the experimental observation shows that at lower

46 ICAMDATA 97 Proceedings
laser intensity, the 405.9 nm emission increases with increasing laser intensity [8]. This

fluorescence rate decreases as the laser intensity increased beyond 1016 photons/cm2 [8]. To

involve the ionization process is essential, as given in equation (1), for a correct analysis of the

measured data since a computation [12] which does not include the ionization process failed in

predicting the decrease of fluorescence rate. Therefore the decreasing of the fluorescence signal is caused by the increasing of the ionization signal.

We have also carried out a laser induced fluorescence measurement of Pb 405.9 nm as a

function of atomic beam density [8]. The result shows that there is a flat value of fluorescence

yield below beam density 108 atoms/cm3. The fluorescence yield increases exponentially for beam

density >108 atoms/cm3 [8]. The laser power was of the order of sub-MW/cm2. At low density the

atomic beam is in thermal expansion. The mean free path among the atoms may be too large to generate laser induced effects. The flat fluorescence value is close to the atomic condition and is recommended for reference data whereas the higher beam density result may have laser induced

effects. This investigation may explain the discrepancies of some of transition probabilities

measured by lasers compared with non-laser methods.

The above modeling was based on laser induced ionization in atomic beams with a density

~108 atoms/cm3 in vacuum. For laser induced plasmas in air with a density > 1012 atoms/cm3

, the

ionization rate is at least two orders of magnitude larger -10 16 cm2. Consequently, the emission

rate is reduced by at least two orders of magnitude. This investigation generates the key result : there is a threshold value of the laser intensity for emission process to be detected. Beyond that

value, the emission process will be quenched and the relaxation process favors ionization. The

low melting point and low ionization limit of Pb also contribute to the excessive generation of laser

induced plasma. Consequently, the excited atom releases its energy via ionization and "quenched"

the emission process. These results explain why certain "fingerprints" of metals based on

laboratory results, e.g. 405.9 nm of Pb failed to show up in the field results using high power laser

induced plasma method.

6 Knowledge Database for Environmental Matrix Effects

The manifestation of environmental matrix effects on the spectral lines are shifts, broadening and

quenching. A knowledge database to store the calibrated data as well as the new fingerprints of

matrix effects is designed. As the Pb 405.9 nm case shows, the calibration based on fingerprints

from a reference database did not guarantee success. However, reliable and quantitative reference

databases are necessary for the first step of any analytic science.

The spectral shifts and broadening of laser induced spectral lines in the presence of high

pressure noble gas are available for Mg [13], Ba[14], Pb[8], Sn[15], Sr[16] and Stark

broadening [17].

References

[1] (a) K. T. Lu and U. Fano, Phys. Rev. A 2, 81 (1970)

(b) K. T. Lu, Phys. Rev. A 4, 579 (1971)

(c) K. T. Lu, in Photophysics and Photochemistry in the Vacuum Ultraviolet, NATO ASI

Series, 217-244 (1985)

1 Databases 47
[2] U. Fano and A. R. P. Rau, "Atomic Collisions and Spectra", Academic Press, New York

(1986)

[3] (a) C. M. Lee and K. T. Lu, Phys. Rev. A 8, 1241 (1973)

(b) M. Aymar, Phys. Reports 110, 163 (1984)

[4] "Atomic Engineering System: version 1 Help Manual", U. S. Copyright No.,TXu 461 487,

Feb. 1991

[5] (a) C. M. Lee , Phys. Rev. A 10, 1598 (1974)

(b) C. Greene and L. Kim, Phys. Rev. A 38, 5953 (1988)

(c) Z. W. Lu and K. T. Lu, Phys. Rev. A 31, 1515-1521 (1985)

[6] C. M. Lee and W, R. Johnson, Phys. Rev. A 32, 979 (1980)

[7] "Multi-spectral Chemical Characterization System: Version 1.0", US Copyrights No. TXu

710-412, Aug. 16, 1995

[8] D. Ding, H. Liu and K. T. Lu, Acta Optica Sinica 8, 404 (1988)

[9] For example: M. E. Wikliffe and J. E. Lawler, J. Opt. Soc. Am. B. 15, 737 (1997)

[10] Leon J. Radziemski, "Review of Selected Analytical Applications of Laser Plasmas and Laser

Ablation, 1987-1994", Microchemical Journal 50, 218-234 (1994)

[11] K. T. Lu, Dennis Baba, Mike Murray and Fang Xu, "Analysis of Matrix Effect of RCRA

Metal Elements in Soil Measured by In-situ Laser Induced Breakdown Spectrometer", in

"American Environmental Laboratory", March 10, 1997

[12] M. A. Boshov, A. V. Zybin, V. G. Koloshnikov and K. N. Koshelev, Spectrochimica Acta 32B,

279 (1977)

[13] J. Y. Zhang et al., J. Phys. B. At. Mol. Phys. 21, 581 (1988)

[14] D. H. Wu, U. F. Yand, and K. T. Lu, J. Phys. B. At. Mol. Opt. Phys. 23, L149 (1990)

[15] M. Jin, D. Ding, et al., in "Twelfth International Conference on Atomic Physics", Abstracts of

Contributed papers VII-8, Ann Arbor, MI, 1990

[16] J. Q. Sun, E. Matthias, et al., Phys. Rev. A 43, 5956 (1991)

[17] C. Clark, K. T. Lu, and A. Starace, "Effects of Magnetic and Electric Fields on Highly

Excited Atoms," in Progress in Atomic Spectroscopy, Part C, p. 247-320, Ed. Beyer and

H. KLeinpoppen, Plenum (1984)

48 ICAMDATA 97 Proceedings
Los Alamos Opacity Web Page

N. H. Magee, Jr. and R. E. H. Clark

Atomic & Optical Theory Group, T-j.

and

Code Integration Group, X-CI

Los Alamos National Laboratory, Los Alamos NM 87545

1 Introduction

The Los Alamos opacity database is now available on the World Wide Web at http://t4.lanl.gov.

The database contains both the original Astrophysical Opacity Library [1] distributed worldwide

in the 1980's (for historical reference) and the new improved opacities from the Light Element

Detailed Configuration OPacity (LEDCOP) code [2]. Users can access the opacity data using the

multigroup opacity code TOPS [3] to obtain Rosseland and Planck gray opacities, group mean

opacities over selected energy ranges, the monchromatic absorption coefficients and the average

ionization over a wide range of temperatures and densities. As described below, these quantities

are available for all of the elements presently on the database and TOPS will provide the same

quantities for any arbitrary mixture of these elements.

2 Short History of the Opacity Database

The Los Alamos opacities have been distributed world wide since the 1960's, mainly for use in

astrophysical modeling. At first, the opacity tables were calculated for each individual request, but

this became very time consuming. All of these tables were individually calculated from scratch for

each new mixture, recalculating the opacities from the individual elements over and over again. In

the late 1970's, it was realized that the energy dependent absorption coefficients could be calculated once for each element and then combined with absorption coefficients of other elements to form as many mixtures as desired. There were only two restrictions for this method.

First, all molecular opacities and abundances had to be removed from the calculations since one must have all of the elemental data in the equation of state (EOS) to form molecular species.

Second, the opacities had been calculated on a temperature-density {T — p) grid, but the calculation

had to be switched from the (T — p) grid to a temperature-electron degeneracy (T — 77) grid. The

electron degeneracy parameter characterizes the electron pressure of the plasma at the ion-plasma

boundary, so two elements calculated at the same 77 "see" the same plasma conditions and can be

mixed together. Extensive comparisons were run in the late 1970's between the mixed opacities

and the ab initio mixture calculations and differences were on the order of a few percent.

The Los Alamos Astrophysical Opacity Library was developed from this change in methodolgy.

The first comprehensive set of elemental opacities was calculated in the late 1970's and distributed

with software programs for mixing the elements together. Most of this distribution was done via

magnetic tapes, with FTP being utilized in the early 1990's. Even with FTP, the data transfer was

very slow since the library contained more than 300,000,000 words with more being added as new

opacity calculations were being done for the library. It was then decided to place all of the detailed

1 Databases 49
absorption coefficient data files on the Web and use the upgraded mixing program TOPS to allow

users to access the full database and download the data in as much detail as they wished.

3 Brief Code Descriptions

The Los Alamos LEDCOP opacity code uses a basis set of detailed LS terms (plus average configuration terms for complex ion stages) to calculate opacities for elements with Z < 31. Each ion stage

is considered in detail and interactions with the plasma are treated as pertubations. Calculations

are done in local thermodynamic equilibrium (LTE) and only radiative processes are included. The

EOS model is based on the Saha equation [4], including degeneracy, where the bound Rydberg

sequences are cut off by plasma corrections [5]. The code does not consider liquid or solid phases,

but uses an explicit ion model [6] to treat all of the bound electron states of every ionization stage.

A self-consistent Hartree-Fock code [7] with relativistic corrections is used to generate both

single configuration LS term energies, radial dipole matrix elements and angular factors for all ion

stages and unresolved transition array (UTA) energies and variances [8] in intermediate coupling

for selected ion stages. Nonhydrogenic photoionization cross sections are calculated for each configuration subshell with / < 5, using distorted wave continuum functions and the same Hartree-Fock

structure calculations as for the bound-bound transitions in order to conserve oscillator strength

across the photo-electric edges. Users should access the web page reference link for more details.

The Astrophysical Opacity Library consists of random access binary files. The TOPS code is the

vehicle for accessing these data files and performing numerical integrations to obtain the Rosseland

and Planck opacities. TOPS can provide opacities for an arbitrary mixture of pure elements. As

mentioned previously the data is stored as a function of T and 77. The TOPS code mixes elements

at similar 77's and then interpolates on 77 to obtain a material density. The user can select an

arbitrary density and, for multigroup opacities, an arbitrary photon energy grid. The temperature

grid is limited to subsets of the temperature grid on which the original data are tabulated; no

interpolation in temperature is allowed in the TOPS code.

4 Database Structure

At present, the database contains monochromatic absorption coefficients for all of the elements

from hydrogen to zinc. Older element calculations are being upgraded and the database may be

extended to higher Z elements in the future. Each element in the library is calculated on a uniform

T, 77 and u (u = hu/kT) grid to allow the mixing of the elements to form mixtures. This provides an almost unlimited choice for users to customize opacity tables from pure elements to two element

mixtures, such as the carbon-iron mix presented in this paper, to complex astrophysical mixtures

containing more than 20 elements. The older 1977 element data is included so that users can

baseline the changes in the opacities over the 20 year span of the calculations. The old element

data can be mixed just like the newer data, and can even be mixed with the newer data since the

older photon grid is a subset of the photon grid used for the newest calculations. The TOPS code

automatically chooses the correct grid when the materials are mixed.

Table 1 lists the temerature, density and u ranges covered by the database. The density range

is shown rather than the electron degeneracy range since the density is a more familiar quantity.

Every element in the library has approximately 1500 T — 77 points, covering the ranges listed below.

Therefore, each element has approximately 12,000,000 words of data. As disk space allows, the

authors hope to expand the number of u grid points from the present 3,900 to 14,900.

50 ICAMDATA 97 Proceedings
Table 1: Ranges covered by t le opacity database.

Quantity Range Comments

Temperature

Density

u

.5 or 1.0 eV to 100,000 eV

10

_ 10 gm/cc to 10+9 gm/cc

0. to 30. or 30,000.

10 temperatures/decade.

1 to 3 densities/decade. Highest

density is temperature dependent.

1977 data stops at u = 30.

5 Sample Web Page Output

A short sample output is shown for a carbon-iron mixture at two temperatures and two densities.

The default output has been chosen, so the table displays the Rosseland and Planck gray opacities

and the the average number of free electrons per atom. Note that a warning message has been

printed, indicating that one of the requested densities was off the table. The TOPS code will use

the values from the highest calculated density for all densities above the last density point.

Table 2: Sample opacity tables for CFe mixture.

TOPS results

Opacities in cm**2/gm, T in keV, density in gm/cc

WARNING - Requested densities went off table boundaries

Temp Den Req Den used

1.0000E-03 1.0000E+00 7.0739E-01

Normalized composition for requested elements

No. Fraction Mass Fraction At. No. Chem. Sym.

5.0000E-01 1.7699E-01 6 C

5.0000E-01 8.2301E-01 26 Fe

Temperature grid used the following 2 points

1.0000E-03 1.2500E-03

Density grid used the following 2 points

1.0000E-01 1.0000E+00

Rosseland and Planck opacities and free electrons

Density

1.0000E-01

1.0000E+00

Density

1.0000E-01

1.0000E+00

Ross opa

4.1416E+05

4.5953E+05

Ross opa

3.3323E+05

3.7040E+05

Planck opa

8.4327E+05

2.5213E+06

Planck opa

1.2938E+06

3.8026E+06

No. Free

5.2602E-02

2.3540E-02

No. Free

1.0226E-01

5.3035E-02

Mat Id. 117831

112142

Av Sq Free

5.2604E-02

2.3541E-02

Av Sq Free

1.0231E-01

5.3057E-02

T= 1.0000E-03

T= 1.2500E-03

6 Critical Evaluation

One of the most difficult tasks in opacity calculations has been assigning error criteria to the final results. The calculations are a complex mixture of atomic physics input data and plasma modeling.

1 Databases 51
The plasma models include the EOS occupancy determination and the broadening of the boundbound line transition profiles. Up to 1988, there was very little organized comparison between the

various theoretical codes and no experimental data. Both of these situations changed in 1988 with

the meeting of the first International Opacity Code Comparison Workshop and with the publication

of the first opacity transmission experiment from RAL [9] in England. Since that year, there have

been three more workshops [10] with more than 15 participating groups, and more than half a dozen experiments from groups around the world.

Opacities from the various codes have changed by factors of 2 to 10 over the years since 1988,

especially in T — p regions where the An = 0 bound-bound line transitions are important. The

authors feel that these large uncertainties are now resolved and that one can place an upper limit of

25 % on the integrated Rosseland opacities for low and moderate densities where LTE is appropriate.

At higher densities, such as a few gm/cc at temperatures of 10 to 50 eV, the agreement between the

independent codes can differ by more than a factor of 2 and there is almost no reliable experimental

data, so it is not possible to set an uncertainty below 50 % for these regions.

References

[1] W. F. Huebner, A. L. Merts, N. H. Magee, and M. F. Argo, "Astrophysical Opacity Library",

LA-6760-M, Los Alamos National Laboratory 1977

[2] N. H. Magee, Jr., J. Abdallah, Jr., R. E. H. Clark, et al., "Atomic Structure Calculations

and New Los Alamos Astrophysical Opacities" Astrophysical Applications of Powerful New

Databases, Astronomical Society of the Pacific Conference Series, S. J. Adelman and W. L. Wiese eds., 78, 51 (1995)

[3] J. Abdallah, Jr. and R. E. H. Clark, "TOPS: A Multigroup Opacity Code", LA-10454-M, Los

Alamos National Laboratory 1985

[4] A. N. Cox, "Stellar Absorption Coefficients and Opacities" Stars and Stellar Systems, L. H.

Allen and D.B. McLaughlin eds., vol. 8, p. 195, University of Chicago, Chicago 1965

[5] J. C. Stewart and K. D. Pyatt, Ap. J., vol. 144, 1203 (1966)

[6] W. F. Huebner, "Atomic and Radiative Processes in the Solar Interior" The Physics of the

Sun, P. A. Sturrock ed., vol. 1, p. 33, D. Reidel Publishing Company, Dordrecht-Holland 1986

[7] J. Abdallah, Jr., R. E. H. Clark, and R. D. Cowan, "CATS: Cowan Atomic Structure Code",

LA-11436-M, vol. 1, Los Alamos National Laboratory 1988

[8] D. P. Kilcrease, J. Abdallah, Jr., J. J. Keady, and R. E. H. Clark, J. Phys. B, vol. 26, L717

(1993)

[9] S. J. Davidson, J. M. Foster, C. C. Smith, K. A. Warburton, and S. J. Rose, Appl. Phys. Lett. 52, 847 (1988)

[10] Third International Opacity Workshop & Code Comparison Study (WorkOp-III;94), MaxPlanck-Institut fur Quantenoptik Report No. 204, A. Rickert et al. eds., (1995)

52 ICAMDATA 97 Proceedings
TOPbase/TIPbase

C. Mendoza

Physics Center, IVIC,

Caracas, Venezuela

C. J. Zeippen

Observatoire de Paris

Meudon, France

1 Introduction

TOPbase/TIPbase is an atomic database service that has been available on the Internet since

January 1993 from both the Centre de Donnees Astronomiques de Strasbourg (CDS), Prance,

http://cdsweb.u-strasbg.fr/OP.html, and HEASARC, Goddard Space Flight Center, NASA,

USA, http://asca.gsfc.nasa.gov/docs/topbase/home.html. Direct access to the commandbased database can be managed by telnet to cdsarc.u-strasbg.fr (IP=130.79. 128.5) in France

and topbase.gsfc.nasa.gov (IP=128.183.126.111) in the USA with account id= topbase and

PW = Seaton+. TOPbase [1, 2] contains term energies, f-values and photoionization cross sections

computed in LS coupling in the Opacity Project (OP) [3] for astrophysically abundant ions (Z=l14; Z=16, Z=18; Z=20; Z=26). This database has averaged over 100 calls a month since it became

operational. TIPbase (under development) will offer the data from the current IRON Project (IP)

[4], namely level energies, radiative transition probabilities, electron impact excitation collision

strengths and rates for fine structure transitions of ions of astrophysical interest, with emphasis on

the iron group. In the present paper, we briefly discuss the atomic data, the database design, work

in progress and some important points that have emerged during our five-year experience offering

such a service.

2 Atomic data

The atomic data contained in TOPbase/TIPbase are calculated by an international group of ex- perts from Canada, France, Germany, UK, USA and Venezuela with more than 15-year experience

in large collaborative computational projects. State-of-the-art numerical methods are used such

as those implemented in the atomic structure codes Civ3 [5] and superstructure [6] and colli- sional approaches based on the R-matrix method [7, 8, 9]. The emphasis is both on accuracy and

completeness of massive datasets thus leading to series of papers where such issues are extensively

discussed, namely the series "Atomic Data for Opacity Calculations (I-XXIII)" in the Journal of

Physics B and the series "Atomic Data from the IRON Project (I-XXVIII)" in Astronomy & Astrophysics. A measure on the quality of the data produced by the OP and IP is given, for instance, by

the large number of f-values computed in the former that have been selected for the NIST reference

compilations (e.g. [10]).

3 Database design

TOPbase was one of the first on-line atomic databases that became operational on the Internet. Due to a general lack of standards and having taken the practical resolution to avoid the commercial packages in order to ensure portability at low costs, the design of the TOPbase database

1 Databases 53
management system has been entirely homemade [1]. It is closely related to the physics of the

atomic data and to the most frequent search patterns that are likely to be repeated by users and

applications. In this respect, a bound state (i) is uniquely addressed by a key defined in terms

of the following attributes: (nz, ne, islp, ilv), where nz and ne are respectively the atomic

number and electron number of the ion; islp gives the quantum numbers (total spin multiplicity, orbital angular momentum and parity) of the spectroscopic series to which it belongs, defined

as islp — 100(25 + 1) + 10L + P\ and ilv is the level energy position within the spectroscopic

series. The key for a transition (i —> j) is similarly given in terms of the attributes (nz, ne,

islp, jslp, ilv, jlv). The input selectors, based on numerical ranges of these keys, and the

index structure have been devised to facilitate searches along isoelectronic and isonuclear series, in

energy or wavelength ranges, within an ionic system or a spectroscopic series, or just for a single

level or transition. As shown in Fig. 1 the data manipulation scheme has been implemented on

two levels: the view where searches and time-consuming block data retrievals are performed from

disk; and the table where fast and versatile functions (sorting, column and row selections, graphic

display) are carried out iteratively in main storage to satisfy user requirements. Both data struc- tures allow display, printing, disk downloading and graphic processing. The present user interface

is command-based providing a fairly powerful yet simple query language. Although most regular

users have not complained about this query environment, it does discourage the occasional user who is not really prepared to invest time in learning the commands. Thus, a web-based user interface has been developed for TOPbase which is to become operational by the beginning of 1998. In

spite of the reduction in interactivity of a web interface, TOPbase keeps most of its design features,

e.g. the numeric access codes and the view and table data structures. Furthermore, the design of

TIPbase will follow the guidelines and scheme of TOPbase.

4 Recent developments

We summarize here recent work that has either been finished or is currrently in progress regarding

updates of the data and improvements of the software.

4.1 Work concluded

• Improved radiative data (e-levels, f- values, photoionization cross sections) for the ions Fe I-IV.

• Improved radiative data for the ions of oxygen.

• The TOPbase web user interface. It will become operational in January 1998.

4.2 Work in progress

® New radiative data for the P and CI isonuclear sequences.

• Radiative data in intermediate coupling for the isoelectronic sequences of Ne and Ar.

• Electron impact excitation rates for fine structure transitions in the isonuclear sequence of

Fe.

• The TIPbase database management system and user interface.

54 ICAMDATA 97 Proceedings
table

descriptor

F ^ cv se database view ex

re so

pt

px

TOPBASE general structure

Figure 1: TOPbase data manipulation scheme showing the two main data structures, the view and

the table, the display and graphic capabilities and query commands.

1 Databases 55
5 Comments

We would like to make here some comments, intended mainly for future entrepreneurs, regarding

the development and maintenance of atomic database services which have arisen in our five-year

experience running such a service.

We have found a sizable need for atomic data in the world-wide scientific community although we feel that the demand would sharply go down if it is addressed on business terms. Therefore it

is unlikely that many outsiders will be attracted by the opportunities offered by the new atomic

database projects, and therefore their development will have to rely mainly on inhouse initiatives

that would have to apply for grants to the traditional funding agencies. In other words, nobody is bound to get rich from running an atomic data business.

In our opinion it is essential to offer atomic database services within the context of a data center. In the case of TOPbase, we have worked out a good relationship and operational terms with both the

CDS and NASA. Furthermore, the concept of a data center appears to be undergoing an interesting

evolution. Rather than being a center for data compilation and publication, it is now becoming a

contractor, promoter and evaluator of distributed database portfolios which should be as close as possible to the data producers. Moreover, the marketing of the data and the establishment of new

client bases are among their new responsibilities.

The general absence of standards surely is a deterement to the proliferation of atomic databases

and makes life very difficult for both users and developers. Apart from the consensus on web-based

user interfaces, we feel that it is timely to sort out some of the remaining key issues: data-entry

and output formats, management systems, interactivity, data transfer and compression protocols,

and documentation.

In the context of electronic data dissemination, there is the implicit responsibility of ensuring

data integrity. Since the latter would eventually be passed on to the data producer, the source

reference must always be quoted in all database transactions.

References

[1] W. Cunto and C. Mendoza, Rev. Mex. Astron. Astrofis. 23, 107 (1992)

[2] W. Cunto, C. Mendoza, F. Ochsenbein, C. J. Zeippen, Astron. Astrophys. 275, L5 (1993)

[3] The Opacity Project Team, The Opacity Project, Vol. 1, IOPP, Bristol (1995)

[4] D. G. Hummer, K. A. Berrington, W. Eissner, et al., Astron. Astrophys. 279, 298 (1993)

[5] A. Hibbert, Comput. Phys. Commun. 9, 141 (1975)

[6] W. Eissner, M. Jones, and H. Nussbaumer, Comput. Phys. Commun. 8, 270 (1974)

[7] P. G. Burke, A. Hibbert, and W. D. Robb, J. Phys. B 4, 153 (1971)

[8] P. G. Burke and W. D. Robb, Adv. Atom. Molec. Phys. 11, 143 (1975)

[9] P. G. Burke, in "Physics of Electronic and Atomic Collisions" (S. Datz, ed.), p. 447, NorthHolland, Amsterdam 1982

[10] W. L. Wiese, J. R. Fuhr, and T. M. Deters, "Atomic Transition Probabilities of Carbon,

Nitrogen, and Oxygen - A Critical Data Compilation", J. Phys. Chem. Ref. Data Monograph 7

(1996)

56 ICAMDATA 97 Proceedings
NIFS Retrieval Display System for Atomic Data

through the WWW

Izumi Murakami, Masatoshi Kato, Takako Kato, NEC nifs team

Data and Planning Center, National Institute for Fusion Science,

Oroshi-cho, Toki, Gifu 509-5292, Japan

Abstract

The Data and Planning Center at NIFS has developed a retrieval display system for atomic data

since 1979. This year we reconstructed our atomic database to be accessible via the World Wide

Web. We introduce our atomic and molecular numerical databases and describe how to use them.

1 Introduction

Data compilation and evaluation of atomic and molecular data for fusion research was initiated

by working groups organized by Professors K. Takayanagi, H. Suzuki et al. in our former institute

(Institute of Plasma Physics, Nagoya Univ.) in 1975 [1]. This work has continued in the Research

Information Center in IPP, Nagoya from 1979 [2] including surface data and in the Data and

Planning Center of the National Institute for Fusion Science since 1989 [3]. The retrieval and

display system for four kinds of numerical data, listed below, was developed as a joint research

program with Drs. Y. Kanada, K. Takasugi and R. Ogasawara et al. This system has been open

for users since 1981 [4, 5] through a main frame computer (FACOM).

In 1997, we changed the database system to be accessible via the World Wide Web, and the

system has become easier to access and retrieve data from.

We have four numerical databases:

AMDIS Cross sections for ionization and excitation of atoms, ions, and molecules by

electron impact

CHART Cross sections for charge transfer and ionization of atoms, ions, and molecules

by collisions

SPUTY Experimental sputtering yields for monatomic solids by ions

BACKS Particle and energy-backscattering coefficients of light ions from solids

Each database has numerical data tables with references and empirical formulas. The

bibliographic information on numerical data contains the method of the experiment or theory, as

well as the authors' names, paper title, journal name, page, and published year. Following, we

describe how to access the new databases, how to use the retrieval display system, and A,provide

examples.

1 Databases 57
2 How to Access the Databases and Retrieve Data

We require users to register and get an account before they access the databases. This does not

mean that we charge users. We need to know who is using the databases and for what purpose.

For registration, access the URL address, http: //dbshino.nifs.ac.ip/. Following the instructions,

go to the brief description page on the databases and regulations, and then go to the registration

page where you may submit your personal information for registration to dbmaster@dbshino. nifs .ac.jp . Do not forget to write your purpose for using the databases. We

opened the databases only for scientific research, and we will determine who is acceptable as a

user. You will receive your account ID and password in a week by e-mail.

At the front page, we also link to our other web site at URL= http:llamdata.nifs.ac.ip/ for

information on the numerical databases. You will find tables showing how many data sets are

stored for each ion species. After clicking the position of the ion you are interested in, you will find

graphs of the cross section from AMDIS. Also, there are examples of data stored in ALADDIN

format with graphs for rate coefficients as well as cross sections.

Here, we briefly describe how to use our numerical databases. The procedure is as follows:

1. Access the system at URL=http://dbshino.nifs. ac.jp, type in your account ID and

password.

2. Choose a database name from the list.

3. Set searching conditions, such as element name, and search.

4. Select process(es) which you are interested in from the list.

5. Select either standard or custom for bibliographic information or numerical data for

tables and graphs and push the display button.

6. Select units for the data to be displayed for AMDIS, CHART, and BACKS and push

the display button.

7. 20 bibliographic data items are shown in one page.

8. For AMDIS, you may choose data one by one to be displayed in tables or graphs.

9. For BACKS, choose angles or energy to be plotted in a graph.

10. Before drawing graphs, you may specify how to draw axes, whether to draw an

empirical curve or not, and the positions for drawing symbol descriptions. A postscript

file of the graphs can be downloaded after they are drawn.

For each step in this procedure, you move on to a deeper web page. To each web page is attached

a help page which pops up as a separate window. In Step 2, you will find CURVE which draws

empirical formulas for specific ions.

3 Examples

Following are examples of searching for ionization cross sections by electron impact and

excitation cross sections (AMDIS).

58 ICAMDATA 97 Proceedings
3.1 AMDIS Ionization

To search for cross sections for a single ionization of neutral Neon, put "Ne" for element, "0" for

initial ionic state, and "+2"for final ionic state, as shown in Fig. 1. In addition, you may specify

author names, published years, and some more conditions or select theoretical, experimental, or evaluated data.

You can make numerical data tables or graphs. The graph of the cross section is shown in Fig. 2

for this case. An empirical curve calculated with Lotz's formula can be drawn together with the

data.

[Help] AMDIS IONIZATION

ISearch Data! iForm Clear]

Element

Initial ionic state: 1 0 1 Number of electrons I I (if you want to search for isoelectronic sequence.)

Final ionic state: I +/ I

Theoretical OExperimental DEvaluated

Author: I I Year of Publication: From IZZZH Tn I I (YYYY)

Additional conditions for search: [Type Table] [Journal Table]

Figure 1: A sample for setting search conditions for AMDIS-IONIZATION.

AMDIS-ION

Ne + 2e

T

1—I I I 1 1

1

970920 15:22

o Krtshnakumar, £. etal.(l966)E

m Krshnakumar.6 el al. (1988)6 * Wetzel. R.C.etal. (1987)6

a McCarthy. I.E. el al.M963)T

* Bleakrwy. W. (1930)6

+ Adamczylt. B. etal.{1966)E

0 Van dor W. MJ elal .(1969)6

1 Nngy. P. e( a) (1960)6 Shcfwnehnln. S.G. el al. (1976)6 • Gaudin.A. el al. (1967)6

« Schram.B.L. el al. (1966)6 * Peach. G.M971)T

/ McGiwe. 6J. (19711T

a Stophan, K et al. (1980)E

Younger, S.M.(1862)T

Younoer. S.M. (1962)T

• OnloVar, K.elsl. (1972)T

10 10 10 Electron Energy CeV)

Figure 2: Cross section for the single ionization of neutral Neon, drawn in AMDIS-IONIZATION.

The Lotz's empirical formula is also drawn.

1 Databases 59
3.2 AMDIS Excitation

Similarly, you can search for the excitation cross section from Is2 X S to ls2p l P for He-like carbon,

for example. Enter "C" for element and "2" for the number of electrons. For the initial state configuration, enter "ls2". For the final state, enter "Is 2p" for the configuration, "1" for the

multiplicity, and "P"for the orbital angular momentum.

When making a graph, you can select either a cross section or collision strength. An example

of the latter is shown in Fig. 3.

AMDIS-EXC 971020 15:22

i2p

1

1 i i i i ii| © Magee.N H. atal. [1977)T

* Nakazaki, S. {1976)T ' * Foster, G. atal. (1977)T a Foster. G elal. (1977)T v MaQW, Jf.NM •lal.(1977)T + Bhatia, A.K. at al. (1977)T * Bhatia,A.K. etaJ.il977)T

n—i—rm

* NakozakJ. 5. ( I83)T m NekazakJ, S. (1963 T

* NakazakJ. S. (19B3 T

* Nakazaki, S. el el. (19B2)T

NakAzaki, S. e( al.ji962)T * M*fts. AX M981)T

» Pmdhan, A.K. rtal. (198I)T b Maaee, N.H.atal. (1977)T a BameJI. N.R. (196S)T MaoM. N.H etal. (19771T Magee. N.H. et al. (1977TT o Batuja. K L. el el. (1980)T Wyrmearden, W.Lvan. t>\ al. M979)T

- Magae, Jr N.H. et al. (1977)t (1977)1

Electron Energy E/AE

Figure 3: Collision Strength as a function of E/AE, drawn in AMDIS-EXCITATION.

4 Remarks

We are interested in atomic data needs and appreciate your comments and requests. We welcome

your suggestions on improving the databases. Please send your requests, questions, and your

data by e-mail to dbmaster@dbshino.nifs.ac.jp . Instructions on data formats are being prepared

and will appear soon. We are grateful to Dr. Y. Kanada, Dr. K. Takasugi, and Dr. R. Ogasawara for creating the

database and retrieval display system and for their help and advice on the new database system.

References

[1] Cross sections for Atomic Processes Vol.1, IPPJ-DT-48 (1975), Vol.2, IPPJ-DT-50 (1976)

edited by K. Takayanagi, H. Suzuki.

[2] IPPJ-AM series, IPP, Nagoya Univ., Japan

[3] NIFS-DATA series, National Institute for Fusion Science, Japan

[4] T. Kato, Y. Itikawa, Y. Kanada, and R. Watanabe, Physica Scripta 23, 198 (1981)

[5] T. Kato et al., J. Nucl. Mater. 128 & 129, 1006 (1984)

60 ICAMDATA 97 Proceedings
Wavelengths of Six Times Ionized

Germanium, Ge VII

L. I. Podobedova1 - 2 and A. N. Ryabtsev2

lNational Institute of Standards and Technology, Gaithersburg MD 20899 U.S.A.

institute of Spectroscopy RAS, Troitsk, 142092 Russia

A compilation of Ge VII wavelengths has been carried out for the NIST Atomic Spectra Database

on the World Wide Web. The compilation is based on our previous analyses of the germanium

spectra: the 3d8 -3d74p transition array in the range 160-210 A, 3p63d8-3p5 3d9 in the range 123-142

A and 3d7 4s-3d7 4p in the range 739-987 A [1-3] and the compilation of energy levels by Sugar and

Musgrove [4]. A Russian publication [1] with the complete list of wavelengths of Ge VII is not well

known; no new data on this spectrum were obtained since our analyses.

The Ge VII spectrum was excited in a three- electrode vacuum spark with the discharge

parameters C=l-10 uF, L= 500-1000 nH, and U= 4-10 kV. Transitions to the ground state, lying

in the region shorter than 200 A, were studied from spectrograms obtained with a 3-m grazing

incidence vacuum spectrograph (angle of incidence 85°) with a 3600 lines/mm grating. When

working in the region longer than 700 A, where transitions between excited states are located, we

used a 6.65—m normal incidence vacuum spectrograph with a 1200 grooves/mm grating. The

standard error for the wavelengths in the short-wave region was estimated at 0.004 A, and in the

long-wavelength region, 0.007 A.

The Ge VII spectrum belongs to the iron isoelectronic sequence, having a ground-state

configuration 3p6 3d8 and the lowly excited configurations 3d7 4s, 3d7 4p, 3p5 3d9 and 3d7 4f. The

3p5 3d9 configuration, with the excitation of an electron from an inner shell, which is unknown at the beginning of the isoelectronic sequence, decreases in energy with respect to valence electron

excitations as the ionization stage increases. As a result, a strong interaction between the

3p63d74p and 3p5 3d9 configurations is observed for a number of ions of the sequence including Ge

VII (Fig. 1). The analysis of the resonance transition array 3d8 - 3d7 4p, located in the region 160-

210 A, has been carried out in [2]. All levels of the ground configuration 3d8 and 85 of 110 levels of

the 3d7 4p configuration have been found. Other levels of the latter configuration either do not

have transitions to the ground configuration or the transitions are very week. These levels can be

found by studying transitions to the 3d7 4s configuration. The analysis of the 3d7 4p-3d7 4s and

3p63d8 -3p5 3d9 transition arrays and the necessary corrections of the 3d7 4p configuration were made in our subsequent work [3] . Thus all levels of the 3d8

, 3d74s, 3s74p and 3p5 3d9 configurations were established. Later, these levels were compiled in [4]

.

The purpose of the present work is to check our previous analysis and to present a wavelength

table in the format of the NIST Database. It should be noted that we interpreted the spectra on

the basis of single-configuration calculations because of our calculation limitations at that time.

Besides, the knowledge of other ions of the Fe-like isoelectronic sequence was very poor. In 1980,

when we started to work on the Ge VII spectrum, the highest well-studied member of this

sequence was Cu TV The spectra Zn V and Ga VI were under study, and only preliminary values

for the levels of the term 3d8 3 F were known. Since that time, a great amount of work has been

done for many spectra of Fe-like ions. Now, the resonance transition array 3d8 -3d7 4p has also

been studied for the Zn V-Br X, Rb XII and Sr XIII ions. The 3p63d8-3p5 3d9 transition array is known for the Ga VI-Br X and Ag XXII-Sn XXV ions. In these latter ions, this transition array

1 Databases 61
- f)

3d74f - cm^xlO3 2000

s3d9 -

1 500

'4 P

-

1 000

500

0

Ni ill Zn V Ge VII Se IX KrXI Sr XIII Figure 1: Average energies of the three lowest odd configurations realtive to that of the ground

configuration along the Fe I sequence.

The Hartree-Fock (HF) and least-square fit (LSF) calculations were carried out for the studied

configurations by means of the Cowan code. The final values of the corresponding parameters and

their ratios are given in Table 1. All 47 energy levels of the even 3d8 and 3d7 4s configurations are included in the LSF calculation, and the mean-square deviation a is 91cm-1

. The effective

parameters (3 and T for the 3d8 configuration were fixed because of the instability of the fitting

process, and the values for them were taken to be the same as for the 3d74s configuration. The

odd configurations 3d7 4p, 3p5 3d9 and 3d7 4f were included in the calculation with their interaction.

As noted above, there is a strong interaction between the 3d7 4p and 3p5 3d9 configurations, even though the average energies of these configurations are separated by 226,640 cm 1

. According to the HF calculation, the 3d7 4f configuration is located 83,680 cm1 higher and also disturbs some

levels of the 3p5 3d9 configuration. All 122 energy levels of the 3d74p and 3p5 3d9 configurations were included in the LSF calculation and the mean square deviation a is 131 cm1

. We increased

the average energy of the unknown 3d3 4f configuration by 3005 cm1 with respect to the HF value

as in the 3d7 4p configuration. All parameters were fixed according to the usual scaling factors

from the HF values: 0.85 for the electrostatic interaction and unity for the spin-orbit interaction.

The configuration interaction parameters were scaled by a factor of 0.85 for both even and odd

configurations. In conclusion, we note that the LSF/HF ratios for all studied configurations are

close to those predicted by extrapolation along the isoelectronic series. It is also interesting to note

that the 3p5 3d9 ^3° level deviates from the computed value by only -7 cm-1

; in the singleconfiguration calculation [1] this deviation was -7155 cm-1

. On the basis of this work, we confirm our previous classifications for all spectral lines and

energy levels except for the 3p63d8 3Pi-3p5 3d9 3Po° transition. Instead of the line at 135.018 A, the

correct line is at 135.008 A. Correspondingly, the 3p5 3d9 3Po° level, having only one transition to the ground state, changes from 769854 cm-1 to 769908 cm-1

. We also added second classifications

62 ICAMDATA 97 Proceedings
for three lines, in accordance with the transition probabilities calculated with the final

parameters of the LSF calculation. Besides, a few misprints in the designations of the classified

lines have been corrected. After checking the analysis, we prepared a table of the classified

wavelengths including more than 520 Ge VII spectral lines. This table will appear in an upcoming

new version of the NIST Atomic Spectra Database.

References

[1] L. I. Podobedova, A. N. Ryabtsev, Reprint ISAN (Institute of Spectroscopy, USSR Academy

Sciences) No.ll, p. 28 (1986)

[2] L. I. Podobedova, A. A. Ramonas, and A. N. Ryabtsev, Opt. Spectrosc. 49, 247 (USSR 1980)

[3] L. I. Podobedova, A. N. Ryabtsev, Opt. Spectrosc. 60, 694 (USSR 1986)

[4] J. Sugar and A. J. Musgrove, Phys. Chem. Ref. Data 22, 1213 (1993)

1 Databases 63
Table 1: Parametric values of the energy integrals and their ratios to the Hartree-Fock values for the

3d8 +3d7 4s and 3d7 4p + 3p5 3d9 + 3d7 4f configurations in GeVII (cm 1 ).

Configuration Parameter LSF Error HF LSF/HF*

3p5 3d9

Eav(3d8) 19212 40 21541 -2329

F2(3d,3d) 130539 311 148806 0.877

F4(3d,3d) 83108 283 93874 0.885

a(3d) 66 007

p(3d) 550 f T(3d) -8 f C(3d) 1948 43 1950 0.999 Eav(3d7 4s) 436151 19 434305 1846

F2(3d,3d) 134696 104 154339 0.873 F4(3d,3d) 87076 203 97613 0.892

a(3d) 68 7 P(3d) 550 121

T(3d) . -8 1 C(3d) 2107 18 2069 1.018 G2(3d,4s) 14097 82 14281 0.987

R2(3d,3d;3d,4s) 11270 f 13259 0.850

CT 91 Eav(3d7 4p) 553079 15 550074 3005

F2(3d,3d) 135781 89 154506 0.879 F4(3d,3d) 87292 193 97730 0.893 a 57 6

p 768 100

T(3d) -9 1 C(3d) 2092 16 2072 1.010

C(4p) 3812 34 3278 1.163 F2(3d,4p) 35302 129 36020 0.980 Gl(3d,4p) 11210 58 11938 0.939 G3(3d,4p) 11284 151 11409 0.989 Eav(3p5 3d9) 779719 57 807033 -27314

C(3p) 23397 124 22166 1.056

C(3d) 1857 62 1946 0.954 Fl(3p,3d) 11686 627

F2(3p,3d) 148729 548 149744 0.993 Gl(3p,3d) 148827 362 181099 0.822 G2(3p,3d) -5981 698

G3(3p,3d) 114830 594 112606 1.020 Eav(3d7 4f) 863400 f 860395 3005

F2(3d,3d) 131967 f 155255 0.850 F4(3d,3d) 83502 f 98238 0.850

C(3d) 2087 f 2087 1.000

C(4f) 8 f 8 1.000

F2(3d,4f) 12868 f 15139 0.850

F4(3d,4f) 4711 f 5542 0.850 Gl(3d 4f) 5841 f 6872 0.850

G3(3d,4f) 3365 f 3959 0.850

G5(3d,4f) 2309 f 2717 0.850

Rl(3d,4p;3d,3d) 12652 f 14885 0.850 R3(3d,4p;3d,3d) 12651 f 14883 0.850

R2(3d,4p;3d,4f) 13408 f 15774 0.850

R4(3d,4p;3d,4f) 4586 f 5395 0.850

Rl(3d,4p;4f,3d) 1655 f 1947 0.850

R3(3d,4p;4f,3d) 1694 f 1993 0.850

Rl(3d,3d;3d,4f) -25658 f -30185 0.850

R3(3d,3d;3d,4f) -13185 f -15512 0.850 a 131

* Differences Eav(LSF)-Eav(HF) are presented for Eav. f - The parameters are fixed.

64 ICAMDATA 97 Proceedings
The ORNL Controlled Fusion Atomic Data Center

D. R. Schultz, P. S. Krstic, F. M. Ownby, F. W. Meyer, C. C. Havener,

M. E. Bannister, W. Liu, D. J. Jeffery, and P. C. Stancil

Physics Division, Oak Ridge National Laboratory

Oak Ridge, TN 37831-6373

Abstract

The principal mission of the Controlled Fusion Atomic Data Center is the collection, evaluation, and dissemination of atomic collision data relevant to fusion energy development. With the

advent of the widespread use of the World Wide Web, the data center's resources are being placed

on-line to facilitate their use by end-users (cf. http://www-cfadc.phy.ornl.gov/). As this development continues, initially disparate, individually compiled resources will be transformed

into integrated tools for retrieving recommended data, or displaying and manipulating the in- formation available. The data center's present capabilities, recent data production/evaluation

efforts, and goals for future development are highlighted here.

1 Introduction

Since its inception at Oak Ridge National Laboratory in 1958 and formal establishment in 1963,

the Controlled Fusion Atomic Data Center (CFADC) has published indexed compilations of bibliographical information and recommended numerical data regarding atomic, molecular, and particlesolid collisions of interest in fusion energy research. Rather than attempting to provide here an

exhaustive history of the CFADC and its activities, we briefly summarize the resources available

through the data center, primarily through the World Wide Web [1].

2 The "Redbooks"

In order to provide convenient recommended sets of atomic, molecular, and particle-solid collision

data to the fusion energy research community, the CFADC has periodically published collections

containing numerical and graphical data. Owing to their red bindings, these series of volumes

have become known in the community as the "Redbooks." Usually a small group of experts

has surveyed the existing experimental and theoretical works within a given range of reactions,

and determined and catalogued recommended reaction cross sections. The latest series of such

collections of recommended cross sections, rates, and numerical fits is entitled "Atomic Data for

Fusion" [2]. Since only 500 copies of each volume were originally printed and distributed, the

number of users to which these collections have been available was limited. Therefore, we have

recently scanned the two most requested volumes and made them available through an indexed set of hypertext links on the data center Web site [1]. Users can view, print, or download the graphical

and tabular data of interest directly from the Web.

Furthermore, the recommended data contained in the Redbooks have been recorded in the

ALADDIN format, for ease of exchange within the fusion energy research community (see below).

In the near future, hypertext linkages of the Redbook pages will allow the user-viewable graphs and

tables to be directly linked to these separately organized ALADDIN data entries, and ultimately to

1 Databases 65
other resources. For example, when a CFADC bibliographic search is performed through the Web

interface, Redbook graphical, tabular, and fit coefficient data will be returned in addition to the

bibliographic listing. The existence of the Web-based version of the Redbooks will allow them to be updated in the future without the necessity of re-distributing new editions. That is, as data of

improved accuracy or for new reactions becomes available which lead to modifications or extensions

of the Redbook recommendations, new pages can easily be placed on the Web site.

3 The CFADC Bibliography

Another principal product of the CFADC has been a series of published bibliographies. Access

to such information is a crucial first step in the process of providing critically evaluated data

for applications like fusion energy research. After a long series of publications beginning in the

1960's, the semiannual CFADC bibliographic updates have recently been published along with

contributions from other foreign data centers through the International Atomic Energy Agency

(IAEA) in volumes entitled "International Bulletin on Atomic and Molecular Data for Fusion."

Convenient cumulative indices to the bibliographic entries were published in 1980 and 1987 through

the IAEA as well [3]. The ever increasing number of collected entries has lead to a succession of computer-based

databases for archiving and organizing this information. Presently, the CFADC makes available

entries dating from 1978 to the present (about 30,000 entries) over the Web [1]. This method of

dissemination is quite effective in that it allows users unlimited direct access to the full, current

database. Efforts are also underway to place the CFADC archival entries (dating from c. 1950 to 1977 and numbering approximately 40,000) on the Web-based system, and to link the bibliographic

search engine with other resources such as the Redbooks and ALADDIN. For the benefit of the

reader, we also mention that a group lead by the Laboratoire de Physique des Gaz et des Plasmas at the Universite Paris-Sud maintains a completely independent general atomic and molecular bibliographic database which can also be searched via the Web (see http : //gaphyor . lpgp . u-psud . fr/).

4 The International ALADDIN Network

Coordinated through the IAEA Atomic and Molecular Data Unit, the CFADC participates in an

international network of atomic data centers whose missions involve the support of fusion energy

research. Among this data center network's primary activities is the maintenance of a standard

format of atomic and molecular data exchange called ALADDIN (A Labeled Atomic Data INterface). Originally developed by Russell Hulse of PPPL, ALADDIN was adopted in 1988 by the

network. Almost two dozen collections of recommended or evaluated atomic collision data and

particle-surface interaction data exist in this format, representing data for hundreds of individual

reactions. This data provides a primary resource for atomic and molecular data for fusion energy

research, often directly linked to plasma modeling codes. Furthermore, ALADDIN possesses a FORTRAN interface code through which searches of the data files for individual reaction data can be made, and tabulations from the fitted data coefficients can be outputted.

The data files, computer code, associated evaluation functions, and dictionaries have been

distributed from the IAEA A+M Data Unit or the CFADC to interested parties, and are now

available through the Web [1] for direct viewing and downloading. Preliminary linkage of the

CFADC bibliographic search engine and the ALADDIN files has been recently accomplished and

ALADDIN can be run directly over the Web. The IAEA maintains an Internet linkage to ALADDIN

and is planning a Web interface. Web-based interfaces will also hopefully lead to flexible, updatable

methods of maintaining and enhancing this valuable resource.

66 ICAMDATA 97 Proceedings
5 The Atomic Data and Analysis Structure

Developed in collaboration between Strathclyde University and the Joint European Torus (JET)

principally by Hugh Summers, the Atomic Data and Analysis Structure (ADAS) is a collisionalradiative modeling suite designed to aid in the interpretation of the spectra of radiating plasmas.

Its primary application has been fusion plasma diagnostics for JET, but has also recently been

employed to aid in interpreting observations by the Solar and Heliospheric Observatory satellite. A consortium, of which the CFADC is a member, has also recently been formed to allow access to

this powerful set of computer codes and data collections for a wider user community. A detailed

description of the ADAS suite can be found on-line at Strathclyde University or mirrored at the

CFADC (see the "links" hyperlink on the CFADC WebSite [1]).

6 The ORNL Multicharged Ion Research Facility

An important aspect of the ORNL atomic physics for fusion program in addition to the CFADC

is the Multicharged Ion Research Facility (MIRF). This facility has a long history of providing

atomic data for electron-ion, ion-atom, and ion-surface collisions. Experiments in each of these

areas are actively ongoing and utilize a state-of-the-art Caprice Electron Cyclotron Resonance ion

source. Descriptions of the MERF experiments are available through the CFADC Web site [1] as are indexed tabulations of certain portions of the data measured there. For example, the data obtained

over the past three decades regarding electron impact ionization of atomic ions has been collected

and organized into a hyperlinked Web resource. Similar work has been initiated for the ion-atom

merged beams experiment, and linkages between these data collections and the bibliographic search

engine will be made in the future.

7 Data Projects

Another aspect of the CFADC's mission is to provide whenever possible new calculations and/or

evaluations of data which is urgently needed in fusion energy research. To this end, we have recently

concentrated on the production of data for use in charge exchange recombination spectroscopy

by computing large collections of state-selective charge transfer cross sections. These have been

considered for a range of ions including those of Be [4] (owing to its low atomic number and

consequent low induced radiation losses, it has been a primary plasma-facing component material

candidate), Ne [5] (due to its introduction into the divertor to beneficially enhance radiation losses

for energy exhaust), and Ar (due to its introduction as a diagnostic species) colliding with primary

plasma components (H, H2, and He).

Also, due to the need to model the momentum transport in the divertor plasma in present and

next-step fusion devices, we have computed and tabulated the elastic and related transport cross

sections for collisions among the isotopic variants of H+ + H, H2, and various other reactions of

interest [6]. Work on production of both charge transfer and transport cross sections is ongoing.

Some of these tabulations are available on the Web site under the "eprints" hyperlink, and future

plans are to more systematically include them in data collections linked to the bibliographic search

engine.

1 Databases 67
8 Towards the Future

Even though the needs of fusion and other applications for collected, evaluated, and recommended

atomic data persist and in fact intensify, the human resources available for such activities continues

to dwindle. Thus, an effective leveraging of these human resources by utilization of the World Wide

Web as a means for disseminating data produced or collected at the CFADC, and across other sites maintained by other data centers, will be a dominant trend in the future. Linkages will be made

between the disparate, individual data collections and resources. This will improve users' ability to find the required information, and will form a powerful aid for data evaluation. For example,

combining in a single graphically oriented Web tool the ability to display existing recommended

data, results from well-established scaling laws, new basic data from linked data collections, and

data contained in other resources even across the Web, will facilitate efforts to carry out projects

to recommend data and provide centralized, updatable files for access by users. Also, recognizing

that the atomic data needs of a wide range of applications are in essence similar, the CFADC has

initiated a program of production and collection of data of importance in astrophysics, an another

important leveraging of resources. These data efforts are complimented by ongoing state-of-the- art modeling of astrophysical environments such as those present in later epochs of supernovae

explosions.

Acknowledgement

The Controlled Fusion Atomic Data Center is supported by the U.S. Department of Energy's Office

of Fusion Energy Sciences through Oak Ridge National Laboratory, managed by Lockheed Martin

Research Corporation under grant number DE-AC05-96OR22464.

References

[1] Entry to the CFADC's on-line resources is through http : //www-cf adc . phy . ornl . gov/ on the

World Wide Web.

[2] "Atomic Data for Fusion", Vol. 1, Collisions of H, H2, He and Li Atoms and Ions with Atoms

and Molecules, C. F. Barnett, ed., ORNL-6086, 1990; "Atomic Data for Fusion", Vol. 3,

Particle Interactions with Surfaces, E. W. Thomas, ed., ORNL-6088, 1985; "Atomic Data for Fusion", Vol. 4, Spectroscopic Data for Iron, W. L. Wiese, ed., ORNL-6089, 1985; "Atomic

Data for Fusion", Vol. 5, Collisions of Carbon and Oxygen Ions with Electrons, H, H2 and He,

R. A. Phaneuf, R. K. Janev, and M. S. Pindzola, eds., ORNL-6090, 1987

[3] "Computer Index to Atomic and Molecular Data (CIAMDA 80)", International Atomic Energy Agency, Vienna 1980; "Computer Index to Atomic and Molecular Data (CIAMDA 87)",

International Atomic Energy Agency, Vienna 1987

[4] D. R. Schultz, P. S. Krstic, and C. O. Reinhold, Physica Scripta T62, 69 (1996)

[5] D. R. Schultz and P. S. Krstic, Atomic and Plasma-Material Interaction Data for Fusion 6,

173 (1995)

[6] D. R. Schultz, S. Yu. Ochinnikov, and S. V. Passovets, Elastic and Related Cross Sections for

Low-Energy Collisions among Hydrogen and Helium Ions, Neutrals, and Isotopes, in "Atomic

and Molecular Processes in Fusion Edge Plasmas", R. K. Janev, ed., Plenum, New York 1995;

P. S. Krstic, D. R. Schultz, and G. Bent, Physica Script T62, 21 (1996)

68 ICAMDATA 97 Proceedings
The Database «SPECTR» on Spectral Properties of

Atoms And Ions

I. Yu. Skobelev, A. Ya. Faenov, and A. I. Magunov

Multicharged Ion Spectra Data Center (MISDC) of VNIIFTRI,

Mendeleevo, 141570 Russia

1 Introduction

r The database «SPECTR» has been created in the Multicharged Ion Spectra Data Center (MISDC)

of VNIIFTRI as a tool to allow the fast determination of information on spectra of atoms and ions.

It is a database containing data on spectroscopic constants of isolated atoms and ions (energy

levels, wavelength of spectral lines, radiative probabilities, ionization potentials) and. some

collision data (dielectronic recombination rates, electron impact excitation cross sections and

rates, electron impact ionization cross sections and rates).

Currently, the database «SPECTR» contains more than 450000 numerical records. The largest

part of the data concern the UV and X-ray spectral regions, X < 100. Besides published data

(experimental and theoretical), the experimental data produced at MISDC for the X-ray spectral

band X < 26 are used in database «SPECTR».

2 MISDC of VNIIFTRI and Database "SPECTR"

The multicharged Ions Spectra Data Center of VNIIFTRI is a research group, working in the field

of X-ray spectroscopy of multicharged ions and its application for the diagnostics of hightemperature plasmas.

Main Fields of Investigations:

A. creation of Bragg and Bragg-Fresnel optical elements for high-resolution X-ray spectroscopy

(see, for example, [1-9]) B. high-precision X-ray spectroscopy of multicharged ions (emission spectra observations,

spectral line identification, accurate wavelength measurements) (see, for example, [6, 10-22])

C. creation of X-ray spectroscopy diagnostic methods and their application to measurements of

different plasma parameters (laser-produced plasmas, Z- and X- pinches, plasma focus) (see,

for example, [23-28])

D. creation of a database on spectra of atoms and ions (database "SPECTR")

Database "SPECTR"

The database SPECTR (DB "SPECTR"), on one hand, contains a great number of data on

characteristics of atoms and ions, and, on the other hand, represents also the software to quickly

find the information needed, to browse on the screen and to make a hard copy.

The information stored in DB SPECTR may be divided into two parts. The first part (and now

the larger one) is the data on properties of isolated atoms and ions, that is, the data on energy

1 Databases 69
level structure, wavelengths of radiative transitions and its probabilities. The second part

contains the data on characteristics of collision processes. The main difference between these two

parts is the following: The first part deals with a set of constants, while the second one deals with

a set of functions. That is, for any radiative transition its wavelength, radiative probability,

energies of upper and lower levels are numerical quantities, but its collisional characteristics are

functions of the relative velocity of the colliding particles. Therefore, the software used to operate on these two different types of data is also somewhat different.

DB "SPECTR" Software

The database "SPECTR" software is based on FoxPro Database Management System. The

information is stored in well-known DBF-format and can be transferred easily into another

formats.

DB "SPECTR" Data

The quantitative characteristics ( 4 May 1997):

Data on spectral lines 397 885 records

Data on energy levels 75 100 records

Data on ionization potentials 2 292 records

Data on excitation cross sections and rates 4 932 records

Data on ionization cross sections and rates 276 records

Data on references 504 records

The total number of records 481 134

Qualitative Characteristics

DB "SPECTR" is a database on the characteristics of isolated atoms and ions, i.e., on spectral lines

(wavelengths and radiative probabilities) and energy levels. The small number of collisional data were included mainly to test the software developed. Since the MISDC research team works in

the field of X-ray spectroscopy, the main part of data (about 75%) refers to the multicharged ions.

Data sources S Published experimental data. For the X-ray region, the database contains practically all published experimental data, for the UV and visible regions only some data.

S Our own experimental data for multicharged ions. The MISDC research group has produced

experimental data on the X-ray spectra of multicharged ions for more than 20 years. For

example, during last 5 years we have produced new accurate data on satellite lines caused byradiative transitions in He-, Li-, Be-, B-, C-, N-, 0-, F-, Na-, Mg- like ions, and on high-n

transitions in He- and Ne-like ions. Producing this kind of information is the main field of

scientific interest of the MISDC group. For this purpose we create new types of X-ray highresolution spectrographs (with spherically bent crystals, for example) and develop new

methods which improve the accuracy of wavelength measurements.

S Theoretical data, both published (not all, of course) and calculated especially for DB

"SPECTR" in some Russian institutes (see, for example, [29]).

70 ICAMDATA 97 Proceedings
DB "SPECTR" Performance

The search operations are executed fast, and some examples are presented in this table:

Database SPECTR

(4 May 1997)

Total number of records 481 134

Pentium-133, 16 MB RAM

QUERY SEARCH

TIME

THE NUMBER OF

RECORDS SELECTED

1 Lines of copper ions in spectral region 10.1 - 10. IX A 2s 9

2 Lines of silver ions in spectral region 10 - 15 A 5s 94

3 Lines of H-like and He-like silicon 4s 3192

4 3d-2p transitions in Ne-like and Na-like silver 2s 313

5 ls2p x Pi - Is2

So transition in He-like uranium 2s 2

6 2s2p6 3p - 2s2 2p6 transitions in Ne-like ions 1 s 411

7 Lines of 01 atom 1 s 441

8 Lines of O-like and N-like iron 3 s 998

References

[I] S. A. Bel'kov, B. A. Bryunetkin, N. V. Zhidkov, I. Yu. Skobelev, N. A. Suslov,

A. Ya. Faenov, Quantum Electronics 24, 253 (1994)

[2] A. Ya Faenov, S. A. Pikuz, A. I. Erko, B. A. Bryunetkin, V. M. Dyakin,

G. V. Ivanenkov, A. R. Mingaleev, T. A. Pikuz, V. M. Romanova, T. A. Shelkovenko,

Physica Scripta 50, 333 (1994)

[3] S. A. Pikuz, V. M. Romanova, T. A. Shelkovenko, T. A. Pikuz, A. Ya. Faenov,

E. Forster, J. Vol'f, O. Verhran, Quantum Electron. 22, 21 (1995)

[4] T. A. Pikuz, A. Ya. Faenov, S. A. Pikuz, V. M. Romanova, T. A. Shelkovenko,

Journal of X-ray Science and Technology 5, 323 (1995)

[5] A. I. Erko, L. A. Panchenko, S. A. Pikuz, A. R. Mingaleev, V. M. Romanova,

T. A. Shelkovenko, A. Ya. Faenov, B. A. Bryunetkin, T. A. Pikuz, I. Yu. Skobelev,

Rev.Sci.Instrum. 66, 1047 (1995)

[6] I. Yu. Skobelev, A. Ya. Faenov, B. A. Bryunetkin, V. M. Dyakin, T. A. Pikuz, S. A.

Pikuz, T. A. Shelkovenko, V. M. Romanova, JETP 81, 692 (1995).

[7] J. P. Geindre, P. Audebert, A. Rousse, J. C. Gauthier, A. Ya. Faenov, T. A. Pikuz,

S.A. Pikuz, T. A. Shelkovenko, Physica Scripta 53, 645 (1996)

[8] A. Ya. Faenov, T. A. Pikuz, A. A. Firsov, L. A. Panchenko, Yu. I. Koval, M. Fraenkel,

A. Zigler, Physica Scripta 55, 167 (1997)

[9] M. Sanchez del Rio, A. Ya. Faenov, V. M. Dyakin, T. A. Pikuz, S. A. Pikuz, V.

M. Romanova, T. A. Shelkovenko, Physica Scripta 55, 735 (1997)

[10] A. Ya. Faenov, S. A. Pikuz, A. S. Shlyaptseva, Physica Scripta 49, 41 (1994)

[II] S. A. Pikuz, D. A. Hammer, D. H. Kalantar, A. Faenov, I. Yu. Skobelev, Phys.Rev.A 49,

3450 (1994)

1 Databases 71

4
[12] B. ABryunetkin, A. Ya. Faenov, M. P. Kalashnikov, P. V. Nickles, M. Schnurer,

I. Yu. Skobelev, J. Abdallah, R. E. H. Clark, JQSRT 53, 45 (1995)

[13] S. Bollanti, P. Di Lazzaro, F. Flora, et al, Physica Scripta 51, 326 (1995)

[14] A. Ya. Faenov, D. A. Hammer, J. Nilsen, A. Osterheld, S. A. Pikuz, T. A. Pikuz,

V. M. Romanova, T. Shelkovenko, I. Yu. Skobelev, Physica Scripta 51, 454 (1995)

[15] A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, G. A. Kyrala, J. A. Gobble, K. D. Fulton,

J. Abdallah Jr., D. P. Kilcrease, Phys. Rev. A. 51, 3529 (1995)

[16] A. Faenov, B. Bryunetkin, V. Dyakin, S. Pikuz, I. Skobelev, U. Safronova, T. Pikuz,

J. Nilsen, A. Osterheld, Phys.Rev.A 52, 3644 (1995)

[17] A. I. Magunov, V. M. Dyakin, A. Ya. Faenov et al, JETP 83, 267 (1996)

[18] A. I. Magunov, V. M. Dyakin, A. Ya. Faenov, et al, Phys. Rev. A 54, 3971 (1996)

[19] A. L.Osterheld, J. Nilsen, S. Ya. Khakhalin, A. Ya. Faenov, S. A. Pikuz,

Physica Scripta 54, 240 (1996)

[20] I. Yu. Skobelev, A. Ya. Faenov, V. M. Dyakin et al, Phys.Rev.E 55, 3773 (1997)

[21] I. Yu. Skobelev, A. Ya. Faenov, A. I. Magunov, A. L. Osterheld, B. K. F. Young,

J. Dunn, R. E. Stewart, Physica Scripta T73, 104 (1997)

[22] J. Abdallah, Jr., A. Faenov, D. Hammer, et al, Physica Scripta 53, 705 (1996)

[23] S. A. Pikuz, B. A. Brynetkin, G. V. Ivanenkov, A. R. Mingaleev, V. M. Romanova,

I. Yu. Skobelev, A. Ya. Faenov, S. Ya. Khakhalin, T. A. Shelkovenko, JQSRT 51, 291

(1994)

[24] T. Pisarczyk, B. A. Brunetkin, A. Ya. Faenov, et al, Physica Scripta 50, 72 (1994)

[25] V. M. Dyakin, A. Ya. Faenov, A. I. Magunov, et al, Physica Scripta 52, 201 (1995)

[26] A. Faenov, V. Dyakin, A. Magunov, T. Pikuz, I. Skobelev, S. Pikuz, A. Kasperczyk,

T. Pisarczyk, J. Wolowski, B. Zielinska, Physica Scripta 53, 591 (1996)

[27] F. B. Rosmej, B. A. Bryunetkin, A. Ya. Faenov, I. Yu. Skobelev, M. P. Kalashnikov,

P. V. Nickles, M. Schnurer, J. Phys. B Lett. 29, L299 (1996)

[28] A. Bartnik, V. M. Dyakin, J. Kostecki, I. Yu. Skobelev, A. Ya. Faenov, H. Fiedorowicz,

M. Szczurek, R. Jarocki, Quantum Electronics 27, 334 (1997)

[29] V. A. Boiko, V. G. Pal'chikov, I. Yu. Skobelev, A. Ya. Faenov "Spectroscopic Data of

Atoms and Ions (Atom Spectra with One and Two Electrons)". CRC Press, 1994

72 ICAMDATA 97 Proceedings
The Plasma Chemistry Database

W. K. Trail, C. W. Davis, and W. L. Morgan

Kinema Research & Software, Monument, Colorado

http:/ /www. kinema. com/kinema

We are developing a comprehensive plasma chemistry database of atomic and molecular

properties and collision data in Java for use on a LAN, or over the World Wide Web. The database

will serve two principal functions: first, it will make this data easily accessible to scientists on the

web through a graphical user interface (GUI), and second it will make the data accessible through

standard SQL database calls in Java thus enabling our plasma chemistry software tools to access appropriate input data across the web or across a LAN during execution. An example of the

current version of this database is on our web site. The database, which currently contains roughly 50 species, provides atomic and molecular

properties such as permanent moments, polarizabilities, electron affinities, heats of fusion,

rotational constants, etc., as well as critically selected experimental or theoretical electron

collision data for a wide range of processes including elastic scattering, rotational excitation,

vibrational excitation, electronic excitation, attachment, dissociative attachment, ionization, and

dissociation. (We will eventually add heavy particle collision data.) The collision cross sections are

in two forms: raw cross sections and coefficients for analytic fits. Because reaction rates are so useful in plasma chemistry the interface provides the ability to calculate them from cross sections over a user-selected temperature range. In addition, it automatically carries out an Arrhenius fit to the resultant reaction rate and displays the coefficients.

gi| Applet Viewer: AppletJavaRates.class

•AppletSelect A Species:

About.

Properties

Collision Data

Add New Species

ArC2H2

C2H4

C2HG

CCI2F2

CCI4

CF4

CH4

CO

C02

Figure 1: The main page of the graphical user interface to the database.

The first stage of this project was to build the GUI. The GUI allows the user to select an atom or molecule, and view the available raw data. All of the data are easily extracted from the interface

using standard cut and paste utilities. In Fig. 1 we show the main page; the user simply selects a

species and chooses to view either 'Properties' or 'Collision Data'. In Fig. 2 we show the properties screen for Cb. In Fig. 3 we show the 'Collision Data' screen for momentum transfer in electron-Cb

1 Databases 73
scattering. The user can view the collision cross sections for other processes by clicking on the

'Next' and 'Prev.' buttons. In addition to displaying a table of cross sections for this process, this screen allows the user to calculate reaction rates from the cross sections over a selected

temperature range. Also on this screen is a built in 2-D plot utility which allows the user to view a

plot of the reaction rates or the cross sections. For example, in Fig. 4 we show a plot of the

reaction rate for vibrational excitation of Cb by electron collisions.

mAtomic and Molecular Properties

Constants Species CI2

Comments

Return to Main

Polarizability Dipole Moment

Mass (AMU) (A"3) (Debye) A(1/cm)

70.9 4:61 0

B (1/cm) Ea(eV) Ip(eV)

0.2438

Hf (eV)

2.38 11.48

Kinema Research andSoftware 199,7

Figure 2: The 'Properties' screen for CI2. This page displays the mass, polarizability, dipole

moment, scattering length, rotational constant, electron affinity, ionization energy, and the heat

of fusion.

Building the Java interface between the database and our plasma chemistry software comprises

the second stage of this project. Because most of our software is written in Fortran 77 and Fortran

90, we will first develop a Java interface that essentially provides a convenient way to move data

from the database to the appropriate input files. The Fortran programs will be executed from this

Java interface.

For the final stage of this project we will migrate our plasma chemistry software to Java. Our

programs will then be able to access the appropriate input directly from the database (over the

Web) during execution. Some further advantages of a Java-only suite of programs include

platform-independence, access to the massive Java class libraries, and ease of distribution (and

execution) over a network.

74 ICAMDATA 97 Proceedings
^Collision Data

Species jQ?

Mol V*1 StatWt

J70.S06

Scale

Reaction

Label

Pol Moment

1

CI2(X)

jMomentum Transfer

Cross Section Data Mom Type EnergyLoss

J4.61 0 Quadrapole L 0 I

(?' Cross Sections C Rates From Lin Fit C Rates From Anl. Fit

12 20.27 15 18.65 20 16.27 25 14.2 30 12.5

Tmin (eV) Tmax(eV) dTe (eV)

Data Set # 1 Ix Axis Log - i 2s«BSj;vSl --[ iPlotXSec: iS&d NexV-^) ry Axis Log - ' -

Eq Type |2 Energy Range 1/2 .

'<,<'Prcyj Nfo.aoij

Add Fit Rarige

Cross Sec Fit Coeffs A fl.02454

0.02592

E min I51E max

|5.5

0.2077

0.5

Figure 3: The 'Collision Data' screen provides information on the collision process displayed in

the 'Label' field. This screen provides tools for calculating reaction rates, coefficients for fits, buttons for selecting other processes, and plotting utilities. The 'Add Reaction', 'Clear Data', and

'Edit Data' buttons in the lower left will allow users to replace, add new, or modify data in the

database.

Figure 4: This is a plot of the reaction rate as calculated from the v = 0-1 vibrational excitation

cross section. The curve labeled 'From Lin. Interp. XSecs' is the reaction rate as calculated from a

linear interpolation of the raw cross section data. An Arrhenius fit to these reaction rates is represented by the circles. The curve labeled 'From Analytic Fit to XSecs' is the reaction rate as

calculated from our analytic fit to the raw cross section data. An Arrhenius fit to these reaction

rates is represented by the X's. (The plots are more easily viewed in color on a computer screen.)

1 Databases 75
Development of an Atomic Spectroscopy Reference

Implemented on a PC Platform under Windows 95

K. Visser and G.E. Hattingh

Physics Department

University of Stellenbosch

STELLENBOSCH

Republic of South Africa

e-mail: kv@maties.sun.ac.za

1 Introduction

Atomic Spectroscopic reference data comprising the characteristic energy levels and their associated

eigenstate descriptions, wavelengths, and transition probabilities are available mostly in printed for- mat. The major computerized databases implemented on the Personal Computer (PC) platform

for Atomic Spectroscopy consist of the NIST Standard Reference Database 38 "Spectroscopic Properties of Atoms and Atomic Ions" and the NIST Standard Reference Database 61 "Database for

Atomic Spectroscopy"'. On the World Wide Web the NIST Atomic Spectroscopy Database, version

1.1, is currently available at http://aeldata.nist.gov/nist_atomic_spectra.html

Our objectives are to develop software providing

• a comprehensive database integrating the available critically evaluated Atomic Spectroscopic

information,

• a search engine serving as input filter to selectively retrieve user-specified information from

the database,

• user-specified custom-designed formatting of the output data both as tabular alphanumeric

text and in graphical format,

• appropriate calculations using the primary data as input to derive secondary parameters.

For the initial phase of the project we decided to develop the software for the IBM and compatible

PC platform under the Windows 95 operating system and used Borland's Delphi 3 compiler to generate a 32 bit application program. The program is developed in a modular way with each

module representing a particular application, which can be activated by clicking on its named tab.

Presently available and operational modules are:

• Energy level tables;

• Wavelength and Multiplet tables;

• Wavelengths calculated from the energy level data and applying user-selectable subsets of the

selection rules for the various radiative transition types.

76 ICAMDATA 97 Proceedings
Upon initiation the program searches for all associated data files (one per element) present. For

each file found it uses an efficient blockread procedure to transfer the file's available data records

as a single block at high speed into memory. These data records are kept memory resident to avoid repetitive reading and swapping of the database information in and out of memory during

subsequent searches. Adding more elements to the program is a simple matter of making their

correctly formatted data files available in the assigned directory. An array of indices referring

to the first and last record for each elemental ionization stage is kept for quick searches in the

appropriate subset of the memory resident list of data records.

The database files for the program use an internal encoding format to decrease their size compared to the original ASCII text files, thereby increasing the efficiency of the program in terms of

speed and smaller data file size. Each variable is enumerated and mapped onto the smallest integer

type which covers its range. For instance, instead of storing the name or chemical symbol of the

element and its ionization stage as ASCII fields in the data records, the hundred plus elements

and possible ionization stages are mapped onto a subset of the integers ranging from 0 to 127

and declared as variables of type Byte. By packing variables of lesser range bit-wise together, to optimally fit into the range of the smallest suitable integer type, memory and mass storage space

are conserved. Strings, such as are used for the description of the electron configuration and parent

term, the term value, the multiplet number, line codes and references to the original source of the

data, are variables which occur repetitively in the database records. They are also enumerated and

the 2 Byte variable, serving as referencing index into the stringlist, is stored in the appropriate

record fields of the database file instead of repetitively storing the longer string of text itself. This

enumeration and internal formatting of the database files led to a 7.2 times reduction of the comparative ASCII text file size for energy levels and a 5.1 times reduction for wavelength files. The

ASCII text files containing the stringlists for configurations, etc., have a size of 80 kb.

The displayed tables can be dynamically reformatted according to the user's choice with respect

to which columns of data are currently visible and which are hidden from view so as to remove

information which the user might consider unnecessary for his current needs. The displayed data

columns/rows in the scrollable tabular list can also be dragged and dropped to change their vertical

and horizontal ordering. The widths of the displayed columns are also dynamically resizable.

2 Energy Levels Module and Wavelength & Multiplet Module

The database currently includes energy level data for 417 atomic/ionic species from 20 elements (O,

Na, Mg, Al, Si, P, S, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Ni, Co, Cu, Kr & Mo) consisting of 33,004 energy

level records. It also contains wavelength data for 47 atomic/ionic species from 4 elements (O, Mg,

Al, Sc) with 11,320 wavelength records. Expansion for the energy levels of another 123 ionic species

from 17 more elements and 17,785 energy level records are underway, as well as wavelength data

for another 186 ionic species from 10 more elements and 23,648 wavelength records.

Single or multiple elements can be selected/deselected via mouse clicks on the element name

buttons arranged to resemble the periodic table, as shown in Fig. 1, with the selected state being

indicated by a change of color. Unavailable elements are grayed out. For ease of element selection an element list is also provided which can either contain the

elements arranged alphabetically by name or chemical symbol and atomic number. A command

button to toggle the selected state for all available elements is also provided.

Single or multiple ionization stages can be selected/deselected by clicking on their individual

buttons. Different ionization stages for each individual element or ionization stages common to all elements can be selected for all actively selected elements. A similar "Select/deselect All" command

1 Databases 11
button is also provided for the ion selection. Additional search criteria that can be specified are the energy/wavelength range; the electron configuration; the term values; parity; total angular

momentum quantum number J; orbital angular momentum symbol L and spin multiplicity ms

.

Na

K

he

Ca

Se ected Elements

W if dividual iom.?atic ifi

;

F E enieflts listed by rrihioi

i

So Ti ¥ Fe Go Mi Cu

t^ercury (80))

Ok Select From List Deselect All Cancel

S CI &r

e m Kr

M E

Figure 1: Selection of elements from the periodic table.

3 Calculated Wavelength Module

In this module theoretically expected wavelengths can be calculated from the energy levels by

applying the Ritz combination principle

he

Xvac =

\Ek-Ef \

to pairs of levels E{ and Ef that might be radiatively connected. Both the energy levels of a single

element and ionization stage can be selected at a time. The user can specify the following criteria

that pairs of levels must meet for selection in the derived wavelength calculation:

• a transition mode from: - absorption from a single lower state, or - emission from a single excited state, or - transitions involving all states;

78 ICAMDATA 97 Proceedings
(For absorption and emission the initial state can be picked from the applicable energy level

list of the selected atom/ion.)

• a wavelength interval in terms of its upper and lower wavelength limits;

• LS-coupling can be activated or ignored to prevent or allow intercombination lines;

• electric dipole (El), magnetic dipole (Ml) and electric quadrupole (E2) radiation types or combinations thereof can be checked to activate their respective selection rules;

• combinations of changes in the total angular momentum 5J can be checked.

For the interval (2 > A >2000 A) wavelengths in air are calculated from

> ^vac

Aair — 7TT

n(A)

with the refractive index of air calculated from the Edlen formula[l]

m , nn.^n , n * 2.406030 xlO6 1.5997 x 104 n(A) = 1 + 8.34213 x 10"5 + —rr^ ^ +

(1.30 x 10 10 - a

2

) (3.89 x 109 - a

2

) with the wavenumber a in cm-1

. The displayed table of calculated wavelengths can sorted according

to wavelength, or energy of the upper or lower state. The module can be used for such applications as theoretical prediction of suitable transitions for a multi-step laser excitation scheme, identification of the states involved in experimentally observed

wavelengths and selection of closely grouped wavelengths from largely different excitation states suitable for spectroscopic temperature determination.

4 Future Development

We plan to develop the program further to include modules for

• transition probability tables,

• Grotrian diagram creation from the energy levels and selection rules,

• calculation of simulated spectra,

• hyperfine structure,

• line profiles and convolution,

• Zeeman splitting.

Other future developments planned, include: expansion of the number of available elements,

allowance for editing of the data fields and insertion of data records by a user which are to be

saved as overlay files so as not to corrupt the original data files, saving and retrieving of the last used options and configurations. We also envision making a demonstration version of the program

available on the World Wide Web.

References

[1] B. Edlen, Metrologia 2, 71 (1966)

1 Databases 79

Data Needs

Absolute Infrared Intensities for:

Standards and Reactive Molecules

Charles Chackerian, Jr. NASA Ames Research Center, Atmospheric Physics

Research Branch, MS 245-4, Moffett Field,

CA 94035-1000

1 Introduction

In recent years laser techniques have provided us with very accurate infrared line positions and

the term "secondary frequency standard" has entered the lexicon of infrared spectroscopy. For

example, line positions of carbon monoxide in the 5um spectral region have been determined

with an absolute accuracy of about 30 KHz [1]. Frequency information is prerequisite for

obtaining accurate intensity information since the determination of transition dipole

parameters from experimental intensity measurements requires numerical values for

transition frequencies, transition initial state energies, and rovibrational partition functions.

Transition frequencies are also used, along with quantum-mechanical models, to obtain the

vibration-rotational state wave functions associated with the transitions of interest. The wave

functions can then be used along with absolute or relative intensity information with an

appropriate quantum mechanical model to determine parameters that describe the dipole

surface of the molecule; some examples are for CO [2], OH [3] and CH3CI [4]. To the best of my knowledge, there are no reports of absolute line intensities of

rovibrational transitions in the literature that could serve as secondary standards to an

accuracy better than ±5%.

I estimate the absolute accuracy that currently could probably be obtained for secondary

infrared intensity standards. Following that, I discuss intensity determinations for unstable

molecular species. I do not attempt to give a rational for the level of accuracy needed for any

particular application or propose specific molecules that could be candidates for use as secondary intensity standards.

2 Primary Intensity Standard

A "perfectly performing" spectrometer does not require a primary intensity standard in order to determine absolute line intensities from absorption measurements. Such an instrument

responds linearly to photons over the appropriate radiative flux range and has negligible

scattered light. However, were we to test the spectrometer's performance we would ultimately

be limited by the accuracy of a primary radiation standard. I will assume here that a black body

can serve this purpose. Blackbodies in operation at the National Physical Laboratory and the

National Institute of Standards and Technology have emissivities equal to 0.999 or better and

operate at temperatures known to about 200 millikelvin. At 5 um our blackbody operating at 450K, with uncertainties in its temperature of 0.2 K and emissivity of 0.1%, would have an

uncertainty in its emitted differential flux (Watts/cm2 - micron-sr) of 0.39%. The latter

uncertainty depends on the temperature of the blackbody and the precise wavelength, but for

2 Data Needs 83
the purposes of the discussion to follow we will assume that our ultimate accuracy for infrared

intensities is on the order of 0.4%.

In some cases it is possible to obtain absolute intensity information via relative intensity

measurements over a large spectral interval, and in this situation a blackbody source is needed

to establish the spectrometer's relative sensitivity with wavelength.

3 Secondary Intensity Standards

Secondary intensity standards have not been established for molecular infrared transitions, but

in this section results obtained by our group are used to illustrate possible sources of errors in

intensity determinations as well as expected accuracies which could be obtained from highquality measurements.

The best way to determine the absolute intensity of rovibrational transitions of a stable

molecule is with conventional absorption spectroscopy. The equations in the Appendix below

show the relationships between the transmission of an individual rovibrational line (Eq. 1) and

the rotationless transition moment for a rovibrational band (Eq. 3). The equations also indicate

that accuracies of transition frequencies, energy levels, gas pressure, composition, broadening

cross sections, absorbing path length, and temperature all play a role in determining the

absolute accuracy of the measured transition moment, and therefore, the accuracy of any of

these quantities will be a factor in determining the accuracy of the individual line intensities.

Table 1 shows the most precise results we have obtained to date for the rotationless

transition moment of a rovibrational band. The four spectra of the (00^2)i*(00^0)l band of

12 C16 0180 were obtained using a natural abundance sample of carbon dioxide and the FTS at the National Solar Observatory, Kitt Peak, AZ. The double-sided interferograms produced

excellent instrumental profiles in the spectral domain.

Table 1: Intensity data* for 4639.5 cm" 1 band of 12 C

160 180 determined via FTS

spectroscopy (carbon dioxide in natural isotopic abundance).

Spectrum Pressure Path | <00°2 | M | 00°0>

(Torr) (meters) (Debye)

KP03 65.0 97.04 0.0014312

KP04 45.0 409.82 0.0014310

KP05 45.0 145.16 0.0014351

KP13 59.7 193.28 0.0014352

*R. Kshirsagar, L. P. Giver, and C. Chackerian, Jr. (private communication, NASA Ames Research Center)

The transition moments obtained from the individual spectra were obtained by plotting the

square root of the reduced intensity of individual lines in the band vs. the m quantum number.

The reduced line intensity is defined in Eq.(2) of the Appendix. The vibration-rotation

interaction term is small enough to be undetermined; the precision of the transition moment

squared determinations is +0.15%. The individual line intensities used in the reduced intensity

plots were obtained via non-linear least-squares fitting of the FTS spectra. The paper of Benner

84 ICAMDATA 97 Proceedings
et al. [5] gives a discussion of this technique which requires knowledge of the instrumental

function as well as in this case the pressure broadening of -^C^O^O by The

isotopic composition is obtained from a standard compilation [6], and the uncertainties for the

above isotopes is negligible. At low pressures errors in pressure broadening are not as important as errors in the instrumental function and inherent errors in the pressure gauge or neglect of thermal transpiration [7] if the gas sample and capacitance manometer are at

different temperatures. The pressure uncertainty of our measurements is about 0.22%. Our

temperature uncertainty is about 0.17% which results in a 0.34% error (the rotational partition

function is proportional to the temperature). This temperature error will also add an additional

0.17% error through the Boltzmann factor. Temperature errors can also cause an error in the

vibration-rotation interaction term, F, of Eq.(7). If the compositional, path length, and data

reduction errors can be assumed to be zero, the error in the absolute intensity would be about

0.75%. The latter estimate is clearly conservative in the sense that it is probably too low but is

still greater than the precision of ±0.30% we have achieved for the above cited intensity

measurements on -^C^O^O. It is probably reasonable to assume that we can achieve an

absolute accuracy of about 2% in the determination of infrared rovibrational line intensities.

4 Unstable/Reactive Molecules

The determination of absolute intensities for reactive molecules is particularly difficult in the

infrared because: (i) the sources that produce the spectra are usually not in LTE, except

possibly for the lowest rotational levels, and (ii) the concentration of molecules in the optical

path is not known. Lifetime techniques are not possible because the infrared radiative lifetimes are longer than collisional deactivation times.

For some diatomic molecules it has been possible to exploit the effect vibration-rotation

interaction has on modifying intensities. Here knowledge of the abundance of the optically

active species is not required, only the ratios of emission line intensities originating in common

upper levels [3,8] or the relative intensities across an absorption band [9]. Eq.(3) taken in ratios

is used for the emission experiments to determine the electric dipole moment function. The

vibrational transition moment squared is determined from these measurements with absolute

errors on the order of ±10%.

5 Conclusions

We have demonstrated that infrared line intensities can be determined with a precision of

about 0.3%. For the particular experiment described the absolute error on the transition

moment squared could be about 1%. It is probably reasonable to assume that we can achieve an

absolute accuracy of about 2% in the determination of infrared rovibrational line intensities of

stable molecules.

The absolute accuracies achieved for a small number of unstable molecules is on the order

of ±10%.

2 Data Needs 85
6 Appendix

The equations which relate the absorption of radiation in an isolated rovibrational line

(centered at the frequency a 0) to its intensity is given by the Beer-Lambert Law,

I(Aa = cr-oro ) = exp -Spl

H(A<7,Y) ln2V2

\ 7t J

(1)

where Io(Ao) and I(Aa) are the intensities respectively, incident on and emergent from the

absorbing gas sample. S is the line intensity, p the partial pressure of the species of interest, / the absorbing path length, and H the line shape. The Voigt line shape parameter,

Y = (y L /y D )Vln2 , is a function of the temperature and pressure. The Doppler broadening, y ,

is a function of the molecular weight of the optically active species as well as the temperature.

The pressure broadening coefficient, Y^ ~ ^PiY^ {T/T) i

, is a function of the temperature,

i T(K), as well as the collisional cross sections between the various species, i. Here y^ is referenced to the standard temperature. The line intensity in Eq.(2) for

f 3

>

^

3hc

'sr Zvr (T)T

exp

hcE

i kT

-hea. •HL(rit rf

)

-l

(2)

= Sreduced = |(v, \M{QX )\vf )\

2 F(vt

, rt ;vf

,rf )

a rovibrational transition between initial and final states, (i,f), depends on the temperature

through the rovibrational partition function Z and exponential factors. T0 is the standard

temperature, iV£ Loschmidt's Number and Gsr a statistical weight. The transition probability

is factored into vibrational, rotational, HL, and rovibrational interaction terms,

h\M(Qx )^ HL(rt ,r^- )F(v(

. , r(. ; v

f

,ry) . Qx represents an appropriate vibrational

coordinate(s). The reduced intensity is related to the individual line intensities, Sif, as well as

1 /p

quantities which can be calculated. A plot of {Sreduced) versus an appropriate rotational

quantum number yields the vibrational transition moment as well as any dependence of the

transition moment on rotational quantum numbers.

Unstable/reactive species molecular spectra are often observed in emission. The volume

emission coefficient, 7, is given by Eq.(3)

/ = K'cr

4 N: e

1 MA) (3)

86 ICAMDATA 97 Proceedings
References

[1] M. H. Wappelhorst, S. Saupe, B. Meyer, T. George, W. Urban and A. Le Floch, J. Mol.

Specrosc. 181, 357-362 (1997)

[2] C. Chackerian, Jr., R. Farrenq, G. Guelachvili, C. Rossetti, and W. Urban, Can. J. Phys. 62,

1579-1585 (1984)

[3] D. Nelson, A. Schiffman and D.Nesbitt, J. Chem. Phys. 93, 7003-7019 (1990)

[4] F. Cappellani, G. Restelli and G. Tarrago, J. Mol. Spectrosc. 146, 326-333 (1991)

[5] D. C. Benner, C. P. Rinsland, V. M. Devi, M. A. H. Smith, and D. Atkins, J. Quant,

Spectrosc. Rad. Transfer 53, 705-721 (1995)

[6] P. De Beaver, M. Galled, N.E. Holder, and I. L. Barrens, J. Phys. Chem. Ref. Data 13, 809-

892 (1984)

[7] K. F. Pointer, M.-J. Rodgers, P. J. Nash, J. T. Thompson and M. P. Perkin, Vacuum 33, 311-

316 (1983)

[8] C. Chackerian, Jr., G. Guelachvili, A. Lopez-Pinero and R. H. Tipping, J. Chem. Phys. 90,

641-649 (1989)

[9] J. B. Burkholder, P. D. Hammer, J. Howard, A. G. Maki, G. Thompson, and C. Chackerian,

Jr., J. Mol. Spectrosc. 124, 139-161 (1987)

2 Data Needs 87
NASA's Laboratory Astrophysics Program

Hashima Hasan and Harley Thronson

Office of Space Science, NASA Headquarters

Washington D.C. 20546

1 Introduction

NASA's Office of Space Science (OSS) operates an active laboratory astrophysics program

conducted primarily at universties, federally funded laboratories, and research institutes. Topic

areas currently supported include electron impact cross sections, photodissociation proceses,

electron-ion collisons, oscillator strengths for a variety of atomic transitions, polycyclic aromatic

hydrocarbons, interstellar grains, and compilation of atomic databases. Related theoretical work

is also supported to complement the laboratory research. The objective of the program is to enable

and maximize the scientific return from the data of NASA's past, present and future space science

missions. A brief description of the scientific program and NASA's needs for laboratory

astrophysics is given in this paper. A workshop encompassing laboratory needs for OSS in the

fields of astrophysics, planetary atmospheres, and space physics is planned on April 1 - 3, 1998 at Harvard University.

2 Program Description

Laboratory Astrophysics needs for NASA are driven by the data from its ongoing and planned

missions, as well as from archival data (Table 1). Currently, the program is split along

wavelength lines into two subprograms. Specific research projects are proposed by the scientific

community in response to solicitations by NASA in the form of NASA Research Announcements

(NRA). An annual solicitation for the Ultraviolet, Visible and Gravitational Astrophysics

Research & Analysis program provides the community an opportunity for a timely response to perform laboratory research for enabling the interpretation of new data from UV/Visible missions.

The Infrared, Sub-mm and Radio Astrophysics program solicits proposals every three years. With

the operation of the Near Infrared Camera and Imaging Spectrograph (NICMOS) and proposed

launch of the Space Infrared Telescope Facility (SIRTF) and the Stratospheric Observatory for

Infrared Astronomy (SOFIA), there may be need for more frequent solicitation in this area. Currently, only one program is funded in High Energy Astrophysics, though with the launch of

the Advanced X-ray Facility (AXAF), there will perhaps be a need to expand this program.

A wide variety of projects, the focus of each of which is to enable the understanding of specific

astrophysical phenomena, such as those within diffuse interstellar couds, stellar atmospheres,

dust grains, etc. are under study. Names of principal investigators, institutions, and project titles are listed in Tables 2 and 3. In a broad sense, the program supports the fundamental science

questions defined by NASA's Structure and Evolution of the Universe and Astronomical Search for

Orgins science themes.

88 ICAMDATA 97 Proceedings
Table 1

NASA's Astrophysics Missions

(partial list)

Currently in operation

Extreme Ultraviolet Explorer (EUVE)

Hubble Space Telescope (HST)

Wide Field and Planetary Camera 2

Space Telescope Imaging Spectrograph (STIS)

Near-Infrared Camera & Multi-Object Spectrograph (NICMOS)

Archival phase

International Ultraviolet Explorer (IUE)

Orbiting & Retrievable Far & Extreme Ultraviolet Telescope (ORFEUS and ORFEUS2)

Interstellar Medium Absorption Profile Spectrograph (IMAPS)

Hubble Space Telescope (HST)

Wide Field and Planetary Camera (WFPC)

Goddard High Resolution Spectrograph (GHRS)

Faint Object Spectrograph (FOS)

High Speed Photometer (HSP)

ASTRO and ASTR02

Ultraviolet Imaging Telescope (UIT)

Hopkins Ultraviolet Telescope (HUT)

Wisconsin Ultraviolet Photo-Polarimeter Experiment (WUPPE)

Missions in development

Sub-millimeter Wave Astronomy Satellite (SWAS)

Stratospheric Observatory for Infrared Astronomy (SOFIA)

Space Infrared Telescope Facility (SIRTF)

Wide Field Infrared Explorer (WIRE)

Space Interferometry Mission (SIM)

Far Ultraviolet Spectroscopic Explorer (FUSE)

Hubble Space Telescope (HST)

Advanced Camera for Surveys (ACS)

Cosmic Origins Spectrograph (COS)

Galaxy Evolution Explorer (GALEX)

2 Data Needs
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D rD2 Daia Needs 91
Atomic Inputs to Calculate Radiative Forces

in Stellar Models

G. Massacrier1

, J.-F. Gonzalez1

, M.-C. Artru 1 G. Michaud2 ' 3

, J. Richer2 - 3, F. LeBlanc4

1 CRAL, 46 allee d'ltalie F- 69364 Lyon Cedex 07, France

2 CERCA, 5160 boul. Decarie, Montreal, Quebec, H3X 2H9, Canada

3 Dep. de physique, Univ. de Montreal, Montreal, H3C 3J7, Canada

4 Dep. de physique, Univ. de Moncton, Moncton, ElA 3E9, Canada

1 Introduction

Photoabsorption processes imply momentum transfer from the radiation flux to the atomic absorbers in a plasma. The resulting radiative forces act selectively on different chemical species.

According to the local imbalance between gravitational g and radiative accelerations gracj in a

star, a given element can diffuse up or down in layers where mixing hydrodynamical processes

are negligible. Effects of chemical stratification occurring during stellar lifetimes are observed as peculiar surface abundances. The diffusion of strongly absorbing species can ultimately influence

the evolutionary path of the star and might affect its pulsational stability.

Standard stellar evolution codes assume homogeneity of chemical composition throughout the

star (except in nuclear reaction zones). Rosseland opacities «r are interpolated from a grid of

plasma conditions in T (temperature), p (density) and X, Y, Z (mass fractions of hydrogen, helium

and 'metals'). The relative abundances of metals are held fixed in Z.

When including atomic diffusion in stellar models, local under- or over-abundances may develop.

Because of their influence on radiative accelerations but also on the Rosseland opacity these local

variations of the metallic relative abundances in Z have to be taken into account. This increases

the number of free parameters and precludes the use of precalculated data. One has to turn to

in-line computations. Very efficient and finely tuned methods must be found as the Rosseland

opacity and the radiative accelerations for many elements must be computed at each layer and

each evolutionary step of the star for several iterative steps.

2 Radiative Accelerations on an Ion

The radiative acceleration on an element A in the ionization state A; at radius r in a star is given

sua) = ^# 3^ f mi« (i)

Anrz c XA,k Jo «(«)

where Lra^(r) / Anr2 c is the total radiative momentum flux at r, kr is the Rosseland opacity, X&^ is the mass fraction of the ionization state, u = is the dimensionless frequency variable, k(u) is the

total opacity at frequency w, and iiA,k( u) 1S tne opacity for the ion under consideration (corrected

for the fact that only that part of the photon momentum absorbed and transfered to the final ion

92 ICAMDATA 97 Proceedings
is needed; see below). V(u) is the normalized black body flux:

15 u eU ^= 4^ W^W (2)

The frequency dependent factor V{u)/k(u) appears because the 'diffusion' approximation for the

radiative flux is assumed. Hence Eq. (1) is relevant only for stellar envelopes. In atmospheres

the actual flux should be used. The value of g^{A) depends on the competition for the photons

between the ion and the other elements. Increasing the abundance of the element leads to saturation

and may also modify the radiative acceleration on the other elements.

Total monochromatic opacities must first be computed:

K ( U) = ^L, Ka(v): J*a{v) = X^'*^)' PKA,k(v) = Yl Ni(Jij(v) . (3)

k

transitions

where N{ is the population density of the absorbing state i (of the ion A, fc), and the cross section for the transition. This requires data for energy levels, oscillator strengths and line profiles

for bound-bound absorptions, as well as photoionization cross sections for bound-free absorptions.

All these data for all main contributors to the Rosseland opacity are now available or can be derived

from recent large atomic data banks.

In the modified opacity KA,k{v) of Eq. (1), bound-bound contributions are summed as in Eq. (3).

But for bound-free absorptions two modifications occur. First, two ionization states are involved

in the process. The state k for which we want the acceleration is the final ion. The photoionization cross sections one has to use are those of the previous (k — 1) state. Second, in such a

process, only a part of the absorbed photon momentum is transmitted to the final ion (the rest goes away with the photoelectron). This implies the use of modified cross sections, usually written

GijW) — f\on,ij(v) crij(v). This second point applies as well to free- free absorptions. /;on is an

atomic parameter almost absent in the literature (more details in an accompanying contribution

[I])-

3 Diffusion of an Element

For reasons of rapidity and efficiency the diffusion of an element A is treated as a whole, and not

through its individual ions. The effective radiative acceleration to be used to study the diffusion of

A is some average of its ion accelerations. The approach is to weight <j£id (^) w*kh ^ ne i°n population

times its diffusion coefficient:

fad.Wtk

-Nki)- (4)

For an ion diffusing in a bath of protons, one roughly has oc l/z%, where Zk is the net charge of

the ion (an estimate for neutrals (zk = 0) leads to an effective approximate value Zk — 0.1). The

process of averaging enhances the weight of less ionized states. Redistribution processes have to be taken into account too. Following a bound-bound absorption, an ion may be ionized through (electronic) collisions before being deflected (by protons). Thus

the ionization state in which the ion diffuses before being deflected may differ from the one in which

the photon was absorbed. As the diffusion coefficients depend on the charge of the ion, the previous

average has to be modified to take this effect into account. Only rough approaches are used at the

moment. Precise computations would require large sets of collisional data.

2 Data Needs 93
4 Calculations of Radiative Accelerations

4.1 Smoothed Background Procedure

Systematic attempts ([2], [3], [4]) to calculate radiative accelerations were performed using the

TOPbase data bank [5] calculated by the Opacity Project group ([6], [7]). The method is that

explained in [8]. The radiative acceleration from each transition is calculated separately and then

summed. The total opacity k(u) is divided into two parts: the opacity of the transition under

consideration and a background opacity. The latter is a constant in the frequency interval Au that

contains the natural frequency of the line. It is computed by evenly distributing other bound-bound

cross sections in the interval.

The method is motivated by the fact that the background opacity has to be computed only once to get the acceleration of all the ions. It allows a good treatment of saturation. Electron

recoil, averages with diffusion coefficients and redistribution can be included. However evenly dis- tributing in an interval all lines falling in that interval artificially fills the valleys in the background

opacity. Thus at low temperatures when line widths are small this method underestimates exact

accelerations. It is also too time consuming to be used in-line in present evolution codes.

4.2 Opacity Sampling Procedure

In [9] and [10] another approach was used to calculate radiative accelerations. At a given temperature and density an opacity spectrum is pre-computed for each element at given points on a certain

frequency grid (opacity sampling). Then Eq. (1) is directly integrated. The method is accurate in

as much as the sampling is sufficient not to miss important lines in the elements. Hence the lower

the temperature, the finer the grid mesh should be. Optimization of the number of grid points and

use of an non-evenly spaced grid are discussed in [11]. Actual computations ([9]) were done based on the OPAL opacities for the 21 most abundant

elements ([12], [13], [14], [15]). Opacities obtained from OPAL are already summed on the ionization

states. Radiative acceleration on an element A is then calculated according to:

/ ,v £rad(Q «R f°° KA {u)

( ( £rad \A) = 2~ — / —r^- V{u) du . 5 47rr^c Xa Jo k(u)

This expression is simply the momemtum absorbed from the radiation. It assumes that this mo- mentum is entirely transfered to the element A. Though the effects of electron recoil, averaging over the ions or redistribution are not included with this use of elemental opacities, the gain in computation time obtained by not treating ions individually allows one to calculate radiative accelerations

in-line in stellar evolution codes for any given chemical composition ([16], [17]). A correction factor can also be pre-computed ([9]) wich is simply the ratio of the radiative accelerations of an element

calculated with and without these corrections.

References

[1] G. Massacrier and K. El-Murr, this volume

[2] G. Alecian, G. Michaud, and J. Tully, Astrophys. J. 411, 882 (1993)

[3] J.-F. Gonzalez, M.-C. Artru, and G. Michaud, Astron. Astrophys. 302, 788 (1995)

[4] F. LeBlanc and G. Michaud, Astron. Astrophys. 303, 166 (1995)

94 ICAMDATA 97 Proceedings
[5] W. Cuiito, C. Mendoza, F. Ochsenbein, and C. J. Zeippen, Astron. Astrophys. 275, L5 (1993)

[6] M. J. Seaton, J. Phys. B: At. Mol. Opt. Phys. 20, 6363 (1987)

[7] M. J. Seaton, Y. Yan, D. Mihalas, A. K. Pradhan, Mon. Not. Roy. Astr. Soc. 266, 805 (1994)

[8] J.-F. Gonzalez, F. LeBlanc, M.-C. Artru, and G. Michaud, Astron. Astrophys. 297, 223 (1995)

[9] J. Richer, G. Michaud, F. J. Rogers, C. A. Iglesias, S. Turcotte, and F. LeBlanc, Astrophys.

J., in press (1998)

[10] M. J. Seaton, Monthly Not. Roy. Astr. Soc. 289, 700

[11] F. LeBlanc, G. Michaud, and J. Richer, in preparation

[12] F. J. Rogers and C. A. Iglesias, Astrophys. J. Suppl. 79, 507 (1992)

[13] F. J. Rogers and C. A. Iglesias, Astrophys. J. 401, 361 (1992)

[14] C. A. Iglesias and F. J. Rogers, Astrophys. J. 443, 460 (1995)

[15] C. A. Iglesias and F. J. Rogers, Astrophys. J. 464, 943 (1996)

[16] S. Turcotte, J. Richer, and G. Michaud, Astrophys. J., submitted

[17] S. Turcotte, J. Richer, G. Michaud, C. A. Iglesias, and F. J. Rogers, Astrophys. J., submitted

2 Data Needs 95
New Electron Temperature and Density Diagnostics

for Photoionized Gas

D. W. Savin1

, T. Bartsch2

, M. H. Chen3, S. M. Kahn1

, D. A. Liedahl3

, J. Linkemann4

, A. Miiller2

, S. Schippers4

, M. Schmitt4, D. Schwalm4

, and A. Wolf4

Department of Physics and Columbia Astrophysics Laboratory, Columbia University,

New York, NY 10027 USA

2Institut fur Kernphysik, Strahlenzentrum der Justus-Liebig-Universitat,

D-35392 Giessen, Germany

^Lawrence Livermore National Laboratory, Livermore, CA 94550 USA

4 Max-Planck-Institut fiir Kernphysik and Physikalisches Institut der Universitat

Heidelberg, D-691 17 Heidelberg, Germany

The ionization and heating of the media surrounding accretion-powered compact sources, such as cataclysmic variables, X-ray binaries, and active galactic nuclei, is dominated by photoionization.

Theoretical models of photoionized gases show that the ionization structure is determined by

photoionization balanced by radiative recombination (RR) and dielectronic recombination (DR).

The electron temperature at which the fractional abundance of a given ion peaks [1] is far below

the temperature where the ion would exist in coronal equilibrium [2,3]. As a result, X-ray line

emission is produced by RR and DR and not by electron impact excitation [1,4]. Also, the radiative

recombination continuum (RRC) of an ion is predicted to appear as a distinct narrow feature just

above the ionization threshold of the ion [5]

.

With the improved spectral resolution offered by the SIS detectors of ASCA [6] it has become

possible to observe some of these unique properties of photoionized gases. From ASCA

observations, the RRC for Ne X has been identified in SIS spectra of the low-mass X-ray pulsar

4U 1626-67 [7] and the Mg XII, Si XIV, and S XVI RRC have been identified in spectra of the

X-ray binary Cygnus X-3 [8]. From the widths of the RRC features, electron temperatures of

-5-100 eV are inferred for the X ray emission line regions. As predicted, these temperatures are

far below the temperatures where these ions are formed in coronal equilibrium.

The upcoming launches of the X-ray astronomy satellites AXAF, XMM, Spectrum-Rontgen

Gamma, and Astro-E are expected to open a new era in the spectroscopy of extrasolar X-ray

sources. The combination of the large collecting area telescopes and high resolution spectrometers on these satellites will produce high quality spectra to which a wide range of plasma diagnostic

techniques will be applied. Of particular interest will be the 0.7-2.0 keV (6-18 A) spectral band

which is dominated by the L-shell transitions (i.e. n >_3 -» n = 2) of Fe XVII to Fe XXIV (the iron

L-shell ions). These ions exist over a wide range of conditions and are expected to provide many

valuable plasma diagnostics.

L-shell iron forms at the same conditions where Ne X, Mg XII, Si XIV, and S XVI form. Thus,

the temperatures measured in 4U 1626-67 and Cyg X-3 largely validate the predicted

temperature range for L-shell iron. However, the exact temperature at which a given ion forms

depends on many variables, such as the metallicity of the gas, the shape of the ionizing spectrum,

the presence of additional heating and/or cooling mechanisms, and radiative transfer effects. These can be expected to vary for different sources. For most iron L-shell ions at these low

temperatures, DR via An = 0 core excitations dominates recombination. It is therefore important

96 ICAMDATA 97 Proceedings
~20

§15

10

a 5

n=6

19 Ss^p^^nl 6f.g.h

120 " - Z&P^ I

n=7 ^4 J

9 10... ZsZp'CS^Jnl

J III I I IIIIIII19 I

20 40 60 80 100 120 Center of Mass Energy (eV) 140

Figure 1: Measured Fe XVIII to Fe XVII

recombination rate coefficient versus collision energy. The nonresonant "background" is due to RR.

10

•s 10"

10"

1

1 t—|

1 , ,—r-| 1 r-

-

" "

'/

/ / /

/ / .'.../. , , 1 10 10 10* 10 Electron Temperature (eV) Figure 2: Fe XVIII to Fe XVII Maxwellian

averaged An = 0 DR rate coefficients. See text for explanation.

that the iron L-shell DR rates be benchmarked over a range which encompasses the predicted

temperature range.

To address the needs for modeling photoionized gases, we have initiated a series of

experiments to measure the An = 0 DR rates for the iron L-shell ions. Measurements are carried

out using the heavy-ion Test Storage Ring (TSR) at the Max-Planck-Institut fur Kernphysik in

Heidelberg, Germany [9]. Here we present our results for An = 0 DR of Fe XVIII [10]. In

particular we have investigated the capture channels

Fe17+(2s2 2p5

[ 2P3/2]) + e- Fe16+(2s2 2p5

[ 2Pi/2]rc/) Fe16+(2s2p6

[ 2 Si/2]n0

(n = 18, ...,oo)

(n = 6, oo). (1)

The radiative stabilization of these autoionizing states to bound configurations of Fe XVII leads to DR resonances for collision energies between 0 and 132 eV.

Fig. 1 shows the measured Fe XVIII DR resonances. We have integrated the measured DR

resonance strengths and energies with a Maxwellian electron velocity distribution to yield a total

Fe XVIII An = 0 DR rate coefficient as a function of electron temperature (Fig. 2, upper solid line).

Various theoretical DR rates are also shown in Fig. 2. At hnTe -15 eV, near where Fe XVIII is predicted to peak in fractional abundance in photoionized gases, our inferred DR rate is a factor of

~2 larger than the calculations of Ref. [11] Gong dashed line), Ref. [12] (dotted line), and Ref. [13]

(short dashed line). These theoretical rates all tend rapidly to zero at kiaTe < 20 eV because they

have not included DR via 2pi/2 —> 2p3/2 core excitations. The calculations of Ref. [11] and Ref. [13]

used LS-coupling and thus do not include fine-structure core excitations. The calculations of

Ref. [12] used intermediate-coupling which can account for fine structure; but that work did not

include the 2pi/2 —> 2p3/2 channel because the calculations were carried out for the high

temperatures of collisionally ionized plasmas (where this channel is unimportant). Also shown in

Fig. 2 are our new calculations [10] which include the 2pi/2 —> 2p3/2 channel (lower solid line). Our

new calculations agree to within -30% with our measurements.

The commonly used models of photoionized gas incorporate DR rates which have been

calculated using either the Burgess formula [14] or LS-coupling. The Burgess formula is known to be inappropriated for low temperatures [15]. And as we have shown, LS-coupling calculations do

not properly account for all possible DR channels at low temperatures where DR can proceed

2 Data Needs 97
250 i

200 '- A

\ nf-3d

150 1—j nd-3p

100

50

0

\ 1 I—\ I

.... i .... i .... i .... i .... i ... . 24 25 26 27 28 29 30 X(k)

Figure 3: Preliminary calculations of the Fe XVII

soft X-ray spectrum produced by Fe XVTII DR via

2pi/2 -> 2p3/2 core excitations. The intensity

(ordinate) is in arbitrary units. The nd -» 3p and

nf -» 3d transition arrays are shown for 18 < n < 100.

25

26.0 26.2 26.4 26.6 26.8 27.0 Uk)

Figure 4: Preliminary calculations of the electron

density dependence of the Fe XVII nd —> 3p

transition array produced by Fe XVIII DR via

2pi/2 —> 2p3/2 core excitations. The transition array

is shown for \ogne = 9, 12, 14, and 15 cm 3

. The

intensity (ordinate) is in arbitrary units.

primarily via nlj —> nl'y excitations of core electrons. A re-evaluation of the recommended low

temperature DR rates is needed to assess for what L-shell and M-shell ions new rates must be

determined.

L-shell iron An = 0 DR via 2s -» 2p core excitations has been proposed as a possible electron

temperature diagnostic for photoionized gas [16,17]. Here dielectronic capture proceeds via a

[2s2 2pk + e~ -> 2s2pk+1 nl] channel. Stabilization typically proceeds via a 2p -> 2s radiative decay.

However, for low enough n, the 2s" 1 core can "freeze", and the outer electron radiatively cascade to the L-shell, filling the 2s 1 hole. These cascades occur in the presence of an excited 2p electron. In

the low density limit, the resulting spectrum is unique to the DR process. Thus, as the

temperature dependence of RR and DR is different, the ratio of lines produced by RR and DR

provide the makings of a temperature diagnostic. Developing these diagnostics requires accurate

knowledge of the DR resonance energies and strengths, which can be provided by measurements

such as those presented here.

Here we propose a new electron temperature and density diagnostic for photoionized gas

which is based on DR via a 2pi/2 -> 2p3/2 core excitation. Because the 2p3/2 -> 2pi/2 radiative

transition is electric- dipole forbidden, DR via this channel stabilizes by a radiative decay of the

captured electron. The energy of the 2pi/2 —> 2p3/2 transition is -15 eV, and the recombining

electrons are captured into high n levels. For Fe XVIII, we find n > 18. These high-lying electrons

have a high branching ratio for undergoing an n -> 3 transition and producing soft X-rays. Fig. 3

shows a preliminary calculated soft X-ray spectrum resulting from Fe XVIII An = 0 DR via

2pv2 —> 2p3/2 core excitations. The resolution is AX = 0.07 A which is comparable to that planned

for the spectrometers of AXAF and XMM. The broad features are due to unresolved n —> 3

transitions. The high energy sides of these transition arrays are due to very high n levels. These

weakly-bound levels can be collisionally ionized before they radiatively decay. The highest bound

n level is a function of the electron density ne. Thus the widths of these transition arrays are

sensitive to ne and can be used to infer the density of the radiating gas. Fig. 4 shows the density

sensitivity for one of the nd -» 3p transition arrays shown in Fig. 3. Further experimental and

theoretical work is in progress to explore this new class of temperature diagnostics.

98 ICAMDATA 97 Proceedings
Acknowledgments

We thank M. Grieser, R. Repnow, and the TSR group for their expert technical support during the

beam time. The authors thank T. R. Kallman, F. Paerels, J. C. Raymond, and D. A. Verner for

stimulating conversations. This work was supported in part by NASA High Energy Astrophysics

X-Ray Astronomy Research and Analysis grant NAGW-4185. Travel to Heidelberg and living

expenses for D. W. S. were supported by NATO Collaborative Research Grant CRG-950911. The

experimental work has been supported in part by the German Federal Minister for Education,

Science, Research, and Technology (BMBF) under Contract Nos. 06 GI 475, 06 GI 848, and 06 HD

8541. Work performed at Lawrence Livermore National Laboratory was performed under the

auspices of the US Department of Energy (contract number W-7405-ENG-48).

References

[I] T. R. Kallman et al., Astrophys. J. 465, 994 (1996)

[2] M. Arnaud and R. Rothenflug, Astron. Astrophys. Suppl. Ser. 60, 425 (1985)

[3] M. Arnaud 'and J. Raymond, Astrophys. J. 398, 394 (1992)

[4] D. A. Liedahl et al., Astrophys. J. 350, L37 (1990)

[5] S. Hatchett, J. Buff, and R. McCray, Astrophys. J. 206, 847 (1976)

[6] Y. Tanaka, H. Inoue, and S. M. Holt, Publ. Astron. Soc. Japan 46, L37 (1994)

[7] L. Angelini et al., Astrophys. J.l 449, L41 (1995)

[8] D. A. Liedahl. and F. Paerels, Astrophys. J.l 468, L33 (1996)

[9] D. Habs et al., Nucl. Instrum. Methods B 43, 390 (1989)

[10] D. W. Savin et al., Astrophys. J. 489, L115 (1997)

[II] L. J. Roszman, Phys. Rev. A 35, 2138 (1987)

[12] M. H. Chen, Phys. Rev. A 38, 2332 (1988)

[13] Dasgupta and K. G. Whitney, Phys. Rev. A 42, 2640 (1990)

[14] Burgess, Astrophys. J. 141, 1588 (1965)

[15] P. J. Storey, in "Planetary Nebulae", ed. D. R. Flower, p. 199, D. Reidel Publishing

Company, Dordrecht 1983

[16] D. A. Liedahl, Ph. D. Thesis, University of California at Berkeley 1992

[17] S. M. Kahn and D. A. Liedahl, in "Physics of Multiply Charged Ions", ed. D. Liesen, p. 169,

Plenum Press: New York 1995

2 Data Needs 99

Data

Production

3,1 Atomic

Structure and

Spectroscopy

The Platinum Group Ion Project

V. I. Azarov, S. S. Churilov, R. R. Kildiyarova, A. N. Ryabtsev1 A. J. J. Raassen, P. H. M. Uylings2

, Y. N. Joshi3, L. Tchang-Brillet4

, J.-F. Wyart5

1 Institute for Spectroscopy, Russian Academy of Sciences,

Troitsk, Moscow region 142092, Russia

2 Van der Waals-Zeeman Instituut, Universiteit van Amsterdam,

Valckenierstraat 65-67, 1018 XE Amsterdam, The Netherlands

3 Physics Department, St. Francis Xavier University,

Antigonish, NS, B2G 2W5, Canada

4 Departement Atomes et Molecules en Astrophysique,

Observatoire de Meudon, 92190 Meudon, France

b Laboratoire Aime Cotton, CNRS II, bat. 505,

Centre Universitaire, 91405 Orsay, France

1 Introduction

Elements of the 5d-sequence show complex spectra and large relativistic effects, reflected in a

strong mixing of levels and high values of the spin orbit interactions. Over the last decade many

investigations focusing on the resonance transitions of 5d-elements were published [1]. One reason

for these investigations is the increase of interest in 5d-elements in astrophysics after the observation

of spectral lines of 5d-elements in chemically peculiar stars, such as x Lupi and k Cancri [2]. Another

reason is the development of sophisticated computational methods, such as the orthogonal operator

approach [3], [4], [5] and the Multi Configuration Dirac Fock code [6]. These new computational

methods allow the successful investigation of the complex systems of the 5d-sequence, thanks to

far better values for initial estimates of the energy level values and transition probabilities. A third reason for exploring the 5d-elements is interest in relativistic effects that appear to be strong for

these heavy elements. The orthogonal operator approach provides the tools to investigate these

small, thus far neglected higher order correlation and relativistic effects quantitatively, as was

recently showed for the 3d-elements [7]. To study these effects properly, however, many data from

different elements in the 5d-sequence and from different stages of ionization are necessary.

Efforts of our team have resulted in many investigations of elements in the platinum group.

The state of these analyses is shown in table 1. These analyses have resulted in experimental

wavelengths and energy level values, as well as calculated transition probabilities. In most of the

spectra indicated in table 1 about 400 lines have been identified. The high dispersive 10m normal

incidence vacuum spectrograph in Meudon was used to obtain the spectrograms. This spectrograph is equipped with a 3600 1/mm grating, resulting in a plate factor of 0.26 A/mm. Other

observational instruments are the 6.6 m normal incidence vacuum spectrograph at the Institute for Spectroscopy in Troitsk and the 3 m normal incidence spectrograph of the St. Francis Xavier University in Antigonish. Spectrograms have been measured with semi-automatic and fully-automatic

comparators in Antigonish and Troitsk, respectively. The analyses were supported by the " package

IDEN" [8], [9] developed in Troitsk.

3.1 Atomic Structure and Spectroscopy 103
2 Present Investigations

The main objective of the project presented here is the extension of the analyses, focussed in

the past on spectra of doubly ionized elements of the platinum group. These lower stages of

ionization are more interesting from the astrophysical point of view, but they are also a challenge

due to the complexity of these systems. The lower stages of ionization are dominated by strong

correlation effects. For this reason the energy matrix has to be extended to (5d^ + 5d 7V_1 6s

+ 5dN-2 6s2

) for the even system and to (Sd^-^p + 5dN"2 6s6p + 5d N-3 6s2 6p) for the odd

system. This extension of the basis will result in complicated calculations of energy level values and

transition probabilities using orthogonal operators along the lines presented in [5]. The transition

probabilities, in combination with the wavelengths calculated from the experimental energy level values, provide a large amount of valuable data.

Another result from these efforts is the possibility to quantize higher order magnetic and electrostatic effects as was done in the 3d-elements [7]. To undertake these studies a large amount of data

is necessary together with a good knowledge of interacting configurations. For the higher stages of

ionization the latter is not that relevant. We show an example of the consistency of small, thus far

neglected 3-particle electrostatic higher order effects, observed in Os V and Au V [10] (see table 2).

Here we have chosen a comparison between two iso- ionic spectra. Iso-ionic comparisons are far more

relevant since they are less sensitive to the reproduction of errors, as is the case for iso-electronic

comparisons. The example given for four times ionized platinum group elements shows the stability

of our computational method in providing reliable estimates for starting the analyses of unknown

systems of doubly ionized 5d-elements. For the strong 2-particle electrostatic interactions and the

1-particle magnetic interactions this stability was already known for years, but the stability of the

small higher order effects in the orthogonal operator approach offers the possibility to extrapolate even these small effects to unknown spectra and to obtain good predictions, necessary to investigate

the complex systems successfully.

References

[1] A. J. J. Raassen, V. I. Azarov, P. H. M. Uylings, Y. N. Joshi, L. Tchang-Brillet, and A. B.

Ryabtsev, Phys. Scr. 54, 56 (1996)

[2] D. S. Leckrone, G. M. Wahlgren, S. G. and Johansson, Astrophys. J. 377, L37 (1991)

[3] A. J. J. Raassen and P. H. M. Uylings, Phys. Scr. T65, 84 (1996)

[4] P. H. M. Uylings and A. J. J. Raassen, Phys. Scr. 54, 505 (1996)

[5] P. H. M. Uylings, A. J. J. Raassen, and J.-F. Wyart, J. Phys. B.: At. Mol. Opt. Phys. 26,

4683 (1993)

[6] F. A. Parpia, C. Froese-Fischer, and I. P. Grant, Comput.Phys.Commun. 94, 249 (1996)

[7] J. E. Hansen, B. R. Judd, A. J. J. Raassen, and P. H. M. Uylings, Phys. Rev. Lett. 78, 3078

(1997)

[8] V. I. Azarov, Phys. Scr. 44, 528 (1991)

[9] V. I. Azarov, Phys. Scr. 48, 656 (1993)

[10] A. J. J. Raassen, R. Gayasov, and Y. N. Joshi, Phys. Scr., submitted

104 ICAMDATA 97 Proceedings
Table 1: State of knowledge of platinum group ion spectra.

w

74

Re

5 Os76

Ir

77

Pt

78

Au

79

1 5d6 5d7 5d8 5d9 5d10 11 5d5 5d6 5d7 5d8 5d9 5d10 111 5d4 5d5 5d6 5d7 5d8 5d9 TV OQ tJU. fid 5 JU. 5d8

V 5d2 5d3 5d4 5d5 5d6 5d7 VI Bd1 5d2 5d3 5d4

5d5 5d6 VII Sd1 5d2 5d3 5d4 5d5 Vlll 5dx 5d2 5d3 5d4 IX 5d* 5d2 5d3 X 5d* 5d2

5d : unknown

5dN : known in past and from others

5d"^ : in progress in our team

5dN : finished in our team

Table 2: Comparison between the 3-particle electrostatic ddp-type parameters in Os V and Au V

Parameter Os V Au V

Tie -25.4 -25.2

Tit 14.5 10.5

Tib -18.2 -16.1

Tio -15.6 -10.0

T20 -38.2 -47.1

T2i -11.5 -19.4

T22 -48.9 -15.1

T23 -12.7 -3.2 T24 -15.1 -17.7

T25 7.9 5.1 T26 -41.6 -33.5

T27 14.2 1.7 T28 59.0 44.6

T29 -30.1 -20.5

T30 8.0 29.6

T31 -5.9 -17.7

T32 -11.0 2.6

T33 14.5 7.2

T34 -40.8 -46.1

T35 -64.0 -65.5

3.1 Atomic Structure and Spectroscopy 105
An Integrated Approach to Bound and Continuum

States: Application to Beryllium-like Ions

Keith A. Berrington and John C. Pelan

Department of Applied Mathematics and Theoretical Physics,

Queen's University, Belfast BT7 INN, U.K.

Modern research in the theory of atomic physics is characterised by a desire to understand

the collective behavior of charged particles and their response to added energy or radiation, from

quantum-mechanical first principles (ab initio); the concomitant aim being the quantitative pre- diction of atomic properties and the establishment of standards for areas of science and technology

where atoms play a role - whether in laboratory plasmas or in environments such as astrophysics.

Because of the implied ab initio approach, the theme of much recent research is the incorporation of more effects into the wavefunction: the unification of processes formerly treated as independent. So atomic properties associated with bound and continuum states, electron impact

excitation and ionization cross sections, photon excitation and ionization, and fine- structure levels, can be calculated in an integrated way. [1] Resonances are perhaps the most obvious manifestation of interference effects in quantum mechanics. One of the most widely used, and perhaps most fully developed, of the sophisticated

models available to atomic physics is the R-matrix approach [2]. This model was first introduced in

nuclear physics specifically to study resonance reactions [3], the idea being that a resonance could

be described in terms of the colliding particles forming a compound state, the total wavefunction

being expanded as a complete set of these states. The complicated interaction zone, the internal

region of configuration space, is delineated by a sphere of radius r = a around the centre of mass,

with the external region reducing to a simpler two-body problem. These ideas were developed for

atomic physics by Burke and others and encapsulated in a computer program package for electron

scattering and photoionization from atoms and ions [4]. It may seem suprising for a method originating in the study of resonances and continuum

processes, but R-matrix techniques - and indeed any multiconfigurational close-coupling approach - can be applied to the bound state problem with great success. This was exploited in the drive for quality data for stellar opacity applications by Seaton and

others [5], who extended the R-matrix method and programs to photoabsorption processes relevant

to stellar envelope opacities, in particular for bound-bound and photoionization transitions. The

Opacity Project (OP) provided an important data base for atomic physics, the TOPBASE facility at the Centre de Donnees Astronomiques de Strasbourg [6]. Within this paradigm, we are now concerned to explore the potential of close-coupling ab initio

methods for high precision atomic structure calculations. Particularly for excited and continuum

states, such methods should eventually be superior to atomic structure methods which use the same

functional basis from r = 0 to r = oo. Recent developments are again based on the R-matrix model,

within the high optimization offered by close-coupling. These include exploitation of the 'QB'

method[7] for systematic resonance analysis, use of target 'core base states' and pseudo-states for accurate representation of inner-shell and continuum processes, and incorporation of radiative and

relativistic effects via the Opacity Project codes together with terms of the Breit-Pauli Hamiltonian.

106 ICAMDATA 97 Proceedings
Table 1: Comparison of 2s2 — 2s2p gf-values for C

++ J = 0

e — 1°, taken from the recent R-matrix

calculation of all bound and autoionizing fine-structure energy levels to n = 10 [10], with other

theories (OP [5], CIV3 [12] and MCHF [13]) and experiments.

Transition Present[10] NIST[8] Other

2s'

2 - 2s2p6 P?

2s2 - 252^°

1.93E-7

0.761

1.87E-7

0.759

1.89±0.07E-7[12], 1.87±0.002E-7[9]

0.780[5], 0.757[13], 0.754±0.014[11]

Oscillator strengths for all ions of C, N and 0 were subject to a review and assessment by

Wiese et al in 1996 [8]. This review, together with a more recent lifetime measurement on C

++

using the heavy ion storage ring at Heidelberg [9], provide a sensitive test of theory. Using the

theoretical techniques described above, a complete set of data has just been calculated [10] for fine- structure energy levels for bound and autoionizing states of the form ls2 2sn/ and ls2 2pnl (J — 0

e and J = 1°) up to n — 10 for the Be-like ion C

++

, together with electric dipole oscillator strengths

whose accuracy is estimate to be within ~3% by comparison with experiment (table 1). Work is progressing on other ions, for example Ne, Ar, P and CI, to upgrade the OP database and to extend

it to fine-structure transitions.

In a higher energy regime, similar theoretical techniques can be used to quantify so-called 'hollow

atom' effects. Although the methods are developed for complex atoms, consider the four-body

problem in atomic physics, which is the simplest system to show hollow atom interference between

direct and indirect ionization involving excitation-autoionization and triply excited intermediate

states. In the particular case of hollow lithium, this occurs when both K electrons from the ground

state configuration become excited into the L shell during a collision, and there has been much

interest in the properties of this system. In a recent application of the R-matrix and QB method

(described above), hollow atom interference effects and resonances in Li have been examined and

quantified. Outer-shell and inner-shell effects, excitation and ionization channels, direct and indirect

ionization processes, resonant and non-resonant behavior are combined for photon and electron

impact processes. This includes resonance analysis (table 2), electron impact ionization of ground

state Li+ and photoionization of Li (table 3), electron excitation and ionization of metastable states and double photoionization. Good agreement with experiment where available is obtained, with a

tabulation of all 480 212Vnl" states for n < 9,1" < 3, and a demonstration of the chaotic behavior

of overlapping series [14]. These bound and continuum state techniques are in progress to being extended to more complex

atoms, particularly for atoms (eg. C, O, Ne, Mg etc.) where there is current interest in the dynamics

of atoms and ions at X-ray energies in astrophysical and technology applications.

References

[1] K. A. Berrington, J. C. Pelan, and L. Quigley, J. Phys. B 30, 4973 (1997)

[2] P. G. Burke and K. A. Berrington (eds), "Atomic and Molecular Processes: An R-matrix

Approach", Institute of Physics Publishing 1993, ISBN 0-7503-0199-6

[3] Wigner, Phys. Rev. 70 15, 606 (1946)

[4] K. A. Berrington, W. B. Eissner, and P. H. Norrington (1995)

[5] The Opacity Project, Institute of Physics Publishing 1995, ISBN 0 7503 0288 7

3.1 Atomic Structure and Spectroscopy 107
Table 2: Li resonances coupled to 2s2 l S: effective n and width (r meV). Identifications (ID) assume a 2s2 core, except those labelled 3 P (2s2p) and Q = 2s2p2

. ID Tll Se r ID Tll Se r ID r

TT\ ID m5e r

2ge 2po /po

Q 1.664 82 2p 1.215 123 Q 1.425 98 4/ 3.985 0.9

3s 2.243 141 2p6 2.239 55 3d 2.968 97 6 P3d 4.490 4.8

3.181 22 3p 2.430 65 36 no P3p 3.244 17 5/ 4.981 0.5

3 P3p 3.677 8.5

3 no ^PdS 2.860 19 A 1 Ad 3.944 C\ o 23 6/ 5.980 0.4

OS A OOQ O.Z 4p 1 Q oa Q 1 O.l 7 ^ <J D.y / y u.z 65 5.212 5.0 hp 4.440 6.9 6d 5.911 3.8 8/ 7.978 0.2

75 6.205 3.1 3 P3d 4.798 5.7 7d 6.888 2.1 9/ 8.977 0.1 85 7.198 2.1 6p 5.387 3.2 3 P4p 7.561 4.9

95 8.187 1.5 3 P45 5.958 3.9 8d 7.976 2.3

3 P4p 9.971 1.9 7p 6.560 2.8 9d 8.933 1.1 8p 7.506 1.5 9p 8.490 1.0

Table 3: Total ionization cross sections (10

18 cm2

) for e +Li+ I52 and 7+Li ls2 2s, as a function

of e~ energy (eV) relative to Li I52. e-(eV): 146.13 147.00 147.02 147.14 147.20 147.33 147.43 150.33 153.93

e-+Li+

7+Li

2.918 2.962 2.962 2.973 2.977 2.975 2.980 3.097 3.244

0.603 0.928 0.962 0.508 0.523 0.606 0.533 0.540 0.512

[6] W. Cunto, C. Mendoza, F. Ochsenbein, and C. J. Zeippen, A&A 275 L5 (1993)

[7] L. Quigley and K. A. Berrington, J. Phys. B 29, 4529 (1996)

[8] W. L. Wiese, J. R. Fuhr, and T. M. Deters, "Atomic Transition Probabilites of C, N and O",

J. Phys. Chem. Ref. Data Monograph No. 7, (AIP) ISBN 1-56396-602-6 (1996)

[9] J. Doerfert, E. Trabert, A. Wolf, D. Schwalm, and O. Uwira, Phys. Rev. Lett. 78, 4355 (1997)

[10] K. A. Berrington, J. C. Pelan, and L. Quigley, Phys. Scr., in press (1998)

[11] N. Reistad, R. Hutton, A. E. Nilsson, I. Martinson, and S. Mannervik, Phys. Scr. 34, 151

(1986)

[12] J. Fleming, A. Hibbert, and R. P. Stafford, Phys. Scr. 49, 316 (1994)

[13] J. Fleming, N. Vaeck, A. Hibbert, K. L. Bell, and M. R. Godefroid, Phys. Scr. 53, 446 (1996)

[14] K. A. Berrington and S. Nakazaki, J. Phys. B 30, in press (1997)

108 ICAMDATA 97 Proceedings
Efficient Method to Account for Correlation Effects

when Generating Atomic Parameters

for Complex Atoms

P. Bogdanovich, G. Gaigalas and Z. Rudzikas

State Institute of Theoretical Physics and Astronomy,

A. Gostauto 12, 2600 Vilnius, Lithuania

1 Introduction

The potential of a simplified method of superposition of configurations for studying the

energy spectra of atoms and ions has been discussed in some earlier papers[l-4]. In this

method a part of admixed configurations, obtained mainly by one-electron excitations, is taken into account directly when calculating the multi-configurational energy matrix,

whereas the correlation corrections, connected with the majority of configurations, obtained

by virtual two-electron excitations, are accounted for in second-order perturbation theory as corrections to Slater integrals and similar quantities [4]. Such an approach allows us to take

into consideration a fairly large number of admixed configurations, preserving a comparatively small order of the matrix to be diagonalized. This is of extreme importance for

calculations of energy spectra of complex configurations.

The possibility to approximately account for a large number of admixed configurations (in

the second order of perturbation theory) has allowed us to avoid the use of solutions of multiconfigurational equations and to employ the so-called transformed radial orbitals, obtained

from Hartree-Fock functions of the configuration considered, with the help of simple

algebraic multipliers of the type of various positive degrees of a radial variable. The main

advantage of this approach is the exceptional simplicity of the generation of the basis

combined with its fairly high efficiency. Recently a similar approach has been also applied to the relativistic Dirac-Hartree-Fock approximation [5,6].

This paper is aimed at exploring the possibility to apply such a method for calculations of

electronic transitions in atoms and ions. We expect a fairly high efficiency because of the

following facts:

1) The transformed radial orbitals are fairly useful for calculations of matrix elements of

the operators of electronic transitions [7]. 2) It follows from the above-mentioned publications that the approach under

consideration allows the determination of fairly accurate wavelengths. This is rather

important when calculating the majority of characteristics of electronic transitions.

3) The high accuracy of the energy levels of a configuration leads to sufficiently accurate

weights of the wave functions of a pure coupling scheme, obtained after diagonalization

of the energy matrix. This also contributes to an increase in the accuracy of the matrix

elements of the electronic transitions.

4) The approach used allows us to include in the multi-configurational wave function

practically all necessary configurations - both giving the principal contributions to the

expansion as well as the most important ones for the electronic transition considered.

3.1 Atomic Structure and Spectroscopy 109
2 Results of the Calculation of the Transition 2s2 2p2-2s2p3 in OIII

Let us consider the electronic transitions 2s22p2 - 2s2p3 in OIII. These transitions were studied

by many authors, therefore we can compare our results with fairly accurate theoretical and

experimental data. Moreover, the role of correlation effects is very important for these

configurations. Therefore, it will be possible to estimate how accurately we are taking them into

account.

The transformed radial orbitals were defined as follows:

k P in' l'

| r) = N r P (nl I r), TR HF

(N is the normalizing factor). They are orthogonalized to all Hartree-Fock and transformed

functions already included in the basis used. The values of n'V, k and nl are presented in Table 1.

Table 1: Parameters of the transformed radial orbitals used

n'V k nl n'V k nl n'V k nl n I k nl n'V k nl

5s 1 2s 5p 1 2s 5d 2 2s 5f 3 2s 4 2s

6s 1 2p 6p 1 2p 6d 1 2p Gf 2 2p % 3 2p

6h 3 2p 7s 2 2s 7P 2 2s 7d 3 2s 7f 4 2s

7? 5 2s 8s 2 2p 8p 2 2p 8d 2 2p 8f 3 2p

8? i 2p 8h 5 2p 9s 1 Is 1 Is 9d 2 Is

The quantum numbers of the radial orbitals which according to [7] play the main role while

refining the matrix elements of the transition operator are underlined. In this approach the

principal quantum numbers n have no physical meanings and they have nothing to do with the

numbers of nodes of the radial orbital considered. Their values starting with n = 5 were used.

While calculating the energy matrix and, correspondingly, multi-configurational wave

function (as in [4] for calculations of the energy spectra), the fairly important quasidegenerate

configuration 2p4 was admixed to 2s2 2p2

, as well as all configurations obtained from these two

by one-electron excitations. Moreover, all configurations necessary to improve the matrix element

of the transition operator and obtained from the configuration 2s2p3 by one electron excitations in

states of opposite parity [7] were automatically included in the matrix. The contributions of the

remaining possible admixed configurations were taken into consideration in second order

perturbation theory in terms of the corrections to the radial integrals of electrostatic interactions

and similar quantities. The configuration 2s2p3 has no configurations of the same parity which

are quasidegenerate to it. When improving it, all possible one-electron admixed configurations were taken into account to form the energy matrix as well as the configurations obtained from

2s2 2p2 and, due to strong mixing, from 2p4 by one-electron excitations in the states of the opposite

parity [7]: 2s2 2pnis; 2s2 2pnid. It is necessary to underline that according to the above-mentioned

list, configurations of the kind 2p3 ms and 2p3 md must be included. However, they already

appeared earlier as the result of one-electron excitation of the configuration considered.

The results obtained for some transitions are presented in Table 2. It contains the

experimental wavelengths and the oscillator strengths (gf) of electric dipole transitions, calculated

in the single-configuration Hartree-Fock (HF) approximation and with the method of simplified

superposition of configurations (SSC) as well as calculated with the usual superposition of

configurations approach with the same radial orbitals accounting for a complete set of possible

admixed configurations (SC). In the latter case the order of the matrix to be calculated and

110 ICAMDATA 97 Proceedings
diagonalized increases many times. The table also contains recommended data on oscillator

strengths [8] as well as the results of multi-configuration calculations [9]. Our results are presented for both the 'length" (L) and "velocity" (V) forms of the transition operator. Moreover,

the upper lines contain ab initio values whereas the lower ones contain data obtained using

experimental energy values.

As seen from Table 2, the results obtained in the SSC and SC approaches differ

insignificantly, especially for the case of the 'length" form of transition operator. They are very

close to the data found using more elaborate methods [8,9] and are not significantly improved

when using experimental energy values. As was expected, the largest discrepancies occur when

calculating intercombination transitions. The SSC data, obtained for the "velocity" form of the

transition operator, are slightly less accurate. This may be an indication that the basis of radial

orbitals used is not sufficiently complete while using this operator.

3 Conclusion

The numerical data presented indicate that the method of simplified superposition of

configurations (SSC), in which only part of the admixed configurations is directly taken into

account when calculating the energy matrix, whereas the majority of admixed configurations,

obtained by two-electron virtual excitations, are accounted for in second-order perturbation

theory, is fairly efficient not only for calculations of the energy spectra, but also for studies of

electronic transitions. This method may be easily applied to study complex electronic

configurations, having several open shells, and, thus, may efficiently contribute to the generation

of accurate atomic data for relevant databases..

References

[1] P. Bogdanovich, G. Zukauskas, Sou. Phys. Collection 23, No. 3, 13-26 (1983)

[2] P. Bogdanovich, G. Zukauskas, S. Sadziuviene, Sov. Phys. Collection 24, No. 3, 27-37 (1984)

[3] P. 0 . Bogdanovich et all, Izvestija vuzov SSSR. Fizika 33, 6-17 (1990)

[4] P. Bogdanovich,G. Gaigalas,A. Momkauskaite, Z. Rudzikas, Physica Scripta 56, 230-239

(1997)

[5] V. A. Dziuba, V. V. Flambaum, M. G. Kozlov, 28th EGAS, Abstracts, 62, 1996

[6] V. A. Dziuba, V. V. Flambaum, M. G. Kozlov, Phys. Rev. A 54, 3948-3959 (1996)

[7] P. Bogdanovich, Lithuanian Physics Journal 31, 79-83 (1991)

[8] W. L. Wiese, J. R. Fuhr, T. M. Deters, J. Phys. Chem. Ref. Data, Monograph 7, (1996)

[9] H. Nussbaumer, P. J. Storey, Astron. Astrophys. 99, 177-181 (1981)

3.1 Atomic Structure and Spectroscopy 111
Table 2: Oscillator strengths igf) for some electri c dlpole transit ions i n QUI.

LSJ-L'S J ?lexp(A) HF SSC SC [81 f9]

3P2

- 3D3 835.289 L 0.841

0.856

0.431

0.433

0.456

0.451

0.438 0.44

V 0.492

0.489

0.464

0.469

3 Po-3Di 832.929 L 0.203

0.207

0.104

0.105

0.110

0.109

0.106 0.107

V 0.118

0.118

0.112

0.114

3P2

- 3P2 703.854 L 0.541

0.550

0.499

0.499

0.524

0.516

0.510 0.505

V 0.515

0.516

0.522

0.530

3 P2

- 3 Si 508.178 L 1.392

1.343

0.906

0.918

0.945

0.932

0.935 0.925

V 1.014

1.002

0.976

0.990

3 Po-3 Si 507.388 L 0.277

0.268

0.180

0.183

0.188

0.186

0.186 0.185

V 0.202

0.199

0.194

0.197

1 D2

- 1 D2 599.590 L 2.682

2.557

1.414

1.438

1.485

1.469

1.455 1.460

V 1.674

1.647

1.557

1.574

525.794 L 1.008

0.972

1.158

1.163

1.209

1.188

1.195 1.160

V 1.199

1.194

1.225

1.246

597.814 L 0.668

0.684

0.241

0.242

0.246

0.244

0.240 0.250

V 0.312

0.311

0.269

0.272

3P2 -!D2 535.481 L

V

1.01-4

.959-4

.440-4

.444-4

.428-4

.424-4

.525-4

517-4

.553-4

.561-4

.555-4 .585-4

1 D2

- 3D3 1002.49 L .347-4

.364-4

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.190-4 .200-4

V .343-4

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.319-4

112 ICAMDATA 97 Proceedings
Relativistic Calculations in the Arsenic Sequence:

Fine- Structure Transitions

E. Charro and I. Martin

Departamento de Quimica Fisica,

Universidad de Valladolid,

47011 Valladolid, Spain

1 Introduction

One of the properties of highly ionized atoms that is a subject of considerable interest for many

fields, such astrophysics and fusion plasma research, is the transition probability between different

electronic levels or the oscillator strength. One of the isoelectronic series of the heavier species which

has not been studied so far, to our knowledge, is that of the arsenic atom. As I has itself been the

object of great interest in the last few years ([4]), given the detection of its 4p2 5s 4 Ps/2 — 4p3 4 S3 / 2 line in the spectrum of Chi Lupi, a HgMn type star, with a spectrometer on board the Hubble Space

Telescope. Other atomic systems that have been found to exist in different ionization degrees in

Chi Lupi are Sr, Y, Zr, Ru and Pd [5], which are potencially members of the As I isoelectronic

sequence, although there are so far no reports on the existence of these elements in As-like form.

For many years we have applied the Quantum Defect Orbital method, both in its non-relativistic

(QDO) [1] and its relativistic (RQDO) [2] versions, to the calculation of oscillator strengths and

photoionization cross sections of a rather large number of atomic species, including several isoelectronic sequences ([3]). Nevertheless, for the reasons given above, we have undertaken the study

of the intensities of all the allowed lines of the 4s2 4p3 — 4s2 4p2 5s transition array in a number of As-like ions ranging from Br III (Z = 35) to La XXV (Z = 57). Two methodologies have

been followed: the aforementioned RQDO method and the multiconfiguration Dirac-Fock (MCDF)

formalism with the GRASP code written by Grant et al. [6] .

2 Relativistic Quantum Defect Orbital Method

The RQDO method has been described in detail [2] . We shall thus only mention here those aspects

of the formalism which are relevant to this study.

The relativistic quantum defect orbitals are the analytical solutions of a quasirelativistic secondorder Dirac-like equation with a model Hamiltonian that contains the quantum defect as a parameter. This model Hamiltonian allows for an effective variation of the screening effects with radial

distance and, as a consequence, the radial solutions behave approximately correctly in the core region of space, and display a correct behaviour at large radial distances. These have been found to be, in many cases, the most relevant regions contributing to the transition integral. The RQDO's

lead to closed-form analytical expressions for the transition integrals, which allows us to calculate

transition probabilities with simple algebra and little computational effort. The RQDO Hamiltonian accounts for core-valence polarization only implicitly, through the

inclusion of the quantum defect. However, it is our experience that the explicit inclusion of the

above effect is often important. As in some previous works (see, e.g., [3] ) we have performed

3.1 Atomic Structure and Spectroscopy 113
two types of RQDO /-value calculations: one with the standard dipole-length transition operator,

Q(r) = r, and another with a core-polarization corrected form of the former [7]:

Q(r)=r l--[l-exp(-r/rc )] 3 (1)

where a is the core polarizability and rcis a cut-off radius, chosen to be in these calculations the

mean radius of the outermost orbital of the core, calculated in accord with an expression given by

Chichkov and Shevelko [8]. The core has been considered in all cases to be Ar 3d10 4s2

. For the

core polarizabilities we have taken the values supplied by Fraga et al [9] , which do not go beyond

Nb IX (Z = 41). For the higher ions in the sequence we have found the core polarizabilities in

atomic units from the following expression

which has been obtained through a fitting of the a-values of Fraga et al. [9] from As I (Z = 33) to Nb IX (Z = 41), with a correlation factor of 0.9967. Z is the atomic number.

In the RQDO context, energy level data are required in order to obtain the quantum defects.

For Br III we have been employed the data provided from a compilation by Kelly [10]. For the

quartet levels of the 4s2 4p2 5s configuration we have taken the experimental energy values of

O'Sullivan [11] for Rb V and O'Sullivan and Maher [12] for Sr VI. No experimental energies have

been found for the remaining levels of these two ions and we have employed the energies obtained

with our MCDF calculations. For the ions Y VII to Mo X we have used experimental energies by

Reader and Acquista [13] . Early energy data measured by Rahimullah et al.[14] for these ions are

in good agreement with those of Reader and Acquista [13] . All the above experimental data have relied on theoretical predictions and observed intensities

for the identification of the lines, as well as an analysis of the systematic trends followed by the level energies along the isoelectronic sequence [11, 12, 13, 14]. O'Sullivan [11] and O'Sullivan and Maher

[12] rely on MCDF calculations. Reader and Acquista [13] employ Hartree-Fock (HF) calculations.

These authors estimate uncertainties in the range from 0.6 cm

-1

to 15 cm

-1

for the levels of the

4s2 4p3 and 4s2 4p2 5s configurations, the uncertainties increasing from the ground to the excited

configurations, and also from Y VII to Mo X.

In order to have a basis on to which test the quality of the energies employed, we have plotted the

energies of the ground and excited configurations, respectively. They present a regular behaviour,

in all cases, along the isoelectronic sequence, and the connection between the present MCDF and

the experimental energies [13] is smooth.

Other input data that are also needed in the RQDO calculations were the ionization energies

of the atomic systems. The corresponding values from As I to Kr IV are supplied by Kelly [10] and

a few more by Fraga et al. [9]. For the remaining ions we have employed an extrapolation formula

obtained by fitting the ionization energies in cm~1 of the previous ions. This formula is

where, again, Z is the atomic number. The correlation factor was 0.9998.

3 Multiconfiguration Dirac-Fock Method

The MCDF method, as implemented in the GRASP code [6], is a generalization of the Dirac-Fock

formalism. For details of the atomic MCDF model we refer to a review by Grant [15].

In a = 38.838 - 10.615 InZ, (2)

Ei = 86.96 Z

3 - 2806.66 Z

2

, (3)

114 ICAMDATA 97 Proceedings
The extended average level (EAL) mode with the Breit and QED corrections [6] has been

employed. The following configurations have been introduced: 4s2 4p3 + 4p5 to describe the ground

configuration, and 4s2 4p2 5s + 4s 1 4p4 + 4s2 4p2 4d1 to describe the excited configuration. The choice

of these configurations has been made on the grounds of the comments by Bieroh and Migdalek

[16] and O'Sullivan [11] and by observing that this configuration mixing leads to a good accord

between dipole-length (Babushkin gauge) and dipole velocity (Coulomb gauge) MCDF oscillator

strengths for most of the transitions studied.

4 Results and Analysis

For each transition, two RQDO sets of /-values are given, one obtained with the standard dipolelength transition operator, Q{r) = r, and the other with the core-polarization corrected transition

operator, Eq. (2.1). The two sets of MCDF oscillator strengths correspond to calculations in

the dipole-length and dipole-velocity forms, respectively. The experimental /-values reported by

O'Sullivan [11] and O'Sullivan and Maher [12] up to Mo X have been considered for comparative

purposes. In all the transitions, our MCDF calculations did not reach convergence both for Br

III and Kr IV. For Rb V, all theoretical as well as experimental /-values are anomalously low in

magnitude. This feature is explained by O'Sullivan [11] in terms of a large configuration mixing

taking place in this particular ion that leads to a major re-distribution of intensity between the

4p — 5s and 4p — 4d transitions. In all studied transitions both our RQDO and MCDF /-values are

in good accord with experiment. As we go down in the sequence, a greater similarity between the

dipole-length and dipole velocity MCDF oscillator strengths is observed. In most transitions, the

effects of correcting the RQDO /-values for core polarization are sizable and bring them closer to the

MCDF oscillator strengths, in particular to those corresponding to the dipole-length calculation.

A sharp increase that occurs in most transitions of Sr VI is apparent both in our calculations and

experiment. O'Sullivan [11] refers to it as "array quenching" and explains it in terms of a sudden

change in eigenvector composition of the 4p2 5s term.

In all transitions, the RQDO /-values are generally greater in magnitude than the MCDF

results, the differences increasing with atomic number, except for the 2 D3/ 2 ~

2Pz/2 transition.

Nevertheless, the RQDO-MCDF relative difference of 96% occurring at La XXV (Z=57) for the

4 S3/2 — 4 Pz>/2 transition is certainly an exception. For the other transitions, the largest RQDOMCDF relative differences in the heaviest of the ions studied range from 15% in Sn XVIII (Z = 50)

for the 2 P3/2 - 2 51/2 transition and Cs XXIII (Z = 55) for the 2 Dz/2 ~

2 ^3/2 transition to 33, 5%

for La XXV (Z = 57) for the 4 S^/2 —

4 P*>/2 transition. Apart from the more correct wavefunctions

supplied by the MCDF approach, as compared to the RQDO wavefunctions, a possible reason for

the discrepancies might be the fact that the LS coupling scheme has been adopted for all the ions

in the RQDO procedure, unlike Biemont and Hansen [17] who adopted an intermediate coupling

scheme in their calculations of magnetic dipole and electric quadrupole transitions in the ground

state of the germanium and arsenic isoelectronic sequences.

In summary, RQDO and MCDF oscillator strengths for the 4s2 4p3 — 4s2 4p2 5s transition

array of a number of As-like ions are presented. When experimental data are available, our results are in good accord with them. Some discrepancies between the RQDO and MCDF /-values are apparent, particularly for the heavier ions, for which we consider the MCDF results to be superior

in quality. Nevertheless, the RQDO procedure has once more proved to be a very useful tool for

estimating transition probabilities. It is particularly adequate in the cases where mass-production

of data is needed, given its cost-efficiency and reasonable correctness. It offers also the advantage

of its analyticity and lack of convergence problems from which elaborate ab initio calculations often

suffer.

3.1 Atomic Structure and Spectroscopy 115
One drawback of the RQDO formalism is that it needs quantum defects from other sources as input. But this can be, in many cases, circumvented by making use of the regularities presented by

the quantum defects both along spectral series and isoelectronic sequences, which allow for inter- or extrapolations.

5 Acknowledgements

This work has been supported by the DGICYT of the Spanish Ministry of Education within Project

No. PB94-1314-C03-03 and the J.C.L. within Project No. VA 21/97.

References

[1] G. Simons, J. Chem. Phys. 60, 645 (1974); I. Martin and G. Simons, J. Chem. Phys. 62, 4799

(1975); Mol. Phys. 32, 1017 (1976)

[2] I. Martin and J. Karwowski, J. Phys. B: At. Mol. Opt. Phys. 24, 1538 (1991); J. Karwowski

and I. Martin, Phys. Rev. A43, 4832 (1991)

[3] E. Charro, I. Martin, and C. Lavin, J. Quant. Spectrosc. Radiat. Transfer 56, 241 (1996);

Astron. Astrophys. Suppl. Series. 124, 1 (1997), and references therein

[4] G. J. Bengston, U. Berzinsh, J. Larsson, and S. Svanberg, Astron. Astrophys. 263, 440 (1992)

[5] D. S. Leckrone, S. Johansson, G. M. Wahlgren, C. R. Profntt, and T. Brage, Phys. Scr. T65,

110 (1996)

[6] I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, and N. C. Pyper, Comput. Phys.

Commun. 21, 207 (1980); K. G. Dyall, I. P. Grant, C. T. Johnson, F. A. Parpia, and E. P. Plummer, Comput. Phys. Commun. 55, 425 (1989)

[7] D. Bielihska-Waz, M. Sc. Thesis, University Nicholas Copernicus, Toruri Poland 1992

[8] B. N. Chichkov and V. P. Shevelko, Phys. Scr. 23, 1055 (1981)

[9] S. Fraga, J. Karwowski, and K. M. S. Saxena, "Handbook of Atomic Data", Elsevier, New

York 1976

[10] R. L. Kelly, J. Chem. Ref. Data 16, Supp.l (1987)

[11] G. O'Sullivan, J. Phys. B: At. Mol. Opt. Phys. 22, 978 (1989)

[12] G. O'Sullivan and M. Maher, J. Phys. B: At. Mol. Opt. Phys. 22, 377 (1989)

[13] J. Reader and N. Acquista, J. Opt. Soc. Am. 71, 434 (1981)

[14] K. Rahimullah, M.S.Z. Chagtai, and S. Khatoon, Phys. Scr. 14, 221 (1976); Phys. Scr. 18, 96

(1978)

[15] I. P. Grant, in "Methods in Computational Chemistry", Vol. 2., p. 1, edited by S.Wilson,

Plenum Press, New York 1988

[16] J. R. Bierori and J. Migdalek, J. Phys. B: At. Mol. Opt. Phys. 25, 4099 (1980)

[17] E. Biemont and J. E. Hansen, Phys. Scr. 33, 117 (1986)

Tables and figures are available upon request to the authors.

116 ICAMDATA 97 Proceedings
Atomic Database for C I from C II

J. Dubau+

, T.Kato*, and U. I. Safronova * + Observatoire of Paris, Meudon, F-92195 MEUDON Cedex, France

* National Institute for Fusion Science, Oroshi-cho, Toki, Gifu, 509-52, Japan

1 Introduction

Carbon is the main constituent of the graphite tiles which cover the inner side of the vacuum

chamber of the latest tokamaks (JET, TFTR, JET-60). Carbon is also one of the most abundant

elements of the Universe. The tokamak spectra are very rich in C lines emitted in the outer

region of the plasma, the coolest part, where C is not completely ionized and can still emit a line

spectrum. The recombination rates will play an important role in the plasma cooling when more

ionized species recombine progressively.

The dielectronic recombination (DR) process for C (C I from C II) can be schematically rep- resented by ls2 2s2 2p + e ls2 2s2p2 n/, ls2 2s2p3 (LS), ls2 2p3 n/, ls2 2p4

ls2 2s2 2p, ls2 2s2p2 + eor ls2 2s2 2p

2

, ls2 2s2 2pn/, ls2 2s2p3 (L' S') + hu , (1)

where LS= 3 5,

1 D, l P for autoionizing states and L'S'=5 S, 3D, 3 P for bound states. An intensity

factor Qd for transitions from autoionizing levels 7=ls2 2s2p2nZ, ls2 2s2p3 (L5), ls2 2p3 n/, ls2 2p4 to excited states j'= ls2 2s2 2p2

, ls2 2s2 2pn/, ls2 2s2p3 (L'S") can be defined as follows:

Qd(T,7>o) = g7Ml, l')

A

^

%

}

(7)

, Ml) - E^r(7,7"), Mi) =EA»(7,«') , (2)

where Ar (7, 7') are radiative transition probabilities and Aa (j,a') is the autoionization rate, with

a'=ls2 2s2 2p, ls2 2s2p2 and a0 = ls2 2s2 2p.

We used the Cowan [1] and SUPERSTRUCTURE codes taking into account 28 even and 29

odd parity configurations Is2 2li2l22l^nl with up to n=6 and 0< / <(n-l). The contributions of the

configurations with 6< n <500 are taken into account in the calculation of all ls2 2/i 2^21^1 [LSJ] states up to n=6. In the present paper we can present only a small amount of our numerical data

due to the limited space.

2 Energy Levels, Radiative Transition Probabilities

We carried out detailed calculations of radiative transition probabilities and autoionization rates

for the intermediate states ls2 2s2 2pnZ, ls2 2s2p3

, ls2 2p

4

, ls2 2s2p2 n/ and ls2 2p3 n/ with n=2 - 6

. The atomic energy levels, radiative transition probabilities and autoionization rates were obtained by using the atomic structure code of Cowan [1]. Table 1 lists energies calculated by

the Cowan (a) and SUPERSTRUCTURE (b) codes, together with theoretical data obtained

by Nahar and Pradhan (c) [2] and recommended data (d) by Wiese et al. [3] for C I with the

ls2 2s2 2p2

, ls2 2s2p3, ls2 2s2 2pnZ intermediate states. The differences in the theoretical data (a)

and (b) can be explained by different refinements of the Hartree-Fock approximation. The Cowan

3.1 Atomic Structure and Spectroscopy 117
code allows the use of scaled factors for radial integrals. We used a scaled factor equal to 0.85. The SUPERSTRUCTURE code is based on a scaled Thomas-Fermi-Dirac-Amadi potential. The

scaling parameter is different for each angular momentum /. These parameters are iterated to give

the minimum energy of a term or a group of terms. It should be noted that both methods did

not take into account correlation effects properly which explains the disagreement of these data

(columns a and 6 in Table 1) with the recommended data (column c) for some states.

3 Total Dielectronic Recombination Rate Coefficients

The total dielectronic recombination rate coefficient is obtained by the sum over all the levels,

(I_h\ 3/2

a<(a0 ) = 3.3 x UP24 Ee ^^(7,7'K)M«o). (3)

The sum over 7 means sum over all autoionization levels. As we already mentioned before we

calculated numerically the Qdil, y'\ao) values with /y'=ls2 2s2 2pnl, ls2 2s2p3

( 5 S, 3 D, 3 P) and

7=ls2 2s2p3

( 3 S, 1 D, l P ), ls2 2p4

, ls2 2s2p2 nZ, ls2 2p3 n/ up to n=6. We take into account the

states with n >6 by scaling Qj. It was shown in Ref.[4] that the largest contribution to Qd for large n are due to the 2s-2p transitions. In our case it is transitions as 2s2 2pnl[LS]-2s2p2 (LS)nl[L'S']. Radiative transition probabilities for these transitions are almost constant for large n and nonradiative transition probabilities (autoionizing rates) are proportional to \:

Ar (2s2 2pnl[LS], 2s2p2 {Ll2 S12 )nl[L'S'Jf]) = Ar {2s2 2pn0 l[LS], 2s2p2 (L uSi 2 )nol[L'S'J']), (4)

Aa (2s2p2 (L l2 Sl2 )nl[L'S'J']\ 2s2 2p

2 P) = {^j Aa {2s2p2 {Ll2 Sl2 )nQl[L' S' J']\ 2s

2 2p2 P) . (5)

Table 2 gives these data for n=4, 5, 6 with /=s, p, d, f, g and all kinds of L'S'J'. We chose for

illustration the data with the largest values of Qd- We can see from this Table that Eqs.(4,5) are

correct for transitions with large values of Ar and Aa .

Acknowledgments

U.I.Safronova would like to thank the members of the Data and Planning Center, the National

Institute for Fusion Science; the Director of the Center, Prof.H.Momota and the Director of NIFS,

Prof.A.Iiyoshi, for their hospitality and financial support.

References

[1] R. D. Cowan, "The Theory of Atomic Structure and Spectra", University of California Press,

Berkeley 1981

[2] S. N. Nahar and A. K. Pradhan, Phys. Rev. A 44, 2935 (1991)

[3] W. L. Wiese, M. W. Smith, and B. M. Glennon, Atomic Transition Probabilities v. 1, NSRDS-4

Washington, DC (1966)

[4] T. Kato, U. I. Safronova, and M. Ohira, Physica Scripta 54 (1996)

118 ICAMDATA 97 Proceedings
Table 1: Energy (103 cm x

) and sum of weighted radiative transition probabilities (^2{gAr ) in sec

-1

) of carbon (C I) for ls2 2s2li2l2{Li2Si2)nl[LSJ] states. Comparison of different methods and

recommended data from Ref.[3]: a-Cowan code, 6-SUPERSTRUCTURE code, c-Ref.[2], d -Ref.[3]

2s2l\nl2 !<12<Sl2 LS J E in 10

»T T EH)

a 0 c d a

9 a2 On2 Lb e*p 3d1 0u nu.uuu ooo 0u.uuu 000 0u.uuu 000 0u.uuu 000 0U.UUUUT^UU 0000-4-00

Lb Zp l un ol 1U.UU1 xo.oyo 10 ^09 101U. 1131Q4 0U.UUUUtUU 0000-4-00

2s2 2p2 l S 0 18.953 20.411 23.023 21.648 0.0000+00

ZS Zpop ( 2 p\ ip ii

fifi 4Qfi oo.^yo DD.OUo fiQ Dy.DDl fifil fia DO.OOO a^a o 9fifii _uoa U.ZDDl-rUO

zs zpop ( 2 p\ 3nu 9Z

fi7 OfiQ o / .uoy fi7 40^ fiQ fi^n oy.Dou fiQ 71 1 oy. <ii U.Ol / Z-f-UO zs zpop i 2 P\ 3c? 11

fi7 77fi fiS D0.4U1 401 71/ 1.000 8^^ 70 744 OU.OK7~\/ ll7-L08 +UO

9ZSc.29Lpop r) q T) ( 2 P\ 3d1

11 70 49Q 70l u.oR7f\ / u 79 799 71 3fi c

l 0u.iooi 1 337-4-OQ Tuy

9 c2o„o^ zs zpap ( 2 P\ Inu 9z 71 Rfi^ 7Q( O.U0771 / 74 948 79 fi1

n 99Q3_i_nQ

2s2 2p3p ( 2 P) l s 0 73.420 76.223 75.992 73.976 0.5352+08

2s2p3

( 4 S) 2 31.866 24.432 32.515 33.735 0.0000+00

2s2p3

( 2 D) *D 2 67.675 66.919 63.943 64.093 0.1710+10

zszp ( 2 P\ 3dr ii 78lo.l7R3Do 7fi 1 Rfi 1 D. -LOO 7fi / O.U14 01 4 7^ 9^fi 0 941 Q-4-1

0

ZS ZpoS ( 2 p\ 3dr

ii 409 oo.Doy fio DU.OoO ^a^i fiO DU.oOO 3^3 Ou.yuo QOfi7-4_OQ / +uy

ZS ApoS l 2 P\ lp ii oy.uou fi1 ^88 fi9 38^ fi1 Qi.yoz Q89 0u. 191 iziy-f-iu Q_i_1 0

2s2 2p3d ll n\

( P) dp 1 75.570 80.375 80.996 79.319 0.4165+09

zs zpao, (2 P\ U 9z 7fi / u.uoy OfiQ 7fi / u.zoo 988 7Q< y.ouu 3^0 77/ 1 .UOl fi81 0 3fi9fi-4-OQ

ZS Lpod ( 2 P\ 3 /~) 9z 7fi fiOfi / u.uuu 77/ / .UJU 0^0 80ou. 1iiy1 Q 78 307 0U. 1lOOUTl" 83R-I-1 0

ZS Lpou, ( 2 P\ oo

7fi fift9

/ D.DOZ 77 433 80 397 78 ^31 0U. 11

7fi7-i-1 1 O / TlU0

zs zpocz ( 2 P\ 3dr

ou

7fi 49Q 7fi id. 73Q / oy 7Q Qfi^ < y.yuo 78 91 fi

/ O.Z 1U 0 308^4-OQ

2s2 2p3d l P 1 76.644 77.653 79.877 78.728 0.2985+09

zs zp*±s ( 2 P\ 3p nU

7fi ^ft^ 7Q fiSO / y.uou 78 1 o^; 1l.^OOT^UO 4^34-08

zs zp*is l 2 P\ lp il

7fi Q^9 7Q/ y.o877/78 33a 7 aofi-4-oa ZS Zp4p ( 2 P\

\ P) i JJn 9Z

QPl Q1 /I 83 1 fia 01. 81 770 1 I U 1 01 9-L.oa 1.U1Z-|-U0

2s2 2o4» ( 2 P) l s o 82.434 83.794 82.252 5 231+07

2s2 2pAd ( 2 P) 1 82.147 85.681 83.830 6.559+08

2s2 2p4d ?P) l F 3 82.241 85.780 83.949 1.989+09

2s2 2p5s ( 2 P) l P 1 82.443 85.661 83.882 3.972+08

2s2 2p5p ( 2 P) l D 2 84.186 87.062 85.400 4.708+07

2s2 2p5p ( 2 P) l S 0 84.613 87.325 85.626 1.312+07

2s2 2p5<2 ( 2 P) l F 3 84.868 88.300 86.450 7.044+08

2s2 2p5d ( 2 P) l P 1 84.860 88.358 86.491 1.335+08

2s2 2p6s ( 2 P) l P 1 84.940 88.253 86.414 2.338+08

2s2 2p6p ( 2 P) 3p 0 85.625 88.877 87.077 4.477+06

2s2 2p6<2 ( 2 P) l D 2 86.127 89.489 87.632 1.786+08

2s2 2p6d ( 2 P) 2 86.160 89.599 87.706 2.013+08

3.1 Atomic Structure and Spectroscopy 119
Table 2: Energy excitation (E$ in eV ), weighted radiative transition probabilities ((gAr ) in sec

-1

), autoionization rate (Aa in sec

-1

) and factor intensities (Qa in sec

-1

) for 2s2 2pnl2s2p2 (Li2Si2)nl(L' S' J') transitions with n=4, 5, and 6.

2s2 2pns

4

56

2s2 2pnp

4

5

6

4

56

2s2 2pnd

4

56

4

56

4

56

2s2 2pnf

Upper level L\ 2 S\2 L' S' J

1 2s2p2 {L 12 S12 )ns(L'S'J')

^D) l D 2

X D 2 (}D) X D 2 2s2p2 (L 12 S12 )np(L'S, J

l ) ?D) 1 F 3

fD) l F 3

Q-D) l F 3

( 3 P) 3 Pa

( 3 P) 3 Pa

( 3 P) 3 Pa

2s2p2 (L12 51 2)nd(L, 5

, J')

05) 3 £> 3

CS) 3 D 3

OS) 3 £> 3

( 3 P)

( 3 P)

( 3 P)

( 3 P)

( 3 P)

( 3 P)

2s2p2 (Ll2 Sl 2)nf(L'S'J')

Aa UAa) gAT UgAr ) Qc ES

3 D

3 D

3 D

3 Fa

3 Fa

3 Fa

'F

X F

'F

7.702+13

3.574+13

2.426+13

3.047+13

4.854+12

2.633+12

2.630+13

2.884+12

1.454+12

1.329+13

3.851+12

2.323+12

4.384+13

1.278+13

6.991+12

4.895+13

1.418+13

8.314+12

1.502+14

7.562+13

5.127+13

3.489+13

7.879+12

4.188+12

6.458+13

2.456+13

1.178+13

1.602+13

7.046+12

4.198+12

4.580+13

1.482+13

8.113+12

5.632+13

1.831+13

1.050+13

2.712+09

3.327+09

2.577+09

5.592+09

4.192+09

5.308+09

2.379+10

2.290+10

2.328+10

1.495+10

1.460+10

1.501+10

2.100+10

2.183+10

2.189+10

3.084+10

3.114+10

3.144+10

1.027+09

1.338+09

1.398+09

4.254+09

3.281+09

3.802+09

2.339+10

2.246+10

2.297+10

1.435+10

1.420+10

1.417+10

2.075+10

2.017+10

2.139+10

2.895+10

3.006+10

3.009+10

8.914+07

1.104+08

1.293+08

6.193+08

3.368+08

3.984+08

1.587+09

4.393+08

4.725+08

1.984+09

1.293+09

1.306+10

3.310+09

1.881+09

3.071+09

4.194+09

3.879+09

3.968+09

7.948

8.599

8.897

8.187

8.710

8.954

12.49

13.03

13.28

10.88

11.22

11.39

12.84

13.18

13.36

12.86

13.19

13.37

4 (3 P) l D 2 3.140+11 3.740+11 2.362+10 2.351+10 3.429+09 12.87

5 ( 3 P) l D 2 1.970+11 1.460+11 2.273+10 2.266+10 2.405+09 13.20

6 ( 3 P) l D 2 1.170+11 1.670+11 2.286+10 2.271+10 2.581+09 13.37

4 ( 3 P) 3 Ga 3 4.201+12 4.233+12 3.003+10 2.990+10 4.940+09 12.87

5 (3 P) 3 Ga 3 7.880+11 9.260+11 3.089+10 3.079+10 4.347+09 13.20

6 (3 P) 3 Ga 3 5.450+11 6.320+11 3.082+10 3.074+10 4.387+09 13.37

4 ( 3 P) l G 4 4.257+12 4.288+12 3.850+10 3.839+10 6.337+09 12.87

5 ( 3 P) l G 4 8.150+11 9.620+11 3.964+10 3.953+10 5.556+09 13.21

6 ( 3 P) l G 4 5.670+11 6.620+11 3.945+10 3.941+10 5.589+09 13.38

2s2 2png 2s2p2 (L l2 S12 )ng(L'S'J')

5 ( 3 P) l G 4 1.6+10 1.8+10 4.021+10 4.015+10 4.766+09 13.21

6 ( 3 P) l G 4 1.8+10 2.0+10 4.020+10 4.016+10 4.923+09 13.38

5 ( 3 P) l H 5 1.9+10 2.5+10 4.870+10 4.862+10 5.231+09 13.21

6 ( 3 P) l H 5 2.1+10 2.7+10 4.813+10 4.810+10 5.366+09 13.38

120 ICAMDATA 97 Proceedings
A Project for Large-Scale Stark Broadening Data

Production: Ca IX and Ca X Spectral Lines

Milan S. Dimitrijevic 1 and Sylvie Sahal—Brechot2

1 Astronomical Observatory, Volgina 7, 11050 Belgrade, Yugoslavia

2 Observatoire de Paris— Meudon, 92190 Meudon, France

1 Introduction

In a series of papers we have performed large scale calculations of Stark broadening parameters

for a number of spectral lines of various emitters [1], [2], [3], [4]. Such data are of interest for a number of problems in astrophysics, physics and plasma technology. One may mention as examples calculation of stellar opacities, stellar atmospheres modelling and investigations, abundance

determinations, interpretation and modelling of stellar spectra, laboratory plasma diagnostics, re- search and modelling, radiative transfer calculations and investigation of laser produced plasmas

and plasmas created in fusion research. In order to satisfy the numerous Stark broadening data

needs for astrophysical and laboratory plasma research and stellar opacities calculations, we are making a continuing effort to provide Stark broadening data for a large set of atoms and ions. Our

calculations are performed within the semiclassical - perturbation formalism [5, 6], for transitions

where a sufficiently complete set of reliable atomic data exists and good accuracy for the obtained

results is expected.

Extensive calculations have been performed up to now [4] for a number of radiators, and consequently, Stark broadening parameters for 79 He I, 62 Na, 51 K, 61 Li, 25 Al, 24 Rb, 3 Pd, 19 Be,

270 Mg, 31 Se, 33 Sr, 14 Ba, 28 Ca II, 30 Be II, 29 Li II, 66 Mg II, 64 Ba II, 19 Si II, 3 Fe II, 2 Ni

II, 12 B III, 23 Al III, 10 Sc III, 27 Ba III, 32 Y III, 10 Ti IV, 39 Si IV, 90 C IV, 5 O IV, 114 P

IV, 19 O V, 30 N V, 25 C V, 51 P V, 33 V V, 30 O VI, 21 S VI, 10 O VII, 10 F VII, 20 Ne VIII,

4 Ca IX, 8 Na IX, 48 Ca X, 7 Al XI, 4 Si XI, Si XII, and 26 V XIII multiplets become available.

Data for particular lines of F I, Ga II, Ga III, CI I, Br I, I I, Cu I, Hg II, N III, F V and S IV

also exist. In continuation of our project, we have calculated within the semiclassical-perturbation for- malism the electron-, proton-, and He Ill-impact line widths and shifts for 4 Ca IX and 48 Ca X

multiplets, as a function of temperature and perturber density.

2 Results and Discussion

A summary of the formalism has been published several times [7], and will not be repeated here.

The energy levels for the Ca IX and Ca X lines have been taken from Bashkin and Stoner [8]. In

addition to electron-impact full halfwidths and shifts, Stark-broadening parameters due to proton-,

and He III- impacts have been calculated. Our results for 4 Ca IX and 48 Ca X multiplets for perturber densities from 1018 to 1022 cm-3 and temperatures from 200,000 to 2,000,000 K will be

published elsewhere [10, 11].

In Tables 1 and 2, we present a sample of results obtained for Ca IX and Ca X, respectively.

We also specify a parameter C [9], which gives an estimate for the maximum perturber density for

3.1 Atomic Structure and Spectroscopy 121
which the line may be treated as isolated when it is divided by the corresponding electron-impact

full width at half maximum. For each value given in Tables 1 and 2, the collision volume (V)

multiplied by the perturber density (N) is much less than one and the impact approximation is valid [5, 6]. When the impact approximation is not valid, the ion broadening contribution may be

estimated by using quasistatic estimates [12, 13]. The accuracy of the results obtained decreases

when broadening by ion interactions becomes important.

We hope that the present results will be of interest for stellar, laboratory, fusion and laser- produced plasma investigations and modeling, as well as for the testing and developing of Stark

broadening theory.

References

[1] M. S. Dimitrijevic and S. Sahal— Brechot, Astron. Astrophys. Suppl. Series 109, 551 (1995)

[2] M. S. Dimitrijevic and S. Sahal— Brechot, Astron. Astrophys. Suppl. Series 115, 351 (1996)

[3] M. S. Dimitrijevic, and S. Sahal—Brechot, Astron. Astrophys. Suppl. Series 119, 369 (1996)

[4] M. S. Dimitrijevic, Zh. Prikl. Spektrosk. 63, 810 (1996)

[5] S. Sahal-Brechot, Astron. Astrophys. 1, 91 (1969)

[6] S. Sahal-Brechot, Astron. Astrophys. 2, 322 (1969)

[7] M. S. Dimitrijevic, S. Sahal-Brechot, and V. Bommier, Astron. Astrophys. Suppl. Series 89,

581 (1991)

[8] S. Bashkin, J. O. Stoner, Jr., "Atomic Energy Levels and Grotrian Diagrams", Vol. 1, North

Holland, Amsterdam 1975

[9] M. S. Dimitrijevic and S. Sahal-Brechot, JQSRT 31, 301 (1984)

[10] M. S. Dimitrijevic and S. Sahal-Brechot, Astron. Astrophys. Suppl. Series, submitted 1997

[11] M. S. Dimitrijevic and S. Sahal-Brechot, Bull. Astron. Belgrade 156, in press (1997)

[12] H. R. Griem, "Spectral Line Broadening by Plasmas", Academic Press, New York 1974

[13] S. Sahal-Brechot, Astron. Astrophys. 245, 322 (1991)

122 ICAMDATA 97 Proceedings
Table 1: Electron- and proton-impact broadening full half-widths (FWHM) and shifts for Ca IX

for a perturber density of 10 18 cm-3 and temperatures from 200,000 to 2,000,000 K. By dividing

C with the full linewidth, we obtain an estimate for the maximum perturber density for which the

line may be treated as isolated and tabulated data may be used.

Perturber Density = l.E+18cm-a Perturbers are: Electrons Protons

Transition T(K) Width(A) Shift (A) Width(A) Shift (A)

Ca IX 3P 5S 200000. 0.768E-03 0.953E-04 0.640E-04 0.103E-03

116.1 A 500000. 0.551E-03 0.932E-04 0.133E-03 0.147E-03

C=0.29E+19 1000000. 0.439E-03 0.893E-04 0.178E-03 0.178E-03

2000000. 0.355E-03 0.766E-04 0.231E-03 0.211E-03

3000000. 0.314E-03 0.671E-04 0.262E-03 0.228E-03

5000000. 0.269E-03 0.562E-04 0.318E-03 0.254E-03

Table 2: Electron- and proton-impact broadening full half-widths (FWHM) and shifts for Ca X

for a perturber density of 10 18 cm

-3 and temperatures from 200,000 to 2,000,000 K. By dividing

C with the full linewidth, we obtain an estimate for the maximum perturber density for which the

line may be treated as isolated and tabulated data may be used.

Perturber Density = l.E+18cm-3 Perturbers are: Electrons Protons

Transition T(K) Width(A) Shift(A) Width(A) Shift (A)

Ca X 3S 3P 200000. 0.498E-02 -0.601E-04 0.302E-04 -0.282E-04

563.1 A 500000. 0.322E-02 -0.532E-04 0.983E-04 -0.676E-04

C=0.56E+21 1000000. 0.238E-02 -0.679E-04 0.179E-03 -0.113E-03

2000000. 0.180E-02 -0.605E-04 0.264E-03 -0.160E-03

3000000. 0.155E-02 -0.581E-04 0.303E-03 -0.188E-03

5000000. 0.130E-02 -0.561E-04 0.351E-03 -0.214E-03

Ca X 3S 4P 200000. 0.481E-03 0.314E-05 0.138E-04 0.190E-05

111.0 A 500000. 0.321E-03 0.343E-05 0.279E-04 0.438E-05

C=0.84E+19 1000000. 0.244E-03 0.303E-05 0.383E-04 0.691E-05

2000000. 0.191E-03 0.315E-05 0.441E-04 0.951E-05

3000000. 0.168E-03 0.310E-05 0.477&04 0.107E-04

5000000. 0.145E-03 0.267E-05 0.529E-04 0.123E-04

Ca X 3S 5P 200000. 0.571E-03 0.831E-05 0.366E-04 0.857E-05

82.8 A 500000. 0.395E-03 0.112E-04 0.574E-04 0.152E-04

C=0.22E+19 1000000. 0.310E-03 0.103E-04 0.666E-04 0.208E-04

2000000. 0.250E-03 0.994E-05 0.761E-04 0.249E-04

3000000. 0.224E-03 0.910E-05 0.817E-04 0.275E-04

5000000. 0.196E-03 0.773E-05 0.890E-04 0.310E-04

Ca X 3S 6P 200000. 0.858E-03 0.227E-04 0.830E-04 0.230E-04

73.2 A 500000. 0.614E-03 0.238E-04 0.111E-03 0.358E-04

C=0.97E+18 1000000. 0.494E-03 0.221E-04 0.126E-03 0.432E-04

2000000. 0.408E-03 0.206E-04 0.142E-03 0.515E-04

3000000. 0.369E-03 0.185E-04 0.151E-03 0.573E-04

5000000. 0.327E-03 0.151E-04 0.164E-03 0.632E-04

Ca X 4S 4P 200000. 0.103 -0.161E-02 0.259E-02 -0.175E-02

1475.2 A 500000. 0.698E-01 -0.234E-02 0.534E-02 -0.336E-02

3.1 Atomic Structure and Spectroscopy 123
Accurate MCHF/MCDF Transition Rates

Charlotte Froese Fischer0

, Per Jonsson", and Stephan Fritzsche6 a Vanderbilt University, Nashville, TN 37235, USA

b Universitat Kassel, Kassel, Germany

1 Introduction

With today's powerful workstations and high performance architectures, it has been possible to improve considerably the accuracy to which atomic properties can be predicted. This is done by

using systematic methods, where wave functions for a series of models including more and more

physical effects axe obtained from expansions defined in terms of an orbital basis of increasing size. Typically, the first model is one that includes only valence correlation. But often core-polarization

is also important in which case a core-valence calculation is need. In some instances, even core-core correlation produces a small correction. By monitoring convergence within the different models

and comparing the converged results themselves, an uncertainty estimate can be obtained. These

methods can be used both for non-relativistic MCHF calculations where Breit-Pauli corrections are added in configuration interaction (CI) calculations, or for MCDF calculations starting with the

Dirac-Coulomb Hamiltonian, adding Breit and leading QED corrections in relativistic CI.

2 Iso-electronic Sequences

A number of iso-electronic sequences have been explored using MCDF. In fact, the recently implemented non-orthogonal methodology allowing for separately optimized initial and final state wave

functions was first tested on the Mg-like sequence [1]. The same MCDF procedures have been applied to the study of the Be-like El transitions

2s2 l S — 2s2p 1,3Pi. For low-Z, the transition rates in Babushkin (length) and Coulomb (velocity)

gauges do not show good agreement [2, 3], though in C III the former is in excellent agreement

with Breit-Pauli [4] and recent experiment [5]. Table 1 shows some results for the sequence. For

the intercombination line (IC) the difference in gauges is decreasing with Z whereas for the allowed resonance transition, the difference is only one or two units in the fourth decimal place for all Z.

A detailed analysis (in preparation) also shows that the frequency dependent Breit correction is important for high-Z.

Other sequences investigated recently using MCHF with Breit-Pauli are the 2s2 1 S — 2s3p 1,3Pi

allowed and intercombination lines for Z < 10 [6, 7]. The experimental data for these transition

rates have been analyzed semi-empirically [8] and values predicted for the sequence. Except for

N IV, our computed values are in closer agreement to the semi-empirical predictions than experiment itself.

3 Spectrum Calculations

Many variational studies have concentrated on accurate, single line, benchmark calculations. The

MCHF+BP and MCDF programs also permit the study of portions of a spectrum. In the latter,

124 ICAMDATA 97 Proceedings
Table 1: Transition energies (in cm-1

) and rates (in s _1) for the 2s2 1 Sq— 2s2p 3 P\ intercombination

(IC) and 2s2 — 2s2p x Pi allowed dipole (El) lines in the Be isoelectronic sequence. In the table

[x] denotes powers of ten.

7 A

1 AIC AIC &EE1 gji 9Jv

7 MCDF 67 301 5.586 [2] 8.597 [2] 131 029 0 6113 0 6118

Exp 67 272 130 694

8 MCDF 82 104 2.212 [3] 3.074 [3] 159 154 0 5122 0 5124

Exp 82 079 i 7QH

9 MCDF 96 899 fi Qfil f*l

lJJ Q D41i 6\ 1 87 994 0 4414 0 4416

Exp 96 861 1lot) £fi S41

10 MCDF 111 730 1 £fi9 T41

L4J T41L4J 91 K OOU 0 3882 0 3884

Exp 111 705 91 4

11 MCDF 126 640 a 4i n T41

L4J 97^ T41L4J 94** 06Q 0 3470 0 3471

Exp 126 612 94** 12 MCDF 141 662 y.ouo T41

L4J 1118L°J 979 1 0 3141 0 3142

Exp 141 631 971 UO f

24 MCDF ^41 252 2.772 [7] 2.824 [7] 667 962 n 1fi23 X.\J CtlJ n 1623

Exp 341 120 667 150

25 MCDF 360 178 3.773 [7] 3.834 [7] 709 557 0 1578 0 1578

Exp 359 970 708 770

26 MCDF 379 363 5.041 [7] 5.118 [7] 753 366 0 1539 0 1540

Exp 379 130 752 502

27 MCDF 398 983 6.631 [7] 6.721 [7] 799 649 0 1505 0 1505

Exp 398 720 799 040

28 MCDF 418 964 8.583 [7] 8.689 [7] 848 677 0 1474 0 1476

Exp 418 720 847 494

orbitals may be optimized for a series of levels. Using this option, the 3s2 3p3

, 3s3p4, 3s2 3p

2 3d

levels of selected elements of the iso-electronic sequence in the range 22 < Z < 32 were computed

along with El transitions between these levels [9]. Some lifetimes for levels of Fe XII, which all show remarkable agreement in length and velocity forms, are reported in Table 2. In Table 3 we report excitation energies of selected levels from Fe XII ions, comparing them

with previous theory and experiment. When both are available, the present MCDF results are generally in better agreement with experiment.

4 Complex Systems

The MCHF+BP and MCDF programs have also been applied to the study of forbidden transitions

among the twelve (12) lowest levels of 3d5 of Fe IV. A re-examination of the data for these levels was

suggested by Rubin et al [11] as a result of an analysis of the the flux of Fe IV {3d5 4P5/2 - 3d5 %/2 ) in the Orion Nebula, using the Goddard High-Resolution Spectrograph. From a theoretical point

of view, an accurate ab initio calculation is extremely complex. The MCHF+BP approach was

restricted to the mixing of the four lowest terms, 6S,

4G, 4P, and 4D, each with a correlated expansion. The resulting Breit-Pauli calculations required almost four hours on a Cray T3E computer

with 32 nodes. Still missing, was the mixing with other quartets and the doublets. In the MCDF

approach, the expansions grow in size rapidly with the orbital set (there being more reiativistic

3.1 Atomic Structure and Spectroscopy 125
Table 2: Excitation Energies and Lifetimes of levels of SsSp4

Fe XII Levels Energy (cm :

) No. J

1

Lifetime (s)

Calc. Exp. Length Velocity

6 5/2 +

7 3/2 +

8 1/2 +

9 3/2 +

10 5/2 +

274620 274373

284131 284005

288431 288307

341076 340020

342949 341703

6.11(-10)

5.70(-10)

5.40(-10)

2.75(-10)

3.02(-10)

6.17(-10)

5.78(-10)

5.49(-10)

2.78(-10)

3.05(-10)

Table 3: Excitation energies for a few selected levels of the 3s2 3p3

, 3s3p4

, and 3s2 3p2 3d configurations for Fe XII ions. All energies (in cm-1

) are displayed with respect to the 3s2 3p3 4 5

,3/2 ground-state level.

Level Designation

of states J

p Huang et al. Ref. 9

Fawcett

Ref. 10

This work Experiment

1 3s2 3pa 4 S 3/2 - 0 0 0 0

2

2 D 3/2 - 45375 42667 41555 ±1

3

2 D 5/2 - 49932 47130 46088 ±1

4

2 P 1/2- 78297 75532 74108 ±1

5 2p 3/2 - 84503 81792

6 3s3p4 4 P 5/2 + 274625 274344 274620

7 4p 3/2 + 284157 283556 284131

8 4p 1/2 + 288345 287737 288431

9

2 D 3/2 + 345263 341076 339761 ±10

10 2 D 5/2 + 347176 342949

21 3s2 3p2 3d 4 D 5/2 + 460430 453305 454327

22 4 D 7/2 + 470196 463593

23 2 G 7/2 + 509637 496836

24 3s3p4 2 P 3/2 + 516954 507969

25 3s2 3p2 3d 4 P 5/2 + 528771 512530 517607 513708 ±10

126 ICAMDATA 97 Proceedings
orbitals) and so the correlation effects had to be restricted. Only after the inclusion of the Breit

correction were computed levels in the observed order. Thus spin-orbit alone cannot predict the

energy structure. The transition rates for transitions within these levels, vary over orders of magnitude. There appears to be good agreement between our theories for some transitions, particularly

for the Ml transitions where the AS = 0 and AL = 0 selection rules are obeyed.

Heavy atoms also are of great interest. They differ from light atoms in that a fully relativistic

Dirac-Fock-Breit formalism may be necessary and correlation exhibited by the mixing of configuration states is very strong. We are currently extending the MCDF codes for larger, more efficient correlation studies. At the same time, open /-shells appear. Correlation studies of such states in

MCDF will be extremely difficult because of the size of the expansions that occur in jj-coupling.

In fact, only the core electrons are "relativistic": it may be possible to describe the outer electrons

in the Breit-Pauli scheme. This approach is being investigated. The MCHF package has been

extended to include an arbitrary number of / electrons. For this purpose, an efficient method is used for finding algebraic expressions for matrix elements. It is based on second quantization in

the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin),

and a generalized graphical technique [13]. Coefficients of fractional parentage are replaced by the

far fewer "reduced" coefficients of fractional parentage. Codes based on this formalism have been

found to be, on average, 2-6 times faster. This research was supported by the Division of Chemical Sciences, Office of Basic Energy

Scinces, Office of Energy Science, U.S. Department of Energy.

References

[1] P. Jonsson and C. Froese Fischer, J. Phys. B (accepted)

[2] P. Jonsson and C. Froese Fischer, Phys. Rev. A (submitted)

[3] S. Fritzsche, A.-M. Maxtensson-Pendrill, and B. Fricke, in Proceedings of the 5th Int. Colloq. on Atomic Spectra and Oscillator Strengths, Meudon, France, 1995, ed. by W.-U.L. TchangBrillet, J.F. Wyart, and C.J. Zeippen, p. 70

[4] C. Froese Fischer and G. Gaigalas, Phys. Scripta 56, 436 (1997)

[5] J. Doerfert, E. Trabert, A. Wolf, D. Schwalm, and O. Uwira, Phys. Rev. Lett. 78, 4355 (1997)

[6] C. Froese Fischer, M. R. Godefroid, and J. Olsen, J. Phys. B 30, 1163 (1997)

[7] C. Froese Fischer, G. Gaigalas, and M. R. Godefroid, J. Phys. B 30, 3333 (1997)

[8] L. J. Curtis, S. T. Maniak, R. W. Ghrist, R. E. Irving, D. G. Ellis, M. Henderson, M. H.

Kacher, E. Trabert, J. Granzow, P. Bengtsson, and L. Engstrom, Phys. Rev. A 51, 4575

(1995)

[9] S. Fritzsche, C. Froese Fischer, and B. Fricke, Atomic and Nuclear Data Tables (accepted)

[10] K.-N. Huang, At. Data Nucl. Data Tables 30, 313 (1984)

[11] B. C. Fawcett, At. Data Nucl. Data Tables 35, 203 (1986)

[12] R. H. Rubin et al., Astrophys. J. 474, L131 (1997)

[13] G. Gaigalas, Z. Rudzikas, C. Froese Fischer, J. Phys. B 30, 3747 (1997)

3.1 Atomic Structure and Spectroscopy 127
Secondly Quantized Multi-Configurational Approach

for Atomic Databases

Gediminas Gaigalas and Zenonas Rudzikas

Institute of Theoretical Physics and Astronomy,

A. Gostauto 12, Vilnius 2600, Lithuania

1 Introduction

Studies of the structure of atoms and ions (ultracold to relativistic included) as well as their twobody interactions with photons, electrons and other particles require accurate methods for the

description of such objects.

In order to obtain accurate values of atomic quantities it is necessary to account for relativistic

and correlation effects. Relativistic effects may be taken into account as Breit-Pauli corrections

or in a fully relativistic approach. In both cases for complex atoms and ions, a considerable part

of the effort must be devoted to integrations over spin-angular variables, occurring in the matrix

elements of the operators under consideration.

Many existing codes for integrating are based on a scheme by Fano [1]. The integrations over spin-angular variables in this case constitute a considerable part of the problem, especially when

atoms with many open shells are treated, and the operators are not trivial. In the papers of

Gaigalas et al[2, 3], an efficient approach for finding matrix elements of any one- and two-particle

atomic operator between complex configurations is suggested. It is free of shortcomings of previous

approaches. This approach allows one to generate fairly accurate databases of atomic parameters

(Froese Fischer et al [4, 5]).

Further development of the approaches by Gaigalas et al [2, 3] for the spin-spin and spin-otherorbit relativistic corrections in the Breit-Pauli approximation is presented in this paper.

2 Matrix Elements Between Complex Configurations

According to the approach of Gaigalas et al [3], a general expression of the submatrix element for any two-particle operator between functions with u open shells can be written as follows:

(LS)\\G\Wk* (L'S')) =

Y, W

bura (LS)\\G (*MjM?' n#) I ( L

' S'V

nili.njlj ,n'V ,n' l'-

rii li ,njlj ,n'j

>n'j IjKu ,<ri2 ,k'12 ,a[ 2

(1)

where A

6TM = (l^Si,

for A

ket and A = Is.

LjSjiL'iS'^L'jSjj

bra

is the array of bra function shells' terms, and similarly

128 ICAMDATA 97 Proceedings
Thus, to calculate the spin-angular part of a submatrbc element of this type, one has to obtain:

1. The recoupling matrix R (X{, Xj, X'i: A^, A

bra

, A

ket

, Tj, which has an analytical expression in

terms of just 6j- and 9j-coefficients.

2. Submatrix elements T (riiXi, rijXj, n^, n'jXp A

bra

, A

ket

, B, Tj for tensorial products of cre- ation/annihilation operators that act upon a particular electron shell. So, all the advantages

of tensorial algebra and quasispin formalism (Rudzikas [6]) may be efficiently exploited in the

process of their calculation.

3. The phase factor A.

4. 0' (riiXi,njXj,n[Xi,n'jX'j,z?J which is proportional to the two-electron submatrix element of

operator G.

Further development of this approach for the spin-spin and spin-other-orbit relativistic correc- tions in the Breit-Pauli approximation is presented in the following section.

3 The Spin-Spin and Spin-Other-Orbit Operators

The spin-spin operator Hss itself contains tensorial structure of two different types, summed over

fe:

lfc+12,112)

(2)

Their submatrix elements are:

l (5)

x (it ||c(A;+1)

||Z;>) (lj |b(fc-1) |k-') ^fc_1 (nihnjlj^i'hmjdf) (3)

(rnXirijXj iHf-^+^^ni^nfX?) = ^(2k + S) {5) x

x (it (lj ||c(fc+1)

||

lf ) Nk ~ 1 (njlj ni li ,nj

rljl ni>li>) , (4)

where we use a shorthand notation (2k + 3)

(5) = (2k + 3) (2k + 2) (2k + 1) (2k) (2k - 1) and radial

integral in (3), (4) is defined as in Glass and Hibbert [7]:

Nk

(niliTijlj^ni'li'Tijilj') =

q,2 roo roo r

k = ~r Pi in) Pj (ra) -^(n - r2 )Pv ( n)Pr

(r2 ) dndr2 ,, 4 Jo Jo r-i (5)

where e(x) is a Heaviside step-function,

3.1 Atomic Structure and Spectroscopy 129
e(x) =

1; for x > 0,

0; for x < 0. (6)

The spin- other- orbit operator H300 itself contains tensorial structure of six different types,

summed over k:

ttsso =- ST rif(*- 1*1,101) . jj{k-lk 1,011) , ri-(fcfcl,101) , o-^M.Oll) , u-(Jfc+lfcl,101) , rr(fc+lfcl,011)l

[ soo T ±J

-soo ' A1 soo ' 11 soo ~ ±1 soo "r" nsoo !•

Their submatrix elements are:

(nAinjAj

ul ' ai<T2l )| n^Aim^Ajv) = 2 • (<7i + 2a2 ) {{2k - 1) (2fc + 1) x

x (h + U> - k + 1) (k - U + &#) (fc + h - h>) {k + h + U, + l)} 1 /2 x

x {k)~ l/2

(li ||c<*)

| Z

f/) (Zj |b<*)|| /j/) iVfe -2 (njljnil^nflfrii'k) ,

(7)

(8)

(riiAinjAj ||#s

( !£

1,<ri<T2l)

| rii/Ai/nj/Aj/) - -2 • (<ti + 2<r2 ) (2fc + 1)

1/2

(z* ||c(*)|| Z?) x

x (Zj- ||c(*>

J Z,v) |(A; (A; + l))"

1 /2

(J, (Z* + 1) - k (k + 1) - lv (h> + 1)) x

x

|

(A; + l)iVfc_2 (rijljnili,nj<lj>ni>li>) — kNk (nilinjlj,ni'liinj>lji)} —

-2 (k (k + 1))

1/2 V

k ~ l (niknjlj^n^krijdf) }

,

H

{k+iki,cria2i)j n. lX .in ., x .^ _ 2 . ( ai + 2<r2 ) {(2fc + 1) (2fc + 3) x

x (k + lv — k) (k — li + Z*/ + 1) (fc + Zf - Z*/ + 1) (fc + h + lv + 2)}

1/2 x x (k + 1)- 1/2

(li ||c(*>|| ^) (Zj Zj/) TV* (mknjlj^knjdj.)

.

The radial integrals in (8)-(10) are (see Glass and Hibbert [7]):

(9)

(10)

V

k (nilinjlj,ni>liinj>lj>) =

fJ2 roo roo r*~l

f) = t/„ /„ "WW^f^Wfl'W*!^ (n)

Now we have all we need (the operators for tensorial structure and their submatrix elements)

for obtaining the value of a matrix element of these operators for any number of open shells in bra

and ket functions. This lets us exploit all advantages of the approach by Gaigalas et al [3]. The spin-spin and spin-other-orbit operators itself generally contain tensorial structure of several

different types. Therefore the expression (1) must be used separately for each possible tensorial

structure for performing spin-angular integrations according to [3]. Each type of tensorial structure

is associated with a different type of recoupling matrix R (Xi, Aj, A^, Xj, A

bra

, A

ket

, and with

different matrix elements of standard tensorial quantities T InjAj, Tlj Aj 5 Tl

j X'i, n'jX'j, A

6rd

, A

ket

, 5, rY.

130 ICAMDATA 97 Proceedings
4 Conclusions

The tensorial forms of the general secondly quantized spin-spin interaction operator (2) and spinother-orbit interaction operator (7) and its submatrix elements ( for spin-spin interaction expressions (3), (4) and for spin-other-orbit expressions (8), (9) and (10)) are presented. In calculating

its matrix elements between functions with u open shells this allows to exploit all the advantages

of method by Gaigalas et al [3]:

1. to obtain both diagonal and off-diagonal elements with respect to the configuration matrix

elements in a unified approach,

2. to use in practical applications the tables of submatrix elements of standard quantities, which

here are both the coordinate representation and the occupation number representation tensorial operators,

3. to apply the quasispin formalism for the occupation numbers parts and make use of it,

4. to make use of having recoupling matrices simpler than in other known approaches.

References

[1] U. Fano, Phys. Rev. A 67, 140 (1965)

[2] G. A. Gaigalas and Z. B. Rudzikas, J. Phys. B 29, 3303 (1996)

[3] G. A. Gaigalas, Z. B. Rudzikas, and C. Froese-Fischer, J. Phys. B 30, 3747 (1997)

[4] C. Froese-Fischer, A. Ynnerman, and G. Gaigalas, Physical Review A 51, 4611 (1995)

[5] C. Froese-Fischer and G. Gaigalas, J. Phys. B 29, 1169 (1996)

[6] Z. B. Rudzikas, "Theoretical Atomic Spectroscopy", p. 410, Cambridge University Press, Cambridge 1997

[7] R. Glass and A. Hibbert, Comput. Phys. Commun. 16, 19 (1978)

3.1 Atomic Structure and Spectroscopy 131
Polarization Profile Calculations for

Plasma Diagnostics

Manuel Angel Gonzalez and Marco Antonio Gigosos

Departamento de Optica, Universidad de Valladolid,

47071 Valladolid, Spain

1 Introduction

Computer simulation techniques have been used to calculate Stark broadened profiles that can

be measured by polarization spectroscopy for the two-photon transition n = 2 -» n = 1 (Lyman-a) of hydrogen. The plasma model and the calculation techniques used in the

simulation are described in Ref.[l]. The fine structure of the level n = 2 has been taken into

account in order to study plasmas at very low electron densities (lower than 1021 m3

j. The

calculations include plasmas of pure hydrogen, pure deuterium, as well as each of these with

heavier perturbers. Also considered has been the -academic- case of static perturber ions. This

allows us to evaluate the effects of ion dynamics, which, for this spectral line, are of

fundamental importance. The plasma conditions considered cover the range for electron

densities between 4.6 x 1019 and 1.0 x 1023 nv3 and for temperatures between 2,000 and

100,000 K.

The computer simulation allows us to directly obtain the emission and absorption profiles

for the two-photon transition between the levels n = 2 and n = 1 of hydrogen. The polarization

profiles can be obtained from these profiles using the Kramers- Kronig relations (see p. 459 of

refs.[2] and [3]). The calculational technique used allows us to obtain the emission and

polarization spectra simultaneously for the diagnosis of different plasma configurations. All in

all, spectra have been obtained for more than 400 conditions of density, temperature and

perturber mass.

2 Polarization Spectroscopy

Polarization spectroscopy is based on the measurement of the change of the polarization state of a probe wave when it passes through a studied medium [2] . Such a change is induced by a polarized

pumping wave. This pumping wave changes the optical behavior of the substance. That is, it changes its refractive index and its absorption coefficient in a non-isotropic way. Up to a point,

polarization spectroscopy is similar to saturation spectroscopy, which is based on the

measurement of the absorption of a probe wave that passes through a substance whose optical

response is changed by a pumping beam.

In the experiment studied in this work, the probe beam detects the induced susceptibility by a two-photon transition [3, 4, 5, 6] between the hydrogen atom levels of the Lyman-a transition. The

pumping beam produces a transition from the state Is to the virtual state I - 1, rn = 1 (p state)

because it is a a

+ polarized beam, which gives a different saturation of the three possible states of

that virtual level: only the m = 1 state is saturated. This is equivalent to an anisotropy in the

medium, because there is no uniform population between the different m sublevels. In the same

process, the probe beam is absorbed, producing a transition between the virtual level and the n =

2 level. The selection rule I Al I =1 forces the arriving level to be the 2s. one, because there is no

level with I = 2 in that energy interval.

132 ICAMDATA 97 Proceedings
3 Calculation process of the polarization profiles

The profile A(a>) of a spectral line can be readily obtained from the autocorrelatian function of the

atomic dipole moment by means of a Fourier transform of its average {

} over a certain statistical

ensemble [7] J

i CO lWt

{c{t)}, C(t) = tr (D • U+(t)DU(t)) . (1)

o

e

The time development operator U(t) obeys the following form of the Schrodinger equation under

the no-quenching approximation:

ih^-U(t) = (HQ +V(t)) U(t), (2) at

V(t) = qE(t) • R , (3)

where Ho includes the fine structure of the level n = 2. qK is the dipole momentum operator of the

emitter, and E(£) is the electric microfield generated by ions and electrons surrounding it. In this work, we are interested in the polarization profiles obtained by a two-photon

absorption process. Such a spectrum is given by the addition of the squares of the absorption and

the dispersion profiles [2]:

P(co) = A(0))2 + D(0))2 (4)

The Kramers-Kronig relations allow us to obtain the dispersion profile from the absorption one:

i V.P. A& dz . (5) n z - co

t/ - ao D(co)

Operating on it, it can be shown that

h co A{co) = - [cos(cot)CR(t) - sm(o)t)Ci(t)] (6) n Jo

AtCO D(co) = - [cos(cot)Ci(t) + sin(o)t)CR(t)] (7)

71 Jo

where C/?(£) = Re C(t) and Ci(t) = Im C(t).

In a computer simulation process, a microfield time sequence is obtained for some selected

plasma conditions, and the numerical integration of equations (2) is a previous step to the

calculation of {C(t)}.

The simulated plasma is made up of a set of Np independent ions and Np independent

electrons placed at random inside a spherical volume in such a way that the homogeneity of the

3.1 Atomic Structure and Spectroscopy 133
spatial distribution of particles is guaranteed. Both electrons and ions move along straight line

trajectories with a Maxwellian velocity distribution, as established in the u-ion model [8]. The

emitting atom is located at the center of the simulation sphere. Details of the particle substitution

technique can be found in Ref. [1]. The electric field of the set of simulated ions and electrons is determined at the center of the sphere and readily carried to the system of differential equations on which the calculation of the evolution operator of the emitter finally depends. Debye screening

has been included in the calculation of the electric field to account for the correlation effects between charged particles of different sign.

The results obtained for low densities yield a dependence of the width and shape of the

spectrum with density and temperature that fits very well with an impact model of the

broadening, both electronic and ionic (see Fig. 1).

100 r

10

0.110 19

1 11 1

' —i—r-| 1 1—r] 1 Jt I

| p

; FWHM

(pm)

•" /y Simulation -*-— // ~ M

// „ A/ 2/3 .

T = 29000 K

. / . . 1 ,

H — H + plasma

, , i , . , i , , , i ,

10 20 10 2 10" 10 23 Nc (m~3

)

Figure 1: Dependence of the full width at half maximum (FWHM) with the electron density. For

low densities, the trend is linear with Ne, which is characteristic of impact broadening.

A-c = 103n m-1

7'

c =42(10 K

0.5 1 AX (pui)

Figure 2: Polarization spectra by two-photon

absorption. The effect of the reduced mass ju of the emitter-perturber pair is shown.

0 5

"-T '1 1 - Nc = 3.2 • 1021 m-3

-i r i >o Simulation -- - T = 8000 K

P\) Exp. ref. [6] o O — D+ plasma

i i i

-20 -15 -10 10 15 20 AA (piu)

— I I 1 - Nc = lO23 rn-^

1 1 1 a Simulation T = 8000 K p \ Exp. ref. [6] o D — D+ plasma dfvS

— i i i i i

-HO -20 -10 10 20 :*0 40 AA (pm)

Figure 3: Two-photon polarization spectrum of the Is -> 2s Lyman-a transition. Comparison of experiment

and simulation.

134 ICAMDATA 97 Proceedings
The obtained results have allowed us to make tables of complete line profiles for plasma

diagnosis. In Fig. 4 the dependence of the full width at half maximum (FWHM) of the studied

transition is shown as a function of the electron density and the temperature of the plasma. The

smooth dependence of AA,i/2 with temperature for the emission profiles allows us to obtain the

density of perturbers from direct measurements of the line width.

Acknowledgments

The authors of this work thank the Departamento de Informatica of Valladolid University for the use of its calculation resources, Dr. Cardenoso for his close collaboration in the development of the

work, and professors Gonzalez Vizmanos and Fuentes Garcia for their collaboration in the

maintenance of the calculations. The attendance of this conference has been partially financed by

the Spanish DIGICYT under grant PB94-0216.

Figure 4: Curves of constant Stark width in a H-H+ plasma (n = 0.5). The numbers close to the lines show the full width at half maximum (in pm) for the transition n - 1 -» n = 2 that can be measured with polarization

spectroscopy by two photon absorption.

3.1 Atomic Structure and Spectroscopy 135
References

[1] M. A. Gigosos and V. Cardenoso, J. Phys. B: At. Mol. Opt. Phys. 29, 4795 (1996)

[2] W. Demtroder, Laser Spectroscopy, (Springer-Verlag, Berlin Heidelberg 1996)

[3] J. Seidel, Phys. Rev. Letters 57, 2514 (1986)

[4] K. Danzmann, K. Grutzmacher and B. Wende, Phys. Rev. Letters 57, 2151 (1986)

[5] Andreas Steiger, Starkverbreiterung des 2S-Zustands von Wasserstoff und Deuterium in

Bogenplasmen niedriger Dichte, Ph. D. Thesis, Berlin (1993)

[6] J. Seidel, A. Steiger, and K. Grutzmacher, Spectral Line Shapes, Vol. VIII, eds. A. D. May, J. R. Drummond, E. Oks, p. 32. (AIP Press, Toronto 1994)

[7] H.R. Griem, Spectral line Broadening by Plasmas, (Academic Press, New York 1974)

[8] J. Seidel and R. Stamm, J. Quant. Spectrosc. Radiat. Transfer 27, 499 (1982)

136 ICAMDATA 97 Proceedings
Laboratory Measurements of Resonant Contributions

to Fe XXIV Line Emission

M. F. Gu1

, P. Beiersdorfer2, G. V. Brown2

, S. M. Kahn1

, D. A. Liedahl2

, K. J. Reed2

, and D.W. Savin1 Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027

2Lawrence Livermore National Laboratory, Livermore, CA 94550

1 Introduction

Recent Advanced Satellite for Cosmology and Astrophysics (ASCA) observations of the Centaurus

cluster of galaxies [1] exhibit discrepancies with the relative line intensities of various Fe XXIII

and XXTV L-shell emission lines predicted by standard plasma codes. This discrepancy is seen with all standard emission codes and is attributed to problems with the atomic physics used in

the emission codes. New distorted wave (DW) calculations of Fe XXIII and Fe XXIV electron

impact excitation (EIE) rate coefficients [2] appear to provide better agreement with the ASCA

observations. Using the Lawrence-Livermore electron beam ion trap (EBIT), Savin et al. [3] measured the relative line emission of several Fe XXIV 3 —» 2 and 4 —» 2 lines and found good

agreement with the calculations of Liedahl et al. These measurements, however, were carried out

at electron energies significantly greater than the excitation threshold energies of the lines

observed. The calculations remain to be experimentally verified for energies at which resonant

processes may be important and for energies near threshold where DW calculations may

overpredict the EIE cross section.

A number of X-ray astronomy satellites are scheduled for launch in the next few years. The

Advanced X-ray Astrophysics Facility (AXAF) is scheduled for launch in 1998, and the X-Ray

Multi-mirror Mission (XMM) and Astro-E in 1999. These satellites will carry spectrometers with

resolving powers in the Fe L-shell emission region over an order of magnitude greater than the

spectrometers aboard ASCA. Interpreting AXAF, XMM, and Astro-E spectra will require atomic

data at an accuracy significantly greater than the data presently used in the standard emission

codes.

To address some of the existing and upcoming needs of X-ray astrophysics, we have continued our studies of Fe XXIV line emission. In this work, we measured Fe XXIV 3^-2 line emission at energies around threshold, using EBIT to examine the resonance contributions to the line

emissivity. Here, we present relative cross sections, at electron energies between 700 and

1500 eV, for producing line emission at wavelength A. = 11.18 A of the Fe XXIV 3g?5/2 -> 2pm

transition.

Various processes can contribute to line emission observed from a collisional plasma. Direct

excitation (DE) is the most important one at energies above the EIE threshold. Below threshold,

dielectronic recombination (DR) produces high n satellites which cannot be resolved from the EIE

line. Resonant excitation (RE) can populate the same levels as DE via dielectronic capture

followed by autoionization to the level of interest. In this work, we have measured the following

processes:

• DE

Fe23+(2s) +e~-> Fe23+(3d5/2) + <r-> Fe23+(2p3/2) +hn+er

3.1 Atomic Structure and Spectroscopy 137
• RE

Fe23+(2s) + er- -> Fe22+(41 'nl") -> Fe23+(3d5/2) + e~ -> Fe23+(2p3/2) +/in + r

• DR

Fe23+(2s) + e- ^ Fe22+{Mmnl r) -» Fe22\2pmnl') + hv2 + e~

Quantum mechanically, there is no way to distinguish between DE and RE, and we measure the

coherent sum of the two processes.

2 Experimental Technique

EBIT [4] uses a magnetically confined electron beam to produce a potential well which traps the

ions in the radial direction. In the axial direction, ions are trapped by voltages applied to the top

and bottom drift tubes. The electron beam is also used to ionize and excite the trapped ions.

Radiative decay of the excited ions results in X-ray emission which is observed by a flat crystal

spectrometer (FCS) through one of the X-ray ports. A thallium hydrogen phthalate (001) crystal is used. The dispersion plane of the FCS is perpendicular to the electron beam. Between the EBIT

and the FCS is a 4 um polypropylene window. X-rays are detected by a flowing gas (90% Ar and

10% CH4 at 1 atmosphere) position sensitive proportional counter with a 4 um polypropylene

window.

After injecting iron into the EBIT, the electron beam energy is kept at 4 keV for 200 ms. Then

every 10 ms the beam energy is swept between 700 and 1500 eV using a sawtooth pattern 2 ms in

length. The intensity of a particular line is I cc J drne(r)nq (r)cn), where ne (r) is the electron density, nq (r) is the ion density, cris the cross section for producing the observed line emission, and v is the

electron velocity. During the sweeping of the beam energy, the charge balance changes

insignificantly because the ionization and recombination time scales at these energies are >100 ms. We maintain a nearly constant ne (r) by varying the anode voltage of the electron gun.

We record the intensity of line emission atX= 11.18 A as a function of beam energy. Because

\ drne (r)nq (r) is kept constant versus E, we can derive cross sections for producing these lines by

normalizing our measurements to theory.

3 Uncertainty Analysis

Uncertainties are listed in Table 1 at the 1 cr confidence level.

Table 1: Uncertainties for observed line emission measurements.

X= 11.18 A

Source (percent)

Statistics 8 - 14

Background Subtraction 5

Polarization Effects 5

Electron Density 2

Normalization 10

Quadrature Sum 15 - 19

138 ICAMDATA 97 Proceedings
There are about 200 counts per beam energy bin ( ~12 eV per bin) for the line emission at X = 11.18 A above the DE threshold. The DR satellites have peak counts of between 50 and 100.

The la statistical uncertainty varies between 8% and 14%.

14.0 r

12.0 -

10.0 - J

o 8.0

a

c 6.0 - £

4.0 -

2.0 -

0.0 -

Total Rate

/ DE Plus RE Rate

/ DR Rate

/

0.5 1.5 ZS

Temperature (keV)

3.5

Figure 1: Normalized cross sections for

producing line emission at X = 11.18 A.

Figure 2: Rate coefficients for

producing line emission at X = 11.18 A.

We observed line emission due to charge transfer (CT) with neutral gas in the EBIT. This signal

is independent of beam energy. At beam energies between 700 and 800 eV, the CT signal is clearly resolved from DR resonances and seen to be constant. We subtract this background from

the total intensity. The relative uncertainty introduced by this subtraction is about 5%.

Line emission produced by a unidirectional electron beam is linearly polarized and anisotropic

[5]. Crystals have different integrated reflectivities for X-rays polarized parallel to and

perpendicular to the dispersion plane [6] . The observed line intensities depend on the polarization

of the emitted lines. This is a function of collision energy. In the energy range covered here,

polarization due to DE does not change significantly. Polarization of the DR satellites should

approach that of DE as the beam energy approaches the DE threshold [7]. RE is expected to be

less polarized than DE emission. We assume the line emission at all energies has the same

polarization. Polarization effects need to be further investigated but are estimated to introduce < 5% uncertainty.

While sweeping the electron beam energy, we try to keep the electron density constant by

ramping the extraction voltage of the electron gun in sync with the beam energy. The measured

beam current indicates that the electron density varies by less than 10% between 700 and

1500 eV. We have corrected the observed line intensities for this variation. The electrons in the

EBIT have a transverse energy of ~ 150 eV [8]. The resulting change of the pitch angle between

the electron velocity and the beam direction results in a small variation of electron density versus beam energy. Using the normalization energy as our reference point, ne varies by ±2% across the

measured energy range due to the changing pitch angle.

Our normalization point lies ~40 eV above the DE threshold and > 40 eV away from all RE

resonances. Given the electron beam energy spread of 50 eV [9], we estimate that emission at the

normalization point is not significantly affected by either DR just below the DE threshold or the

RE resonances. Thus we assume the line emission is completely due to DE at this energy and use HULLAC (Hebrew University/Lawrence Livermore Atomic Code) [2] calculated cross sections.

3.1 Atomic Structure and Spectroscopy 139
Statistical uncertainties at the normalization energy introduce uncertainties of -10% in the cross sections for line emission at X = 11.18 A.

4 Results

Fig. 1 shows the normalized cross section for producing X = 11.18 A line emission. The error bars on the data points show the la statistical uncertainties. The normalization point is presented

without an error bar. The 3151' and 3161' DR resonances are well separated. All other DR

resonances between 1.0 keV and the DE threshold are unresolved and appear as a continuous

increase in the cross sections. The RE resonance at a beam energy of about 1.25 keV is produced

by dielectronic capture into the Fe XXIV 4151' level followed by autoionizing to the 3cfe/2 level. Using the relative cross sections obtained above, we calculate the rate coefficients of each

process. The DE rate is calculated by using HULLAC [2] cross sections. For experimentally

inferred rates, only line emission within the measured energy range is included. Fig. 2 shows the

experimentally inferred rates for DR, DE plus RE, and the total rates. The total rate includes the

experimentally inferred DR, DE plus RE, and the theoretical DE rates at energies outside of our measured range. The theoretical DE rates do not include the cascade contributions. At a temperature of 1.7 keV, near where Fe XXIV emissivity peaks, DR contributions amount to -20%

for the X = 11.18 A line emission. RE enhances the rates by -5%. However, the unmeasured RE

contributions at higher energies can be expected to increase the rates further. Thus, plasma

emission codes which do not include the effect of DR and RE on line emissivities can be expected

to underestimate the line intensity by at least -25%.

5 Acknowledgements

The authors wish to thank S. T. Manson for stimulating conversations and P. A. D'Antonio, E. W.

Magee, and D. H. Nelson for their expert technical support. Work at Lawrence Livermore

National Laboratory was performed under the auspices of the U.S. Department of Energy

(contract W-7405-ENG-48). This program is supported by a NASA High Energy Astrophysics

X-Ray Astronomy Research and Analysis grant NAGW-4185 (Columbia University) and work

order W-19127 (LLNL).

References

[1] Fabian, A. C. et al., ApJ 436, L63 (1994)

[2] Liedahl, D. A. et al., ApJ 438, LI 15 (1995)

[3] Savin, D. W. et al., ApJ 470, L73 (1996)

[4] Levine, M. A. et al., Phys. Scr. T22, 157 (1988)

[5] Percival, I. C, and Seaton, M. J., Philos. Trans. R. Soc. London A 251, 113 (1958)

[6] Henke, B. L., Gullikson, E. M., and Davis, J. C, At. Data Nucl. Data Tables 54, 181 (1993)

[7] Inal, M. K. and Dubau, J., J. Phys B. 22, 3329 (1989)

[8] Marrs, R. E., (private communication)

[9] Beiersdorfer, P. et al, Phys. Rev. A 46, 3812 (1992)

140 ICAMDATA 97 Proceedings
Modeling Electromagnetic Interactions

in Quantized Electronic Systems

Verne L. Jacobs

Complex Systems Theory Branch,

Condensed Matter and Radiation Sciences Division,

Naval Research Laboratory,

Washington, D. C. 20375-5000

1 Introduction

We have been developing a density- matrix approach [1] that provides a convenient framework for

the systematic computer simulation of the electromagnetic spectra emitted or absorbed by a quantized electronic system. A quantized electronic system is characterized by discrete

energy-level structures, which correspond to bound or quasi-bound states, and by radiative

transitions that produce line-like spectral features, which are advantageous in the development of sources of coherent electromagnetic radiation.

Extensive applications of our density- matrix approach have been made to radiative

transitions of many-electron atomic systems in strong fields [2, 3], and detailed spectral

simulations have been provided for K-alpha dielectronic satellite spectra of highly charged atomic

ions in electron-ion beam interactions [4] and in high-temperature plasmas [5]. In these

simulations, it has been necessary to assemble a very large data base of atomic energy levels and

transition probabilities. We have also been interested in applications to radiation processes

involving energetic electron beams propagating in strong electric and magnetic fields, as in

free-electron lasers and electron cyclotron masers or gyrotrons, and in crystal fields, giving rise to electron channeling radiation and coherent bremsstrahlung [6]. Currently, we are adapting our

density-matrix approach to coherent electromagnetic interactions in low-dimensional

semiconductor microstructures [7], such as quantum wells, quantum wires, and quantum dots.

These structures have been referred to as quantum-confinement systems, because they can give

rise to discrete or quasi- discrete levels and to radiative transitions that are closely analogous to the spectral-line transitions in atomic systems. In contrast to natural atomic systems, which may

be treated as identical, the quantum dots that are often referred to as "artificial atoms" may occur

in arrays, and their geometric and physical properties may vary in a random manner.

Consequently, our microscopic description is expected to be most appropriate for the investigation

of the properties of a single microstructure, where the homogeneous line-broadening mechanisms

and elementary relaxation processes may be examined.

The numerous device applications of the electromagnetic processes of interest include laser

systems, electro-optical components, optical communications technologies, and radiation

detectors. New quantum-optics applications include quantum computing, coherent control, and

quantum cryptography. In addition, this fundamental study forms the basis for the spectroscopic

investigation of basic material properties and interactions.

3.1 Atomic Structure and Spectroscopy 141
2 Density-Matrix Organization of the Spectral Simulation

The starting point for a detailed spectral simulation should be a realistic determination of the

quantized electronic structure for the single-electron or many-electron subsystem of interest. The

complete spectrum of electronic states may include discrete bound states, continuum states, and

quasi-bound states or autoionization resonances. These electronic states may be taken to be

eigenstates of a Hamiltonian in the presence of an external (classical) electric or magnetic field or an internal crystal field that can be represented by a local potential function. The correct treatment of coherent electromagnetic interactions usually involves the self-consistent

determination of the radiation fields, as solutions of the coupled dynamical equations governing

the interacting quantized electronic subsystem and the electromagnetic field. The effects of many-particle interactions can be treated as self-energy corrections to the

single-particle energy levels. In the description of many-electron atomic systems, the starting

point is usually a many-electron approximation, which must be systematically improved. In the

treatment of electrons (or holes) in ideal crystals or in semiconductor microstructures, the initial

single-particle description must also be systematically improved to take into account the effects of

the electrostatic interaction between charged particles, which are referred to as correlation

effects. The inclusion of these effects leads to dielectric screening and to band-gap

renormalization. The effects of lattice vibrations may be described, within the framework of

many-body quantum field theory, in terms of electron-phonon collisional interactions.

The total probabilities for the various radiative transitions can be evaluated using the

familiar Fermi Golden-Rule formula, which is obtained from the lowest-order perturbation theory

describing the interaction of the electronic subsystem of interest with the quantized

electromagnetic field. The familiar radiation parameters include the (Einstein) spontaneous

emission rates and the cross sections for the induced emission and absorption processes. In order

to describe the spectral line shapes, it is necessary to employ a high-order, non-perturbative

description of the interaction of the electronic system with the quantized electromagnetic field

and with the multitude of perturbing particles or quasi-particles. In order to accomplish this

objective, it is necessary to adopt a quantum statistical description of the interaction of

electromagnetic radiation with the charged particles.

A complete non-perturbative statistical description of the interaction between the quantized

electronic subsystem of interest and the quantized electromagnetic field, as well as its interaction

(or entanglement) with a much larger quantum system representing the surrounding

environment, is provided by the density- matrix approach. In the time domain, the equation of

motion for the density operator representing the combined, enlarged system provides the starting

point for the general quantum dynamical description. It is often desirable to introduce a transformation to the frequency domain, in which the basic quantity is the Liouville-space

resolvent operator. In order to obtain a practical formulation, it is necessary to introduce reduced

density- matrix descriptions, in which the interactions of the subsystem of interest with the

environment are treated stochastically, as collisional and radiative relaxation processes. In this

manner, reduced density operators are defined for the electronic subsystem and for the

electromagnetic radiation field. If coherent interactions are of interest, the reduced system must

be defined to include the coherently coupled subsystems.

Our density- matrix description [1] may be viewed as a comprehensive framework for the

systematic organization of the basic collisional-interaction and radiation-transition data. In order

to obtain the electronic-level populations from the traditional data set of transition probabilities

and cross sections, it is necessary to simplify the equations of motion for the reduced density

142 ICAMDATA 97 Proceedings
operators. The Markov or short-memory-time approximation leads to the conventional rate or Master equations for the electronic-level populations, together with the electronic-state

coherences. In the case of free or quasi-free particles, non-equilibrium distribution functions can

be determined. A separate reduced density-matrix equation for the radiation field must be

included in order to provide a self-constant treatment of the non-linear behavior that is characteristic of coherent electromagnetic processes.

In the frequency-domain formulation of the density-matrix description, it is convenient to introduce a generalized Fermi Golden-Rule formula for the evaluation of the spontaneous

radiative emission rate, as well as for the various cross sections of interest. This formula is expressed in terms of the initial-state density operator for the electronic subsystem and the

final-state projection operator appropriate to the relevant photon detection process. The

Liouville-space reduced transition operator occurring in this formula is defined in terms of a

Liouville-space resolvent operator, which may be evaluated to give the spectral-line shape

produced by an array of radiative transitions. This is a standard procedure in the isolated-line

approximation, but it may be necessary to employ an overlapping-line description. The

Liouville-space self-energy operator provides the open-system description of the collisional and

radiative relaxation processes. In order to include Stark and Zeeman broadening, it is necessary

to evaluate the line-shape formula using the "atomic" data that has been determined from

electronic eigenstates in the presence of static or dynamic external electric and magnetic fields. In

order to make comparisons with experimental observations, it is usually necessary to include

either thermal or turbulent Doppler broadening.

3 Spectral Simulations

Spectral simulations have been carried out for many-electron atomic systems in electron-ion beam

interactions [4] and in high-temperature plasmas [2, 3, and 5]. An ultimate goal in these

simulations has been to employ the same set of atomic data consistently in the description of the

non-equilibrium atomic-population kinetics and in the determination of the spectral-line shapes.

These atomic spectral simulations have been found to be useful in determinations of electric-field

and magnetic-field distributions and for diagnostics of plasma densities and temperatures.

Spectral simulations for coherent radiation processes of energetic electrons in crystal lattices,

such as coherent bremsstrahling and channeling radiation [6], can provide information on the

elementary microscopic interactions and on the local crystal environment. Our density-matrix

approach [1] may provide a comprehensive framework for detailed and systematic spectral

simulations of electromagnetic interactions in low- dimensional semiconductor electronic systems

[7], such as quantum wells, quantum wires, and quantum dots.

Acknowledgments

This work has been supported by the Department of Energy and by the Office of Naval Research.

3.1 Atomic Structure and Spectroscopy 143
References

[1] V. L. Jacobs, J. Cooper, and S. L. Haan, Phys. Rev. A 50, 3005 (1994).

[2] L. A. Woltz, V. L. Jacobs, C. F. Hooper, and R. C. Mancini, Phys. Rev. A 44, 1281 (1991).

[3] V. L. Jacobs, J. Quant. Spectrosc. Radiat. Transfer 54, 195 (1995).

[4] V. Decaux, P. Beiersdorfer, S. M. Kahn, and V. L. Jacobs, Astrophys. J. 482, 1076 (1997).

[5] V. L. Jacobs, G. A. Doschek, J. F. Seely, and R. D. Cowan, Phys. Rev. A 39, 2411 (1989).

[6] A. W. Saenz, A. Nagl, and H. Uberall, Phys. Rev. B 37, 7238 (1988).

[7] H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties

Semiconductors, Second Edition, (World Scientific, Singapore, 1993).

144 ICAMDATA 97 Proceedings
Relativistic Oscillator Strengths in Chlorine

I. Martin, C. Lavin, A.M. Velasco

Departamento de Quimica Fisica, Facultad de Ciencias,

47005 Valladolid, Spain

1 Introduction

Models of interstellar chlorine chemistry can be used to constrain models of interstellar clouds. One

difficulty in confirming the basic ideas of this model is that the analyses have been based on rather

poorly known oscillator strengths for CI I, as has been emphasized by Keenan & Dufton [1] and Morton

[2]. We have followed the Relativistic Quantum Defect Orbital (RQDO) procedure [3] with and without

explicit inclusion of core-valence correlation. The observations [4] of the CI I spectrum show that LS

coupling is valid for the deepest 3p4 ns, np and nd configurations whereas pair coupling is progressively better satisfied for higher I and n values. In our calculations of oscillator strengths, we

have followed the LS coupling scheme, except for the 3p4

( 3P)4f - 3p4

(3P)5g lines, for which the Jd

coupling scheme seems clearly to be more appropriate.

2 Method of Calculation

The absorption oscillator strength for an electric dipole transition between an initial state, I i), and a

final state, I j>, is given by

_2 (E] -El )

where (Ej - Ei) is the transition energy (in atomic units), 2J + 1 is the degeneracy of the initial level and

S is the so-called line strength (in atomic units). In a one-configuration treatment, such as ours, the

angular and radial parts of the line strength can be separated. Within LS coupling, the line strength

is written as follows:

S(ySLJ, YS'L'J')

(2)

SSS' Scc'Rline (SLJ, S'L'J') RmuU (yL, y'L')(-l ) I (r) RnT (r)rdr

where J and J',L and L',S and S', and y and y 'represent the quantum numbers required to complete

the specification of the states I i) and | j), respectively. The subscripts c and c ' refer to the core. The

integral in (2) contains the radial parts of the initial and final wavefunctions only. The line factor, Rune,

3.1 Atomic Structure and Spectroscopy 145
Ru 42J 4 U2J> + K-i )s + J + L' + 1 ^1 J

L,j,} (3)

is given by the above expression, where the symbol in braces is a 6-j symbol. (Rune)2 gives the relative

strength of the lines within a multiplet. In (2), nl and n'Y are, respectively, the principal and orbital

angular momentum quantum numbers of the jumping electron, and /> indicates the larger of the two

orbital quantum numbers, / and /

', involved in the transition.

The multiplet factor, Rmuit, depends upon the particular configurations involved in the transition:

- for 3s23p4nl-3s23p4n'V the multiplet factor adopts the form

Rmult = V^T7 (-1 )t< +L+l' +

* j^j

-and for 3s23p5-3s23p4n'l' the multiplet factor is

Rmult = V5V2L + U2L' + 2f-i^+L+/' +i |^,^p5 LS{\ p

4 (Lc Sc )PLS)

where (p5LS{/p4(Lc Sc)pLS) is the coefficient of fractional parentage, CFP.

The expression for the line strength in the Jd coupling scheme is

(4)

(5)

S = (2J + 1)(2J' + 1)

kLj

2

J' IK'

\ l>\lRnlRnTrdrf (6)

where Jc is the total angular momentum quantum number of the electron core 3p4 3P level; Kresults

from the coupling of the orbital angular momentum, /, of the valence electron with Jc , and J is obtained

through the addition of the spin of the valence electron to K.

3 Results

3P5 2po _ 3p

4(sp) 4S 2p Transitions

Some lines of the 3p5 2 P° - 3p4

(3P)4s 2 P multiplet of neutral chlorine have been the object of several

theoretical studies, as well as measurements, because of their importance in astrophysics. Table 1 contains fine structure oscillator strengths for the 3p5 2P° - 3p4

(3P)4s 2P transitions in CI I. In this table

we display, together with the RQDO results [5], the f- values calculated by Biemont et al. [6] with the

SUPERSTRUCTURE (SST) computer program, taking the most important configuration interaction

and relativistic effects into account, as well as the results of Ojha & Hibbert [7], who used large

multiconfiguration expansions in the atomic structure code CIV3. Biemont et al. and Ojha & Hibbert

report f- values calculated in dipole length and velocity approaches.

146 ICAMDATA 97 Proceedings
The most accurate laboratory data are the measurements of Schectman et al. [8] using beam-foil

spectroscopy. These authors estimated that their results should be accurate to about 7%. The present

results, without explicit account for polarization, are in good accordance with the most accurate

theoretical and experimental results. Our f-values for the 3p5 2 P°3/2 - 3p4

(3 P)4s 2P3/2 and 3p5 2 P°i/2 - 3p4

( 3P)4s 2 P3/2 lines are larger than the earlier measurements for these transitions and confirm the

recent experimental data of Schectman et al. For the remaining transitions, our f-values are in good

accord with the measurements of Clyne & Nipp [9]

.

3p4(

3P) 4f- 3p4(

3P) 5g Transitions

In Table 2, we display RQDO f-values for 3p4

(3P)4f - 3p4(3P) 5g transitions calculated in the Jd coupling

scheme [5] . No comparison data have been found in the literature. The level designations in this table are given according to the notation 3p4

(2S+1Ljc) nl [K]j where Jc is the total angular momentum

quantum number of the electron core 3p4 3P level; if results from the coupling of the orbital angular

momentum, /, of the valence electron with Jc , and J is obtained through the addition of the spin of the

valence electron to K. According to Quinet et al. [10], in pure Jd coupling, the energies of a pair of

levels for a given Jc should fall on a parabola when plotted against h=l/2[K(K+l) - JC (JC+1) - 1(1+1)].

This approximation is verified in the cases of 4f and 5g electrons.

Acknowledgements

This work has been supported by the D.G.I.C.Y.T. of the Spanish Ministry of Education and Science,

under Project No.PB94-1314-C03-03

References

[I] Keenan F.P., Dufton P.L., MNRAS 242, 52p (1990)

[2] Morton D.C., ApJS 77, 119 (1991)

[3] Martin I., Karwowski J., J. Phys. B 24, 1539 (1991); Karwowski J., Martin I., Phys. Rev. A 43,

4832 (1991)

[4] Radziemski L.J.Jr., Kaufman V., J. Opt. Soc. Am. 59, 424 (1969)

[5] Lavin C, Velasco A.M., Martin I., Astronomy and Astrophysics, in press

[6] Biemont E., Gebarowski R., Zeippen C.J., A&A 287, 290 (1994)

[7] Ojha P.C., Hibbert A., Phys. Scr. 42, 424 (1990)

[8] Schectman R.M., Federman S.R., Beideck D.J., Ellis D.G., ApJ 406, 735 (1993)

[9] Clyne M.A.A., Nip W.S., J. Chem. Soc. Faraday Trans. II 73, 161 (1977)

[10] Quinet P., Palmeri P., Biemont E., Brault J.W., Phys. Rev. A 49, 2446 (1994)

[II] Wiese W.L., Smith M.W., Miles B.M., Atomic Transition Probabilities, Vol.11, U.S. Govt. Print

Off., Washington D.C., NSRDS-NBS 22 (1969)

[12] Schwab J.J., Anderson J.G., J. Quant. Spectr. Rad. Transfer 27, 445 (1982)

3.1 Atomic Structure and Spectroscopy 147
Table 1: Oscillator strengths for the 3p5 - 3p4

(3P)4s fine structure transitions in CI I. RQDO RQDOb SSTC CIV3d CO Experiment

3p 2P°3/2 - 4S 2P3/2 0.1368 0.1281 0.147 0.1324 0.114 0.100±0.030f

0.109±0.010e

0.153+0.011h 3p 2P°3/2 - 4s 2Pl/2 0.0249 0.0240 0.0299 0.0264 0.0233 0.028±0.006f 3p 2P°l/2 - 4S 2 P3/2 0.0561 0.0523 0.0530 0.0474 0.0418 0.03810.006^

0.055±0.004h

3p 2 P°l/2 - 4s 2 Pl/2 0.1017 0.0980 0.116 0.1051 0.088 0.093±0.016f

aRQDO without explicit polarization correction [5];

bRQDO with explicit polarization correction [5];

cBiemont et al. [6], length form; dOjha & Hibbert [7], length form e Critical compilation, Wiese et al. [11]; fClyne & Nipp [9]; ^Schwab &

Anderson [12]; h Schectman et al. [8].

Table 2: Oscillator strengths for the 3p4

( 3 P2)4f [K]j - 3p4(3P2)5g [K]j transitions in CI I.

RQDO RQDO RQDO RQDOb

[5] 11/2 - [6] 13/2 1.2217 1.2211 [3] 7/2 - [4] 9/2 1.0697 1.0691

[5] 11/2 - [6] 11/2 0.1031 0.1030 [3] 7/2 - [4] 7/2 0.0307 0.0306

[5] 9/2 - [6] 11/2 1.2354 1.2348 [3] 5/2 - [4] 7/2 1.0989 1.0983

[5] 11/2 - [5] 11/2 0.1031 0.1030 [3] 7/2 - [3] 7/2 0.2247 0.2246

[5] 11/2- [5] 9/2 0.0016 0.0016 [3] 7/2 " [3] 5/2 0.0083 0.0083

[5] 9/2 - [5] 11/2 0.0019 0.0019 [3] 5/2 - [3] 7/2 0.0111 0.0111

[5] 9/2 " [5] 9/2 0.1028 0.1027 [3] 5/2 - [3] 5/2 0.2220 0.2219

[5] 11/2 - [4] 9/2 0.0040 0.0040 [2] 5/2 - [3] 7/2 1.0668 1.0662

[5] 9/2 - [4] 9/2 0.0001 0.0001 [2] 5/2 - [3] 5/2 0.0532 0.0531

[5] 9/2 - [4] 7/2 0.0040 0.0039 [2]a/2 - [3] 5/2 1.1201 1.1201

[4] 9/2 - [5] 11/2 1.1263 1.1257 [l]a/2 - [2] 5/2 1.1216 1.1209

[4] 9/2 - [5] 9/2 0.0209 0.0208 [l]3/2 - [2] 5/2 0.2691 0.2690

[4] 7/2 - [5] 9/2 1.1481 1.1475 [l]l/2- [2] 3/2 1.3466 1.3459

[4] 9/2 - [4] 9/2 0.1802 0.1801 [2] 5/2 - [2] 5/2 0.2051 0.2050

[4] 9/2 - [4] 7/2 0.0041 0.0041 [2] 5/2 - [2] 3/2 0.0149 0.0149

[4] 7/2 - [4] 9/2 0.0052 0.0052 [2]a/2 - [2]5/2 0.0224 0.0224

[4] 7/2 - [4] 7/2 0.1794 0.1793 [2]a/2 - [2]3/2 0.0897 0.0897

[4] 9/2 " [3] 7/2 0.0093 0.0093

[4] 7/2 - [3] 5/2 0.0089 0.0089

[4] 7/2 " [3] 7/2 0.0004 0.0004

aRQDO without explicit polarization correction; bRQDO with explicit polarization correction [3].

148 ICAMDATA 97 Proceedings
Oscillator Strengths of Rydberg Transitions

W Mende and M Kock

Institut fur Atom und Molekiilphysik, Abteilung Plasmaphysik,

Universitat Hannover, Callinstrasse 38,

D-30167 Hannover, Germany

1 Introduction

In the present extended abstract we will describe a novel experimental technique which allows the

determination of absolute oscillator strengths of transitions into high-lying Rydberg states where

in current experiments the main quantum number n varies from 30 to 60. The largest attainable

upper quantum number is limited by the spectral width and the incremental scanning step size of

the laser system. The lower limit of n results from the requirement that the ionization probability

must be very nearly equal to unity for atoms being in a high Rydberg state. Absolute f-values are obtained from a measured photoionization cross section exploiting the fact that the discrete

f-values are continuously merging into the differential ones.

2 Procedure

By means of laser spectroscopic techniques we investigate transitions from the Sr I 5s5pl P° reso- nance state into Rydberg states as well as into the continuum near the the first ionization threshold.

The first laser is set to the resonance wavelength of 460.7 nm while the second laser is tuned over the Rydberg states into the continuum. Our experimental arrangement to study Rydberg lines has

been described elsewhere (Willke and Kock 1991, Mende and Kock 1996). The detector for the

laser- produced ions is our metal vapour oven designed as a thermionic diode. A cross section of our oven is given in Fig.l.

The oven was typically operated at a temperature of 520 °C with argon as a buffer gas at pressures

between 10 and 15 hPa. At such pressures the ionization probability for Rydberg states with n > 20

is pn = 1. For n < 20 it is no longer guaranteed that the ionization probability is still unity, thus

setting a lower limit for our measuring procedure. As long as the condition, pn ~ 1, is fulfilled there is a simple relationship between /-value and photoionization cross section (see Mende and

Kock 1996):

1 ire

2 Sln uln l+

-fin = T^X a U)

47T£o mc S

l+ ui + The equation holds under the additional assumption that the absorption of the lines occurs in an

optically thin layer. The /-value f\n is then directly related to the photoionization cross section a

1+

measured at frequencies vi + and z/i n , respectively, the ratio of the ion signals S

ln due to absorption

in the line, and the direct absorption into the continuum, 5

1+

. The necessary absolute photoionization cross section o~ l+ at the first ionization threshold was

determined with the saturation method (see e.g. Burkhardt et al 1988, He et al 1991, Mende et al 1995). Within the excited vapour column the second laser pulse, when tuned to a fixed wavelength

3.1 Atomic Structure and Spectroscopy 149
in the ion spectrum, produces the following number of photoions:

Z = j N0 (l - exp (-ol+

g(p)(j>) ) dV . (2)

Here g(p) is the spatial distribution of the laser pulse while <j) is the time-integrated number of

photons of the ionizing laser pulse. By fitting this expression to a saturation curve, N0 and a

1+ can be obtained on absolute scales provided the spatial distribution g(p) is known. The influence

of different spatial laser profiles g(p) on saturation behaviour can be seen in Fig.2. A top-hat, a Gaussian and a modified Lorentzian function g(p) are used with the saturation function given in

equation (2):

9top— hat (P)

(3)

gLorentz (P) TrAp2 (p

2 + Ap2

) 2

Only with a top-hat shaped laser pulse can complete saturation be achieved. Incidently, the wings

in the Gaussian and Lorentzian curve are responsible for the fact that the curves in Fig. 2 do not

reach complete saturation.

Fig. 3 displays a measured saturation curve together with a least-squares fit of equation (2). Note

that it is not sufficient to describe the spatial distribution by a top-hat function. The actual

distribution must be taken instead. We monitored the distribution with a CDD camera and fitted

150 ICAMDATA 97 Proceedings
C/2

0

I 1 1 1 1 1 1 1

1

1

1 i i

1

i

1

/

/ ^

1 /

top hat

; Gauss

' Lorentz

laser

profile

o

/

/,•' /

'

1

: \

ll \\

', : \

\\

i.i.i.i, i i.i,

0.2 0.4 0.6 0.8 1.0

g*<|) (cm

2

)

-0.2 0.0 0.2

P (cm)

Figure 2: Saturation function with different spatial laser profiles.

| 200

I

1

1

• experimental points

i •

Gauss g(p)

top-hat g(p) •

" —1

J?

//

//

r

//

0.0..i.i 50.0 100.0 150.0 200.0

energy (|iJ)

Figure 3: Saturation behaviour of the ion signal versus energy variation of the ionizing laser pulse

at 412 nm. The full curve is a least-squares fit of the data points with the saturation function

given in Eq. (2). Due to the wings of the Gaussian shaped laser pulse, complete saturation was

not achieved.

it to a bell-shape curve. We have calibrated our f-values with the 176 Mb±20% cross section we

found with the saturation technique. The accuracy to which we can determine absolute f-values

is mainly limited by the saturation technique. Since only a small saturation could be obtained

3.1 Atomic Structure and Spectroscopy 151
Tablel. Absolute oscillator strengths of the Sr I 5s5p 1 P° —> bsnd l D2 transitions.

n f- value n f-value

30 6.76E-4 46 2.44E-4

31 5.96E-4 47 2.46E-4

32 5.56E-4 48 2.50E-4

33 4.92E-4 49 2.19E-4

34 4.38E-4 50 2.02E-4

35 4.79E-4 51 2.13E-4

36 4.19E-4 52 1.88E-4

37 4.07E-4 53 1.77E-4

38 3.97E-4 54 1.65E-4

39 3.55E-4 55 1.57E-4

40 3.50E-4 56 1.55E-4

41 3.33E-4 57 1.32E-4

42 3.35E-4 58 1.28E-4

43 3.01E-4 59 1.23E-4

44 2.84E-4 60 1.01E-4

45 2.66E-4

with our laser system, the uncertainty of 20% is relatively large. With higher laser energy available

the uncertainty could be easily reduced to 10%. Nevertheless, in the present experiment it is the

dominant contribution to the total uncertainty of (22 — 24)% in the f- values given in table 1 for the

Rydberg transitions 5s5p l P° —> bsnd 1 D2 with n = 30 — 60.

References

Burkhardt C.E., Libbert J.L., Xu J., Leventhal J. J., and Kelly J.D., Phys. Rev A 38, 5949-52

(1988)

He L.W., Burkhardt C.E., Ciocca M., and Leventhal J.J., Phys. Rev. Lett. 67, 2131-4 (1991)

Mende W., Bartschart K., and Kock M., J. Phys. B: At. Mol. Opt. Phys. 28, 2385-93

(1995)

Mende W. and Kock M., J. Phys. B: At. Mol. Opt. Phys. 29, 655-663 (1996)

Willke B. and Kock M., Phys. Rev A 43, 6433-5 (1991)

152 ICAMDATA 97 Proceedings
Atomic Data for Lighting Applications

Gillian Nave, Craig Sansonetti, Joseph Reader

National Institute of Standards and Technology,

Gaithersburg, MD 20899, U.S.A.

1 Introduction

Although lighting accounts for about 20% of U.S. electric power consumption, even the best white

light sources convert only about one third of the power they consume to usable light. Improved

discharge sources are a promising avenue for development of more efficient lighting, but lack of basic

atomic data places fundamental limitations on this research. NIST is currently establishing a new

experimental program aimed at determining atomic wavelengths, energy levels, and branching ratios

that are needed for lighting applications. The centerpiece of this effort is a high resolution Fourier

transform spectrometer recently installed at NIST. Its broad spectral coverage, high resolution, and

linear intensity response will permit observation of almost all spectroscopic data of interest.

2 Atomic Data of Interest to Lighting

Rare earth metals are commonly used in metal halide lamps to provide a white light spectrum

similar to that of natural light. Three elements of interest are thullium, holmium and dysprosium.

These metals have very rich atomic spectra, with many thousands of lines throughout the visible

region, but relatively little radiation in the ultraviolet and infrared regions. In many cases the

atomic data for these elements are missing. Many energy levels remain to be found and many

lines are unclassified. Transition probability data are needed, even for the strongest lines in the

spectrum.

Fourier transform (FT) spectrometry offers many advantages for measuring these atomic data.

Accurate measurements of line intensities are possible with the large dynamic range (~ 105

) and lin- ear intensity response. A FT spectrometer measures all of the lines in the spectrum simultaneously,

minimizing the effects of source drift, and its wide wavenumber coverage permits the measurement

of all of the decay channels from a particular upper level simultaneously. The high resolution and

signal-to-noise ratio allow blended lines to be easily distinguished and minimize the errors due to mis-identification of spectral lines.

3 The NIST Fourier Transform Spectrometer

Three years ago, NIST acquired a high-resolution FT spectrometer from the Los Alamos National

Laboratory [1, 2]. The instrument has a spectral resolution of 0.0025 cm-1 and we currently have

optics and detectors to cover the wavelength range from 200 nm to around 8 /im.

Two major improvements have been made since we acquired the spectrometer. First, the

instrument has been installed in a new vacuum chamber. A vacuum chamber is needed both to eliminate the effects of air turbulence in the optical path, and to allow operation in the infra-red,

where there are molecular bands from water vapor and carbon dioxide.

3.1 Atomic Structure and Spectroscopy 153
300

o

<D

.<2 200

o

c

I o

I

.!> 100

CO

0

19337 19338 19339

Wavenumber (cm

-1

)

Figure 1: Comparison of the Dy line at 19338 cm-1 (4f10

(5 I)6s 6

I 17/2 - 4f9

( 6 H°)5d6s 6 H°

5/2 ) in

the hollow cathode and electrodeless discharge lamp.

The second change has been a complete replacement of the data acquisition system. The

new system, based on the method of Brault [3], uses two 20 bit A/D converters to sample the

interferogram at a fixed sampling rate of 39.9 kHz. Laser fringes are recovered from the servo system

used to control the catseye retroreflectors. Both the fringes and the A/D samples are referenced

to the same 40 MHz clock, and the interferogram can then be recovered by using an interpolating

digital filter. The digital filter increases the signal-to-noise ratio as it greatly reduces noise from

outside the spectral region of interest. The new system is also much less sensitive to vibrations

than the previous system, and hence ghosts from non-uniform sampling of the interferogram are reduced.

The instrument has been operating in the region from 250 nm to 2.5 /um since March, 1997. In

addition to our observations of spectra of rare earth elements of interest to the lighting industry, we

have been studying spectra of mercury, bismuth and krypton, which are of astrophysical interest.

4 The Spectrum of Dysprosium

The first spectra we are investigating in connection with our program of atomic data for lighting are those of neutral and singly-ionized dysprosium. Dysprosium is used in metal halide lamps,

and accurate transition probability data are needed for modelling the lamp discharge. We are collaborating with Wickliffe and Lawler, of the University of Wisconsin, to measure branching

ratios with our FT spectrometer, which will be combined with the Wisconsin lifetime data [4] to provide transition probabilities.

We have recorded spectra of high current hollow cathode lamps from 8500 cm-1

to 30000

cm-1

(1.2 /Lim to 330 nm) using our FT spectrometer. The cathode was a 60 mm long cylinder

154 ICAMDATA 97 Proceedings
of natural dysprosium with an 8mm diameter bore. Currents ranged from 100 mA - 500 mA

and the carrier gas was 200 Pa of Ar. Radiometric calibration was done with a tungsten strip

lamp. Dysprosium spectra were also recorded with the Chelsea FT 500 vacuum ultraviolet Fourier

transform spectrometer at Lund University, Sweden. These covered the range 25000 cm-1

to 50000

cm

-1 and were radiometrically calibrated with a deuterium lamp.

Natural dysprosium has four isotopes, and the spectral lines from the hollow cathode lamps are thus complicated by isotope structure. To assist in the analysis of these spectra we also recorded

the spectrum of an electrodeless discharge lamp containing the single isotope 162 Dy. However the

electrodeless discharge lamp is not as useful as the hollow cathode lamp for measuring branching

ratios, as many spectral lines are strongly self-absorbed. Radiometric calibration is also less reliable as it is not possible to measure the transmission of the lamp envelope. Figure 1 compares a line in

the hollow cathode lamp and the electrodeless discharge lamp. Although the line in the electrodeless

discharge lamp is wider than the line in the hollow cathode lamp, it is not complicated by isotope

structure. So far we have obtained wavelengths for roughly 4000 Dy I and Dy II lines observed in the 162 Dy

electrodeless discharge lamp. These have been used to revise the energy level values of 376 energy

levels in 162 Dy I and 228 energy levels in 162 Dy II. Initial branching ratios have been obtained

for some of the lower Dy II levels and even parity Dy I levels. These show good agreement with

the preliminary branching ratios of Wickliffe and Lawler[5] , who have used a different calibration

technique, giving increased confidence in the radiometric calibration.

Acknowledgments

We are grateful to U. Griesmann for his assistance with the FTS data acquisition system and the

hollow cathode. We thank U. Litzen of the University of Lund for assisting in the use of the FTS

by one of us (G.N.). We thank E. Worden for providing the electrodeless discharge lamp. This

work is partially supported by the Electric Power Research Institute.

The identification of commercial products in this paper does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the

items identified are necessarily the best available for the purpose.

References

[1] D. Hof, B. A. Palmer, Rep. LALP-88-39, Los Alamos National Laboratory, Los Alamos, NM,

Oct. 1988

[2] J. Simons, B. A. Palmer, D. E. Hof, R. C. Oldenborg, J. Opt. Soc. Am. B 6, 1097 (1989)

[3] J. W. Brault, it Appl. Opt. 35, 2891 (1996)

[4] J. J. Curry, E. A. Den Hartog, J. E. Lawler, J. Opt. Soc. Am. B, in press

[5] M. E. Wickliffe, J. E. Lawler, private communication

3.1 Atomic Structure and Spectroscopy 155
Investigation of the Autoionization Spectra of

Samarium from 48800 cm-1

to 51200 cm-1

Hyunmin Park, Hyim-chae Kim, Yong-joo Rhee, and Jonginin Lee

Laboratory for Quantum Optics, Korea Atomic Energy Research Institute,

P.O. Box 105, Yusong, Taejon 305-600, Korea

1 Introduction

The autoionization state is a quasi-bound state of an atom which lies above the ionization threshold

of the outer valence electrons. This state plays a great role in the photoionization of atoms in

plasmas and astrophysics. Hence, the investigation of the autoionization states has been of interest

and a number of experimental and theoretical results have been reported recently.

The spectrum of the rare earth metal Sm is complex because of its partially filled 4/ shell and the

structures of the [4/

6 6s2

] 1 F ground term. To our knowledge, there are only few results reported on the autoionization state of the Sm [1], [2]. In this paper, we report the autoionization spectra of

atomic samarium(Sm) in the region from 48800 cm-1

- 51200 cm-1

, obtained from the three-step

excitation. We measured the energy levels of the odd autoionization states.

2 Experiments and Results

Three-step excitation was used to investigate the autoionization state of Sm. The first excitation

step was fixed at a transition from the ground state, [4/

6 6s2

] 7Fi, to the first excited state [4/

6 6s6p]

7 F®, the energy of which is 17190 cm-1

. Then the even states with the energies 34522 cm

-1

, 34420 cm-1

, and 34399 cm-1 were chosen as the intermediate levels. Finally, the energies of the

autoionization state were obtained by scanning the wavelengths of the ionization laser from 600nm

to 700nm.

The experimental setup for three-step excitation is well described in Ref.[3]. The setup consists

of a laser system, a time of flight mass spectrometer, and a detection system. For the first and the

second excitation step, we used two single-mode dye lasers pumped by a frequency-doubled Nd:YAG

laser. The transition to an autoionization state from the second excited state was made by using

another broadband dye laser pumped by the same Nd:YAG laser. Two commercial wavemeters

having resolutions of 200 MHz were used to measure the wavelengths of the two single-mode dye

lasers. Additionally, to calibrate the ionization laser, a small portion of the dye laser beam was used

to observe the optogalvanic spectrum of a Sm-Ar hollow-cathode discharge lamp. The frequencies

of the single-mode pulse lasers were stabilized within 100 MHz during an experiment by a feedback

system which consisted of two fabry-perot etalons and a piezoelectric transducer(PZT) attached to the oscillator of the laser. For step-wise excitation, the lasers were made to interact with the Sm

atoms with a time delay of 10 ns, respectively.

The atomic beam of samarium was produced by a resistively heated tantalum boat containing

the natural solid Sm up to a temperature of about 1000 K in a vacuum chamber. The generated

Sm atomic beam was collimated by two slits and directed perpendicularly to the laser beam path

156 ICAMDATA 97 Proceedings
Table 1: List of the investigated autoionization states Intermediate Ionizing Laser Autoionization Fano Width signal

state(cm_1

) wavelength(nm) state(cm_1

) q-parameter (cm- 1

) strength

601.367 51022.9 m

604.574 50934.8 32.7 23.7 s 604.995 50923.3 w

607.195 50863.4 ra 611.276 50753.5 w

612.171 50729.5 w i 613.285 50699.9 w

621.263 50490.6 w

624.497 50407.3 w

625.611 50378.8 w

627.732 50324.8 w

34399 629.152 50288.9 m

(J=l) 632.072 50215.5 w

633.200 50187.3 w

634.378 50158.0 w

635.273 50135.8 w

643.565 49932.9 w

647.099 49848.1 52.9 5.1 s 654.862 49664.9 w

656.428 49628.5 w

663.415 49468.1 m

666.181 49405.6 m

669.106 49340.0 m

670.169 49338.5 m

683.314 49029.3 m

685.258 48987.8 48.6 5.0 s 685.437 48984.0 56.2 6.4 s 698.932 48702.4 w

602.733 51007.0 m

603.408 50988.5 w

34420 615.171 50671.6 41.1 6.0 s (J=2) 615.967 50650.9 64.6 7.8 s 624.580 50426.8 w

626.324 50382.3 w

635.038 50163.2 w

642.951 49947.8 w

624.082 50541.3 w

628.314 50433.4 ra 34544 630.376 50381.4 109.5 8.1 s (J=3) 630.774 50371.3 22.4 6.0 s 639.332 50159.2 -8.0 22.4 s 652.319 49728.5 -87.8 9.1 s

3.1 Atomic Structure and Spectroscopy 157
in order to reduce the Doppler broadening to 30 MHz. The photo ions of Sm were detected at the

end of the flight tube by a microchannel plate(MCP). Finally, the ion signals were averaged by a boxcar averager and the mass spectrum was recorded by a digitizing oscilloscope.

The experimental results showed a large number of autoionization lines in the region 48800

cm-1

- 51200 cm

-1

. Neglecting the small lines, all experimental results are summarized in Table

1. In Table 1, s, m, and w represent strong, medium, and weak transition strengths, respectively.

By fitting the experimental data against Fano's formula [4] , we obtained the resonance energy(Er ) and the linewidth(F) of the autoionizing states. Fano's formula is expressed as follows:

Vtotal{£) = 0~<x o i 1 + ab £

£ + 1

with e = (E — £V)/(r/2), where atotal represents the transition cross section, q is the Fano parameter, E is the incident photon energy, and aa and crj, are the fitting parameters. Most q parameters

recorded in Table 1 are much larger than 1 because the measured autoionization spectra exhibit

nearly symmetric line profiles. In the energy range investigated in this work, we can observe ten

relatively strong transition lines. Those lines can be used for efficient photoionization of Sm.

We presume that the measured autoionization lines are from [4/

6 6s5<i] configurations. However,

to identify the measured lines, we need more experimental and theoretical efforts.

3 Summary

We investigated the autoionization spectra of atomic samarium by three-step excitation. In this

study, we measured the energy levels of the odd autoionization states located in the region from

48800 cm" 1 - 51200 cm"1

. The first resonant step was fixed at a transition from the ground state, [4/

6 6s2

] F\, to the first excited state [4/

6 6s6p] 7 F$, the energy of which is 17190 cm-1

. The even states with energies of

34522 cm

-1

, 34420 cm-1, and 34399 cm

-1 were then chosen as the intermediate levels. Finally, the

energies of the autoionization states were obtained by scanning the wavelengths of an ionization

laser from 600nm to 700nm.

As a result of this work, forty-two autoionization states were found in the investigated range

from 48800 cm-1to 51200 cm-1

. Among the observed lines, Some lines are analysed by Fano's

formula and q parameters are determined.

References

[1] V. E. Dobryshin, N. A. Karpov, S. A. Kotochigova, B. B. Krynetskii, V. A. Mishin, O. M. Stel- makh, and V. M. Shustryakov, Opt. Spektrosk. 54, 415 (1983)

[2] Hu Sufen, MEI Shimin, ZHANG Sen, CHEN Xing, and XU Yunfei, Chinese Phys. Lett. Vol. 6,

No. 2 (1989)

[3] Hyunmin PARK, Hyun-chae KIM, Jong-hoon YI, Jae-Min HAN, and Jongmin LEE, J. of Korean Physical Society. Vol. 30, 453 (1997)

[4] U. Fano, Phys. Rev. 124, 1866 (1961)

158 ICAMDATA 97 Proceedings
Upgrading the Atomic and Molecular Database for

Astrophysics and Atmospheric Physics by Fourier

Transform Spectroscopy

J. C. Pickering, R. Schermaul, G. Cox, J. Rufus, A. P. Thorne, and R. C. M. Learner

Spectroscopy Group, Blackett Laboratory, Imperial College, London, SW7 2BZ, UK

email: j.pickering@ic.ac.uk

P. L. Smith

Harvard-Smithsonian CfA, Cambridge, MA 02138, USA

Abstract

There is currently a great demand for improvements to the atomic and molecular databases

for astrophysics, atmospheric physics, and theoretical physics. At Imperial College (IC), the

VUV Fourier Transform (FT) Spectrometer, with its high resolving power (up to 2 million at 2000 A), broad spectral range and unique wavelength range (down to 140 nm), is used in a

continuing program to improve the accuracy and completeness of both atomic and molecular

data of importance for astrophysics and atmospheric physics.

1 Atomic Spectroscopy

Until recently it was generally assumed that the atomic spectra of elements such as the transition

group were well known; the existing tables of data were thought to be adequate by users such

as astronomers. But now, with a new generation of telescopes equipped with spectrometers of

high resolving power, the situation is very different. Many of the atomic spectra of relevance to astrophysics were last investigated back in the 1930s and 1940s using grating spectrographs and

photographic plates. Accuracies of the resulting wavelengths, and line intensities estimated by eye, simply cannot meet the needs of either the astronomers, who wish, for example, to interpret the high

resolution stellar spectra now accessible with the Hubble Space Telescope's (HST) spectrographs,

or meet the needs of the modern atomic theorists, who with greater computing power can now carry

out calculations of unprecedented sophistication. Improvements of at least an order-of-magnitude

in accuracy of wavelengths and energy levels are urgently required.

Accurate transition wavelengths are of vital importance in the identification of new atomic en- ergy levels and the correction of known energy levels. These wavelengths and energy levels are used

in the identification of stellar spectral line features, and they also feed into semi-empirical calculations in atomic physics which rely heavily on experimental data of high quality. High accuracy of

wavelengths, energy levels and transition probabilities, as well as knowledge of hyperfme structure

and isotope shifts, is essential in generating reliable synthetic stellar spectra and in disentangling

blended features and weak lines of abundant elements in astrophysical spectra of objects ranging

from chemically peculiar stars to supernovae remnants. In particular, the dramatic improvements

in the quality of UV stellar spectra, observed using the GHRS and STIS spectrographs of the HST,

have highlighted the inadequacy of the laboratory atomic data base needed to interpret these observations, especially in the VUV region (below 2000 A), where stellar spectral lines from doubly

3.1 Atomic Structure and Spectroscopy 159
and singly ionized species predominate. The IC FT spectrometer, with its unique short wavelength

cut-off, is ideal for recording these spectra.

In recent years, high resolution FT visible and UV spectra of the line rich, astrophysically

important neutral and singly ionized transition group elements (Fe, Ni, Cr, Co, Ti, and V) have

been recorded at IC using water-cooled, hollow cathode lamps as sources. In all cases, these data

have been supplemented by IR observations at the NSO National Solar Observatory, USA, typically

out to hfim. Analyses of the spectra of Fe I, Ni I, Co I and Co II, led to improvements of at least an order of magnitude in accuracy of wavelengths and atomic energy levels and the identification

of hundreds of new levels [1], [2], [3], [4], and, for Co I, the determination of hyperfine structure

(hfs) constants [5]. The analyses of the spectra of Cr I, Cr II, V I and V II await completion at IC. With the FT spectrometer and suitably reliable intensity calibration, accurate branching ratios can be measured, which, when combined with lifetime measurements, yield oscillator strengths.

Isotope shifts can also be observed, and the VUV platinum spectrum was recorded at IC so that

accurate studies of isotope shifts could be made. A new project studying doubly ionized spectra is underway, initially beginning with Fe III, excited using a Penning discharge source.

1.1 Term Analysis

The dramatic improvement that can be achieved in the database is illustrated by the cobalt spectrum. Visible-VUV (140-600 nm) spectra recorded at IC were used together with FT IR (600-

3000 nm) spectra recorded at Kitt Peak NSO. For strong transitions the wavenumber accuracy is within 1-2 mK, (1 mK = 0.001 cm-1

). In the Co I spectrum analysis [3], over 60 new energy levels were found and several hundred lines identified for the first time. Hfs splitting factors for Co I were found for over 82% of the known energy levels (see Section 1.2). For Co II, the improvement is even more dramatic; over 170 new energy levels were found, and the number of identified transitions

doubled [4], [6] . The new experimental data was used in theoretical calculations to give calculated

transition probabilities [7]. The vast improvements in knowledge of these spectra were not limited

to the visible-VUV spectral regions, -most of the IR transitions were reported for the first time.

1.2 Measurements of Hyperfine Structure

Knowledge of hfs in iron-group elements is important not only for theoretical atomic physics but

also for determinations of elemental abundances in stellar atmospheres. It has been noticeable in

work reporting on stellar abundances that elements with hfs have often been neglected because of

the lack of good laboratory atomic data. For the iron-group elements with odd atomic number, such

as Co, the effect of hfs as a line broadening mechanism must be taken into account in abundance

studies when using both curve-of-growth methods and spectrum synthesis methods. It is also

important to correctly allow for any hfs in the resolution of blended lines in stellar spectra.

Although hfs has been studied for many years, the methods used, such as laser spectroscopy,

atomic-beam magnetic resonance and Fabry-Perot interferometry, allowed observations of only a few selected lines, and so the hyperfine interaction constants A (magnetic dipole) and B (electric

quadrupole) were known for relatively few levels. However, with the FT spectrometer, combining

high resolution and a wide spectral range, thousands of lines may be observed. Co I was investigated

[5] in the first use of high resolution FT spectrometry for comprehensive measurements of hfs over a wide spectral range, 3.8 jum to 180 nm. Computer fits of line profiles of over 1000 Co I transitions

yielded A factors for 297 energy levels with an uncertainty of between 0.2 and 3 %. For 208 of

these A factors no previous measurements are known. Approximate values of the B factors were

also found. Currently, studies of hfs in Co II and V II are also underway at IC.

160 ICAMDATA 97 Proceedings
1.3 The Measurement of Branching Ratios and Oscillator Strengths

The FT spectrometer is an ideal instrument for measuring accurate branching ratios because of

its broad spectral range and smoothly varying response. Branching ratios can be reliably obtained

for lines widely differing in wavelength. The limit in accuracy is determined by the uncertainty in

the calibration of the VUV radiometric standard lamp, and we estimate the limit in uncertainty in

relative intensities for strong lines to be about 4%. Measurements of Ti II branching ratios have

been made and have yielded oscillator strengths when combined either with experimental lifetime

measurements where these exist, or with calculated lifetimes. More branching ratio measurements

will be made in the future depending on current interests in the astronomical community.

1.4 Doubly Ionized Spectra

The defects in the database for neutral and singly ionized species apply even more strongly for the

third spectra. The accuracy of the current wavelength data is about 10 mA whereas wavelengths

are now needed to an accuracy of 1 part in 107

- or 0.2 mA at 2000 A. Two recent advances

in laboratory techniques now make it possible to obtain vast improvements in wavelength and

oscillator strength measurements of third spectra:

i The extension of the wavelength range of the FT spectrometer into the VUV region (down

to about 140 nm) with the development of a MgF2 beamsplitter at IC [8].

ii The development of a light source, a dc Penning discharge, that is compatible with the FT

spectrometer and that excites third spectra and lines from high-lying levels of second spectra

that cannot be produced in dc hollow cathode discharges. These have traditionally been

excited using pulsed hollow cathode lamps and sliding sparks, but the poor "shot-to-shot"

reproducibility of these sources makes them unsuitable for use with an FT spectrometer. The

Penning discharge source used was originally developed as a VUV radiometric standard by

Heise et al. [9]

.

Preliminary measurements were made at IC using this source, and results in the region 150-

220 nm using iron cathodes have yielded Fe II and Fe III spectra with signal-to-noise ratios (SNRs)

of several hundred for the stronger Fe III lines. The improvement in wavelength accuracy is at least an order of magnitude over the existing data. Ni III will also be recorded. Analyses of these spectra

should yield dramatic improvements in accuracy of energy levels and wavelengths, as well as many

new energy levels. The spectra will be intensity calibrated so that branching ratio measurements

can be obtained, and these may be combined with either theoretical or experimental lifetimes to give oscillator strengths. In the future, other transition group elements will also be measured.

2 Molecular Spectroscopy

FT spectrometers are also used to record absorption spectra of species important in studies of the

earth's atmosphere and other planetary atmospheres. Recent projects include:

2.1 Measurements of UV Absorption Cross Sections of S02

In order to avoid underestimating absorption cross sections, the sharpest features in the absorption spectrum need to be fully resolved. With support from ESA, the absorption spectrum of

SO2 was measured at high resolution using the IC FT spectrometer between 280-330 nm. These

3.1 Atomic Structure and Spectroscopy 161
measurements are of direct application to pollution measurements by downward-looking satellites

such as GOME (Global Ozone Monitoring Experiment) and SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) . Work is also in progress, in collaboration

with the Harvard-Smithsonian CfA and Wellesley College, USA, on measurements of the far UV

(190-220 nm) bands of SO2. The resulting accurate absorption cross sections will enable planetary

astronomers to reliably interpret SO2 in HST spectra of the atmosphere of Io and Venus.

2.2 Measurements of VUV Absorption Cross Sections of 02 and NO

For accurate modeling of the penetration of solar radiation into the upper atmosphere in the wavelength region 220-175 nm, computations involving O2 and minor species, notably NO, must be

carried out on a line-to-line basis. This requires both accurate wavenumbers and high resolution in

order to obtain true line profiles and absolute cross sections. Good SNRs for absorption measure- ments require a background continuum of high photon flux, and in the VUV the best such source

is synchrotron radiation. For this purpose, the IC VUV FT spectrometer was taken to the Photon

Factory (KEK) in Japan, and spectra of O2 and NO were recorded from 195-160 nm at resolution

matched to the Doppler widths of about 0.12 cm-1. Analysis of these spectra is in progress.

2.3 Precise Line Parameter Measurements in the Visible A Band Spectrum of O2

The oxygen A band shows a weak absorption in a relatively empty portion of the atmospheric

spectrum and is well suited for atmospheric remote sensing. Accurate O2 data is crucially important

for remote sensing of cloud-top height and coverage for satellite retrieval of atmospheric ozone, which is utilized by the GOME and the SCIAMACHY. They are also needed for the measurement

of middle atmosphere ozone from O2 A band airglow emission measurements proposed for the High

Resolution Doppler Instrument.

The spectrum of the oxygen A band, b

l Y,+ (v = 0) 4— ^ 3 £~ (v = 0), has recently been

measured and analysed in order to improve the currently available data on this band. The measurements were carried out at the Rutherford Appleton Laboratory (UK) using a high-resolution

Bruker FT spectrometer, together with a long pathlength multireflection absorption cell. Spectra were recorded at two different temperatures, various O2 pressures, and absorption pathlengths in

order to retrieve information on temperature and pressure dependent effects. Spectra recorded

using the FT spectrometer at the NSO were also included in the analysis. Precise line intensities

with an accuracy of approximately 0.3% and pressure-broadening coefficients (accuracy approx.

2-3 %) were retrieved including their temperature dependence. This data enabled us to determine the A band transition moment and the Einstein transition probability with standard errors of approximately 0.1 %. The spectra were of sufficient quality that the line intensities, broadening

coefficients, and the transition probability for the corresponding band in the isotopomer 16 0

18 0

could be determined.

Acknowledgements

The work on doubly ionized spectra was supported in part by the Smithsonian Astrophysical

Observatory IR&D Grant, and by NASA grant NAG5-4348 to Harvard University. JCP and PLS

thank D. S. Leckrone and W. Parkinson for their support, and R. Kling, W. Mende and M. Kock

for their assistance. PPARC of the UK provides financial support for much of the laboratory

astrophysics program at IC. RS and RCML thank J. Ballard for making the Molecular Spectroscopy

Facility at RAL available on several occasions. The scientific support by D. Newnham and the

162 ICAMDATA 97 Proceedings
technical support by M. Page and P. O'Brien is most gratefully acknowledged. RS and RCML also

thank J. Brault for his help in making the observations at the NSO. We also apreciate the financial

support of the oxygen project by NERC of the UK.

References

[1] G. Nave, S. Johansson, R. C. M. Learner, A. P. Thome, and J. W. Brault, ApJS 94, 221

(1994)

[2] U. Litzen, J. W. Brault, and A. P. Thome, Physica Scripta 47, 628 (1993)

[3] J. C. Pickering and A. P. Thome, ApJS 107, 761 (1996)

[4] J. C. Pickering, A. J. J. Raassen, P. H. M. Uylings, and S. Johansson, submitted ApJ (1997)

[5] J. C. Pickering, ApJS 107, 811 (1996)

[6] J. C. Pickering, Physica Scripta, in press (1997)

[7] A. J. J. Raassen, J. C. Pickering, and P. H. M. Uylings, submitted Astron. & Astrophys. (1997)

[8] A. P. Thome, Physica Scripta T65, 31 (1996)

[9] C. Heise, J. Hollandt, R. Kling, M. Kock, and M. Kiihne, Applied Optics 33, 5111 (1994)

3.1 Atomic Structure and Spectroscopy 163
Calculations of Oscillator Strengths for Singly Ionized

Iron Group Elements by Means of the

Orthogonal Operator Approach

A. J. J. Raassen and P. H. M. Uylings

Van der Waals-Zeeman Instituut, Universiteit van Amsterdam,

Valckenierstraat 65-67, 1018 XE Amsterdam, The Netherlands

1 Introduction

The relatively high abundances of iron group elements in stellar objects stimulates interest in these

elements. The need for accurate laboratory data is further increased due to the launch of high

dispersive space laboratories such as the Goddard High Resolution Spectrograph on board the

Hubble Space Telescope [1]. Being an odd-Z number element cobalt is far less abundant than the even-Z iron group elements,

Cr, Fe and Ni. However, Co II lines appear up to OB-type stars and are observed in absorption in

the interstellar medium (ISM). This requires accurate transition probabilities (oscillator strengths)

for transitions from the low lying levels in the (3d8 + 3d7 4s) system, which is responsible for the

absorption lines. State of the art experimental values from radiative lifetimes and branching fractions are accurate, but restricted to a limited number of transitions [2]. Advanced computer codes exist to calculate energy level values and wave functions ab initio. These codes allow the introduction of very many interacting configurations. Ab-initio calculations are powerful in relatively simple systems with one term outside the closed shell only. In that

case the system is dominated by electrostatic interactions, mixing levels of different configurations

having the same term names.

In iron group and other transition group elements, in which we deal with several d-electrons the

systems show many terms of different multiplicity and total angular orbital moment (L) within a

relatively small energy range. Including more and more correlation is not the point in calculations

of transition elements. These systems are dominated by magnetic interactions, of which the SpinOrbit interaction is strongest. These magnetic interactions are responsible for the mixing of levels with the same total angular momentum J, but with different multiplicity (2S+ 1) or different orbital

angular momentum (L). This effect strongly affects transition probabilities or oscillator strengths

and is responsible for the appearance of intercombination lines. Therefore, for the iron group

elements, it is far more important to describe well the magnetic mixing that appears from the

spacing between levels of the same J- value and the non-diagonal magnetic matrix element between

them, than to include more configurations.

The orthogonal operator approach, developed over the last years [3], provides the possibility to describe spacings between levels far more accurate by than other computational methods. The or- thogonal operator approach is a semi-empirical method, in which the eigenvalues of the Hamiltonian

are fitted to experimental energy values by adjusting the electrostatic and magnetic interactions of

the Hamiltonian. The method is basically founded on the Slater-Condon Theory. However, their

interactions, as used by the Cowan method, are orthogonalized in our method. This stabilizes the

164 ICAMDATA 97 Proceedings
fitting, makes the operators as independent as possible and offers the possibility of adding higher

order electrostatic and magnetic effects; thus far, these interactions had to be left out as they cor- rupted the least squares fitting procedure. The extension of the Hamiltonian results in a far smaller

average deviation. This implies a better description of the level structure, i.e. the spacings between

the levels, resulting in optimal eigenvector compositions. These intermediate eigenvectors are used

to sandwich the pure LS-transition probabilities. Afterwards these quantities are multiplied by the

electric dipole transition integrals. The latter (see Table 1) are obtained by means of the MCDF

code of Parpia et al. [4] and corrected for core-polarization.

2 Results

As input for the fitting procedure, level values obtained by Pickering et al. [5] were used. The levels included covered (3d8 + 3d74s + 3d6 4s2 + 3d74d + 3d7 5s + 3d7 5d + 3d7 6s) for the even system and

(3d7 4p + 3d6 4s4p + 3d54s2 4p + 3d7 5p + 3d74f) for the odd system. For studying the resonance

transitions in the (3d8 + 3d74s) - 3d74p transition array only the three lowest configurations in

both systems are relevant. In the even system the mean deviation, the average deviation between

the calculated eigenvalues and the experimental energy values, is 39 cm-1

, mainly due to some

larger deviations in the 4d- and 5d configuration. For most of the levels in the the lowest even

configurations the deviation is only a few cm-1

. In the odd system the mean deviation is 19

cm-1. Using the level values and eigenvector compositions of the two lowest even and the lowest

odd configuration results in a large number of oscillator strengths and wavelengths, which will be

published elsewhere [6]. Here we restrict ourselves to giving the oscillator strengths for lines from

the lowest even multiplets recently measured by Mullman et al. [2] and kindly provided to us by

Lawler, present at the ICAMDATA conference. In Table 2 our values are given together with the

experimental values of Mullman et al. and values from the Kurucz database [7]. Our results agree

very well with those of Mullman et al., solving some large discrepancies between Mullman and

Kurucz data. These discrepancies not only concern weak intercombination lines but also the strong resonance transitions between the lowest even term 3d8 3 F levels and 3d7

( 4 F)4p 3 F and 3 G levels (see lines at 2027.040 Aand 2025.760 A). For sixteen of the twenty-eight lines, given by Mullman

et al. [2], our values are within Mullmans error bars, and nineteen are within 10%. Only a few

weaker lines with log(gf) values around -2.0 show larger deviations.

Acknowledgements

It is a pleasure to thank Dr J. E. Lawler for sharing his results with us in advance of the publication.

Table 1: Values for the electric dipole transition integrals in Co II calculated by means of MCDF

including core polarization

3d8 3d7 4s 3d6 4s2 3d7 4d 3d7 5s 3d7 5d 3d7 6s

3d7 4p

3d64s4p

3d5 4s2 4p

3d7 5p

3d74f

0.22 0.03 - 4.88 -6.41 -6.00 4.89

0.19 - - -5.56 - 7.32

.79 -2.65 - -3.20 2.13 -0.79 0.57

0.65 -2.44

0.55

3.1 Atomic Structure and Spectroscopy 165
Table 2: Comparison between theory and experiment" of log(gf)-values for the (3d8 +3d74s) —>• 3d74p transitions involving the lowest even multiplets.

A(A) experiment" present Kurucz'' TJ

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3.0 1 ATAO OO* 10708.33* O I 4 TP \ 3 TP 2|3F)°F 4.0 49697.68* 1 P or en Ana 2559.405 A A 1 -0.21 n 1 t -0.17 A 1 T 0.17 A A

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3.0 50381.72* 1 3 F 1 H A C A £2 1 A 2546.160 1 G 1 -l.bl 1 a a -1.64 1 a 1 -1.61 A A

2.0

i i /jri AO* 11651.28* 1 I 1 TV\ A A

2.0 50914.32* 1 If

OCOO £ 1 a ZOZO.DlO A A£ 0.0b C\ 1 n

0.10 A OA O.o2 A A

4.0 AO 1 A 0£?* 9812.86* O l4 TP\ 3 TP A A4.0 49348.30* 1 3F rG

2524.974 A AZ? -0.06 A AAO 0.003 A aa r 0.005 A A2.0 11001 o * 11321.86* o 1 4 "n \ 3 n 2|3F)°F 2.0 50914.32* 1

i3t-i or 1 a ooo 25iy.82o A 1 /I -0.14 A 1 1 -0.11 A T£ -0.7b O A

o.O 1 ATAO OO* 10708.33* o l4 tp\ 3tp Z\^r )°r O A3.0 50381.72* 1

l3"T?

1 - X

1 2506.464 A AC 0.05 A A/?A 0.062 A A T

-0.47 A A

4.0 A O 1 A O/?* 9812. 8b* o 1 4 tp\ 3tp A A4.0 49697.68* 1

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3F i3n

X? 248b.441 -0.54 A ri -0.51 n a o -0.48 o n 3.0 1 ATAO O O* 10708.oo* A l4 TP\ 3 T7* 2| 3 F) °F A A

2.0 50914.32* 1

A3F

a /i a a 1 nn n a o -0.4z n on -0.39 n aa -O.bb a n 4.0 AO 1 A 0£J * 9812.8b* A l4 TP\ 3t_P 2|§F)°F O A

O.O 50381.72* 1 3F,

L 3 TP

i°.b no yic 1 on 224D.12y -0.35 n on -0.Z9 n c 1 -0.51 a n

4.0 /1AAO AA* 4028. yy

A l4 TP\ 5 TP 2| 3 F)°F C A

5.0 48556.05* 1 If, 1 G

OOOO ATO 2262.072 1 AO -1.08 1 A£? -1.06 1 OA -1.89 o n

3.0 A C CC\ TA* 4560.79* o 1 4 tp\ 5tp 2I3I1 /I A4.0 49348.30* 1 If; °G

OO 1 A TAO 2214.793 1 AO -1.02 1 AO -1.03 A AT -0.97 O A

3.0 A ET O A TA* 4560.79* 0 1 4 tp'\ 5tp 2 j^I"

) J F

A A

4.0 49697.68* 1 If 3t^

| h OO 11 A OO 2211.428 1 O 1 -1.21 1 OO -1.22 1 o o -1.38 r a

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OOAA /i A 1 2200.421 1 A C -1.45 -1.45 1 OA -1.39 A A

2.0 4950.06* 0 1 4 t*i

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3.0 50381.72* 1 If;

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4.0 /IAAO AA* 4028.99* 0 1 4 tp ^ 5 tp 2I3P )°F >1 A4.0 49697.68* 1

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3tti

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1 O 1 OT AO A 2187.039 A AO -2.03 1 A

1

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1.0

f Af\ A r~rr\ * 5204.70* O 1 4 TP '\ 5 TP 2|3F) d F

O A

2.0 50914.32* 1 P',

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2065.542 -1.07 -1.11 -0.85 3.0 950.32* II2F) 4.0 49348.30* 1 p| 3 G

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2027.040 -0.57 -0.57 -0.29 2.0 1597.20* 1||F) 2.0 50914.32* 1 P:

3 F

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3 F

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2000.793 -2.15 -1.92 -1.68 3.0 950.32* 1||F) 2.0 50914.32* 1 P,3 F

a Mullman et al. [2]

6 Kurucz [7]

References

[1] D. S. Leckrone, S. Johansson, G. M. Wahlgren, and S. J. Adelman, Phys. Scr. T47, 149 (1993)

[2] K. L. Mullman, J. C. Cooper, and J. E. Lawler, Ap.J (accepted)

[3] A. J. J. Raassen and P. H. M. Uylings, Phys. Scr. T65, 84 (1996)

[4] F. A. Parpia, C. Froese-Fischer, and I. P. Grant, Comput. Phys. Commun. 94, 249 (1996)

[5] J. C. Pickering, A. J. J. Raassen, P. H. M. Uylings, and S. Johansson, Ap.J., to be published

[6] A. J. J. Raassen, J. C. Pickering, and P. H. M. Uylings, AhA suppl. series, to be published

[7] R. L. Kurucz, Phys. Scr. T47, 110 (1993)

URL address: http://cfa-www.harvard.edu. /amp/data/stats/kurucz.html

166 ICAMDATA 97 Proceedings
Autoionizing Rates for Excited States of

Many-Electron Ions

U.I. Safronova and W.R. Johnson

Department of Physics, University of Notre Dame, Notre Dame, IN 46556

1 Introduction

The most important difference between autoionization states and other excited states is an additional broadening of levels caused by the decay of these states (e.g. 2ln(! => Iskl"). One can

express the autoionizing widths of a level as the square of the decay amplitude:

Here k is the momentum of the ejected electron in the continuum state (aohlLS), and aLS describes

the autoionizing state. When a nonrelativistic basis is used, relativistic corrections must be taken

into account perturbatively. A nonrelativistic basis was used for calculations of autoionization

rates in the MZ code [l]-[2], in the model-potential method (superstructure code) [3], and in

the multiconfiguration Hartree-Fock method (Cowan code [4]). The purpose of this paper is to obtain simple formulas for autoionization rates for any atomic

system by averaging over (LSJ) . These calculations will be carried out using screened hydrogenic wave functions. The purpose of these calculations is to provide accurate, but easily used, atomic

data.

2 Results and Discussion

Autoionization changes the state of two atomic electrons which initially can belong to either two

different groups or to the same group of equivalent electrons. One of the electrons makes a transition

to the continuous spectrum, and the other changes its state in the atom. Therefore, to calculate

the probability of an autoionizing decay in a general multi-electron ion, it is sufficient to study the

change of state in two systems: (nih)Pl (n2 h)P2 {n^hY3 and (ni/i)Pl (n2Z 2 ) P2 . We must study two

types of transitions:

(1)

aokl where

(nrhnn^YHnshr3 => {n.hY^i^hY^^hY^kt

{nihY'{n2 l2 )^ (n1

/ 1 r-2 (n2 / 2 r+1 A;£.

For LS averaged autoionization decay probabilities, one obtains in each case:

(3)

[(n1/ 1 )P 1 (n2 /2 ) P2 W3 ) P3 =* (ni/i)Pl - 1 (n2 /2 ) P2 - 1 (n3

/3 )P3+1 H = (4)

3.1 Atomic Structure and Spectroscopy 167
and

?N [(n^r^r => (nihri -2 (n2 l2 r

2+1 ke\ = (5)

ipi(pi - 1) -

j^J

A(nilin1 h',n2hkt) ,

where TVj = 2(2/j + 1) and where A{riilin2 l 2 ; n3 l 3 k£) is the two-electron decay probability.

A(nilin2h;n3kkl4) (6)

y(2Z3 +

l)(2/4 + 1) E (2/+l)P^ni/in2/2;n3f3 ^4) +

(2/ + l) ^2(nifin2f2;fc/4n3Z3)

A(ni/ini/i;n3 i 3 «4) = ^ *

1| + l)(2/4 + 1) E

2 Pi{nihn2 l2 \nzhkh) (7)

L(2/ + l)

/J I3 \ ^Pi{n\hnih\n^hkU)Pv {nilinili\kUn2h)

Here can be described as a product of a radial integral and 3j-Wigner coefficients:

Pl (n1 hn1lv,n3l3 kh) = Rl (n1 l1 n^^ ^

4 lQ

) K2 £ O (8)

Results of our calculations of A(nilin2 l2 ; n^kU) and A{nil\riil2 ; n^kh) are given in Tables

1 and 2 for mh, n2 l 2 with 7 > m > 1, (m - 1) > h > 0, 7 > n2 > 1, (n2 - 1) > h > 0. The

value of 723 was chosen such that J > 0 and (7T3 — 1) > I3 > 0. The value of I4 was

V

n3 n l n2 defined by the triangle rule for the 3j-Wigner coefficient in Eq. (9). The value of k was given by

k = yz^^J^z — — ^r, where Z is the nuclear charge and a is a screening constant.

In total, 8116 kinds of A{n\lin2 l 2 ; nzhkU) and A(nil\n\l2 \ 713/3/^4) were calculated. We have

selected the results with the largest values of A for illustration.

Acknowledgements

The work was supported by Grant No. B336454 from the Lawrence Livermore National Laboratory.

References

[1] L. A. Vainshtein and U. I. Safronova, At Data Nucl. Data Tables 21, 49 (1978); ibid. 25, 311

(1980)

[2] U. I. Safronova, Physica Scripta T26, 59 (1989)

[3] F. Bely-Dubau, A. N. Gabriel and S. Volonte, Mon. Not. R. Astron. Soc. 186, 405 (1979),

ibid. 189, 801 (1979)

[4] R. D. Cowan, The Theory of Atomic Structure and Spectra (Berkeley, 1981)

168 ICAMDATA 97 Proceedings
Table 1: Autoionizing rates A{n\l\n2l2\ n^hkU) in s as function of Z and a

Z = 26

cr = 0

Z = 26

a = 1

16

1 Z= 10

a = 1 Z = 6

£7 = 1 a

2s2s

2s2p

2p2p

2p2p

2s3s

2s3p

2p3s

2p3p

2sAs

3s3s

3p3p

3p3d

3d3d

3s3s

3s 3p

3s3d

3p3d

3p3d

3d3d

3sAp

3pAs

3pAp

3pAd

3dAp

3dAd

3dAd

3dAf

3p5s

3pbp

3p5d

3d5p

3dhd

3dbf

3p6p

3p6d

3dQd

3d6f

3plp

3dld

ApAp

ApAd

AdAd

Adhd

lsks

lskp

lsks

Iskd

lsks

lskp

lskp

lskd

lsks

lsks

2pkp

2pkd

2pkf

2pkp

2pks

2pkf

2pks

2pkg

2pkp

2pks

2pks

2pkp

2pkd

2pkd

2pkp

2pkf

2pkg

2pks

2pkp

2pkd

2pkd

2pkf

2pkg

2pkp

2pkd

2pkf

2pkg

2pkp

2pkf

2pkp

2pkd

2pkf

2pkf

2.057E+14

6.088E+13

1.039E+13

1.245E+14

2.604E+13

1.736E+13

1.252E+13

2.381E+13

1.050E+13

1.284E+13

2.805E+14

1.576E+14

4.147E+14

3.169E+13

8.273E+13

1.811E+13

1.839E+13

1.138E+13

3.333E+13

1.794E+13

3.325E+13

7.195E+13

5.530E+13

4.024E+13

1.042E+13

9.831E+13

4.169E+13

1.665E+13

3.318E+13

2.643E+13

1.731E+13

4.263E+13

2.425E+13

1.828E+13

1.479E+13

2.276E+13

1.450E+13

1.120E+13

L369E+13

2.440E+13

1.351E+13

2.875E+13

1.117E+13

2.004E+14

5.886E+13

9.544E+12

1.160E+14

2.528E+13

1.667E+13

1.220E+13

2.208E+13

1.018E+13

1.245E+13

2.776E+14

1.565E+14

4.057E+14

3.106E+13

8.207E+13

1.823E+13

1.791E+13

1.130E+13

3.251E+13

1.768E+13

3.261E+13

7.028E+13

5.411E+13

4.021E+13

9.845E+12

9.423E+13

3.854E+13

1.625E+13

3.225E+13

2.570E+13

1.742E+13

4.067E+13

2.221E+13

1.772E+13

1.433E+13

2.168E+13

1.323E+13

1.084E+13

1.303E+13

2.366E+13

1.332E+13

2.722E+13

1.054E+13

968E+14

753E+13

014E+12

104E+14

477E+13

621E+13

199E+13

097E+13

964E+12

218E+13

2.757E+14

1.558E+14

3.997E+14

3.063E+13

8.162E+13

1.831E+13

1.758E+13

1.125E+13

3.196E+13

1.750E+13

3.216E+13

6.915E+13

5.330E+13

4.015E+13

9.470E+12

9.150E+13

3.653E+13

1.598E+13

3.161E+13

2.520E+13

1.746E+13

3.934E+13

2.091E+13

1.734E+13

1.402E+13

2.094E+13

1.242E+13

1.059E+13

1.258E+13

2.316E+13

1.316E+13

2.619E+13

1.012E+13

1.908E+14

5.533E+13

8.184E+12

1.016E+14

2.390E+13

1.545E+13

1.162E+13

1.918E+13

9.599E+12

1.172E+13

2.723E+14

1.545E+14

3.895E+14

2.988E+13

8.084E+13

1.846E+13

1.704E+13

1.115E+13

3.104E+13

1.719E+13

3.141E+13

6.723E+13

5.190E+13

3.994E+13

8.863E+12

8.692E+13

3.336E+13

1.552E+13

3.054E+13

2.434E+13

1.746E+13

3.711E+13

1.887E+13

1.669E+13

1.349E+13

1.969E+13

1.115E+13

1.018E+13

1.181E+13

2.231E+13

1.288E+13

2.449E+13

9.419E+12

1.785E+14

5.098E+13

6.716E+12

8.548E+13

2.212E+13

1.396E+13

1.084E+13

1.591E+13

8.852E+12

1.078E+13

2.654E+14

1.517E+14

3.688E+14

2.828E+13

7.922E+13

1.878E+13

1.595E+13

1.090E+13

2.918E+13

1.655E+13

2.985E+13

6.328E+13

4.896E+13

3.919E+13

7.716E+12

7.781E+13

2.765E+13

1.456E+13

2.835E+13

2.256E+13

1.719E+13

3.264E+13

1.524E+13

1.538E+13

1.239E+13

1.718E+13

8.892E+12

9.340E+12

1.025E+13

2.057E+13

1.218E+13

2.116E+13

8.040E+12

1.364E+14

3.691E+13

3.316E+12

4.511E+13

1.613E+13

9.349E+12

7.853E+12

7.845E+12

6.346E+12

7.601E+12

2.394E+14

1.402E+14

2.981E+14

2.212E+13

7.306E+13

2.019E+13

1.239E+13

9.623E+12

2.303E+13

1.411E+13

2.418E+13

4.941E+13

3.810E+13

3.367E+13

4.557E+12

4.963E+13

1.390E+13

1.114E+13

2.081E+13

1.627E+13

1.422E+13

1.909E+13

6.866E+12

1.092E+13

8.578E+12

9.609E+12

3.793E+12

6.502E+12

5.587E+12

1.454E+13

8.990E+12

1.153E+13

4.119E+12

3.1 Atomic Structure and Spectroscopy 169
Table 2: Autoionizing rates AlnJ^h', n^kl^) in s

1 as function of Z and <r Z = 26

C7 = 0

Z = 26

a = 1 Z = 16

(7=1

Z = 10

tr = 1 Z = 6

a = 1 Z = 6(7 = 2 4/5/ 3dkg 1 647E+14 1 626E+14 1 612E+14 1 587E+14 1 .534E+14 1 .338E+14

Asbd 3dks 1 572E+13 1 565E+13 1 560E+13 1 551E+13 1 .533E+13 1 .464E+13

Apbd 3dkp 2 090E+13 2 081E+13 2 075E+13 2 064E+13 2 .040E+13 1 .947E+13

4d5s 3dks 3 719E+13 3 697E+13 3 682E+13 3 656E+13 3 .600E+13 3 .385E+13

4d5p 3dkp 4 649E+13 4 619E+13 4 599E+13 4 564E+13 4 .491E+13 4 .205E+13

4dbd 3dkd 8 276E+13 8 211E+13 8 166E+13 8 090E+13 7 .928E+13 7 .309E+13

4^5/ 3dkf 8 039E+13 7 983E+13 7 944E+13 7 878E+13 7 .735E+13 7 .172E+13

4d5g 3dkg 1 309E+13 1 291E+13 1 279E+13 1 259E+13 1 .217E+13 1 .076E+13

4/5p 3dks 1 263E+13 1 232E+13 1 212E+13 1 178E+13 1 .108E+13 8 .755E+12

4/5p 3dkd 7 060E+12 7 362E+12 7 569E+12 7 922E+12 8 .659E+12 1 .133E+13

4fbd 3dkp 1 789E+13 1 752E+13 . 1 728E+13 1 686E+13 1 .602E+13 1 .312E+13

4/5d 3dkf 6 984E+13 6 990E+13 6 992E+13 6 993E+13 6 .987E+13 6 .858E+13

4/5/ 3dkd 1 575E+13 1 548E+13 1 529E+13 1 497E+13 1 .432E+13 1 .203E+13

4/5<? 3dkh 9 714E+13 9 476E+13 9 317E+13 9 049E+13 8 .509E+13 6 .713E+13

4d6s 3dks 2 084E+13 2 057E+13 2 037E+13 2 005E+13 1 .935E+13 1 .669E+13

4d6p 3dkp 2 589E+13 2 552E+13 2 527E+13 2 483E+13 2 .391E+13 2 .038E+13

4d6d 3dkd 4 157E+13 4 085E+13 4 035E+13 3 951E+13 3 .773E+13 3 .111E+13

4d6/ 3dkf 4 038E+13 3 970E+13 3 923E+13 3 842E+13 3 .671E+13 3 .020E+13

4/6d 3dkp 1 066E+13 1 017E+13 9 847E+12 9 316E+12 8 .292E+12 5 .290E+12

4f6d 3dkf 3 347E+13 3 368E+13 3 379E+13 3 391E+13 3 .391E+13 3 .146E+13

4/6/ 3dkg 7 623E+13 7 435E+13 7 305E+13 7 080E+13 6 .607E+13 4 889E+13

4/65 3dkh 5 976E+13 5 693E+13 5 505E+13 5 197E+13 4 .600E+13 2 .856E+13

4/6/i 3dkk 1 726E+13 1 595E+13 1 512E+13 1 380E+13 1 142E+13 5 689E+12

4d7s 3dks 1 288E+13 1 265E+13 1 250E+13 1 224E+13 1 168E+13 9 556E+12

4d7p 3dkp 1 594E+13 1 565E+13 1 545E+13 1 510E+13 1 436E+13 1 156E+13

4d7d 3dkd 2 443E+13 2 388E+13 2 351E+13 2 286E+13 2 152E+13 1 660E+13

4^7/ 3dkf 2 368E+13 2 314E+13 2 278E+13 2 215E+13 2 082E+13 1 591E+13

4f7d 3dkf 1 914E+13 1 936E+13 1 947E+13 1 959E+13 1 958E+13 1 733E+13

4/7/ 3dkg 4 287E+13 4 162E+13 4 075E+13 3 922E+13 3 596E+13 2 430E+13

4/7<? 3dkh 3 744E+13 3 531E+13 3 390E+13 3 160E+13 2 718E+13 1 495E+13

4/7/i 3dkk 1 526E+13 1 390E+13 1 304E+13 1 169E+13 9 325E+12 4 040E+12

5d5rf 3dkd 2 636E+13 2 581E+13 2 543E+13 2 478E+13 2 342E+13 1 828E+13

5d5/ 3dkf 2 233E+13 2 212E+13 2 196E+13 2 166E+13 2 091E+13 1 717E+13

5/5/ 3dkg 4 754E+13 4 584E+13 4 468E+13 4 273E+13 3 876E+13 2 564E+13

5/5^ 3dkh 1 310E+13 1 246E+13 1 204E+13 1 135E+13 1 004E+13 6 215E+12

5dQd 3dkd 1 117E+13 1 087E+13 1 067E+13 1 033E+13 9 598E+12 6 887E+12

5d6f 3dkf 1 066E+13 1 049E+13 1 036E+13 1 012E+13 9 566E+12 7 094E+12

5/6d 3dkf 1 035E+13 1 029E+13 1 024E+13 1 010E+13 9 723E+12 7 484E+12

5/6/ Sdkg 1 1 onnu1

1 1 0 yuy.b+io 1 1

r7CCOT7l

1 1 Q /OZ-Cj+lo 1 r COXT11 1 O oozr!v+io y1 1 TW I 1 O 5/7/ 3dkg 1 109E+13 1 058E+13 1 024E+13 9 646E+12 8 439E+12 4 635E+12

5/7s 4fks 2 128E+13 2 122E+13 2 118E+13 2 112E+13 2 097E+13 2 041E+13

5/7p 4fkp 2 444E+13 2 437E+13 2 433E+13 2 425E+13 2 408E+13 2 341E+13

5/7d 4fkd 3 .005E+13 2 995E+13 2 989E+13 2 977E+13 2 953E+13 2 857E+13

5/7/ 4/fc/ 4 .241E+13 4 225E+13 4 214E+13 4 195E+13 4 154E+13 3 993E+13

170 ICAMDATA 97 Proceedings
Complete Atomic Data Base for Autoionizing Levels

of B-like ions with Z = 6 - 54

U. I. Safronova and A. S. Shlyaptseva

Department of Physics, University of Nevada, Reno

Reno, NV 89557

M. Cornille and J. Dubau

UPR 176 CNRS, DARC Observatoire de Paris

92195 Meudon Cedex , France

1 Introduction

In this paper, we calculate the autoionization decay of doubly excited ls2s2 2p2

, Is2s2p3

, andls2p4

states via channels ls2 2s2 l S; ls2 2s2p 1 P, 3 P; and ls2 2p23P, 1 D, l S of B-like ions for a broad range

of nuclear charge Z — 6 — 54. Recently, absolute energies of the autoionizing and non-autoionizing

(ground and singly excited) levels and the total autoionization rates have been calculated for Li-,

Be- and B-like ions with Z = 6 — 54 using the MZ method [1]. Not only the total autoionization

rates, but also the amplitudes and rates of autoionization decay via channels, so-called partial rates, are very important in atomic kinetic calculations, for the modeling of dielectronic satellite spectra

and, in particular, for polarization spectroscopy of astrophysical and laboratory high-temperature

plasmas.

2 Calculational Methods

In the present paper we use two different calculational methods, namely MZ (the perturbation theory method) and AUTOLSJ (SUPERSTRUCTURE including configuration interaction). Earlier, we compared non-relativistic and relativistic energies calculated by these two methods for 4 to 10

electron systems of Ar and Fe ions [2].

2.1 MZ Code

The perturbation theory method is the basis of the MZ code developed by Vainshtein and Safronova

[3, 4]. This method uses Z-expansions to calculate various atomic characteristics. The energy matrix

is constructed in the LS-coupling scheme, including non-relativistic and relativistic parts. The nonrelativistic part takes into account three or four terms of the Z-expansion. The relativistic part is constructed using Breit-Pauli operators. In the first step all these terms are calculated for diagonal

and nondiagonal elements. In the second step, the energy matrix is diagonalized. The energies

(eigen values) and the mixing coefficients (eigen vectors, C

J

) are obtained. In the third step these

mixing coefficients are used to obtain all the matrix elements in the intermediate coupling scheme.

In the intermediate coupling scheme the partial autoionization rate Aaut in decay channel i can be

expressed through amplitudes 7 [1] (in a.u.):

3.1 Atomic Structure and Spectroscopy 171
A?ut (QLSJ,Qi) = 2v/2tt £ C

J (QLS,QiLiSi) ^QiL^Qi^S,) x (1)

Q1Q2L1S1

x-y(QiLl Sl ,Q2 Ll S1 ) C

J

(Q2 Ll S1 ,QLS)

Here QLSJ are the quantum numbers characterizing the autoionizing level, Qi is relevant to the

channel z, C

J {QLS,Q\LySi) are eigenvectors mentioned above, and 1 a.u.=4. 134 x 10 16 s~K To

calculate the total autoionization rates we must sum up the partial rates Afut over all decay

channels.

2.2 AUTOLSJ Code

The AUTOLSJ package coordinates the calculation of energy levels, as well as radiative and autoionization rates. In the first step, the code determines non-relativistic wavefunctions by diagonalization of the non-relativistic hamiltonian on a set of chosen configurations. The single-electron

wavefunctions are calculated in "scaled" Thomas-Fermi-Dirac-Amaldi potentials which are different

for each angular momentum /. The scaling parameters are iterated to give the minimum energy of a term or of a group of terms. These potentials depend closely on the configurations. In our case two

complexes ls2s2 2pk + ls2pk+2 and Is2s2pk+lare considered. To derive the non-relativistic and

relativistic energies, the program diagonalizes the matrices relevant to the corresponding operators.

In the second step (part of the AUTOLSJ package developed by Dubau et al 1981 [5]) we use the

level mixing coefficients obtained by the energy matrix diagonalization to calculate the data.

3 Results

In Tables 1 and2 the results of our calculations of partial rates are presented for six decay channels,

namely ls2 2s2 l S ; ls2 2s2p l P, 3 P , and ls2 2p2 1 S,

3 P, l D, respectively. They are computed by

the MZ (a) and AUTOLSJ (b) codes. Also, for comparison we use the Cowan program [6] and the

data by Chen et al [7]. Thus, we compare the data (both partial and total autoionization rates)

from four different codes. The comparison is, in general, good. Nevertheless, some disagreements

appear due to levels with relatively weak autoionization rates (< 10 13 s -1

). Moreover, we study

the Z-dependences of partial rates for each complex of autoionizing levels with J = 1/2,3/2 and

5/2. In general, they show smooth trends. But the Z-dependences for levels with J = 3/2 of the

configuration Is2s2p3 (with a maximum value of eight levels in one complex) have a non-smooth

form with maxima and minima.

References

[1] U. I. Safronova and A. S. Shlyaptseva, Physica Scripta 54, 254 (1996)

[2] M. Cornille, J. Dubau, and U. I. Safronova, Physica Scripta 49, 69 (1994)

[3] V. L. Vainshtein and U. I. Safronova, Atomic Data Nuclear Data Tables 21, 44 (1978)

[4] V. L. Vainshtein and U. I. Safronova, Atomic Data Nuclear Data Tables 25, 311 (1980)

[5] J. Dubau and M. Loulergue, Physica Scripta 23, 136 (1981)

[6] R. D. Cowan, "The Theory of Atomic Spectra", University of California Press 1981

[7] M. H. Chen and B. Crasemann, Atomic Data Nuclear Data Tables 38, 381 (1988)

172 ICAMDATA 97 Proceedings
Table 1: Partial autoionization rates of B-like Fe decaying via the channels ls2 2s2 l S, ls2 2s2p

l P and ls2 2s2p 3 P, calculated by MZ (a) and AUTOLSJ (b) codes. Designations: 7" = ls2s2 2p2

, J = ls2p4

, K = 2p3

[4 S]2s[5 S]ls, T = 2p3

[4 S]2s[3 S]ls, K = 2p3

[2 P]2s[3 P]ls, Q = 2p3[ 2 P]2s[1 P]ls,

K = 2p3

[2

JD]2s[3 D]ls, Q = 2p3

[2 D]2s[l D]ls

ls2 2s2 1 S ls'2 2s2p l P U2 2s2p 3P

XjC VtJl i ct h Ct Ku u

1 T LI 1 10 oU.U3rqi1 1119 L.L Li* 9 fi3 9 43 0 Q3 9it.OO 33

01til 1 10 0 ^90 0U. 71t XyuQO 0U. 71/ lo^ 0u.uuy fiOQ 1 4 fi 1Lit.O 0 3 AT l/Z 1 /9 fl 1 4 8O.ZXO 913 8 99 fi 73 9 ^ 0 90

OJ 1l/Z/9 U.UU l V 0U.UUZu 009^ 0u. 110 x xu 0u. 1xuo03 0u.x1 8Qoy 0U.U1X 041 7i

1l/Z/9 0 0499 o 0041 0 0^4Q 0U.UU0^1LO3 0 1 87 0u. 1xuuRO

8OJT l/Z 0 39Q 0u.uuzu 009fi 0 439 0 3494 0u. 1xuyOQ 0u.uy0Q9Qiiv

1 1 K 1l/Z/9 0 nu 0 ^19 0u.^xuy 40Q 91 fi 91iiL. 7t

1 3 ft" L G_fY 1L/Z/9 u U.UUUZ 0 0009 0 0499 0u.uuzy 009Q 90 8 11 71 .u0

1 /9 n 0 0844 1 2^ 1X .UU 0fi1X 1 Q 2 1 4 0

1L TV1

1L/Z/9 nu 0 OQQfi 0 Q4Q fi 33 0U. 1XO81X 0u.iuy 40Q

180 1/2 0 0.2667 18.0 9.05 2.07 3.09

1 T LI o I

i. 4Lk. 1Lu^ O.L 3 119Lit O.3 771 t O.LI 3 17 9it , 44L±

t-L X1 .di* Q9

OTZl 03 /9 j

ii 0 0Q1 7 0U.UUIO 0fi48 0u.u0793 / zo 0u.uuo 0^8 1XtJ.U ^ fi 1 3 9

01 Oj3 10i* 1X*±. 4 X1 XX. 1 1 Ol31 8 19 fiu.ou8fi 9 OQ 1X .ou 80

OJ OjZ 3 10 U. 1U1 0u.uuoo 0038 0u.u071/ xyQ 0u.uuoy O^fiQ 0 031

9

u.uoxz 0 09^3

Oj3 10z ou.uuyo ooqs 0U.UUUiJy OOO^Q 0u.uu007Qt y 0u.uxou 01 3^ 0 99^1 0u. 1x Q1y x 7 7 / J 3 /9 0/ z 0U. 1lO871 0u.uuuz 0009 0U.X117X / 0u.xux 101 0 04fi3 0 0497

1 Oft" 3Oj/9z u 0 0038 1L.OO3^ 0 049Q fiu.ou3fi v.XJU

1X 1XxVK Oj3 10Z nu nu 0 41

U.'i XI 0 998 1 8 Q 1 8 fi

1 2/f 3/2 0 0447 4 40 0\J • 920 %J Z-i\J 13.8 19.06

13if 3/2 0 0.0017 3.41 0.0778 14.1 15.8

14K" 3/2 0 0.0019 10.6 11.3 10.5 7.74

15Q 3/2 0 0.0014 17.6 13.2 15.1 6.13

16T 3/2 0 0.0190 0.828 1.55 6.36 3.15

18Q 3/2 0 0.3050 17.6 12.5 1.43 3.42

2/ 5/2 2.29 1.660 1.24 0.955 14.1 12.0

3/ 5/2 16.1 12.82 8.71 7.30 3.70 3.19

6J 5/2 0.0082 0.00228 0.0045 0.0176 0.285 0.247

7J 5/2 0.286 0.0040 0.115 0.117 0.0316 0.0322

9K 5/2 0 0 0.005 0.005 0.708 0.549

UK 5/2 0 0 0.095 0.095 21.7 21.3

12K 5/2 0 0 0.433 0.125 21.7 21.2

UK 5/2 0 0 1.19 1.06 19.6 17.1

UK 5/2 0 0 20.5 21.7 1.66 1.03

UK 7/2 0 0 0 0 22.3 23.4

3.1 Atomic Structure and Spectroscopy 173
Table 2: Partial autoionization rates of B-like Fe decaying via the channels ls2 2p2 1 S, 3P and

l D, calculated by MZ (a) and AUTOLSJ (b) codes. Designations: I = ls2s2 2p2

, 7 = ls2p4

, K = 2p3

[ 4 S]2s[5 S]ls, T = 2p3

[4 S]25 [3 S

r]l5, K = 2p3

[2 7>]2s[3 P]ls, Q = 2p3

[2 P]2s[1 P]ls, K =

2p3

[2

7J>]2s[3 7)]ls, Q = 2p3

[2

7J>]2s[

1 7>]ls

l52 2p2 l s ls2 2p l52 2p

Level J a b a b a b

17 1/2 1.38 0.934 8.52 9.15 0.146 0.145

27 1/2 1.01 0.588 8.76 12.1 0.093 0.080

47 1/2 12.6 7.07 1.57 1.80 1.51 1.22

5J 1/2 0.749 0.735 29.7 22.3 4.07 3.86

67 1/2 0.338 0.318 32.1 24.5 2.00 1.81

87 1/2 4.54 3.71 7.24 6.24 23.3 18.6

UK 1/2 0.071 0.051 0.228 2.19 0.088 0.068

13K 1/2 0.051 0.003 2.63 2.23 0.006 0.004

UK 1/2 0.218 0.166 9.09 7.76 0.272 0.214

17T 1/2 0.214 1.69 10.5 5.45 0.268 2.23

18Q 1/2 7.60 4.60 4.11 6.66 9.50 6.07

1/ 3/2 0.031 0.072 7.19 8.33 2.17 2.37

27 3/2 3.0-4 0.002 9.35 10.3 0.048 0.044

37 3/2 0.068 0.336 2.19 2.24 7.34 8.19

57 3/2 2.60 1.96 20.0 16.6 19.8 13.6

67 3/2 0.107 0.243 34.0 25.2 0.826 1.59

77 3/2 3.43 3.14 15.2 10.9 26.3 21.3

10K 3/2 0.234 0.067 4.56 3.10 0.829 0.118

UK 3/2 0.003 0.01 0.866 2.06 0.115 0.029

Y1K 3/2 0.455 0.778 5.18 9.63 6.54 3.27

137T 3/2 0.257 0.031 4.50 4.38 1.42 0.044

UK 3/2 1.86 0.025 7.33 4.19 8.09 6.50

15Q 3/2 0.227 0.029 3.28 4.10 1.90 5.80

16T 3/2 0.311 0.325 18.3 18.8 1.93 0.432

18Q 3/2 4.76 5.24 2.51 6.63 7.55 7.85

27 5/2 0.009 0.059 8.19 9.25 1.19 1.16

37 5/2 0.089 0.356 1.15 1.28 8.36 9.42

67 5/2 0.046 0.325 34.4 24.6 0.363 2.09

77 5/2 6.10 5.01 0.265 1.58 46.5 34.4

9K 5/2 0 0 0.091 0.072 0.002 0.001

UK 5/2 0 0 0.468 2.19 0.025 0.019

Y1K 5/2 0 0 0.225 9.05 1.24 1.86

137C 5/2 0 0 1.89 2.22 0.212 0.137

15Q 5/2 0 0 0.098 0.583 16.8 13.4

\\K 7/2 0 0 0 2.21 0 0

174 ICAMDATA 97 Proceedings
Inner-Shell Excitation Energies for C-, N-, O-,

and F-like Ions with Z == 6 - 54

U. I. Safronova and A. S. Shlyaptseva

Department of Physics, University of Nevada, Reno

Reno, NV 89557

1 Introduction

In this paper we continue to study the atomic characteristics for doubly-excited states. In our

previous paper [1] we developed a method for the calculation of energies for systems with three,

four and five electrons such as ls2sn 2pn (n + n'=2-4). This method was based on a perturbation

theory starting with nonrelativistic hydrogenic basis functions. Moreover, the diagram technique was used. We treated these systems as states with an empty core and three, four and five electrons

interacting with the nucleus and with each other. For such states only diagrams without loops give

contributions to the nonrelativistic part of the energy. Here we study ls2sn 2pn (n + n'=5, 6, 7, 8) states. Following the same approach, we must consider the states with an empty core and 6, 7, 8

and 9 electrons interacting with the nucleus and with each other. Obviously, it is more convenient

to use hole representation, which allows to consider these states as systems with 8 — n — n' holes

and a non-empty core with two closed shells. In this approach we can treat these systems as states with a ls2 2s2 2p6 core and 4, 3, 2 and 1 electrons interacting with the nucleus, the core and with

each other. To describe the interaction of electrons with the core we have to take into account also

diagrams with loops. For singly-excited states, these diagrams were studied in detail for systems

with one electron above the core in many papers by Johnson et al (see, for example, [2]), and with

two and three electrons above the core in papers [3, 4]. In these papers [2, 3, 4] relativistic basis

functions were used, and all angular reductions for diagram contributions were given using the

jj-coupling scheme. For two electrons above the core, the LS-coupling scheme was implemented in

the paper by Safronova et al [5] . The first study of doubly-excited states using perturbation theory

with including the first and second order diagram contributions (relevant to nonrelativistic energy) was presented in papers [6, 7].

2 Energies of ls2sn 2pn' States with n + n'=5, 6, 7, 8 in the Hole

Representation

The field formulation of perturbation theory allows to construct the function of the n-hole system

similar to the function of a n-electron system, replacing an operator of creation with an operator

of annihilation apk: %f=% £ Cl^n aPl ...a^o ' (1)

U- /3i .../?„ Here $o and Q relate to the core and an atomic system with quantum numbers L, S, M, Ms , respectively. Index /?,- describes a one-hole system with quantum numbers nilinnmsi, and ^

3.1 Atomic Structure and Spectroscopy 175
coefficients provide the antisymmetry in all indexes of the wave function <E>^ (for detail see [5]). Using this determination of a hole-function we can carry out all calculations of diagram contributions. The functions of doubly-excited states ls2sn 2pn'[LSJ] with n + n'=5, 6, 7, 8 are written as

follows

*? = h Eft cga^o, = h. Eft/?2 cgftOftflft^o,

(2)

$3 = k Eftftft Cft/32 /33 a/?i a/?2 aft3>0, = ?! Eftft^ft C^^^^Oft aftOftttft^o

The nZ quantum numbers for $f , <E>^, and $f should be equal to Is, ls2/, ls2/2/' and Is2l2l'2l"

accordingly. Briefly, we can represent our states as U2s2 2p6 -+ ls- 1 ^,

ls2s2 2p5 -> ls-^p- 1 ^, l52s2p6

->• ls-^s-^o,

ls2s2 2p4 ls-^p-2 ^, Is2s2p5 ^ ls-^s-^p-^o, ls2p6 -> Is^s"2 ^,

ls2s2 2p3 -> Is- 1 2p-3 $0 ,l52s2p4 -» ls-^s-^p"2 ^, ls2p3 -> ls- 1 2 S -2 2p- 1 $0

-

3 Results and Discussions

Tables 1,2,3 illustrate our results of calculations of the energies of N-, O- and F-like ions, respectively. The intermediate LS energies are shown only in the case of two identical terms belonging

to one complex ( the states with one parity and the same J but different QLS), for example, for

Is2s2pn with n=4, 5 ( 3 P terms for C-like ions; 2 P terms for N-like ions). The same inter-electron

interactions mix terms belonging to different configurations: ls2s2 2pn + ls2pn+2

( 3 P, l P terms for n= 4 and 2 S term for n= 5) and ls2 2s2 2pn + ls2 2pn+2 1 D, 3P terms for n= 4,

2 P term for n=

5 and l S term for n= 5). This mixing can be described by a first order perturbation theory diagram

for the correlation part of the energy [5] and can be calculated by any computer method. The next

part of the correlation energy can be obtained by using virtual configurations, both discrete and

continuous. The advantage of the MZ program is to take into account this part of the correlation

energy in the framework of second order perturbation theory. As a result, we believe that data

obtained by this method for 2-10 electron systems are more precise than other methods.

We conclude that the absolute energy data given in Tables 1-3 can be used for many applications, particuarly in electron and photon emission spectroscopy.

References

[1] U. I. Safronova and A. S. Shlyaptseva, Physica Scripta 54, 254 (1996)

[2] W. R. Johnson, M. Idrees, and J. Sapirstein, Phys. Rev. A 35, 3218 (1987)

[3] M. S. Safronova, W. R. Johnson, and U. I. Safronova, Phys. Rev. ,453, 4036 (1996)

[4] M. S. Safronova, W. R. Johnson, and U. I. Safronova, Phys. Rev. A 54, 2850 (1996)

[5] M. S. Safronova, U. I. Safronova, N. Nakamura, and S. Ohtani, Physica Scripta 53, 689 (1996)

[6] U. I. Safronova and V. N. Kharitonova, Optic and Spectroscopy 27, 550 (1969)

[7] U. I. Safronova, A. N. Ivanova, N. V. Rabinkina, and V. N. Kharitonova, Optic and Spectroscopy 28, 841 (1970)

176 ICAMDATA 97 Proceedings
Table 1: Absolute values of the energy (E in 104 cm l ) for N-like systems. Designations:

E=ls22s22p3

, F=ls2 2p5

, C=ls2 2s2pA, I=ls2s2 2p4, J=ls2p6, Q=2s2p5

[

1 P]ls, K=2s2p5

[3 P]ls

AT TCI LbJ ry Z = 1 o 12 Z = 14

ry z = 16ry -in Z = lory c\r\ Zj — ZU Z = 22 Z = 24 Z = 26

hi 4 c

^3/2

/i 1 1 1 4111 650 5778.113 7707 7737 /IOC 435 nno A OAO 9984.808 12523.56 15355 35 18482 17 21906 01

E

2 r> •^3/2 4106 1 0£? 136 5771.217 TTAA 7729 OAT 207 aatc oo£* 9975.336 1 A C 1 A A^? 12512.96 15343 73 18469 54 21892 12

E Ai/2 4106 137 5771.190 7729 AOT 087 OAT A AA A 9974.994 1 A PJT 1 A 1 A 12512.19 15342 26 18467 07 21888 39

E 2 Dn/2

a 1 oo 4103 307 5767 f+ f~h C\ 632 TTO /* 7724 794 A A/? A AO 9969.953 1 A ET A£? O O 12506.38 15335 66 18459 65 21880 12

E 2 D

^3/2

a 1 oo 4103 297 5767 577 TTA ^ 7724 /•AO 608 A A£? A A d A 9969.462 i nrrAC AO 12505.28 15333 52 18455 87 21873 95

C

4 H./2

A O O f* 4086 o oo 832 5746 795 7699 505 A A vl A AA O 9940.093 1 A A 71 O

12471.81 15296 22 18415 18 21828 46

C

4 o

-^3/2

A O O f* 4086 659 5746 424 7698 798 A AO O OCA 9938.859 1 A A

d

A TA 12469.79 15293 08 18410 50 21821 73

c

4 D

^5/2 4086 567 5746 230 7698 /ion 439 A AO O OCO 9938.258 1O/|/?0 07 12468.87 15291 76 18408 74 21819 55

(7

2 Un

Z/2

A f\ r7r7 4077 487 5735 064 7685 O 1 A 314 AAOO 007 9923.337 1 A A C A O /I 12452.34 15273 86 18389 68 21801 54

2 r-> ^5/2 4077 490 5735 062 7685 OOP" 295 O OO O C\f*f* 9923.266 1 A A r* O 1 r 12452.15 15273 43 18388 83 21799 87

c

2 c3 1/2 4071 480 5727 631 7676 A OO 482 O O 1 O 1 A rf 9913.147 1 O A A O OP* 12440.85 15261 09 18375 65 21786 14

c

2 TO Pl/2 4069 O O o 223 5725 t a r\ 140

<—j r> r-f c\ 7673 769 A A 1 A A A 1 9910.201 1 A A O T /? A 12437.62 15257 52 18371 62 21781 53

c

92 n

^3/2 4069 019 ^79-4 Do / 7672 873 O OO O P" ft A 9908.574 1 O >1 O A O T 12434.87 15253 13 18364 97 21771 88

2 D

^1/2 4046 439 5695 997 7638 127 o o/1 >"7 o /* a 9867.868 1 O O O O O *7 12388.37 15201 08 18307 71 21709 88

92 n

A/2 4046 170 5695 411 7637 OOo 003 O Ci f ooo 9865.900 1 a o o p* 1 r* 12385.15 15196 09 18300 32 21698 21

T

i

2 c* 3 1/2 3071 o TO 879 4335 644 5825 308 7535.612 A /I A O A1 9469.301 11627 34 1 4m a yo 16621 10

T

1 ~1/2 3074 837 4339 087 5829 303 7^40 389 Q47c

i 9QQ 11635 28 14021 71 16635 77

I 2p

^3/2 3075 046 4339 475 5829 901 7541.141 9476.049 11635 .73 14021 52 16634 63

I

4 -Pl/2 3082 650 4348 944 5841 .125 7554.032 9490.582 11651 98 14039 72 16655 21

I

4 -p3/2 3082 763 4349 172 5841 529 7554.678 9491.529 11653 27 14041 34 16657 11

I 4jP5/2 3083 028 4349 705 5842 .496 7556.308 9494.115 11657 .17 14046 97 16664 89

I

2 -°3/2 3076 258 4341 136 5832 .071 7543.975 9479.830 11640 .86 14028 50 16643 94

I ^5/2 3076 .328 4341 222 5832 .121 7543.869 9479.355 11639 .72 14026 31 16640 33

J $1/2 3018 .043 4268 472 5744 .511 7440.884 9360.351 11503 .91 13872 78 16468 02

Q

2 Pl/2 3039 .916 4296 820 5779 .363 7482.305 9408.425 11558 .72 13934 39 16536 46

Q

2P3/2 3040 .060 4297 113 5779 .906 7483.251 9409.990 11561 .20 13938 15 16541 .95 K 2 Pl/2 3046 .697 4304 596 5788 .186 7492.281 9419.742 11571 .68 13949 44 16554 .16 K 'PS/2 3046 .837 4304 .877 5788 .681 7493.072 9420.909 11573 .30 13951 57 16556 .91 K 4 Pl/2 3055 .555 4315 .850 5801 .737 7507.982 9437.387 11591 .00 13970 .09 16575 .81 K 4p

^3/2 3055 .724 4316 .188 5802.348 7509.007 9439.014 11593.47 13973 .71 16580.94

K 4p

5/2 3055.942 4316 .630 5803.151 7510.349 9441.110 11596.57 13978 .10 16586.89

3.1 Atomic Structure and Spectroscopy 111
Table 2: Absolute values of the energy (E in 104 cm_1

) for O-like systems. Designations:

£=ls2 2s2 2p4

, F=ls2 2p6, C=ls2 2s2p5

, J=ls2s2 2p5, K=ls2s2p6

AT iV TOT LlJ J Zi — 1Z Zj — 14 17 1 0

Zj — 10 ry iq Zj = lO

ry r)A

Zj = ZU

ry OO Zj = ZZry 0 a Z = 24 ry c\n Z = 26

TP Hi 3p a ooc; ft/i ft 4ZZ0.040 t>y < o.y / 0 oU4o.ozd 1 r\A 1 n no lU41y.yz 1 0 1 1 n 10 lollU.lo 1 a 1 1 c 0 lOllO.DO 1 n a 0 0 c 19438.5b 23080.73

TP Hi 3p

"l

/l OOK /I Cft 4ZZ0.400 Kfl7ft KK/1 oy <D.oo4 oU4Z.0U4 in/|io /IK lU4lo.4o IOI C\ r7 C7 13107. 67 1/J111 rrr 16111.75 19432. 5o 23071.88

E 3rPn0 4225 378 5Q76 3Q4 8042 232 1041 8 Ofi 1 31 07 99 1 fil 1 1 49 1 Q439 73 93073 ZoU 1 ft

I O.IO

E 4222.031 5972.297 8037.476 10412.72 13101.30 16104.81 19425.10 23063.94

E % 4217.892 5967.002 8030.995 10404.98 13092.16 16094.00 19412.17 23048.21

C

3 P2 4197.247 5940.518 7998.601 10366.63 13047.87 16043.88 19356.54 22987.61

C 4197.078 5940.145 7997.886 10365.38 13045.85 16040.81 19352.08 22981.41

c 4196.986 5939.944 7997.494 10364.68 13044.67 16038.92 19349.17 22977.03

c

L P1 4185.870 5926.373 7981.640 10346.75 13024.92 16017.64 19326.69 22953.72

F l Sb 4158.585 5891.295 7938.581 10295.47 12965.10 15948.94 19248.71 22866.02

I

3 Po 3207.524 4561.043 6162.524 8007.970 10098.58 12436.31 15022.67 17859.08

I

3 Pi 3207.718 4561.432 6163.234 8007.970 10098.58 12436.31 15022.67 17859.08

I

3 P2 3208.004 4562.005 6164.260 8009.653 10101.16 12440.02 15027.74 17865.68

I

l Pi 3203.409 4555.788 6156.323 7999.842 10089.24 12425.65 15010.42 17844.70

K 'So 3171.617 4515.824 6107.959 7942.803 10023.21 12350.30 14925.43 17749.79

K 3 Si 3178.780 4525.024 6119.232 7956.190 10038.76 12368.06 14945.46 17772.16

Table 3: Absolute values of the energy (E in 104 cm-1

) for F-like systems. Designations:

£=ls2 2s2 2p5

, C=ls2 2s2p6

, 7=ls2s2 2p6 N LSJ Z = 12 Z = U Z = 16 Z = 18 Z = 20 Z = 22 Z = 24 Z = 26

E 2 P3/2 4313.938 6142.588 8308.343 10806.40 13640.12 16811.20 20321.64 24173.43

E 2 P1/2 4313.703 6142.062 8307.314 10804.58 13637.10 16806.49 20314.60 24163.28

C

2 S1/2 4282.778 6102.162 8257.820 10745.74 13568.86 16728.78 20227.29 24065.98

J

2

ff1/2 3296.441 4734.311 6438.257 8408.919 10648.28 13156.65 15935.70 18978.92

178 ICAMDATA 97 Proceedings
Accurate Lifetime Measurements

of Fine-Structure States of Neutral Lithium

by Beam-Gas-Laser-Spectroscopy

A. Schmitt, U. Volz, and H. Schmoranzer

Fachbereich Physik, Universitat Kaiserslautern

67653 Kaiserslautern, Germany

Abstract

The radiative lifetimes of the 2p 2P, 3s 2S, and 3d 2D terms of neutral lithium were measured

at improved precision (±0.14%, ±0.23%, and ±0.1%, respectively) by means of beam-gas-laserspectroscopy. We also give the line strengths for the corresponding transitions 2s-2p, 2p-3s,

and 2p-3d. For all three transitions we find an excellent agreement with recent large-scale ab

initio calculations.

1 Introduction

The three-electron atom lithium has always been a testing ground for atomic-structure calculations

[1]-[11]. Its comparatively simple structure allows for very accurate calculations of line strengths by

ab initio methods. State-of-the-art ab initio calculations using methods like CI-Hylleraas expansions

(Yan and Drake [9]), multi-configuration Hartree-Fock (Froese Fischer et al. [11]) or all-orders manybody perturbation theory (Blundell et al. [2]) now have the potential to determine line strengths

for the lithium atom with relative uncertainties at the 10

-4

level and better. The results obtained

by the various methods are generally in very good mutual agreement.

The longstanding disagreement between ab initio theories and the experimental result of Gaupp

et al. [12] for the 2p lifetime was resolved recently in favor of theory by a new beam-gas-laserspectroscopy lifetime measurement performed in our group in 1995 (Volz and Schmoranzer [13]).

This result, however, as well as the lifetime result for the 3s level of lithium reported in the same

paper, were of preliminary character and left some room for improvement. In the present work we

give the final results of a set of new, improved lifetime measurements on the lithium levels 2p, 3s,

and 3d. The uncertainties have been narrowed down to ±0.14%, ±0.23%, and ±0.1%, respectively.

Due to the limited space, only a brief description of the experiment and the improvements made

will be given here. A full report including more experimental details and a more comprehensive

discussion will be published in the near future [14].

2 Experimental method

In beam-gas-laser-spectroscopy (see e.g. [15, 16]) a monoisotopic ion beam with an energy of about

160 keV is partially neutralized and unselectively excited by collisions in a gas cell. The beam

then passes perpendicularly through the resonator of a linearly polarized cw dye laser in which

the atomic level of interest is excited. The fluorescence photons emitted by the excited atoms

are collected by a movable fiber-optics detection system, transmitted to the entrance slit of a

3.1 Atomic Structure and Spectroscopy 179
monochromator, and finally detected by a photomultiplier. A similar fixed fiber-optics detection

system serves as a monitor to normalize the signal of the movable system. Laser- and ion-beam

choppers are used together with digital lock-in counting techniques to obtain a purely laser-induced,

background free and cascade free signal. A decay curve consists of 30 data points at equidistant

positions of the movable detector along the beam and covers at least three lifetimes. For a lifetime

measurement, about 30 decay curves are recorded and evaluated by means of a least-squares fit. Zero-field quantum beats due to unresolved hyperfine-structure are included in the fit function if needed. Finally, the lifetime (before corrections) of the excited level is obtained from the averaged

individual decay constants, using the precisely measured beam velocity as conversion factor.

3 Corrections and uncertainties

The largest systematical effect in beam-gas-laser-spectroscopy arises from the divergence of the

atom beam which causes a slight decrease in the total detection efficiency for the fluorescence

photons as the fibre-optics detector is moved downstream along the beam. As a result the decay

of the excited state fluorescence appears to be faster and the lifetime appears to be shortened

by, typically, a few 0.1%. The correction procedure for this effect was a major contributor to the uncertainties in our previous measurements [13]. The procedure used there was based on an

approximation of the atom beam profiles and of the spatial detection efficiency of the photon

collection system by Gaussian-shaped model functions [15]. This resulted in a simple analytic

expression for the beam divergence correction in which the measured parameters of the atom

beam (widths, divergence angles) and of the fluorescence detector (width of the spatial detection

efficiency) were inserted. In the present work the measured profiles of the atom beam and of the

photon detection efficiency were fed into a computer program which calculated the beam divergence

correction by numerical integration. This reduces the uncertainty in the correction by a factor of

2. The corrections applied are (+0.62 ± 0.07)% for the 2p level, (+0.94 ± 0.10)% for 3s, and

(+0.33 ± 0.04)% for 3d.

Another important error source in lifetime measurements is the occurence of quantum beats.

The geometry of the detection system in our experiment is designed to suppress quantum beats by

a magic angle geometry. Nevertheless, residual quantum beat modulations may appear in the decay

curves due to the finite acceptance angle (±5°) of the detection system. A small modulation with an amplitude of ±1% of the total signal found on the decay curve of the 2p level could be assigned

to the hyperfine-structure of the 2p

2P$/2 state. In this case the proper theoretical expression for the quantum beat was included into the fit function. An evaluation of the decay curve without

accounting for quantum beats would have yielded a lifetime about 0.3% shorter than the true value.

In the case of the 3d level quantum beats cannot be ruled out. However, the measured decay curve

displayed no significant departure from an exact exponential behavior. For the 3s level, finally,

quantum beats are absent due to the low J of 1/2.

Other error sources included in the uncertainty estimates are the beam velocity, adjustment

and linearity of the detector drive, changes in the light-guide transmission, detector saturation,

quenching by residual gas, Zeeman quantum beats, and finally, statistical uncertainties. The total

uncertainties of ±0.14% (2p), ±0.23% (3s) and ±0.10% (3d) result from a quadratic addition of the

individual contributions and should be interpreted as single standard deviations (la). Compared

to our previous results for the levels 2p and 3s [13], the uncertainties could be narrowed down

further, in particular for the 3s lifetime. This reduction in uncertainty is for the most part due

to the improved correction procedure for the atom beam divergence effect. In the case of the 3s

level, increased count rates and therefore lower statistical uncertainties also contributed to the

improvement.

180 ICAMDATA 97 Proceedings
4 Results and discussion

The results of our lifetime measurements and the corresponding line strengths are shown in Table

1 together with a selection of other experimental results with quoted uncertainties below ±1%. For

the 2s-2p transition our result matches two recent more accurate results obtained by Martin et al.

[19] and

Table 1: A selection of experimental line strengths Sif and upper state lifetimes Tj for transitions

in neutral lithium (uncertainties in parentheses).

Transition Authors(year) Ref. Method Tj(ns) <%(a.u.)

2s-2p Gaupp, Kuske, and Andra (82) [12] BGLS 27.29(4) 32.78(5)

Carlsson and Sturesson (89) [17] pulsed laser 27.22(20) 32.86(24)

Volz and Schmoranzer (96) [13] BGLS 27.11(6) 33.00(7)

McAlexander et al. (96) [18] mol. spectr. 27.102(9) 33.008(11)

Martin et al. (97) [19] mol. spectr. 27.13(2) 32.97(2)

this work BGLS 27.09(4) 33.02(5)

2p-3s Volz and Schmoranzer (96) [13] BGLS 29.72(17) 17.84(10)

this work BGLS 29.84(7) 17.77(4)

2p-3d Schulze-Hagenest et al. (77) [20] BGLS 14.60(13) 76.9(7)

this work BGLS 14.589(14) 76.98(8)

McAlexander et al. [18], the latter reporting an uncertainty of only ±0.033%. Molecular spectroscopy was used in these works to determine the 2s-2p line strength from the long-range interaction potential of the molecular A

1 S+ state. The earlier lifetime measurement by Gaupp et al. [12] differs from all the new measurements by more than four of its standard deviations and can thus

be safely ruled out. For the levels 3s and 3d our new results improve the most accurate previous

measurements by Volz and Schmoranzer [13] and by Schulze-Hagenest et al. [20] by factors of 2.5

and 9, respectively.

Among the theoretical work listed in Table 2, only two approaches, namely the quantum Monte

Carlo simulation by Barnett et al. [8] and the Brueckner approximation by Liaw and Chiou [7], fail to agree with experiment. The other theoretical line strengths for the three transitions investigated

are in excellent agreement with the experimental results which confirms the high quality level reached by ab initio calculations for neutral lithium.

References

[1] G. Peach, H. E. Saraph, and M. J. Seaton, J. Phys. B 21, 3669 (1988)

[2] S. A. Blundell, W. R. Johnson, Z. W. Liu, and J. Sapirstein, Phys. Rev. A 40, 2233 (1989)

[3] A.-M. Martensson-Pendrill and A. Ynnerman, Physica Scripta 41, 329 (1990)

[4] A. W. Weiss, Can. J. Chem. 70, 456 (1992)

[5] J. Pipin and D. M. Bishop, Phys. Rev. A 45, 2736 (1992)

[6] K. T. Chung, AIP Con}. Proc. 274, 381 (1993)

[7] S.-S. Liaw and F.-Y. Chiou, Phys. Rev. A 49, 2435 (1994)

3.1 Atomic Structure and Spectroscopy 181
Table 2: Large-scale ab initio calculations of line strengths Sjf for transitions in neutral lithium

(pair entries L/V denote length and velocity form).

Transition Authors (year) Ref. Method %(a.u.)

2s-2p Peach et al. (88) [1] Close coupling 33.03

Blundell et al. (89) [2] RMBPT all orders 32.99/33.02

Martensson-Pendrill et al. (90) [3] Coupled clusters 33.01

Weiss (92) [4] CI 33.03/33.12

Pipin and Bishop (92) [5] CI-Hylleraas 33.00

Chung (93) [6] FCPC 33.00/33.00

Liaw and Chiou (94) [7] Brueckner approx. 33.11/33.08

Barnett et al. (95) [8] Monte Carlo sim. 32.83(3)

Yan and Drake (95) [9] CI-Hylleraas 33.0056

Godefroid et al. (96) [10] MCHF 33.00/33.00

Froese Fischer et al. (97) [11] MCHF+Breit-Pauli 33.0024

2p-3s Peach et al. (88) [1] Close coupling 17.77

Blundell et al. (89) [2] MBPT all orders 17.76/17.75

Chung (93) [6] FCPC 17.75

Liaw and Chiou (94) [7] Brueckner approx. 17.89/17.89

Froese Fischer et al. (97) [11] MCHF+Breit-Pauli 17.7505

2p-U Pipin and Bishop (92) [5] CI-Hylleraas 76.97

Chung (93) [6] FCPC 77.00/77.01

Yan and Drake (95) [9] CI-Hylleraas 77.0098

Froese Fischer et al. (97) [11] MCHF+Breit-Pauli 77.0133

[8] R. N. Barnett, E. M. Johnson, and W. A. Lester Jr., Phys. Rev. A 51, 2049 (1995)

[9] Z. C. Yan and G. W. F. Drake, Phys. Rev. A 52, R4316 (1995)

[10] M. R. Godefroid, C. Froese-Fischer, and P. Jonsson, Physica Scripta T 65, 70 (1996).

[11] C. Froese-Fischer, M. Saparov, G. Gaigalas, and M. Godefroid, At. Data Nucl. Data Tables, to be

published

[12] A. Gaupp, P. Kuske, and H. J. Andra, Phys. Rev. A 26, 3351 (1982)

[13] U. Volz and H. Schmoranzer, Physica Scripta T 65, 48 (1996)

[14] A. Schmitt, U. Volz, H. Liebel, M. Kohl, R. Henkel, H. Schmoranzer, to be published

[15] U. Volz, D. Marger, H. Roth, and H. Schmoranzer, J. Phys. B 28, 579 (1995)

[16] U. Volz, M. Majerus, H. Liebel, A. Schmitt, and H. Schmoranzer, Phys. Rev. Lett. 76, 2862 (1996)

[17] J. Carlsson and L. Sturesson, Z. Phys. D 14, 281 (1989)

[18] W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, Phys. Rev. A 54, R5 (1996)

[19] F. Martin, M. Aubert-Frecon, R. Bacis, P. Crozet, C. Linton, S. Magnier, A. J. Ross, and I. Russier,

Phys. Rev. A 55, 3458 (1997)

[20] D. Schulze-Hagenest, H. Harde, W. Brand, and W. Demtroder, Z. Phys. A 282, 149 (1977)

182 ICAMDATA 97 Proceedings
Accurate Atomic Data for S I, S II, and S III

S. S. Tayal

Department of Physics

Clark Atlanta University, Atlanta, GA 30314

1 Introduction

Prominent S I emission lines have been observed from Jupiter's satellite Io and the Io torus [1]. Absorption lines from neutral sulfur have been reported in the interstellar gas towards Oph [2]

.

S I emission features are also observed in the far- ultraviolet spectra of a Orionis [3] by the

Goddard High Resolution Spectrograph (GHRS) on board the Hubble Space Telescope. Several

S II and S III emission lines have been detected in ultraviolet (UV) spectra of the Io plasma torus

in the magnetosphere of Jupiter by the Voyager ultraviolet spectrometers, the International

Ultraviolet Explorer, and more recently by the high-resolution Hopkins Ultraviolet Telescope

aboard Astro- 1 and by the GHRS on board Hubble Space Telescope. The UV S III lines are important in temperature diagnostics of solar and stellar transition regions. Comprehensive

laboratory analysis of S II [4] and S III [5] spectra are available. New S III lines from the 3p3d

3F>, 3pAd 3P°, 3p4p 1 S, lP, l D, 3p3d ip>, W>, ipo, and 3p5d l P° terms have been identified in the

laboratory spectrum.

In order to give a correct interpretation of the observational data from the plasma, accurate

values of oscillator strengths and electron excitation collision strengths of the constituent ions are needed. In recent years, we have carried out a program to calculate accurate atomic data for S I, S II, and S III. These studies are motivated not only because of the importance of atomic data in

Io torus and stellar plasma modeling, but also to resolve existing discrepancies between the

available calculations and between calculations and measurements. For example, our calculation

resolved long-standing large discrepancies in f-values between theory and experiment for the

3p4 3p . 3p34s' 3Z)0 transition in S I at 1479 A [6], and most of the existing discrepancies between

available calculations for f- values of S III were resolved [7]. Theoretical calculations of cross sections for electron impact excitation of S II [8] and S III [9] have been carried out in concert with

the experimental measurements by A. Chutjian and his co-workers at the Jet Propulsion

Laboratory [10]. The measurements are made using the electron energy-loss, merged-beams

method. Good agreement between theory and experiment for available low-lying transitions

provides us confidence in the accuracy of our calculations and the theoretical models used in these

calculations.

2 Oscillator Strengths and Transition Probabilities

Oscillator strengths and transition probabilities of electric-dipole-allowed and intercombination

transitions from fine-structure levels of the terms belonging to the 3s2 3p4

, 3s2 3p3 4s, 3s2 3p3 5s,

3s2 3p3 3d, 3s2 3pHd configurations of SI, 3s2 3p3

, 3s3p4

, 3s2 3p2 3d, 3s2 3p2 4s, and 3s2 3p2 4p

configurations of S II, and 3s2 3p2

, 3s3p3, 3s2 3p3d, 3s2 3p4s, 3s2 3p4p, and 3s2 3p4d configurations of

S III are calculated using extensive configuration-interaction wave functions. Relativistic effects in intermediate coupling are incorporated by means of the Breit-Pauli Hamiltonian. Small

3.1 Atomic Structure and Spectroscopy 183
adjustments to diagonal elements of the Hamiltonian matrices have been made so that the energy

splittings are as close as possible to the experimental values. Our results of excitation energies,

oscillator strengths, and transition probabilities are compared with other available calculations

and with measurements to assess the quality of atomic data.

The atomic state wave functions are represented by the J-dependent CI expansions of the

form

M

( JMj) = ^ bij $j ( ajLjSjJMj), (1)

;' = i where each of the M single-configuration functions (j)j is constructed from one-electron functions,

and CLj defines the coupling of angular momenta of the electrons. The sum over j includes all configurations in which the orbital Lj and spin Sj angular momenta couple to give the total

angular momentum

J = Lj+Sj. (2)

Each one-electron function is the product of a radial function, a spherical harmonic, and a spin

function. The radial part of each orbital is expressed in analytic form as a sum of

Slater-type-orbitals

k

;=i where n and 1 are, respectively, the principal and orbital quantum numbers and cjni, £jni, and Ijni are the expansion coefficients, exponents, and powers of r, respectively.

The Is, 2s, 2p, 3s, and 3p radial functions are chosen as the Hartree-Fock functions of the

3s2 3p4 3P, 3s23p3 4S°, and 3s23p2 3P ground states of S I, S II, and S III, respectively, and other

radial functions have been obtained with the computer code CIV3 [11]. We used flexible radial

functions and included a large number of configurations in the configuration-interaction (CI)

expansions to ensure convergence. The calculated energy levels are in close agreement with

laboratory measurements. There is usually good agreement between the length and velocity

forms of oscillator strength except for weak and a few other transitions. In cases of discrepancies

between the length and velocity values, the length value is recommended because it normally

remains stable with respect to the addition of more configurations.

3 Collision Strengths and Collision Rates

Electron collisional excitation strengths for inelastic transitions in S II and S III have been

calculated using the R-matrix method in a 19-state (3s2 3p3 4S°, 2D°, 2Po, 3s3p4 4P, 2D, 2S, 3s2 3p2 3d

2P, 4F, 4D, 2F, 4P, 3s23p2 4s 4P, 2P, 3s2 3p2 4p 2 S°, 4D<>, 4P°, 2D°, 4 S°, 2P°) and a 17-state (3s23p2 3P, lD,

1 S, 3s3p3 5 S°, 3D°, 3P°, lF>, 3 S°, Wo, 3s2 3p3d lD°, 3F», 3P», »D>, lF°, l F°, lP°, 3s2 3p4s 3P°, lP°)

close-coupling approximations, respectively. Rydberg series of resonances converging to the

excited state thresholds are explicitly included in the scattering calculations. Resonances are found to make substantial enhancements in collision strengths at low energies for several

transitions. Cross sections in our 19-state calculation for S II [8] show very good agreement with

the recent merged-beams energy loss experiment [10] for the forbidden 3s2 3p3 4 S° - 3s2 3p3 2D)

, 3s2 3p3 4 S° - 3s2 3p3 2P°, and resonance 3s2 3p3 4 S° - 3s3p4 4P transitions and also with the 18-state

184 ICAMDATA 97 Proceedings
R-matrix calculation [12]. A similar multistate R-matrix calculation for electron impact excitation

of inelastic transitions in neutral sulfur is planned.

Collision rates are obtained from the total collision strengths by integrating over a Maxwellian velocity distribution. Effective collision strengths are presented for electron

temperatures from 5,000K to 100,000K, suitable for astrophysical applications, for all 136

inelastic transitions among 17-LS states of S III [9] and for all 171 inelastic transition transitions

among 19-LS states of S II [8]. Our results are believed to be accurate to about 10% for transitions

among low-lying excited states but may be less accurate for transitions involving higher excited

states.

Acknowledgments

This research was supported by the National Aeronautics and Space Administration.

References

[I] S. T. Durrance, P. D. Feldman, and H. A. Weaver, Astrophys. J. (Letters) 267, L125 (1983)

[2] S. R. Federman and J. A. Cardelli, Astrophys. J. 452, 269 (1995)

[3] K. G. Carpenter, R. D. Robinson, G. M. Wahlgren, J. L. Linsky, and A. Brown, Astrophys. J. 428, 329 (1994)

[4] J. E. Pettersson, Phys. Scr. 28, 421 (1983)

[5] E. Johansson, C. E. Magnusson, I. Joelsson, and P. 0. Zetterberg, Phys. Scr. 46, 221 (1992)

[6] S. S. Tayal, J. Phys. B 30, L551 (1997); S. S. Tayal, Ap. J., in press (1997)

[7] S. S. Tayal, J. Phys. B 28, 5193 (1995); S. S. Tayal At. Data and Nuclear Data Tables,

in press (1997)

[8] S. S. Tayal, Ap. J. Suppl. Ill, 459 (1997)

[9] S. S. Tayal, Ap. J. 481, 550 (1997)

[10] C. Liao, S. J. Smith, D. Hitz, A. Chutjian, S. S. Tayal, Ap. J. 484, 979 (1997)

[II] A. Hibbert, Comput. Phys. Commun. 9, 141 (1975)

[12] A. Ramsbottom, K. L. Bell, and R. P. Stafford, At. Data and Nuclear Data Tables 63, 57

(1996)

3.1 Atomic Structure and Spectroscopy 185
Precise Atomic Lifetimes Measured at a

Heavy-Ion Storage Ring

E. Trabert

Ruhr-Universitat Bochum

D-44780 Bochum, Germany

1 Technique

A new experimental technique, derived from beam-foil spectroscopy, has been developed for

the measurement of long atomic lifetimes in ions. The ions are produced in a standard ion source and then, after a first acceleration step, collisionally excited in the gas or foil stripper

of an accelerator. A beam of charge-state selected MeV-ions is transported to and then stored

in the clean ultra-high vacuum conditions of a heavy-ion storage ring. This storage has been

combined with straightforward optical detection (Fig. 1) to make precise and accurate atomic

lifetime measurements in the millisecond range. As any element can be collisionally excited,

the method is very versatile and may be used to study a number of cases which are of

fundamental atomic structure or astrophysical and terrestrial plasma diagnostic interest.

A major advantage of the new technique is that the ion excitation on one hand and the

trapping and detection on the other are spatially separated and can be individually

optimized. The experiment works in fixed geometry. Thus there are no mechanically moving

parts and no explicit dependence of the decay curves on the ion beam velocity. All that is needed to reach high precision are a reliable clock frequency, a measurement of the ion beam

storage time (to correct the photon signal for ion beam losses during the measurement cycle),

and a photon data rate somewhat higher than the detector dark rate. We employed a

solar-blind photomultiplier and an interference filter to suppress possible stray light from ion

getter pumps in the vacuum vessel. There is no need for higher spectral selectivity, as the

transition of interest is often the only one of extreme longevity of the upper level in a given

ionization stage of the element under study. Thanks to this longevity, measurements may

begin after higher-lying levels have decayed to the ground state or to the metastable level of

interest, and consequently there is practically no cascade problem. No ion-beam related

background was detected. Further improvements would be possible by increasing the

detection efficiency, for example by using several photomultipliers in parallel.

Figure 1: Schematics of the experimental arrangement

186 ICAMDATA 97 Proceedings
The new technique has been applied to several intercombination (El, AS=1) transitions and to a few forbidden (Ml) transitions. The selection of test cases matches the wavelength range (A, 190 to 270 nm) of our low-noise photomultiplier (with a dark rate of about 1 count/s) and the vacuum

vessel window material and wavelength filter ranges.

2 Cases Studied

2.1 Intercombination Transitions

2 1 3 0 Among the systems studied are the 2s S0 - 2s2p P 1 intercombination transition in the Be-like

ions B+ and C2+

, the 3s

2 a S0 - 2s2p

3F°l transition in the Mg-like ion Al

+

, and the 2s

22p2

3P1

- 2s2p

3 5 S°2 transitions in C-like N

+

.

2 1 3 0 The 2s S0 - 2s2p P y intercombination transition in the doubly charged carbon ion (Be-like) is of

particular interest as a test case for fundamental atomic structure calculations and for some

astrophysical applications (see Fig. 2). After the notable scatter of the early theoretical data, we

note that some later calculational results seemingly followed experiment, even as early data from

radiofrequency ion trap experiments varied considerably and appear mutually contradictive.

These earlier lifetime results are now being surpassed in accuracy and precision because of the

much cleaner experimental trapping conditions available at the heavy-ion storage ring, by the

new experimental result of(x = 9.714±0.013 ms) [1]. In the most recent calculations by the groups at Belfast and Nashville, however, very different

theoretical approaches yielded rather similar results and were quoted with intrinsic error estimates in the few-percent range. These similarities, however, were furthered by semiempirical

adjustments to experimental energy level and fine structure data. No fully ab initio calculation of

this system so far comes close to the experimental precision and accuracy. An example is set by

the case of B

+

: Two approaches (configuration interaction [2] and MCHF/MCDF [3] calculations)

3 0 led to lifetime results for the 2s2p P x level which were claimed to have 2% uncertainties but

differed from each other by about 6%. This discrepancy boils down to the use of different

3 0 experimental values for the 2s2p P fine structure intervals. With the same (right) choice of

atomic structure reference data, the lifetime calculations perfectly agree with each other and with

experiment (x = 97.7 ± 1 ms). Assuming the validity of the theoretical treatment, our lifetime

measurement with its poor spectral resolution can thus be seen as an indirect, but sensitive test on difficult to obtain experimental fine structure data.

3 0 + The intercombination decay of the 3s3p P 1 level in Mg-like Al may be seen as an analog to the above two ions in the Be sequence. In this case, our experiment (x = 305 ± 10 jj.s) [4] confirms

the lifetime result of an earlier radiofrequency ion trap study [5] (which used laser ablation of Al

and thus operated at a lower ambient pressure than is possible with gases). However, the latest

calculations do not match the experimental data, and the results of earlier calculations have been

stated with considerable uncertainties.

2 2 3 3 5 0 For the 2s 2p Plj2 - 2s2p S 2 transition in C-like N , which appears in auroral spectra of the

upper atmosphere, a series of calculations and ion trap measurements finally led to lifetime data

which agreed with each other and were quoted with about 6% uncertainty. Our storage ring data

(x = 5.87 ± 0.03 ms) [6] reach 0.5% uncertainty and are just outside the previously given 5% (la) error ranges of both the latest ion trap data and the most advanced theoretical treatment [7]

.

3.1 Atomic Structure and Spectroscopy 187
70 80 90 100 110 120 130

Transition probability / s

T

T

T

TT

T

T

T

T

T

E

E

T

ET

T

T

T

T

T

E

TT

Garstang & Shamey 1967

Nussbaumer 1972

Muhletaler & Nussbaumer 1976

Lin & Johnson 1977

Nussbaumer & Storey 1978

Glass & Hibbert 1978

Laughlin, Constantinides &

Victor 1978

Cheng, Kim & Desclaux 1979

Glass 1982

Cowan, Hobbs & York 1982

Kwong era/. 1983

Smith era/. 1984 — Curtis 1991

Kwong era/. 1993

Chou, Chi & Huang 1994

Fleming, Hibbert & Stafford 1994 Froese Fischer 1994

Ral'chenko & Vainshtein 1995

Ynnerman & Froese Fischer 1995

Brage, Fleming & Hutton 1996

Doerfert etal. 1997

Jonsson & Froese Fischer 1997 Froese Fischer & Gaigalas 1997

2+ Figure 2: Intercombination transition probability in the C ion. T Theory, E Experimental data.

Our experiment is denoted "Doerfert et al. 1997" [1].

2.2 Forbidden Transitions

Of forbidden (Ml) transitions we have studied test cases of interconnects within the ground state

12+ complex of several ions. In F-like Sc our experiment aimed at the forbidden transition which

2 5 2 0 connects the 2s 2p P 3/2 1/2 fine structure levels. The signal statistics was limited by the

achievable ion beam current and thus the result limited to 3% precision. The available calculation

[8] matches the experimental transition rate result of (1000 ± 30) s"* [4] only after a 2% correction

2 2 2 4 1 for experimental fine structure data. For the much longer lived 2s 2p and 2s 2p D2 levels in

C-like Si and O-like Si our storage ring data corroborate theory on the forbidden transition

rates [9,10] at the 3% level, yielding lifetimes of 38.8 ± 0.5 ms and 65 ± 3 ms, respectively [6]. The

experimental precision on these long atomic lifetimes is limited by the ion beam dynamics after

injection into the storage ring: Although the long-term beam storage time constant may be as high

as 40 s (which would cause little trouble), the initial transitory behavior of the ion beam

necessitates larger corrections with notable uncertainties.

188 ICAMDATA 97 Proceedings
3 Conclusion

The lifetimes already measured with the new technique range from 0.3 ms to 100 ms. Depending

on the experimental conditions (it is mostly the available ion beam current which determines the

signal rate), the results have errors in the range 3% to 0.13%. At such a level of precision, several

of the new benchmark data test theory. Concerning intercombination transition rates, our data

are found to corroborate only the latest, most extensive calculations. Even these, however, have

not been obtained fully ab initio, but use various adjustments to experimental atomic structure

reference data. Concerning forbidden transition probabilities, theory seems much better off. Here,

however, the predicted transition rates strongly depend on the assumed level splittings, and

theories falling short by a few percent on this account easily yield 10% errors of the lifetime

results. Such errors are clearly resolvable by the new experimental lifetime measurement

technique.

Judging from our test cases, the forbidden transition rates apparently are under better

theoretical control than the intercombination transition rates (after managing the term

differences), probably because rather similar wavefunctions of initial and final states are involved

and not the more dissimilar ones of the intercombination transition problem. However, we note

that earlier on there were order-of-magnitude differences between differently calculated forbidden

transition rates. The project has been financially supported by German BMFT/BMBF and DFG research

grants and by the Alexander von Humboldt Foundation.

References

[1] J. Doerfert, E. Trabert, A. Wolf, D. Schwalm, O. Uwira, Phys. Rev. Lett. 78, 4355 (1997)

[2] J. Fleming, K.L. Bell, A. Hibbert, N. Vaeck, M. Godefroid, MNRAS 279, 1289 (1996)

[3] C. Froese Fischer, G. Gaigalas, M. Godefroid, J. Phys. B 30 (1997). (in print)

[4] E. Trabert, A. Wolf, J. Linkemann, X. Tordoir (work in progress)

[5] B. C. Johnson, P. L. Smith, W. H. Parkinson, Ap. J. 308, 1013 (1986)

[6] E. Trabert, A. Wolf, J. Linkemann, E. H. Pinnington, E. J. Knystautas, A. Curtis,

N. Bhattacharya, H. G. Berry (work in progress)

[7] T. Brage, A. Hibbert, D. S. Leckrone, Ap. J. 478, 423 (1997)

[8] K. T. Cheng, Y. -K. Kim, J. P. Desclaux, At. Data Nucl. Data Tables 24, 111 (1979)

[9] C. Froese Fischer, H. P. Saha, Phys. Rev. A 28, 3169 (1983)

[10] K. L. Baluja, J. Phys. B 18, L413 (1985)

3.1 Atomic Structure and Spectroscopy 189
Light Ion Absorption, Probed with High Spatial,

Temporal, and Spectral Resolution: The Spectrum of C II

Paolo Villoresi and Piergiorgio Nicolosi

Laboratorio di Elettronica Quantistica - D.E.I.

Universitd degli Studi di Padova - Padova, Italy

e-mail: pavil@dei.unipd.it

Abstract

We present a facility for the spectroscopic measurement of the photoabsorption of light

ions in the region 30-100 nm. The optical design of the experiment and the characteristics of

the backlight continuum source allow a spatial resolution of the absorbing medium of about

0.3-0.5 mm and a duration of its irradiation of about 20 ns. Therefore the absorption of a

selected ionization stage of an element can be measured and, in addition, by the use of a high

resolution spectrometer, its photoabsorption and photoionization spectra can be recorded with

spectral resolution of 5000-8000. The facility is composed of a laser produced plasma acting as backlight continuous source, a stigmatic optical system with toroidal mirror and grating, and a UV CCD in the focal plane. The spectrum of C II is reported as example. The ground state has been effectively populated and both discrete series and continuous spectra with several Fano

profiles were measured. From the calculated f-values, it will be possible to estimate the absolute

photoionization cross section.

1 Introduction

Despite the vast amount of data available for neutrals, little photon absorption spectroscopy

has been done for the elements in ionic stages, especially for the multiply charged ones [1, 2, 3]. The difficulty is that of generating a suitable column of ions for the energy level to be probed.

In this context, the twin laser produced plasmas are a well established technique for almost two

decades.

The laser produced plasma (LPP) characteristics as absorbing medium are the following:

• the generation of the ion is obtained by focusing a pulsed laser onto a plane target of the

element under study,

• by varying the laser power density on the target, almost all the ionic stages can be produced

for a large number of elements,

• in the LPP, the various ion species show different temporal and spatial evolution.

As continuum source, the LPP also shows relevant characteristics:

• the duration of the emission is comparable with that of the laser pulse: consequently,

measurements with time resolution of order of 20 ns are possible,

• the emission in the spectral regions from VUV to the XUV may be either discrete or continuous, according to the choice of the target element and the laser power density

focused onto the target,

• as a continuous backlighter, it has a well defined and small physical size, corresponding to the laser focal spot in transverse direction and a longitudinal expansion of a few tenths of a mm,

190 ICAMDATA 97 Proceedings
Detector

Toroidal Grating

Figure 1: Optical setup, BR: background radiation, PC: plasma column

• it has very high brightness, due to the high plasma temperature and density,

• the emission is usually characterized by high reproducibility and stability,

• there is no requirement for ultra-high vacuum and there is no thermal load on the optics.

To exploit conveniently the LPP as backlighter in the EUV spectral range, an optical design

with high optical aperture and a spectral resolution in the range 5000-10000 is needed.

2 Aims of the present experiment

In this contribution we present the measurement of the discrete and continuous spectra originating from the ground state 2s2

(

1 S) 2p 2 P° of the first ion of carbon. The experimental technique

is based on the two laser produced plasmas, applied in the normal incidence spectral region.

The spectral range spans from 38 nm to 80 nm, where the complete 2p 2 P°-ns 2 S and 2p2 P°-nd

2 D series, as well as the series 2s2 2p 2 P°-2s2p np 2 P appears. The first ionization limit is the 2s2

1 S state at 50.8 nm . The following photoionization spectrum has several resonances, giving rise to Fano profiles. The photoionization cross section has been calculated by the London group

[4]- As already mentioned, the "knobs" that can be used to optimize the parameters of the

experiment are the laser power density on the backlighter target and on the absorbing medium,

the graphite target: for these, we have used the values of 2xl012 and lxlO10 W/cm2 respectively.

The focal spot on the absorbing medium target was chosen in order to increase the ion column

density, and is obtained by a spherocylindrical lens, to produce a line focus of 0.1x7 mm2 area. The delay between absorbing medium generation and backlight plasma generation has been

varied between 50 and 120 ns, by retarding the laser pulse in an optical delay line up to about

40 m long. The distance from the graphite target to the spot where the backlight beam was

probing the plasma has been varied between 0.3 and 2 mm, corresponding to noticeably different absorbing plasma densities and temperatures. In particular, with a delay of 58 ns between the

formation of the two plasmas and at 1.7 mm from the C target, the ground state of C II was

selectively populated and correspondingly the spectrum showed negligible contributions from

neutral carbon absorption and only some isolated contributions from excited states of CII and

from CIII.

3 Description of the setup

The optical setup, shown in Fig. 1, is composed of two toroidal optics setups: a mirror and

a grating. The mirror, with meridional and sagittal radii of 1.26 m and 1.04 m, respectively,

operates at 24.6°. This is used as a condenser optics, gathering the backlight emission with

3.1 Atomic Structure and Spectroscopy 191
0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.10

"i

1 r i i i i i i i i i i r

I I I X

40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

Wavelength (nm)

Figure 2: Absorption spectrum of C II: the discrete part begins at 50.8 nm

about f/10 and focusing it onto the spectrograph entrance slit. The grating with 3600 lines/mm

of radii 1.011 m and 0.992 m operates between 10° and 14° . It provides stigmatic imaging of

the absorption region with a dispersion of 6.7 pm per detector pixel. The latter is a cooled UV

CCD made by Princeton Instruments, with 16 bit of conversion, and 512x512 square pixel of

24 /j,m of size. The laser is a Q-switched Nd:YAG, and the typical energies used for the plasma

generations are 3.8 J on the backlight radiator and 1.2 J on the absorbing medium. The high

S/N ratio and the very low residual optical aberrations of the acquired spectra allowed the use

of deconvolution techniques to improve the limit of resolution up to 5 pm.

4 Results and discussion

The C II spectrum was taken in contiguous spectral intervals, each of about 3.8 nm and averaged

over 20 shots. The complete reconstruction of the spectrum, the evaluation of the relative

oscillator strengths of the series and the photoionization cross-section is in progress, and the

preliminary results are shown in Fig 2. The spectrum has been taken at 2.3 mm from the target

surface and with a delay of 58 ns after the plasma generation. The discrete series are converging

to the limit at 50.8 nm. The transitions of the type 2s2 2p 2 P°-2s2 nd 2 D and ns

2 S can be

observed for n larger than 10, and show the effect of a strong perturbation about the 7d state. For these experimental conditions, the ground state absorption of the next ionization stage,

C III, is noticeable. For instance, the strong 45.9 nm multiplet appears in the middle of the

Fano profile originating from the interaction of 2s2 2p 2 P°-2s2p4p 2 D and 2s2p (*P) 3p 2 D with

the (2s2 1 S) kd 2 D open channel.

The strong variation of the plasma density with the distance from the target and how it affects the observed spectra is clearly shown in Fig. 3, where the transition 2s2 2p 2 P°-2s2 6d

2 D at 54.338 nm for different distances from the target and with the same delay of 58 ns is presented. The profiles show the large variation, that occurred in less than a millimeter of

displacement, of the absorption coefficient, whose integral changes by more than one order of

magnitude, and of the linewidths. For the assessment of the data quality, many efforts are made both during the acquisition

and the data analysis. Particular attention is paid, during the measurements, to the absorbing

plasma and the backlight continuum shot-to-shot reproducibility. Consequently, we have verified the conservation of the ratios between lines in a single spectral segment within a few percent. In

addition, we are adopting an acquisition scheme in order to average over the target condition,

in its shot-to-shot ageing, for all the quantitative measurements. In the profile integration,

particular attention is paid to the extended wings and possible external contributions.

192 ICAMDATA 97 Proceedings
Ab 1.5

S.

Co

eff.

y=7.4 mm

10 _ y=1.7 mm

y-2.3 mm

0.5-

0 0 Laa \--^T,-"f r-y -\ i Y i 1 V

'*- -lTi~ r

- - i —

'53.9 54.0 54.1 54.2 54.3 54.4 54.5 54.6

Wavelenght (nm)

Figure 3: 2p-6d absorption at different distances from the target

5 Conclusions

A new experiment for absorption spectroscopy of ionized species with the dual LPP technique

has been realized in the VUV spectral range. The optical setup is stigmatic in an extended region, in order to achieve a fine spatial probing

of the absorbing medium. This characteristic has shown a noticeable improvement of the species

selection and then of the data quality.

Preliminary measurements of the CII photoabsorption and photoionization spectra has been

performed. The analysis of the experimental data is in progress, in particular an estimate of the

absolute photoionization cross-section. This is obtained through the evaluation of the column

density. The latter is derived from the photoabsorption coefficients of strong suitable discrete

transitions, whose oscillator strengths have been calculated [5, 6]. Moreover, the oscillator strengths for high n terms of the p-s and p-d transitions will be estimated with respect to known terms.

Finally, we are working on the identification of the perturbations in the photoionization

cross section, in order to extract information on the level energies and the matrix element of

the interaction.

The authors wish to express their gratitude to Prof. G. Tondello for the support and the

useful suggestions as well as to Dr. E. Jannitti and to ing. R. Tesser for help in the data acquisition. This work was performed within the framework of the EC-HCM program: Investigation

of the Structure and Dynamics of Atoms and Ions by Inner-Shell Excitation.

References

[1] P. Nicolosi et al., J. de Physique IV CI suppl. 1, 89 (1991)

[2] J. T. Costello et al, Physica Scripta T34, 77 (1991)

[3] F. J. Wuilleumier et al., N.I.M. B 87, 190 (1994)

[4] Y. Yan and M. J. Seaton, J. Phys. B 20, 6409 (1987)

[5] W. L. Wiese et al., J. Phys. Chem. Ref. Data Monograph 7 (1995)

[6] Y. Yan et al., J. Phys B 20, 116 (1987)

3.1 Atomic Structure and Spectroscopy 193
Systematic Studies of the n=2 to n=3,4 Transitions in

the Ions of Elements Cu through As Isoelectronic with

Li I through Na I Produced by

Laser Irradiation

J.F. Wyart2- 1

, T. Missalla1

, J.C. Gauthier1

, and C. Chenais-Popovics1 ^aboratoire pour I 'Utilisation des Lasers Intenses, Ecole Polytechnique,

91128 - Palaiseau, France

2Laboratoire Aime Cotton, CNRS II, bdtiment 505, centre universitaire,

91405 - Orsay, France

1 Introduction

Laser produced plasmas provide rich X-ray spectra. Their identification is of importance for the

physics of ICF and X-ray lasers, of laboratory X-ray sources and of hot astrophysical objects. X-ray

spectra of 5 elements (Z=29 through 33) have been measured at the LULI laser facility as part of a systematic investigation of the medium-Z elements. The laser pulse conditions were 600 ps

duration, frequency-doubled and 8 to 35 J focused on 80 um focal spots, leading to irradiations of

2xl014 to 1015 Wcm~2

. Spectra were recorded in the ranges 6-8 A and 7.55-9.55 A by means of two

flat crystal spectrographs (respectively PET and ADP crystals). The size of the plasma limits the

linewidths to about 0.004 A. The laser beam was focused at normal incidence onto the target

surface. The spectra were recorded on films with an observation direction perpendicular to the

laser axis and to the main plasma expansion.

Magnesium has been used as a tracer element for wavelength calibration, some targets being

a mixture of Mg and the element being investigated. Only the Lya doublet (X8.4194/8.4253 A) and

Mg XI Hea (A.9.1682 A) were obtained, and they were supplemented by theoretical wavelengths of

well-resolved lithium-like lines at the short wavelength end of our observations. The wavelength

uncertainty is 0.003 A for well-resolved lines but most of the emission peaks are blends of several

transitions whose relative intensities depend on plasma conditions.

2 Atomic Structure Calculations and Classification of the Lines

In these conditions of irradiation, the ions have charge states beyond 20+, and their emission

spectrum below 10 A contains characteristic transitions between upper configurations having one

electron with principal quantum numbers larger than 2 and lower levels of the ground complex

(2s+2p)N. Since Kelly's compilation [2], the status of the spectra being investigated has remained

almost unchanged. For all ions involved, the levels with principal quantum numbers n=2 have

been accurately described by Edlen from comparisons along isoelectronic sequences between

observed and ab initio MCDF transition energies (n=2, An=0) in the vuv region [1]. These

"recommended" level values are available for checking the accuracy of theoretical models and

approximations. We have used the atomic structure codes of HULLAC [3] based on the relativistic

194 ICAMDATA 97 Proceedings
parametric potential method [4] for deriving transition energies and probabilities between full complexes

(2)

N, i.e. 2s2 2pN- 2 + 2pN

and in opposite parity 2s 1 2pN" 1

(2)

N1 31

, i.e. 2s2 2pN3 3p1 + 2s2pN" 3 3d1 + 2s 1 2pN" 2 3px + 2pN-* 3s 1 + 2pN-* 3d1 and in opposite parity

2s2 2pN- 3 3pJ + 2s1 2pN- 2 3s 1 + 2s 1 2pN~ 2 3d1 + 2pN1 3p*

(2)N-i 41 being the same as (2)

N" 1 31 with quantum number 4 instead of 3.

The processing of full complexes is needed to take into account the most important configuration

mixing effects. In Table 1, wavelengths, transition probabilities, and combining levels are reported for the prominent lines of the spectrum of carbon-like copper Cu XXIV which had not

been reported earlier in the wavelength range 6.9-7.7 A.

Table 1: Theoretical and observed transitions between complexes of configurations (1)

2 (2)

4 and

(1)

2 (2)341 in carbon-like copper Cu XXTV.

(A)

gA

(io 1 ^- 1

) (1000cm-1)

J° (1000cm" 1

)

J

e ^exp

(A)

Int

(arb. units)

6.9578 23.39 634.6 2.0 15007.0 3.0 6.959 5

7.0341 30.60 1027.6 3.0 15243.9 4.0 7.031 30 Bl XXV

7.1099 23.76 14439.2 3.0 374.4 2.0 7.115 45 Bl XXV

7.1532 21.58 14169.5 2.0 189.7 2.0 7.148 30 Bl XXV

7.1533 27.16 14169.3 3.0 189.7 2.0

7.1647 21.14 14086.0 2.0 128.6 1.0 7.166 35 Bl XXV

7.3333 21.58 964.9 1.0 14601.3 2.0 7.325 20 w

7.3346 20.24 973.5 2.0 14607.4 3.0 7.3353 22.63 1170.0 1.0 14802.7 2.0 7.332 15 p

7.3481 44.33 634.6 2.0 14243.5 1.0 7.349 25 p

7.3501 53.83 634.6 2.0 14240.0 2.0 7.3529 35.89 634.6 2.0 14234.6 3.0 7.3571 33.06 13592.2 1.0 0.0 0.0 7.354 20 Bl 7.3598 21.17 13777.1 2.0 189.7 2.0

7.3630 21.52 973.5 2.0 14554.8 1.0 7.359 20 Bl 7.3640 60.58 13769.2 3.0 189.7 2.0 7.3673 28.14 973.5 2.0 14547.0 2.0

7.3947 26.77 1027.6 3.0 14550.8 4.0 7.394 40

7.3947 33.10 964.9 1.0 14488.1 2.0 7.3954 25.10 973.5 2.0 14495.4 3.0 7.3971 46.76 634.6 2.0 14153.4 3.0 7.4000 58.38 1027.6 3.0 14541.1 3.0 7.4032 63.46 1027.6 3.0 14535.3 4.0

3.1 Atomic Structure and Spectroscopy 195
(cont.)

7.4299 37.31 13587.7 2.0 128.6 1.0 7.427 20

7.4384

7.4460

7.4499

20.79

30.14

116.48

15605.8

634.6

13797.5

1.0 2.0

3.0

2162.0

14064.7

374.4

1.0 3.0

2.0

7.446 30

7.4559

7.4612

7.4632

96.39

25.00

51.52

1422.9

13777.1

13588.7

2.0

2.0

3.0

14835.1

374.4

189.7

3.0

2.0

2.0

7.459 18

7.4735

7.4822

32.12

24.21

15512.8

15621.5

1.0 2.02132.2

2256.5

0.0

2.0

7.471 6

7.4848

7.4887

7.4888

75.11

26.99

20.69

15617.0

15362.0

1204.1

3.0

1.0 2.0

2256.5

2008.6

14557.4

2.0

2.0

3.0

7.488 6

7.4977

7.4979

7.4993

7.5029

23.69

55.99

25.85

53.32

15499.5

15345.6

1170.0

15336.8

2.0

2.0

1.0 3.0

2162.0

2008.6

14504.6

2008.6

1.0 2.0

2.0

2.0

7.504 5

7.5238

7.5275

36.12

32.69

1204.1

13800.9

2.0

1.0

14495.4

516.2

3.0

0.0

7.520 15

7.5343

7.5365

7.5403

32.56

76.01

29.83

15281.1

1591.0

1352.0

3.0

1.0

1.0

2008.6

14859.8

14614.1

2.0

2.0

2.0

7.53 Bl

7.5488

7.5503

7.5505

7.5517

36.41

104.59

25.45

23.66

1027.6

1027.6

15500.7

1591.0

3.0

3.0

3.0

1.0

14274.6

14272.1

2256.5

14833.0

3.0 4.0

2.0

1.0

7.540 25

7.5662 79.44 973.5 2.0 14190.1 3.0 7.556 8

7.6055

7.6105

7.6135

7.6165

7.6207

7.6253

7.6281

7.6308

38.44

48.55

38.96

46.00

74.37

91.18

60.89

59.03

1422.9

15301.9

1422.9

964.9

15130.7

15370.8

15365.9

15654.3

2.0

2.0

2.0

1.0 3.0

3.0

2.0

1.0

14571.2

2162.0

14557.4

14094.3

2008.6

2256.5

2256.5

2549.6

2.0

1.0 3.0 2.0

2.0

2.0 2.0

0.0

7.600

7.61

7.62

30 Bl

Bl

Bl

7.6508

7.6528

7.6900

33.89

26.94

20.91

1204.1

1204.1

15136.1

2.0

2.0

1.0

14274.6

14271.3

2132.2

3.0

2.0

0.0

ICAMDATA 97 Proceeding;
As XXIV, As XXIII 2-3 at280eVLTE

9.0 9.1 92 9.3 9.4 9.5

Spectrum of laser irradiated arsenic

9.0 9.1 9.2 9.3 9.4 9.5

Figure 1: Comparison of observed spectrum of laser-irradiated arsenic (right) with theoretical 2-3 resonance transitions of Ne-like As XXTV and Na-like As XXIII satellites (left). The levels of As

XXIII are assumed to be populated according to LTE at 280 eV and not to decay via

autoionization. The relative population of As XXIV and As XXIII is an adjustable parameter.

3 Conclusion

Owing to the narrow linewidths and the high signal-to-noise ratio displayed in Fig. 1, the present

observations add valuable data to many earlier observations of medium-Z elements. The detailed

analysis of these spectra should help in studying ionic charge distribution in laser-produced

plasmas. A database with classified lines is under preparation. The ICAMDATA community will

be informed when it is available.

References

[1] B. Edlen, Physica Scripta 28, 51 (1983); 28, 483 (1983); 30 ,135 (1984); 31, 345 (1985); 32, 86

(1985)

[2] R.L. Kelly, J. Phys. Chem. Ref. Data, 16, supp.l (1987)

[3] M. Klapisch, A. Bar-Shalom and W.H. Goldstein, HULLAC computer codes, unpublished

[4] E. Koenig, Physica 62, 393 (1972); M.Klapisch, J.-L. Schwob, B.S. Fraenkel and J. Oreg, J. Opt. Soc. Am. 67, 148 (1977)

3.1 Atomic Structure and Spectroscopy 197
Self-Consistent Sets of Oscillator Strength

for Ultraviolet Lines in C i, S i, and Ni n

J. Zsargo*, S. R. Federman* and J. Cardelli*

* Department of Physics and Astronomy

University of Toledo, Toledo, OH

^Department of Astronomy and Astrophysics

Villanova University, Villanova, PA

1 Introduction

High quality spectra of interstellar absorption from C I, S I and Ni II toward several lines of

sight 1 were obtained with the Goddard High Resolution Spectrograph on HST. A curve-of-growth

analysis yields adjusted sets of oscillator strengths (Federman & Cardelli 1995; Zsargo, Federman,

& Cardelli 1997; Zsargo & Federman 1998) if the uncertainties are dominated by the errors in

the atomic properties. Our GHRS spectra with signal-to-noise ratios greater than 100-200 were

used to perform such an analysis. Our astronomically derived oscillator strengths were compared

with available information in our papers noted above. Here comparisons with the compilations of

Morton (1991) and Verner et al. (1996) are presented.

2 Analysis

We assumed simple Maxwellian line profiles to find the theoretical curves of growth, and the values

for column densities and Doppler parameters were obtained by least-squares fit where the data for

each line was weighted by the relative uncertainty in W\ [<?(W\)/W\] and in the /-value. The

oscillator strengths for the lines of a given species then were adjusted to have the best overall fit to the corresponding curves of growth. For C I and S I, precise laboratory data for several multiplets

allowed us to place the results on an absolute scale; such was not the case for Ni II.

3 Discussion

3.1 Neutral Carbon

As revealed in Table 1, our analysis yields significant revisions to /-values for 24 lines when comparison is made with previous work. Above 1200 A only forbidden lines needed significant adjustments

to their oscillator strengths. This result is not surprising since most multiplets in this range had well

defined /-values and most of the weak lines were forbidden. Below 1200 A few reliable measures

of /-value exist. Therefore significant changes in multiplet oscillator strengths could be expected.

Comparison with the compilation of Morton (1991) shows reasonable agreement (within 3<r) for

about half the lines. Many of the differences involving dipole- allowed transitions arise because

1 /3

1 Sco, p Oph A, and x Oph for C I; C Oph for S I; x Oph, C Oph and p Oph A for Ni II

198 ICAMDATA 97 Proceedings
LS coupling may not apply. Our astronomical observations indicate that LS coupling is not applicable to the lines at AA1194, 1156, and possibly A1189. Verner et al. (1996) corrected the

tabulated results from the Opacity Project by using laboratory wavelengths in converting A-values

into /-values. Their /-values are similar to those listed by Morton (1991), except for A1156.

Table 1 Comparison of Oscillator Strengths for Lines of Neutral Carbon

Wavelength (A) Transition /(ZsFC)a /(M)6 /(VVF) 1

'

1287.608 zp 3p* 1 — OQ 1.66 x 10" 4 6.38 X 10 -5

1279.498 9n2 zp 3p„^2 — Oil 3 F° 9.03 x 10"-4 (1.98 ±0.50) x 10"-4 1279.229 9r>2 Zp 3p„ — OQ 3 F§ 3.24 x 10"-3 (3.60 ±0.90) x 10"-3 1279.056 9n2 zp 3 P,^1 _— ou 3 F£ 2.02 x 10"-3 (7.33 ± 1.83) x 10"-4 1276.750 zp 3p*l Ac lpo 2.39 x 10-3 2.87 x 10-3 1276.483 2p2 3 Po - 4s lpo 1.68 x 10"-3 4.50 x 10~3 1274.109 2P

2 3 P2 - 3d 5.39 x 10"-4 4.90 x 10-4 1270.408 2p2 3 P1 - 3d lporl 2.06 x 10"-4 6.54 x 10-5 1270.143 2p2 3 Po - 3d lpo 4.28 x 10--4 3.88 x 10-4 1193.996 2P

2 3 Po - 5s 3po 7.50 x 10"-3 (9.41 ± 0.81) x 10"-3 1.05 x 10--2

1193.679 2p2 3 Pi - 5s 3por2 9.00 x 10"-3 (3.92 ±0.34) x 10- 4.45 x 10~2

-3 4.40 x 10"-3 1193.031* 2P

2 3 Po - 4d 3 D° 6.23 x 10"-2 4.76 x 10"-2 1193.009* 2p2 3 Pi - 4d 3 D£ 4.68 x 10"-2 3.34 x 10-2 3.56 x 10"-2 1192.218 2p2 3 Po - 5s lpo 8.77 x 10"-4 (2.63 ±0.51) x 10"-3

1189.631 2p2 3 P2 - 4d 3por2 1.38 x 10"-2 (1.26 ±0.11) x 10"-2 9.69 x 10"-3 1189.447 2P

2 3 P2 - 4d 3por 1 4.59 x 10'-3 (4.19 ±0.36) x 10"-3 3.23 x 10 -3

1158.324 2p2 3 Po - 6s 3por 1 5.83 x 10"-3 (3.42 ±0.30) x 10"-3 5.57 x 10"-3

1158.130* 2p2 3 P1 - 5d 3 D° 1.90 x 10"-3 (5.44 ±0.47) x 10--3 6.10 x 10"-3 1158.019* 2p2 3 P2 - 5d 3 D°u3 6.41 x 10"-3 (1.83 ±0.16) x 10"-2 2.05 x 10"-2

1157.910* 2p2 3 Po - 5d 3 D° 7.63 x 10"-3 (2.18 ±0.19) x 10"-2 2.44 x 10--2

1157.770* 2p2 3 P1 - 5d 3 D°. 5.71 x 10"-3 (1.63 ±0.14) x 10"-2 1.83 x 10"-2

1156.028 2p2 3 P1 - 5d 3po 3.45 x 10'-3 (4.31 ± 0.37) x 10"-3 1.52 x 10"-3

1155.979 2P

2 3 P1 - 5d 3po 4.60 x 10"-3 (5.75 ±0.50) x 10"-3 2.01 x 10--3

1155.809 2p2 3 Po - 5d 3po 3.04 x 10"-3 (1.73 ±0.15) x 10"-2 6.05 x 10"-3

Notes:

a Our values (Zsargo et al. 1997). Typical uncertainties range from 10% to 20%; the weakest lines have the

greatest uncertainty.

6 Morton (1991) compilation.

c Verner et al. (1996).

d LS coupling seems to apply.

3.2 Neutral Sulfur

The comparison for the 25 S I lines appears in Table 2. Unlike the situation for C I, LS coupling

adequately describes line strengths within a multiplet. In about 1/3 of the cases, substantial

differences exist with the values quoted by Morton (1991). There is good agreement with most of

3.1 Atomic Structure and Spectroscopy 199
the results of Verner et al. (1996), except for several multiplets with 3 D° upper states (AA1479,

1274, 1256).

Table 2

Comparison of Oscillator Strengths for Lines of Neutral Sulfur

Wavelength (A) Transition f(FC) a f(M) b /(VVF)C 1807 311 i 4 3p - 4s 9.6 x 10 -2 d (1.11 ± 0,10) x 10"-l 8.45 x 10"-2 1474.571 3p4 - 4s'

3 D° 1J. . UuST xAs 10" J_ \J 3

flI X.iiX 21 ±_1_ 0 24^ x 10" \J.Lj\ J As XU

-3 4.09 x 10 -4

1 474 ^70 3p4 3 P2 - 4s'

3 D£ 11. 7Q1 x 10~ i/ A XU 2 (i (io a. n on\ y in1 l.UO —1— \J*xJ£/j As XU

-2 6.14 x 10"-3

~\AT\ QQ4 o 4 3p4 - 4s'

3 D° smv O.UO As in- 1U 2

(i 71 .UU on 4-

—1— 1

i- . 42^ X Li I yAs ID" XU

-2 3.44 x 10"-2 1472 Q71 3p4 3 P2 - 3d 2& . 18x10~ X O As J.U 2 n Qi + o w x 10"-2

1X^t^t^r. 444 9Qfi £j\j\J n 4 3p 3 P2 - 4s' 1D§ 1 24 x 10~ 3 lO.lO ^-L X.tJi/J As XU

-4 142^ 21Q o 4 3p 3 P2 - 3d 3 D° X . f U A lu 3 90 -L n 4«N y If)- 1 a.OO —L— U.t:U / /N XU

-3 1.44 x 10"-3 1425 1 IlJL/. 188 1UU 3p4 3 P2 - 3d 3 D£ 2 fiQ y 1(1- 2

I"} «c _i_ fl 71 \ x in1 O.UU —L. U. 1 ± J

As XU

-2 2.16 x 10"-2 1425 n^n 3p 3p - 3d 3r)0 u3 1.41 x 10" 1 H Q2 ± 0 t7^ x 10" 1 lii/A _J_ U.U I / As XU

-1 1.21 X

i ri- ll) -1 1401.514 3p4 3 P2 - 5s 3 S° 1.49 x 10" 2 (1.61 ± 0.31) x 10--2 1.42 x 10"-2 1316.622 3P

4 3 P2 - 4d 3 D? 4.54 x 10" 4 (4.11 ± 0.80) x 10'-4 2.69 x 10"-4 1316.615 3P

4 3 P2 - 4d 3 D^ 6.79 x 10" 3 (6.15 ± 1.20) x 10"-3 4.03 x 10"-3 1316.543 3P

4 3 P2 - 4d 3 D3

° 3.81 x 10- 2 (3.45 ± 0.67) x 10"-2 2.26 x 10"-2 1303.430 3P

4 3 P2 - 6s 3 S? 5.06 x 10" 3 (2.91 ± 0.57) x 10--2 4.60 x 10"-3 1296.174 3p4 3 P2 - 4s" 3 P? 2.2 x 10~2 d (4.08 ± 0.80) x 10"-2 2.78 x io-

-2 1295.653 3P

4 3 P2 - 4s" 3 P£ 8.7 x 10-2 d (1.23 ±0.24) x 10" 1.00 x 10-2

-1 8.36 x 10"-2 1270.787 3P

4 3 P2 - 5d 3 D£ 1.64 x 10" 3 6.21 x 10"-4 1270.780 3p4 3 P2 - 5d 3 D£ 9.02 x 10- 3 5.51 x 10~2 3.47 x io-

-3 1270.769 3P

4 3 P2 - 5d 3 D

o 1.09 x 10" 4 6.62 x 10-4 4.14 x 10"-5 1262.860 3P

4 3 P2 - 7s 3 S? 2.59 x 10" 3 2.00 x 10"-3 1247.160 3p4 3 P2 - 6d 1.64 x 10" 3 3.24 x 10-2 7.44 x 10"-5 1247.134 3P

4 3 P2 - 6d 3 D£ 2.90 x 10" 4 5.77 x 10-3 1.33 x 10"-5 1247.107 3P

4 3 P2 - 6d 3 D? 1.92 x 10" 5 3.81 x 10-4 8.86 x 10"-7 1241.905 3p4 3 P2 - 8s 3 S° 1.06 x 10- 3 1.02 x 10'-3 1224.544 3p4 3 P2 - 8d 3 D°u3 < 9.6 x 10 -4

1.23 x 10-2 1.07 x 10"-3

Notes:

a Our values (Federman & Cardelli 1995). Typical uncertainties range from 10% to 20%; the weakest lines have the greatest uncertainty.

6 Morton (1991) compilation.

c Verner et al. (1996).

d Experimental results of Beideck et al. (1994).

3.3 Singly-ionized Nickel

Table 3 shows the adjusted oscillator strengths together with Morton's (1991) values. The adjusted

and the original /-values differ by less than 30% in most cases, implying that the theoretical calculations of Kurucz (1989) are reliable (in a relative sense). There are several lines with considerable

differences, those for AA1477, 1415 and 1345. Since we measured these lines in only one direction,

200 ICAMDATA 97 Proceedings
higher than average uncertainties could arise. These three lines are among the weakest observed

by us, and it is not unreasonable to find the largest discrepancies here between our results and the

predictions of Kurucz (1989) from intermediate coupling calculations. Work is in progress to place

these results on an absolute scale.

Table 3

Comparison of Oscillator Strengths for Lines of Singly-ionized Nickel

Wavelength (A) Transition /(ZsF) a f(M) b 1741.549 3dy 'D5/2 --4p'!r\o U5/2 7.76 X 10"-'1 1.04 X 10"-l 1709.600 3d9 2 D5/2 -- 4p ; b

5/2 6.66 X io-

-2 6.88 X 10"-2

1477.222 3d9 2 D5/2 -- 4p" 2 TX> *5/2 1.82 X 10"-3 1.06 X 10"-3

1467.756 3d9 2 D5/2 -- 4p" b

7/2 1.81 X io-

-2 2.27 X 10"-2

1467.259 3d9 2 D5/2 -- 4p" 2 D

o U3/2 1.13 X 10"-2 1.11 X 10"-2

1454.842 3d9 2 D5/2 -- 4p" U5/2 5.16 X 10"-2 5.95 X 10"-2

1449.997 3d9 2 D5/2 -- 4p" 2-po r

3/2 3.27 X 10"-3 3.53 X 10"-3

1415.720 3d9 2 D5/2 --4p' U5/2 5.97 X 10"-3 4.13 X 10"-3

1412.886 3d9 2 D5/2 --4p' U7/2 6.65 X io-

-3 6.65 X io--3

1393.324 3d9 2 D5/2 --4p' U5/2 1.89 X 10"-2 2.22 X 10"-2

1370.132 3d9 2 D5/2 --4p' 2por 3/2 1.44 X 10"-1 1.31 X 10"-1

1345.878 3d9 2 D5/2 --4p' 4 Coa3/2 1.44 X 10"-2 6.43 X 10"-3

Notes:

a Our values (Zsargo and Federman 1998). Typical uncertainties 30%.

6 Morton (1991) compilation.

References

[1] D. J. Beideck, R. M. Schectman, S. R. Federman, and D. G. Ellis, ApJ 428, 393 (1994)

[2] S. R. Federman, and J. A. Cardelli, ApJ 452, 269 (1995)

[3] R. L. Kurucz (1989) - see Morton (1991)

[4] D. C. Morton, ApJS 77, 119 (1991)

[5] J. Zsargo, and S. R. Federman, ApJ, in press (1998)

[6] J. Zsargo, S. R. Federman, and J. A. Cardelli, ApJ 484, 820 (1997)

[7] D. A. Verner, E. M. Verner, and G. J. Ferland, Atomic Data Nucl. Data Tables 64, 1 (1996)

3.1 Atomic Structure and Spectroscopy 201

Data

Production

3.2 Collisions

Electron Impact Ionization and Surface Induced

Reactions of Fusion Plasma Edge Constituents

KBecker*, F.Biasioli, G.Denifl, H.Deutsch**, T.Fiegele, V.Grill, T.D.Mark, C.Mair,

S.Matt, D.Muigg, P.Scheier, M.Sonderegger, A.Stamatovic, R.Worgotter

Institut fiir lonenphysik, Technikerstr.25, A-6020 Innsbruck, Austria

H'Dept.Physics, Stevens Institute of Technology, Hoboken, NJ 07030, USA

**Fachbereich Physik, Universitdt Greifswald, D-17487 Greifswald, Germany

1 Introduction

Recent studies in the field of thermonuclear fusion based on the magnetic confinement of high

temperature plasmas have demonstrated that the conditions at the plasma periphery ("plasma

edge") play an important role for achieving, sustaining and controlling the thermonuclear fusion

plasma [1]. In order to understand and elucidate the role of the radiative and collisional processes

in the plasma edge region, in particular their influence on the plasma properties and dynamics

and their use for controlling the plasma conditions, it is essential to have available a detailed and

quantitative knowledge on these elementary processes such as cross sections, reaction rate

coefficients etc. Because of the relatively low temperature in the plasma edge the plasma contains

- besides electrons and atomic ions - also a significant number of neutral hydrogen atoms, lowcharged atomic and molecular impurities (produced and introduced for instance via plasma/wall

interactions [2], via diagnostics or via cooling). According to Janev [1] the most important collision

processes (from a standpoint of their effects on plasma edge properties and behavior such as

ionization balance, plasma energy, plasma transport etc.) are electron impact excitation/ionization

reactions with plasma edge atoms, ions and molecules [3-5]. The impurities present in such an

edge plasma obviously will depend on the materials used for the plasma facing components (first

wall, protective tiles, divertor plates, antennas for rf heating etc.) and on the gases introduced for cooling and diagnostic purposes. Janev [1] has given a list of atomic and molecular impurities to be considered in such studies including the rare gases, Li, Be, B, C, Al, Si, Mg, Ti, Cr, Fe, Ni, Cu,

Mo, Nb, Ta, W, and CO, CO2, CH4, C2H2, CnHm, H2O. Some of these impurities may reach levels of

about 1 to several percent of the plasma density.

Whereas electron impact ionization of neutral and ionized atomic targets is a well studied and

documented subject [3,4] (save for a few targets and for some cases involving multiple and stepwise ionization ), the situation in case of molecular targets is far from satisfying. According to Tawara [5], who reviewed electron impact ionization of hydrocarbon molecules many data

(concerning total and partial ionization cross sections) appear to be of relatively low accuracy or have not yet been measured. The latter applies in particular to hydrocarbon molecular ions,

where almost no experimental (and theoretical) studies exist (see also Ref [6]). Moreover, the

subject of electron impact induced ionization of molecular ions has so far received very little attention (in contrast to the field of electron impact ionization of atomic ions [7]). A similar

situation exists for the area of plasma/wall interactions [2], where an understanding of the

individual "surface erosion processes" for the various target materials, in particular under typical

reactor edge plasma conditions, is a crucial prerequisite for designing the thermonuclear fusion

reactor.

3.2 Collisions 205
The present long term data study is dedicated to provide this quantitative information for the

various plasma edge constituents including, (i) experimental and theoretical studies about the

ionization of neutrals and ions, and (ii) reactive interaction of molecular ions with surfaces. The

present studies constitute on the one hand a continuation of previous research in our laboratories

(i.e., on the experimental determination of accurate ionization cross sections for neutral molecules

and on theoretical concepts for the prediction of ionization cross sections for various targets, i.e., atoms, molecules and clusters [8]) and on the other hand an extension of recently started

experiments on the inelastic interaction of electrons with molecular ions [9] and on reactive

scattering of molecular ions on surfaces. These previous studies (and the available techniques)

and also these preliminary and exploratory studies will be summarized and based on this

background an outline of the present research will be given.

2 Electron Impact Ionization Of Neutral Molecules:

Experimental Determination of Cross Section,

Kinetic Energy Release and Ionization Energy

A detailed description of the apparatus and the experimental procedure used in our laboratory for

the accurate measurement of partial ionization cross sections of atoms and of molecules has been

given previously [10]. Briefly, the experimental set-up consists of a modified Nier-type electron

impact ion source, a molecular beam source (either a Knudsen-type oven or a nozzle expansion

source) and a high resolution double focussing Nier-Johnson sector field mass spectrometer. The

performance and operating conditions of this apparatus have been continuously improved over

the past 15 years. Today it is possible to measure (absolute) partial ionization cross section

functions for atomic and molecular parent ions as well as partial ionization cross section functions

for fragment ions formed with excess kinetic energy with high accuracy up to electron energies of

1000 eV [10]. This was tested recently in detail with CF4 [10] and used recently for the study of

C2H6 [11], C3 H8 [12] and Ceo [13].

As shown and discussed in [10] it is necessary (in order to account quantitatively for

discrimination effects in the case of fragment ions produced with excess kinetic energy in the ion

source) and possible to measure the kinetic energy release distributions (KERD) of the fragment

ions formed by electron impact ionization in the ion source using a method developed over the

years in our laboratory. This ion beam deflection method is based on the fact that the extracted

ion beam shape contains information on the original ion kinetic distribution [10-12]. Detailed

studies about KERDs and the average total kinetic energy release (KER) deduced from these

distributions have been performed recently for C3H8 [14] and C60 [15] and are presently also

carried out employing a new experimental method using the apparatus described in section 5. Moreover, using monochromatized electrons in a newly constructed high resolution ion

source/mass spectrometer apparatus we were able to (i) measure in great detail the ionization

threshold region and thus to (ii) deduce ionization energies; first examples of this include

ionization energies of singly-and multiply-charged parent [16] and fragment [17] fullerene ions

and ionization energies of CO clusters [18].

206 ICAMDATA 97 Proceedings
3 Electron Impact Ionization/Dissociation of Mass Selected

Molecular Ions

In order to study electron induced ionization and dissociation of mass selected molecular ions, we

have recently modified [19] our two-sector-field mass spectrometer system in such a way as to allow with help of a newly constructed high performance electrun gun the study of inelastic

interactions between electrons and ions in the ion beam focus of the second field free region (half

way between the magnetic and the electrostatic field). Ions passing this second field free region

have already been mass selected by the magnetic sector field. Because ions are produced in this

set-up by an ordinary electron-impact ionization Nier type ion source, the primary ion currents

available after mass selection are in the order of about 10 pA. With the present electron gun (with

electron currents of about 10 mA) mounted between the two sectors it became possible to investigate electron induced ionization and fragmentation of mass selected ions. In particular we

used the MIKE-scan (mass analysed ion kinetic energy scan) technique [20] (which can be used

also to study the spontaneous decay of molecular ions in the metstable time regime) in order to identify and analyse fragment ions in terms of their mass and charge state and their kinetic

energy release. The position of the respective MIKE peaks allows an unambiguous identification

of the parent and fragment ion peaks produced and from the shape of a MIKE peak it is possible

to derive the total kinetic energy release distribution (KERD) of a specific decay reaction. In a further step the average total kinetic energy release (KER value) of the decay reaction can be

determined by calculating the first momentum of the KERD. So far we have used this technique

to study the properties of singly-and multiply-charged fullerene ions [19].

4 Calculation of Ionization Cross Sections for

Multiple Ionization of Atoms and Atomic Ions

Scaling laws and semiempirical methods can be powerful tools to predict electron impact

ionization cross sections for neutrals and ions for modelling purposes in particular for those

targets where experimental data do not exist and/or rigorous theoretical calculations are inconvenient or impossible. Many practical applications require either a quick estimate of a large

number of ionization cross sections or ionization cross section functions in analytical form [21].

Such needs can often be satisfied best (i.e., most economically and least time consuming to the

practitioner) through the use of scaling laws and other simple methods. Because classical, semiclassical and semi-empirical formulae fail in certain even simple cases [22], we have suggested in

1987 [23] the use of a semi-classical approach based on a combination of the binary encounter

approximation and the Born-Bethe approximation. Although originally devised for the single

ionization of ground state atoms [22,23], this concept has been successfully extended to the single

ionization of excited atoms, free radicals , molecules, clusters and fullerenes and atomic ions and

to the ionization of specific shells of atoms (for more details see accompanying paper in this

conference). Very recently, we have also started to apply this concept to the case of multiple

ionization of atoms, so far including double and triple ionization [24] and quadruple and

quintuple ionization [25], and very recently even to charge states higher than 5 of neutral atoms

[26].

3.2 Collisions 207
5 Reactive Interactions of Molecular Ions with Surfaces

Recently we have constructed in our laboratory a new tandem mass spectrometer [27] consisting

of an ion source, a two sector field mass spectrometer, deceleration ion optics, a surface collision

chamber and a time of flight mass spectrometer. This apparatus allows us to study the various

surface induced reactions such as surface induced dissociation, ion surface reactions and chemical

sputtering as a function of collision energy (from threshold up to about 3 kV). Thus we are able to obtain information about the mechanisms, the kinetics and the energetics of the reactions

occurring. After first tests we have so far studied reactions of acetone and benzene ions and their

respective cluster ions [27-30], fullerene ions and various other fusion relevant ions with

hydrocarbon covered stainless steel surfaces.

This work was supported by OEAW/EURATOM, FWF, OENB, BMWFK, Wien, Austria and, in

part by the Division of Chemical Sciences, Office of Basic Energy Science, Office of Energy

Research, US Department of Energy and the US National Science Foundation.

References

[I] R. K. Janev, Ed., "Atomic and Molecular Processes in Fusion Edge Plasmas", Plenum, New

York 1995

[2] W. 0. Hofer and J. Roth, Eds., "Physical Processes of the Interaction of Fusion Plasmas with

Solids", Academic Press, San Diego 1996

[3] T. D. Mark, Chapter 4 in Ref. [1], p.59

[4] P. Defrance, M. Duponchelle, and D. L. Moores, Chapter 7 in Ref. [1], p. 153

[5] H. Tawara, Chapter 16 in Ref. [1], p.461

[6] D. Gregory and H. Tawara, "Book of Abstracts, 15th ICPEAC", New York 1989, p.352

[7] G. H. Dunn, Chapter 8 in "Electron Impact Ionization", T. D. Mark and G. H. Dunn, Eds.,

Springer, Wien 1985, p.277

[8] T. D. Mark, Plasma Phys. and Controlled Fusion 34, 2083 (1992)

[9] T. Rauth, 0. Echt, P. Scheier, and T. D. Mark, Chem. Phys. Lett. 247, 515 (1995)

[10] H. U. Poll, C. Winkler, D. Margreiter, V. Grill, and T. D. Mark, Int.J.Mass Spectrom. Ion

Proc. 11, 1 (1992)

[II] V. Grill, G. Walder, P. Scheier, M. Kurdel, and T. D. Mark, Int.J.Mass Spectrom.Ion Proc. 129, 31 (1993)

[12] V. Grill, G. Walder, D. Margreiter, T. Rauth, H. U. Poll, P. Scheier, and T. D. Mark,

Z.Phys.D 25, 217(1993)

[13] S. Matt, B. Diinser, M. Lezius, H. Deutsch, K. Becker, A. Stamatovic, P. Scheier, and

T. D. Mark, J.Chem.Phys. 105, 1880 (1996)

[14] V. Grill, S. Matt, H. U. Poll, N. Abramzon, K. Becker, P. Scheier, and T. D. Mark, Int.J.Mass

Spectrom.Ion Proc, submitted (1997)

[15] D. Muigg, G. Denifl, P. Scheier, K. Becker, and T. D. Mark, J.Chem.Phys., in print (1997)

[16] D. Muigg, P. Scheier, K. Becker, and T. D. Mark, J.Phys. B29, 5193 (1996)

[17] S. Matt, O. Echt, R. Worgotter, V. Grill, P. Scheier, C. Lifshitz, and T. D. Mark,

Chem.Phys.Lett. 264, 149 (1997)

[18] G. Denifl, D. Muigg, A. Stamatovic, and T. D. Mark, to be published (1998)

208 ICAMDATA 97 Proceedings
[19] S. Matt, 0. Echt, T. Rauth, B. Diinser, M. Lezius, A. Stamatovic, P. Scheier, and T. D. Mark,

Z.Phys. D40, 389 (1997)

[20] R. G. Cooks, J. H. Beynon, R. M. Caprioli, and G. R. Lester, "Metsatble Ions", Elsevier,

Amsterdam 1973

[21] S. M. Younger and T. D. Mark, Chapter 2 in "Electron Impact Ionization", T. D. Mark and

G. H. Dunn, Eds., Springer 1985, p.24

[22] D. Margreiter, H. Deutsch, and T. D. Mark, Int.J.Mass Spectrom.Ion Proc. 139, 127 (1994)

[23] H. Deutsch and T. D. Mark, Int.J.Mass Spectrom.Ion Proc. 79, Rl (1987)

[24] H. Deutsch, K. Becker, and T. D. Mark, Contr.Plasma Phys. 35, 421 (1995)

[25] H. Deutsch, K. Becker, and T. D. Mark, J.Phys. B29, L497Q996)

[26] H. Deutsch, K. Becker and D. P. Almeida, and T. D. Mark, Int.J.Mass Spectrom.Ion Proc, in

press (1997)

[27] V. Grill, R. Worgotter, J. H. Futrell, T. D. Mark, Z.Phys. D, in press (1997)

[28] R. Worgotter, V. Grill, Z. Herman, H. Schwarz, and T. D. Mark, Chem.Phys.Lett. 270, 333

(1997)

[29] R. Worgotter, C. Mair, T. Fiegele, V. Grill, T. D. Mark, and H. Schwarz, Int.J.Mass

Spectrom.Ion Proc. 164, Ll(1997)

[30] R. Worgotter, J. Kubista, J. Zabka, Z. Dolejsek, T. D. Mark, and Z. Herman, Int.J.Mass

Spectrom.Ion Proc, in press (1997)

3.2 Collisions 209
The Role of Electron Impact Ionization Cross Sections

in Low-Temperature Plasmas

K.Becker, V. Tarnovsky, H. Deutsch*, and T.D. Mark"

Department of Physics, Stevens Institute of Technology, Hohoken, NJ 07030, USA

*Fachbereich Physik, Universitdt Greifswald, D- 17487 Greifswald, Germany

**Institut fur Ionenphysik, Technikerstr.25, A-6020 Innsbruck, Austria

1 Introduction

The use of non-equilibrium, low-temperature plasmas for materials processing is the key to the

advancement of many rapidly developing technologies. The selective and highly anisotropic

etching of materials and the controlled deposition of thin films in the fabrication of

microelectronic structures is one important area of plasma-assisted material processing. Plasma

polymerization and plasma-assisted surface modification are other areas of great technological

importance. Plasma-based processes are used in about 35% of the steps involved in the

manufacture of semiconductor chips and "the more sophisticated the chip, the larger the number

of steps relying on plasma technology" [1]. The past five years have seen an increased level of

activity in efforts to provide a more scientific underpinning of low-temperature plasma processing, a development stimulated by the 1991 National Research Council (NRC) report on "Plasma

Processing of Materials: Scientific Opportunities and Technological Challenges" [1] and several

related reports. Despite these efforts, low-temperature plasma technology (LTPT) today remains

a discipline where technological advances routinely outpace the fundamental understanding of

the key processes at a microscopic level. Even though process and reactor modeling and plasma

diagnostics techniques made very promising advances, a serious lack of sufficient and sufficiently

reliable collisional and spectroscopic data often prevents the exploitation of the full potential of

modeling codes, CAD tools, and plasma diagnostics techniques. This has been noted in a recent

follow-up NRC report on "Modeling, Simulation, and database Needs in Plasma Processing" [2]. The report cites three main reasons for the poorly developed status of the database, (i) the

continued comparatively low level of research efforts in this area, (ii) little coordination between

the activities of the few groups working in this field, particularly poor coordination between

experimental efforts and theoretical calculations, and (hi) a very serious lack of communication

between the community that generates the data and the community that uses the data.

2 Background

A low-temperature plasma is a system far from thermodynamical equilibrium. The electron

temperature is much higher than the gas temperature (which is often close to the ambient

temperature) and can drive "high temperature" chemistry without the adverse effects of high

ambient temperatures on the processed materials. The reactive species in a processing plasma,

primarily chemically active neutral and ionic radicals and molecules and atomic ions, result from

the collisionally induced break-up of the parent feedstock molecules. A quantitative and detailed

understanding of the processes leading to the formation of the reactive plasma constituents and of

210 ICAMDATA 97 Proceedings
their structure is important for three reasons, (i) to determine the composition of the plasma and

thus the plasma properties and the key plasma chemical reaction pathways, (ii) to determine the

flux of reactive plasma species to the wafer or substrate and thus the utility of a particular

plasma for a specific processing application, and (iii) to provide the basis for optical and mass

spectrometric diagnostics of the relevant gas phase and surface processes as well as for state-of- the-art computer simulations and CAD tools for process modeling and reactor design.

Electron and photon interactions with reactive plasma constituents under single collision

conditions are a versatile probe of the structure and dynamics of the parent plasma constituents as well as of the dominant secondary plasma species such as chemically reactive radicals which

are produced by collision-induced dissociation and ionization of the parent molecules. With

average electron energies of 0.5 eV to 5 eV for typical technological low-temperature plasmas, the

high energy tail of the electron energy distribution function (eedf) extends well into the impact

energy regime above the thresholds of the cross sections for the electron-impact dissociation and

ionization of the parent plasma constituents. The overlap of the eedf and the near-threshold

regions of these cross sections determines the efficiency of the formation of the various neutral

and ionic plasma species. The experimental determination of electron-impact cross sections for

the dissociation and ionization of the parent molecules, particularly the low-energy, near- threshold regions of the cross sections and measurements of all types of cross sections for electron

collisions with chemically reactive neutral and ionic plasma radicals are of crucial importance in

any effort to understand, describe, model, and characterize the properties of a particular

processing plasma. The gas phase processes, in turn, determine the flux of ions and neutrals to the wafer or substrate and, therefore, indirectly determine the surface processes as well.

3 Current Activities

Our group at the City College of New York, which has recently been relocated to the Stevens

Institute of Technology in Hoboken, NJ, in collaboration with the group of Prof. Mark in

Innsbruck, Austria and Prof. Deutsch in Greifswald, Germany has been engaged for several years

in a comprehensive effort aimed at the experimental and theoretical study of elementary

processes and the generation of basic collisional and spectroscopic data relevant to lowtemperature processing plasmas

3.1 Experimental Activities

The main focus of the experimental part of the research project is the study of the collisionally

induced ionization, dissociation and dissociative ionization of selected molecules and free radicals.

The choice of target molecules to be investigated is based on two considerations which are given

roughly equal weight, (1) the relevance of the particular species in low-temperature plasmas and

(2) common features among the targets from a more basic collision physics viewpoint (e.g.

interesting and/or similar molecular or electronic structure, members of a particular

molecular/radical sequence, etc.). The project up to now has studied primarily molecular and

radical targets of the form ABx with A = C, N, Si, B = F, H, and x = 1 - 4 (see tables below). The

work for the fluorine-containing targets has been completed except for SiF4 which will be studied

in the near future employing a mass spectrometric technique (see below). All other experiments

3.2 Collisions 211
were carried out in our well-characterized fast-beam apparatus [3,4]- Comparisons between the

ionization behavior of the various targets have been made from several viewpoints:

1 . along each row in the above table

2. along each column in the above table

3. between the various rows in the above table

4. between the various columns in the above table

'able 1: Fluorine-containing Species

CF4 « CF3 CF2 CF

NF3 NF2 NF

SiF4

2) SiF3 SiF2 SiF

x) This molecule was studied by several other groups, but not as part of this project

2)This molecule will be investigated in the near future

It was the objective to correlate the ionization properties (magnitude of total and partial

ionization cross sections, peak ionization cross section values, cross section shapes, ratio of parent

to fragment ionization cross sections, mechanisms of fragment ion formation, etc.) with the

molecular and electronic structure

of the targets. We subsequently investigated the corresponding hydrides.

'able 2: Hydrogen-containing Species

CH4 CH3 CH2 CH

NH3 NH2 NH

SiH4 SiH3 SiH2 SiH

(For reasons of experimental convenience we frequently substituted the deuterated

compounds in our experiments. This is of no consequence for the results and their

interpretation, since ionization cross sections are insensitive to isotope effects to a very high degree of approximation.)

By replacing the F atoms by the lighter H atoms, we essentially go from a multi-center to a quasi

single-center molecule. Furthermore, by replacing the very electronegative fluorine atoms by

hydrogen, the molecular and electronic properties of the targets were modified significantly.

The most recent experimental work focused on NDX (x=l-3) and silane, SiH4. There are some

notable similarities between the NDX ionization data and the previously obtained SiDx and CDX data. Similar to the case of SiDx and CDX, the ionization of the NDX targets is dominated by the

formation of the respective parent ions and the parent ionization cross section has essentially the

same value for all three targets. Furthermore, dissociative ionization, although a less important

process, is, in turn, dominated by a single channel, viz. the removal of a single D atom for all three

targets. Lastly, all fragment ions (except for D+

) are formed with little excess kinetic energy.

There is also two notable differences between the CDX and NDX data on one side and the SiDx data on the other side. For one, the SiDx ionization cross sections are significantly larger (more than a

212 ICAMDATA 97 Proceedings
factor of 2) than the NDX and CDX ionization cross sections, which, in turn, are of very similar

magnitude. Secondly, in the case of SiDx, the cross section for the dominant dissociative

ionization channel had the same value for all three SiDx species, while there is a systematic

decrease in the dominant disociative ionization cross section for NDX and CDX with decreasing

value of x, i.e. the ND+/ND2 and CD+/CD2 cross sections are smaller than the ND2VND3 and

CD2VCD3 cross sections, while the N7ND and C

+/CD cross sections are the smallest.

Silane, SiFU, is in the same class of molecule as e.g. SiF4 and CF4 in the sense that it does

have a stable parent ion. As a consequence, the fast-beam method is not suitable to study SiH4.

A mass spectrometric technique had to be employed (in collaboration with the group of Dr. M.

Schmidt at the INP Greifswald, Germany) to investigate this molecule. There had been three

earlier studies of the ionization of silane carried out by three different groups using three different

techniques, but the agreement was very poor (more than a factor 3 difference in some partial and

in the total ionization cross section). Great care was exercised in the characterization of our mass

spectrometer and in the analysis and minimization of possible sources of systematic errors. As a

result, we believe that the apparatus is capable of measuring absolute molecular ionization cross sections at the 15-20% level of accuracy. As expected, our experiments revealed that dissociative

ionization processes are the dominant ion formation mechanisms and all molecular fragment ions

(except for H2+

) are formed with little excess kinetic energy. By contrast, the H+ fragment ion is formed with a broad distribution of kinetic energies peaking at several electronvolts per fragment

ion.

3.2 Cross Section Calculations

We have also developed and refined various semi-empirical and semi-classical methods for the

calculation of total single ionization cross sections of molecules and radicals. The main effort is on

the development and refinement of a modified additivity rule which allows predictions of total

single ionization cross sections of complex molecules for which more rigorous calculations are

difficult. This model expresses the molecular ionization cross section in terms of the ionization

cross sections of the constituent atoms and empirically determined weighting factors which

account for molecular bonding. Up to now, our efforts focused on refining the additivity concept

for molecules of the form ABn. We are also working on the extension of this concept to more

complex molecules of the form AxBy and AxByCz.

This work was supported in part by the Division of Chemical Sciences, Office of Basic Energy

Science, Office of Energy Research, US Department of Energy, by the US National Science

Foundation, and by the US National Aeronautics and Space Administration (NASA).

References

[1] "Plasma Processing of Materials: Scientific Opportunities and Technological Challenges",

National Academy Press 1991

[2] "Modeling, Simulation, and Database Needs in Plasma Processing", National Academy Press

1996

[3] R. C. Wetzel, F. A. Biaocchi, T. R. Hayes, and R. S. Freund, Phys. Rev. A 35 559 (1987);

R. S. Freund, R. C. Wetzel, R. S. Shul, and T. R. Hayes, Phys. Rev. A 41 3575 (1990)

[4] V. Tarnovsky and K. Becker, Z. Phys. D 22 603 (1992); V. Tarnovsky, P. Kurunczi,

D. Rogoshnikov, and K. Becker, Int. J. Mass Spectrom. Ion Proc. 128 181 (1993)

3.2 Collisions 213
Atomic Data: Energy Levels, Transition Rates, and

Collision Strengths; An Example of Mg VIII

A. K. Bhatia

Goddard Space Flight Center, Greenbelt Maryland 20771

A number of satellites have been launched to observe radiation from various astrophysical

sources. Line radiation is emitted when the levels in ions/atoms excited by electron or proton

impact decay to lower levels by photon emission. From this radiation, the physical parameters,

such as electron temperature and density of astrophysical plasmas, can be inferred. Electron

impact excitation is, in general, more important than proton impact excitation except for fine

structure levels in the ground levels. A number of methods have been used for calculating

excitation cross sections: most commonly used are distorted wave (DW) approximation and the

R-matrix approach. In DW approximation, channel coupling and resonances are neglected, and

therefore the method is considerably simpler than the R-matrix approach. Rate coefficients and

collision strengths, averaged over a Maxwellian distribution, are accurate to nearly 20% in DW

approximation and 10% in R-matrix approach. A comparison of collision strengths in Ca XIII calculated in these two approximations is given in Ref. [1]. Proton excitation rate coefficients are

calculated by semi-classical approximation [2] . With a number of collaborators, I have carried out

DW calculations for a number of ions. In addition to excitation cross sections, energy levels,

oscillator strengths, and transition rates are required. A number of papers have been published on atomic data for various ions. Cumulative indexes of Atomic Data And Nuclear Data Tables, 64,

321 (1996) alone list 15 publications. Recent publications [3,4] are on Fe XV. The atomic data in

Ref. [3] have been used to investigate the rocket spectrum of a solar flare in the 10 - 100 A range

and to identify the strong line at 69.65 A. The atomic data in Ref. [4] have been used to calculate

intensity ratios in the EUV range and compare with those observed by SERTS in an active region

of sun. The calculated results should also be useful in analyzing observations from SOHO.

The atomic data are required not only to study intensities of emitted lines but also to study

elemental abundances and opacity. Atomic data have also been used to study the Bowen

fluorescence mechanism (e.g. in O III [5] and N III [6]). The atomic data are also of importance in

planetary atmospheric studies, laser physics, and for diagnostics of Tokomak plasmas.

To calculate the atomic data, a set of programs developed at University College has been used

extensively: the Superstructure and DW programs. In the Superstructure program, configuration

interaction can be taken into account, and the radial functions are calculated in a modified

Thomas-Fermi potential. Spin-orbit interactions, which give fine structure splitting, and

relativistic corrections are treated as a perturbation to the nonrelativistic Hamiltonian. It is important to choose target configurations carefully in order to obtain accurate energy levels,

oscillator strengths, and transition rates. The same radial functions are used in the DW

calculation to calculate the excitation cross sections.

As an example, our most recent calculation is on the Mg VIII ion carried out in collaboration

with Dr. R. J. Thomas [7] . EUV spectral lines of Mg VIII have been observed from the solar corona by Skylab, by SERTS, and more recently by SOHO. SERTS flights [8] were in 1989, 1991, and in

1993, and lines for which intensities were measured are 311.78, 313.74, 315.02, 317.01, 339.00,

430.44, and 436.73 A. All these lines, with the exception of 430.44 and 436.73 A, have been

214 1CAMDATA 97 Proceedings
measured by SOHO [9] flown in 1995. The figure in Ref. [7] shows a comparison of active region

spectra taken by SERTS-89 and by CDS on SOHO.

Twenty levels are included by using the configurations 2s2 2p, 2s2p2

, 2p3

, 2s2 3s, 2s2 3p, and

2s2 3d in the Superstructure program described by Eissner et al. [10]. Optimum Thomas-Fermi

potential is obtained by minimizing the sum of term energies. The energy levels, oscillator

strengths, and radiative rates have been calculated in intermediate coupling. These are given in

Tables 1 and 2 of Ref. [7]. The potential obtained in the calculation of energy levels, oscillator

strengths, and transition rates is used in the DW program described by Eissner and Seaton [11].

Reactance matrices are calculated in LS coupling and transformed to intermediate coupling by

using term-coupling coefficients [12] obtained from the Superstructure program. It is not practical

to include a very large number of incident partial waves. Therefore, contribution from higher

incident partial waves to dipole-allowed collision strengths is included using Coulomb-Bethe

approximation [13]. Collision strengths are calculated at five incident energies (15.0, 22.5, 30.0,

37.5, and 45 Ry), and they are given in Table 2 of Ref. [7]. The temperature of maximum abundance for this ion is logTe = 5.9 K. The rate coefficients are

calculated at this temperature by averaging the collision strengths over a Maxwellian

distribution. Level populations are calculated by the solving statistical equilibrium equations at a particular electron density, and intensity ratios are calculated using

Iij = nj Aji AEij (energy units)

where iij is the fractional level population, Aji is the transition rate, and AEij is the energy

difference between the levels j and i. A comparison with relative intensities observed by SERTS-89 in an active region is given in

Table 1. The calculated intensity ratio 1(313.74) / 1(317.01) = 1.69 agrees reasonably well with the

observed value 1.40. Inclusion of three more configurations, 2s3p3s, 2s2p3p, and 2s3p3d does not

change the above calculated ratio appreciably. These lines originate from the same upper level,

and therefore the ratio depends only on transition rates. This indicates that the calculated

transition rates are reliable. The relative intensities of 436.73 and 430.44 A remain in some

disagreement with the calculated values. However, the intensity ratio 1(436.73) / 1(430.44) is found to be density sensitive, and at logNe = 9.2 (interpolated), its value is 1.68 which is the

observed value from SERTS-89 (Thomas and Neupert ). This density is comparable to the value of

logNe = 9.6 derived by Brickhouse, Raymond, and Smith [14] from the same SERTS-89 spectrum,

except using Fe IX line ratios formed at a similar temperature to those of Mg VIII.

This work was supported by NASA-ATOP grant 432-38-53-14.

3.2 Collisions 215
Table 1: Relative Intensities Observed by SERTS-89 compared to Calculated Values at Te=8xl05K

Transition X(A) lobs leal iQg(Ne)

i j 6 7 8 9 10c

1 10 311.778 0.313a ± 0.056 0.199 0.199 0.199 0.199 0.199

1 9 313.736 0.317 ±0.049 1.380 1.062 0.540 0.395 0.378

2 10 315.024 1.000 ±0.123 1.000 1.000 1.000 1.000 1.000

2 9 317.008 0.227 ±0.052 0.816 0.628 0.319 0.233 0.223

1 8 335.230 — b 0.437 0.357 0.225 0.188 0.184

2 8 339.000 0.213 ±0.033 0.627 0.511 0.322 0.269 0.263

1 6 430.445 0.159 ±0.019 1.614 1.208 0.542 0.356 0.334

2 7 436.726 0.267 ±0.032 0.108 0.255 0.498 0.566 0.574

a Blended with Ni XV, see Thomas & Neupert (1994)

b Masked by Fe XVI 335.40 A

c Above log(Ne) = 10, ratios do not change

References

[I] S. O. Kastner and A. K. Bhatia, Astron. Astrophys. 71, 211 (1979)

[2] K. S. Baliyan and A. K. Bhatia, J. Phys. B 27, 4281 (1994)

[3] A. K. Bhatia, H. E. Mason, and C. Blancard, Atomic Data and Nuclear Data Tables 66, 83

(1997)

[4] A. K. Bhatia and H. E. Mason, Atomic Data and Nuclear Data Tables 66, 119 (1997)

[5] A. K. Bhatia, S. O. Kastner, and W. E. Behring, ApJ 257, 887 (1982)

[6] S. O. Kastner and A. K. Bhatia, ApJ 287, 945 (1984)

[7] A. K. Bhatia and R. J. Thomas, ApJ 497, 483 (1998)

[8] R. J. Thomas and W. M. Neupert, ApJS 91, 461 (1994)

[9] R. A. Harrison et al., Solar Phys. 162, 233 (1995)

[10] W. Eissner, M. Jones, and H. Nussbaumer, Comput. Phys. Commun. 8, 270 (1974)

[II] W. Eissner and M. J. Seaton, J. Phys. B 5, 2187 (1972)

[12] H. E. Saraph, Comput. Phys. 15, 247 (1978)

[13] A. Burgess and V. B. Sheorey, J. Phys. B 7, 2403 (1974)

[14] N. S. Brickhouse, J. C. Raymond, and B. W. Smith, APJS 97, 551 (1995)

216 ICAMDATA 97 Proceedings
Collisional and Spectroscopic Data Relevant to

the Fundamental Processes in Plasmas Containing

Si-Organic Admixtures

R. Foest, R. Basner, M. Schmidt, P. Kurunczi*, and K.Becker*

Institut fiir Niedertemperatur-Plasmaphysik,

Robert-Blum Str. 8-10, D-17489 Greifswald, Germany

*Department of Physics, Stevens Institute of Technology,

Hoboken, NJ 07030, USA

1 Introduction

Silicon-organic molecules are used in various plasma-assisted deposition and polymerization

applications [1,2]. The most commonly employed monomers [3-7] include tetraethoxysilane

(TEOS), Si(0-CH2 -CH3) 4, tetramethylsilane (TMS), Si(CH3) 4, and hexamethyldisiloxane

(HMDSO), (CH3) 3-Si-0-Si-(CH3)3. TMS is among the simplest Si-organic compounds, whereas

HMDSO is the simplest of the siloxane compounds, which are characterized by a -Si-O-Si- bridge

in their molecular structure. In spite of the practical importance of plasma-assisted material

processing using discharge mixtures containing Si-organic admixtures, little is known about the

fundamental physical and chemical processes in these plasmas and about the collision-induced

decomposition of these molecules in the plasma. Ionization studies under single collision

conditions combined with mass spectrometric studies in the actual plasma have shed some light on the processes in TMS-containing plasmas [8,9] and similar studies are currently underway for

TEOS and HMDSO [10]. In addition to mass spectrometry, optical plasma diagnostics methods

can also shed light on the fundamental plasma processes [11]. Optical emissions from plasmas

containing Si-organic molecules have been studied to some extent [12]. Optical emissions in the

visible and near-ultraviolet region of the electromagnetic spectrum produced by controlled

electron-impact under single collision conditions on TMS, TEOS, and HMDSO have been studied

recently in our group [13,14].

Researchers at the Institut fur Niedertemperatur-Plasmaphysik (INP) in Greifswald,

Germany have been engaged in a comprehensive series of experimental studies aimed at (i) the

measurement of absolute partial ionization cross sections for various Si-organics under controlled

single collision conditions, (ii) in-situ studies of the behavior and properties of the neutral and

ionic components in realistic deposition plasmas containing Si-organic admixtures, and (hi)

correlating the single collision observations with the plasma observations. This effort is complemented by studies of the visible, near-ultraviolet, and vacuum ultraviolet emissions

produced by controlled electron impact on these Si-organic cmpounds carried out at the Stevens

Institute of Technology in Hoboken, NJ, USA.

2 Experimental Details

The experimental apparatus and the data acquisition and analysis procedures for the

photoemission studies employs a crossed beam arrangement where the interaction region is defined by the intersection of the electron beam and the gas beam. A five-element electron gun

3.2 Collisions 217
produces a spatially well defined electron beam with a current of typically 80 uA at 100 eV. The

energy of the electron beam can be varied over the range of 5 - 200 eV with an energy spread of

about 0.8 eV (full width at half maximum) at an energy of 100 eV. A multicapillary array

produces the gas beam which crosses the electron beam at right angles. The estimated gas density

in the interaction region is of the order of 1012 molecules/cm3

. A precision leak valve controls the

backing pressure in the gas line to the multicapillary array. This pressure was monitored by a Baratron capacitance manometer. The analysis/detection system for the vacuum ultraviolet

(VUV) emissions is positioned mutually perpendicular to both the gas beam and the electron

beam. The VUV emissions are spectrally analyzed using a Minuteman model 302-VM 0.2m

vacuum monochromator of the Seya-Namioka design and the VUV photons are subsequently

detected with by a channel electron multiplier (CEM). The output signal of the CEM is fed into a standard circuit for single photon counting. The monochromator is equipped with a holographic

grating for the wavelength range from 50 to 250 nm. The monochromator and detector are evacuated to a pressure of 5 x 10'7 Torr under operating conditions. The main vacuum chamber

which houses the crossed-beam set-up is evacuated to a pressure in the low 10" 7 Torr range

without gas load which rises to about 2-5 x 10 5 Torr under operating conditions.

At the INP, Dr. Schmidt and his co-workers have a high-resolution (m/Am = 40 000) double

focusing sector field mass spectrometer MCH 1310 with a Nier-type electron-impact ion source

[15,16]. The target gas pressure in the ion source, which is typically in the range 0.1 to 1 mPa

compared to a background pressure of 0.001 mPa, is measured with a spinning rotor viscosity

gauge. The electron gun is operated with a stabilized electron beam current of 10 OA emitted from

a directly heated tungsten band cathode. The impact energy can varied from 5 eV to 100 eV. The

energy spread of the electron beam, which is collimated by a weak longitudinal magnetic field of

200 G, is about 0.5 eV (FWHM). The ions are extracted from the ionization region by a penetrating electric field. The acceleration voltage between the ion source and the entrance slit of

the mass spectrometer is 5 kV. Argon, which is used as reference gas, is always added to the

target gas under study for calibration purposes. The ion efficiency curves (relative ionization cross

sections) are measured simultaneously for Ar and the target gas in a well-defined mixture in an

effort to ensure equal operating conditions for the detection of all ions. The measured relative

partial ionization cross sections are put on an absolute scale by normalizing the total single

ionization cross section for a given species relative to the total Argon ionization cross section of

2.77 x 10- 16 cm2 at 70 eV.

Recently, the ion optics for the extraction, acceleration and deflection of the product ions was

rebuilt based on ion trajectory simulations [16] in conjunction with in-situ experimental studies in an effort to minimize and/or quantify the discrimination of energetic fragment ions. The modified mass spectrometer can now be operated either in a high mass resolution mode (with significant

discrimination effects present) or in a high extraction efficiency mode (by partially sacrificing the

high mass resolution capability). All measurements routinely employ a sweep of the ion beam

across the entrance slit of the mass spectrometer and absolute cross sections are obtained by

integrating the ion signal over the complete ion beam profile. The advantage of the INP

instrument is its superior mass resolution and a very large dynamic range which allows very

small ionization cross sections (down to 1 x 10 20 cm2

) to be measured with high precision. On the

other hand, even with the new ion extraction optics, the instrument has a limited capability of

extracting and detecting energetic fragment ions and, of course, it can only investigate stable

targets.

Very recently, a second apparatus has become available at the INP, a time-of-flight mass

spectrometer, which will be operational by the end of this year. The new instrument combines the

218 ICAMDATA 97 Proceedings
capability to extract and detect very efficiently energetic fragment ions with a large dynamic

range, but its use is still limited to stable targets and has a much reduced mass resolution

compared to the high-resolution instrument.

The in-situ plasma measurements are carried out in a 13.56 MHz rf capacitively coupled

discharge reactor. The two electrodes, which have a diameter of 12.8 cm each, are separated by a gap of 4 cm. Typical rf powers are from 15 to 150 W. The pressure in the reactor ranges from 1-20

Pa and typical gas flow rates are 10 seem of the carrier gas (Ar) and 0.1- 0.2 seem of the

Si-organic admixture. The reactor is coupled to a VG SXP 300H plasma monitor (mass

spectrometer) which is also equipped with an ion energy analyzer in order to determine the

kinetic energy distribution of the various ions in the plasma. The plasma monitor, whose mass

dependent detection sensitivity has been carefully calibrated, can be used to probe either the

neutral or the ionic plasma component.

3 Some Selected Results

The ionization cross section measurements for TMS have been completed. It was found that by far

the most dominant channel is the formation of the Si(CH3)3+ fragment ion with a maximum cross section value of about 1 x 10' 15 cm2 which accounts for about 50% of the total TMS ionization cross

section. The maximum TMS parent ionization cross section is less than 2% of that value. Based on

our measured partial ionization cross sections for more than 20 fragment ions and on their

measured appearance energies we proposed a collision-induced decomposition scheme for the

TMS molecule in low-temperature plasmas. Three major decomposition routes were identified

which all involve the total or partial removal of a CH3 methyl group.

Ionization cross section studies for the other two Si-organics have also been completed and the

results are in many respects similar to what was found for TMS, viz. very small parent ionization

cross sections, a dominance of dissociative ionization processes, a small number of fragment ions

with comparatively large ionization cross sections. In contrast to TMS, the ionization data for

TEOS and HMDSO are more difficult to interpret on account of the much more complicated

cracking pattern and the much larger number of fragment ions with appreciable cross sections for

their formation.

Detailed in-situ studies in realistic deposition plasmas containing Ar as the carrier gas and

small (1-2%) admixtures of TEOS and HMDSO revealed a variety of noteworthy findings: whereas

the ionic plasma component in both cases still reflected to some extent the cracking pattern of the

parent molecule, there was little evidence of the parent cracking pattern in the neutral

component. A common feature was the significant increase (in some cases by 2-4 orders of

magnitude) of certain small fragment ions in the plasma compared to calculated ion abundances

using the single collision ionization cross sections. Furthermore, we found ample evidence of the

formation of "new" ions in the plasma by various plasma chemical reactions. This indicates that

secondary processes such as dissociation into neutral ground-state fragments followed by

subsequent electron collisions and ion-molecule reactions play a very important role in the plasma

chemistry of deposition plasma containing Si-organic admixtures.

The comparatively large values of the ionization cross sections for TMS, TEOS, and HMDSO

(relative to e.g. Ar) and the relatively low appearance energies of many fragment ions (7-10 eV

compared to 15 eV for Ar) explain why a small TEOS admixture of 2% to an Ar plasma leads to a

situation where the ionization balance in the plasma is completely determined by the Si-organic

admixture.

3.2 Collisions 219
The photoemission studies involving TMS, HMDSO, and TEOS in the various spectral regions

(vacuum ultraviolet, near-ultraviolet, and visible) revealed several common features:

(1) the vacuum ultraviolet spectra are completely dominated by the H Lyman series

(2) the Lyman-a and Lyman-(3 lines are heavily influenced by cascading from higher H

states

(3) the measured appearance energies indicate that partial fragmentation processes are the dominant break-up mechanisms leading to the formation of excited H fragment

atoms

(4) the near-ultraviolet and visible spectra contain mostly the hydrogen Balmer series and

emissions from the excited CH radical

(5) the TMS and HMDSO emission spectra show also the presence of atomic Si emissions

(6) in general, the measured emission cross sections are comparatively small

Future work will focus on a continuation of the work in TEOS and HMDSO and will eventually

also involve other Si-organics, e.g. dimethylsilane, (CH3)2SiH2 , which is used in processing

applications which require environmentally "green" processing gases.

This work was supported in part by the US National Science Foundation.

References

[I] "Plasma Deposition, Treatment, and Etching of Polymers", R. D'Agostino, ed., Academic Press, San

Diego 1990

[2] S. Peter, R. Pintaske, G. Hecht, and F. Richter, Surf. Coat. Technol. 59, 97 (1993)

[3] H. Yasuda, "Plasma Polymerization", Academic Press, London 1985

[4] D.A. Dougherty and A. Gallagher, J. Appl. Phys. 67, 139 (1990)

[5] A.W. Luft and S. Tsuo, Appl. Phys. Comm. 8, 1 (1988)

[6] I. Tajama and M.Y. Yamamoto, J. Polym. Sci. A: Polym. Chem. 25, 1737 (1987)

[7] P. Favia, R. Lamendola, and R. DAgostino, Plasma Sources, Sci. Technol. 1, 59 (1992)

[8] R. Basner, R. Foest, M. Schmidt, F. Sigenegger, P. Kurunczi, and K. Becker, Int. J. Mass Spectrom.

Ion Proc. 153, 65 (1996)

[9] R. Basner, R. Foest, M. Schmidt, P. Kurunczi, K. Becker, and H. Deutsch, "Contributed Papers of

the XXII. International Conference on Phenomena in Ionized Gases", Hoboken, NJ, USA 1995,

editors: K. Becker, W.Carr, and E. Kunhardt, Stevens Institute of Technology Press, Hoboken

1995, p. IV-31

[10] R. Basner and M. Schmidt, private communications (1996, 1997); see also R. Basner, R. Foest, M.

Schmidt, F. Hempel, and K. Becker, "Contributed Papers of the XXIII. International Conference on Phenomena in Ionized Gases", Toulouse, France 1997, editors: M. C. Bordage and A. Gleizes,

University of Toulouse Press, Toulouse 1997, p. IV-196

[II] see e.g. J. E. Lawler, M. A. Childs, K. L. Menningen, L. W. Anderson, S. D. Bergeson, and K. L. Mullman, in "Phenomena in Ionized Gases", editors: K. Becker, W.E. Carr, and E. Kunhardt,

American Institute of Physics Press, New York 1996, p. 1 [12] M. Schmidt, R. Foest, R. Basner, and M. Hannemann, Acta Phys. Comen. 35, 217 (1994)

[13] M. Ducrepin, J. Dike, R. Siegel, V. Tarnovsky, and K. Becker, J. Appl. Phys. 73, 7203 (1993)

[14] P. Kurunczi, A. Koharian, K. Becker, and K. E. Martus, Contr. Plasma Phys. 36, 723 (1996)

[15] R. Basner, M. Schmidt, H. Deutsch, V. Tarnovsky, A. Levin, and K. Becker, J. Chem. Phys. 103,

211 (1995)

[16] R. Basner, R. Foest, M. Schmidt, F. Sigeneger, P. Kurunczi, K. Becker, and H. Deutsch, Int. J. Mass Spectrom. Ion Proc. 153, 65 (1996)

220 ICAMDATA 97 Proceedings
Measurements of the Absolute Cross Sections of

Inelastic Processes for Slow Atomic Collisions

M. R. Gochitashvili, B. I. Kikiani, R. A. Lomsadze

Tbilisi State University, Tbilisi, 380028 Georgia

Measurements of the absolute cross-sections of inelastic processes in ion-atom and ion-molecule

collisions in the energy range from several hundred to a thousand electron volts are connected

with experimental difficulties (low values of cross sections, scattering of the primary ion at large

angles, problems with the total collection of the formed energetic products of the collisions). This

accounts for discrepancies between the data of different authors. On the other hand, these data

are necessary for solution of many fundamental and applied problems (plasma and upper

atmosphere physics, gas discharge physics and so on).

Below are described the experimental methods and arrangements that have been developed

and applied in our laboratory to measure absolute total and differential cross sections of excitation

aex, ionization Gi, charge transfer ac and electron loss (stripping) as processes.

The main parts of the our mass-spectrometer arrangement are (Fig. 1): an ion source H, an

accelerating and focusing system L (quadrupole lenses), a magnetic mass-analyzer M, collimating

slits (S0-S3), a collision chamber C and a detector of ions D. The target gas pressure in chamber C

(about 104 torr) could be varied according to the single collision condition. The differential

pumping system V achieved a vacuum of about 106 torr in another part of the arrangement.

When measuring cross-sections of excitation processes, the radiation emitted at the collision was

observed under a 90° angle to the direction of the primary ion beam. The spectral analysis of this

radiation was performed in the visible (by a MDR monochromator) and vacuum ultraviolet

spectral regions (by a Seya-Namioka monochromator). The intensity of the radiation was detected

by photo-(PEM) and secondary electron (SEM) multipliers. A system of polaroid and quarterwave plates P was used for checking the polarization of the radiation in the visible region. The

investigations were carried out by different types of ion sources: alkali metal ions were generated

in a surface ionization ion source; and H+

, H2+, Hg+, He+

, 0+

, N+ ions by gas discharges and

electron bombardment ion sources.

Figure 1

3.2 Collisions 221
The optimum regime for the operation of these sources has been established by special control

experiments. For example, in the case of the H3+-He pair it was determined that the vibrational

excitation of H3+* molecules strongly influences the efficiency of the excitation of the La line

(A=120.0 nm) in the dissociation processes. The control experiment showed that by increasing the

hydrogen pressure in the gas discharge ion source this efficiency is decreasing and reaches the

saturation region at a pressure of about 3xl0-3 torr. Under these conditions the deexcitation of

vibrational excited H3+* molecules takes place in the time of collisions with H2. The H3+ ions are formed in the ground state only [1]. Particular attention was devoted to the reliable determination and control of the relative and

absolute spectral sensitivity of the recording system for the emitted radiation. This was done by

measuring the output signal of the molecular bands and atomic lines excited by electrons in the

collisions e+H2, N2, O2. The relative spectral sensitivity and hence the values of the absolute cross sections were obtained by comparisons with cross sections for the same lines and molecular bands

reported by other authors [2-6]. The spectra for e+tta and e+N2 collisions at an electron energy

E=200 eV are presented in Fig. 2.

Figure 2

The transfer electrical field method (see for example [7]) is modified to measure the absolute

values of total cross sections of ionization and charge transfer processes. The target gas ions and

free electrons (secondary particles), arising as a result of collisions, are collected by the

homogeneous electrical field of a plane capacitor K (Fig. 1). Absolute cross sections for the

production of these particles, a+ and a-, are connected with cross sections (Ji, ac, as by the following

relations: ai=ai+ac , o-=cn+as. For the fixed homogeneous part of the field ("collision length") the

capacitor electrode was divided by small plane parallel sections (1-10) and the charge distribution

was studied with them. In front of the electrodes a grid G is placed to suppress the secondary

electron emission from the surface of the sections. This grid is used to receive information about

the energy spectrum of scattering particles by a "stopping potential," too. In Fig. 3 the ion current,

scattering on the section closest to the entrance slit of chamber C (section 1, curves 3, 4) and on

the middle section (section 5, curves 1, 2), is plotted as a function of the stopping potential for a K+-Ar pair at energies E=l keV and E=5 keV (curves 1, 3 and 3, 4 respectively). Considerable

differences between these currents are caused by the strong possibility that the scattering

primary ions are hitting the middle section. Therefore, section 1 was chosen for the measurements

222 ICAMDATA 97 Proceedings
0 20 40.- 60 BO iOO ev. Figure 3

Absolute cross sections for the stripping processes as were measured in separate experiments by mass spectrometer analysis of the primary beam after passing through the collision chamber.

To determine the energetic and angular dependences of differential cross sections a "Box" type

electrostatic analyzer was used [8] . The primary ion beam crossed a narrow thermal energy beam

of targeted particles, formed in the neutral particle source N (Fig. 1). The ion beam is then

separated (slit S4) and directed into analyzer A. The automatic regulation of the analyzer

potential allows that ions with energy loss in the 0-100 eV region pass through outlet slit S5

(lxlO 4 mm2

). The energy resolution of the analyzer is about 500. The whole analyzer system may

be revolved in a horizontal plane around the center of the collision region in the angle interval of

±15°, with a resolution of about 0.5°. During the time of measuring the charge transfer cross sections ac, the charged component of scattered primary beam is removed by a plane capacitor

and the neutral component is detected by SEM.

References

[1] B. Peart, K. T. Dolder, J. Phys. B 7, 1567 (1974)

[2] E. J. Stone and E. C. Zipf, J. Chem. Phys. 56, 4646 (1972)

[3] M. J. Mumma and E. C. Zipf, J. Chem. Phys. 55, 1661, (1971)

[4] J. M. Ajello and B. J. Franklin, Chem. Phys. 82, 2519, (1985)

[5] K. H. Tan and J. W. McConkey, Phys. Rev. A 10, 1212 (1974)

[6] K. H. Tan et al., Can. J. Phys. 52, 786 (1971)

[7] N. V. Fedorenko et al., Sov. Zh. Tekh. Fiz. 26, 1929 (1956)

[8] V. P. Afanasev, S. Y. Yavor, "Electrostatic Analyzer for Charged Particles Beam",

Moscow 1978

3.2 Collisions 223
Ionization, Charge Transfer, and Stripping Cross

Sections for Alkali Metal Ion Collisions with

Inert Gas Atoms and H2 and N2 Molecules

in the 0.5-7.0 keV Energy Range

B. I. Kikiani, R. A. Lomsadze

Physics Department, Tbilisi State University

Tbilisi, 380028 Georgia

The absolute values of the total and differential cross sections for various inelastic processes in

slow collisions of species with closed electron shells are measured. Ionization and charge transfer

cross sections, ai and ctc, are obtained by an improved transfer electric field (condenser) method;

stripping (primary ion electron loss) cross sections as by recording doubly charged primary ions,

produced as a result of collisions; and differential cross sections da/dQ by a "BOX" type

electrostatic analyzer [1]. Because of the realization of these processes at small internuclear

distances of colliding particles R, primary ions are scattered through relatively large angles and

this is accompanied by the formation of much more energetic secondary particles (target gas ions

and free electrons) than is usual. This circumstance has not been considered in earlier papers,

which must raise doubts about the reliability of the measurements themselves and of the

conclusions drawn from them.

An estimate for the uncertainty in the absolute values of cross sections given below is about

15%.

The energy dependences of the absolute cross sections ai for Na+-He, Ne, Ar and <rc for Li+-He,

Ne, and Ar collisions are plotted, as an example, in Figs. 1 and 2. It appears that the discrepancies

between our results and those of other authors [2,3] are considerable. The reasons for this are the

experimental difficulties mentioned above. For example, we determined that in Na+-Ne collisions

about 25% of the target gas ions have energies higher than 40 eV, and about 15% of the free

electrons have energies above 30-35 eV.

The interpretation of our results by plotting schematic correlation diagrams of diabatic terms

of the system of colliding particles [4] and the use of model representations [5,6] has made it possible to express certain conclusions about the mechanisms of the relevant processes. It was

found that in Li+-Ar collisions, an electron is captured mainly into ground state of the lithium

atom Li(2 S), at an internuclear distance R-1.5 a.u. For the Li+-Ne pair, the charge transfer

process is realized through an intermediate state Li+-Ne(2p5 3 S) at relatively large internuclear

distances R.

A comparison of our data for Li+-He collisions with the cross sections for emission of the resonance line of lithium atoms (transition 2 P —»

2 S, X=670.8 nm), reported in [7], shows that ac

includes a considerable (-50%) contribution from the cross section for electron capture by an

excited state of the lithium atom, Li(2p).

The contributions of the various channels to the total cross sections ai were estimated to define the mechanism of the ionization process. For direct ionization channels such contribution

was estimated by calculations of partial cross sections using a procedure described in ref. [6] . For an estimate of the contributions of molecular and atomic autoionization channels [8] experimental

data for the spectrum of free electrons were used. We found that for the Na+-Ar pair the direct

224 ICAMDATA 97 Proceedings
ionization channel is dominant, whereas for the Na+-Ne pair the process of atomic autoionization

of neon is about 30% and direct ionization about 10%. In the case of Na+-He pair the atomic

autoionization channel of helium is the main one.

Figure 1: Ionization (Na+-He) - 1) our Figure 2: Charge Transfer: (Li+-He) - 1) our

results, V) [2]; (Na+-Ne) - 2) our results, 2') results, V) [11], 1") [2], 1"') [3]; (Li+-Ne) - 2)

[2], 2") [3] 2"') [10]; (Na+-Ar) - 3) our our results, 2') [2], 2" [3]; (Li+-Ar) - 3) our

results, 3') [2]. results, 3') [2].

In Fig. 3, our experimental (curves 1, 4) and calculated data (curve 3) of stripping cross sections

for the collisions K+-He, Ne are compared with experimental data for the excitation cross sections

of ten autoionization states of K+ ions for the collision K+-He reported in ref. [9] (curve 2) in

arbitrary units. The comparison shows that the main realization of the stripping process, at least

for the K+-He pair in the investigated energy region, is connected with the direct ionization

mechanism.

The energy and angular dependences of the differential cross sections of elastic scattering were defined for various pairs of particles. As an example, in Fig. 4 our results for K+-H2, N2, Ar

pairs are presented at an energy E=2keV. We use reduced coordinates: p(x)=BsinG do7dQ

7 *eV

Figure 3: Stripping: (K+-He) - 1) our results,

2) [9], 3) [6]; (K+-Ne) - 4) our results.

3 : VWVWVVV"

2 -4

E=2keV

1 1 1

1

1 1 1

1

1 1 1 1 1 1 21 26

Figure 4: Differential Cross Sections:

(K+-Ar) - 1) elastic scattering; (K+-H2)

- 2; (K+-N2) - 3; (K+-Ar) - 4) charge transfer.

3.2 Collisions 225
(impact parameter), and x=EG (reduced angle), where E, 9 are the collision energy and scattering

angle in the mass-center system. For definite absolute values, the total charge transfer cross sections (restored from differential cross sections) were normalized to the one for the K+-Ar

collision, which was measured by the condenser method. It appears that the angular dependence

of the charge transfer cross sections has a threshold behavior (curves 2, 3, 4). The abrupt decrease

of the elastic scattering cross section at t~5-7 keV is due to reaching the internuclear distance R

at which the inelastic processes get excited. Our results indicate that the charge transfer

processes in these collisions are connected with mechanisms of the pseudo-crossing of the

quasimolecular potential energy terms of corresponding states. Because of the significance of the

mass-ratio, the internuclear distance in the region of nonadiabatic collisions for K+-H2 is smaller.

That is why for this pair the absolute cross sections ac are smaller for K+-N2, Ar pairs, as shown

by our results.

References

[I] B. I. Kikiani, R. A. Lomsadze, et al., Sov. Zh. Tekh. Fiz. 55, 1612 (1985); See also the

contributed paper by M. R. Gochitashvili, B. I. Kikiani, R. A. Lomsadze, "Measurements of

the Absolute Cross Sections of Inelastic Processes in Slow Collisions", in these proceedings

[2] I. P. Flaks, B. I. Kikiani, and G. N. Ogurtsov, Sov. Zh. Tekh. Fiz. 35, 2076 (1965); Sov. Zh.

Tekh. Fiz. 36, 491 (1966)

[3] Z. Z. Latypov and A. A. Shaporenko, Sov. Zh. Eksp. Teor. Fiz. 69 (1944) (1975); Zh. Eksp.

Teor. Fiz. 18, 4303 (1973); Zh. Tekh. Fiz. 43, 1300 (1973)

[4] M. Barat and Litchen, Phys. Rev. A 6, 211, (1972)

[5] B. M. Smirnov, "Asymptotic Methods in the Theory of Atomic Collisions", Chap. 6 & 6.1,

Moscow 1973

[6] E. A. Solov'ev, Sov. Zh. Eksp. Teor. Fiz. 81 (1681)

[7] S. Tsurubuchi and T. J. Iwai, Phys. B 14, 243 (1981)

[8] W. Weizel and V. 0. Beeck, Z. Phys. 76, 250 (1932)

[9] H. Aizawa, K. Wakiya, et al., J. Phys. B 18, 289 (1985)

[10] J. O. Olsen, T. Andersen, M. Barat, et al., Phys. Rev. A 19, 1457 (1979)

[II] J. van Eck, F. J. de Heer, J. and Kistemaker, Physica 26, 629 (1960)

226 ICAMDATA 97 Proceedings
Atomic Data for Recombination Calculations

R. Kisielius and P. J. Storey

Department of Physics and Astronomy, University College London,

Gower St., London, WC1E 6BT, UK

A. R. Davey

Mullard Space Science Laboratory, University College London,

Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK

1 Introduction

There exists a significant discrepancy in the abundances of carbon, nitrogen, oxygen, and neon

ions that are derived for photoionised nebulae from recombination lines and from collisionally

excited forbidden lines. This discrepancy emphasises the need for accurate theoretical work on bound-bound and bound-free radiative data for atomic ions. Such data were generated by the

Opacity Project, using the i?-matrix formulation of the close-coupling approximation, but are

often inadequate for the calculation of recombination coefficients due to the presence of narrow, but

important near-threshold resonances which are inadequately resolved and inaccurately positioned.

We report on a programme of systematic new calculations of radiative data and line recombination

coefficients for singly-ionised atoms of the astronomically most abundant elements (C, N, O, Ne)

which uses quantum defect techniques to accurately map resonances.

2 Photoionisation Cross-sections

We treat the (N + l)-electron scattering problem in the close-coupling (CC) approximation. Bound

states and continuum states of the system are determined using the i?-matrix method (see Berrington et al [1]) and from the resulting wave functions, radiative data for values (bound-bound

transitions) and photoionisation cross-sections (bound-free transitions) are calculated.

Configuration-interaction (CI) wave functions for the iV-electron target systems are computed

with the SUPERSTRUCTURE code of Nussbaumer and Storey [2]. In the Opacity Project calculations, the CI expansion of the taxget wave functions consists of Is, 2s, 2p spectroscopic orbitals

for C, N, O, Ne ions. We expand the configuration basis by adding 3s, 3p, 3d, 4/ pseudo orbitals for

C III target and all 3/ and 4/ pseudo orbitals for N III target. In photoionised nebulae, the electron

temperature is generally below 20000 K, so only the near threshold resonances are important in

determining recombination coefficients. The non-physical resonances that arise from the use of

non-physical correlation orbitals are not a problem at low energies.

The photoionisation cross-sections typically exhibit resonances due to photoexcitation of the

core electrons followed by autoionisation. A simple example for C II ions is

2s2 n/ + hv-> 2s2pnl' -) 2s2 + el". (1)

We use quantum defect theory to determine resonance positions and widths. Resonances are due to poles in the scattering matrix S described by a matrix x which varies slowly with energy

3.2 Collisions 227
and contains functions pertaining to both open (o) and closed (c) channels:

S = Xoo~ Xoc[Xcc ~ exp(-27rii/]" 1 Xco- (2)

Diagonalisation of the matrix Xcc yields the effective quantum numbers, v related to the complex

quantum defect // c

/j, c = ac + i/3c (3)

by v = n — /j, c. The energy of the pole e(pole) is given by

eipole) =£c -(n- a)"2 -

\p (4)

where 7 = 4/3 (ro — a) -3

is the autoionisation width of resonance and ec

is the appropriate target

energy.

In contrast to the OP data, we use a variable step energy mesh for photoionisation cross- sections that delineates all resonances to a prescribed accuracy. In the first step of the calculation, we determine resonance positions and widths using a coarse energy mesh. In the second step, we

determine a new fine energy mesh of variable step length Ae assuming a Lorentzian profile for the resonance: =

(£ _ £(po, e))2 + (ir 09

To calculate recombination coefficients, we integrate the photoionisation cross-sections using a

3-point Simpson's rule. If we specify a required accuracy as AF, we can find the necessary energy

interval for a given resonance: 90 x AF

where F^(£) is the 4th derivative of the Lorentzian function. The adopted step length is the

smallest value of Ae obtained for any resonance. In the third step we calculate photoionisation

cross-sections using the new variable step mesh.

The Opacity Project photoionisation data were generated using a relatively coarse energy mesh.

These data sometimes have poor resolution in resonance areas. In Fig.l, we show the photoionisation cross-sections for the 2s2p2 2 D state of the C II ion. One can notice a difference in the number

of energy points and in the resonance resolution. As a result, the area under the cross-section for the 2s2p2 2D state (Fig.l) is 1.585 Mb-Ry from the Opacity Project data and 4.573 Mb-Ry from

our data. These differences are reflected directly in the recombination coefficients.

All ab initio calculations of the photoionisation cross-sections position the resonances incorrectly.

An error of a few thousand inverse centimetres in a resonance position is typical and may significantly affect the resulting recombination coefficients, particularly at low temperatures (10000 K

or less). It is worth noting that earlier work on low-temperature dielectronic recombination (e.g.

Storey, [3]), which treats the resonances as bound states, uses the experimental resonance positions

and is not vulnerable to this uncertainty, although the quality of the wave functions and hence

the radiative data, was certainly inferior. Therefore for C II ions, where near-threshold resonances

2s2p( 3 P°)3d 2 F° and 2 P° make important contributions to the recombination coefficient, and the resonance positions are experimentally known, we adjust the resonance positions to their experimental values: 3301 cm-1 and 5523 cm-1 above the 2s2 X S threshold instead of theoretical values

of 3778 cm

-1 and 6127 cm-1

. This is done by calculating the resonance contribution to the recombination coefficient from a Fano profile fit to the cross-section near the resonances rather than from

the calculated cross-sections themselves. The resonance positions can then be adjusted within the

fit. These adjustments bring about an increase of 20% in the total recombination coefficient for the

2s2p2 2 D state at temperatures below 5000 K.

228 ICAMDATA 97 Proceedings
1000 r

1.2 1.3 1.4 1.5 Photon Energy (Ry)

Figure 1: Comparison of the C II photoionisation cross-section for 2s2p2 2 D calculated by the

Opacity Project (top) and this work. The OP cross-section consists of 199 points, based on a quantum defect mesh, whilst the latter is based on an energy mesh of 3281 points.

3.2 Collisions 229
3 The Level Population Problem

We calculate recombination coefficients for C II, N II, O II and Ne II ions. We determine both the

total recombination coefficients and the effective recombination coefficients for particular spectral

lines as functions of electron temperature Te and electron density Ne

. In our model, recombination

rates are determined using the -LS-coupling scheme for ion states and, therefore, assuming no

radiative transitions between states of different multiplicity.

Because of the very large number of levels included into the model, we have to partition the

calculation of level populations according to the principal quantum number n. We define a principal

quantum number n — rid, such that for n < rid, the population structure is determined solely by

radiative processes. Collisionally induced transitions for these levels can be neglected. The value

of rid depends on plasma density and temperature.

For n > rid, the population depends on n and /-changing collisions and populations are taken

from purely hydrogenic calculation of departure coefficients, bni by Hummer and Storey [4]. For

10 < n < rid, populations are still determined only by radiative transitions but no accurate atomic

data are available. Various approximate methods (quantum defect method, Coulomb approximation, hydrogenic approximation (when I > 3)) are used to obtain the necessary rate coefficients.

For n < 10, all atomic terms are included in the calculation of populations, irrespective of their

parentage. It is assumed that the population is determined solely by recombination and radiative

cascading from higher states.

4 Theoretical Emission Spectra and Ion Abundances

The calculated level populations together with ^/-values are used to calculate theoretical emission

spectra. Lines arising from 3d — Sp and 4/ — 3c? transitions in O II ions are prominent in observed

spectra of some astrophysical objects. Comparing the measured intensities of these lines with those

for hydrogen lines, we are able to determine abundances of 0

2+ ions in observed objects.

Theoretical spectra were determined using intermediate coupling (IC) and LSJ-coupling schemes.

For intermediate coupling (IC) spectra, we use level populations determined in LS'-coupling and

^/-values calculated using the Breit-Pauli Hamiltonian with spin-orbit interaction included. Alternatively, L5J-coupling spectra are computed using the same LS-coupling level populations and

splitting multiplet intensities using angular algebra only.

Relative intensities of various multiplets are used to determine the 0

2+ ion abundances in the

planetary nebulae NGC 7009 and NGC 3242. The need for IC calculations was demonstrated by

the comparison of the theoretical spectra with observed data by Liu et al [5]. Use of IC reduced

significantly the scatter of the derived abundances demonstrating a breakdown of LSJ-coupling.

Using IC yields considerable improvement in the consistency of the derived abundances.

References

[1] J. Phys. B. 20, 6379 (1987)

[2] A&A 69, 139 (1978)

[3] MNRAS 195, 27 (1981)

[4] MNRAS 224, 801 (1987)

[5] MNRAS 272, 369 (1995)

230 ICAMDATA 97 Proceedings
Unified Electron-Ion Recombination Cross Sections

and Rates

Sultana N. Nahar, Honglin Zhang, and Anil K. Pradhan

Department ofAstronomy, The Ohio State University

Columbus, Ohio 48210, U.S.A.

1 Introduction

Calculations of unified electron-ion recombination cross sections are described within the

framework of the close coupling (CC) approximation using the R-matrix method. It is emphasized

that the unified treatment subsumes and computationally unifies "radiative" recombination (RR)

and "dielectronic" recombination (DR) processes. Calculations are carried out in non-relativistic

and relativistic approximations for C V, C VI, 0 VIII and are compared with available accurate

experimental measurements on ion storage rings and electron beam traps with very good

agreement. Radiation damping of autoionizing resonances is included for these ions and found to be significant for H-like and He-like ions, although unlikely to be of importance in other ionic

species. A comprehensive and self-consistent set of new atomic data of photoionization and

recombination rate coefficients for oxygen ions is also obtained. These are for direct applications

to astrophysical models. Sample results are presented. Complete datasets will be available

electronically.

2 Theoretical Summary

Extending the CC approximation and the R-matrix method [1] to electron-ion recombination, and

using the DR theory by Bell and Seaton (BS) [2], Nahar and Pradhan [3] have developed a computationally unified approach to obtain total e+ion recombination cross sections, <jrc, and rate

coefficients, «r(T). The approach entails: (a) computation of photo-recombination cross sections

from photoionization cross sections, <jpi, for all bound states with v< v0 « 10 (v is the effective

quantum number) via the Milne detailed-balance relation and (b) DR cross sections from

radiatively damped high-n resonances, v0 < v < oo, using analytic expressions for both the

detailed and the resonance averaged cross sections derived from the BS theory. The computations

are highly involved and, for example, include in (a) <jpi of several hundred bound states of the

(e+ion) system with low-n autoionizing resonances (up to v«v0) delineated at several thousand

photon energies. This method yields total <jrc in an ab initio and unified manner, including the

background RR and the resonant DR. Physically, there is no separation between the two

processes, therefore the present total (unified) cross sections can be compared directly with

absolute experimental measurements in the entire energy range. The Gfc(T) are obtained through

maxwellian averaging over the recombination cross sections.

Experimental measurements of <7rc for carbon and oxygen ions, C V, C VI, 0 VIII, using the

Test Storage Ring (TSR) at Heidelberg, exhibit detailed resonance structures observed at very

high resolution in beam energy [5]. The experiments measure absolute cross sections and

therefore provide ideal tests for theoretical methods, as well as the physical effects included in the

3.2 Collisions 231
calculations. The present work aims to demonstrate the accuracy of the unified method for

electron-ion recombination, on par with the CC treatment of photoionization and electron impact

excitation, by comparing cjrc with the measured values.

One additional consideration in the present work is the inclusion of radiation damping of

low-n resonances of C IV, C V, and 0 VIII since damping of resonances is known to be important

for highly charged H-like and He-like ions. The reason is that for the dipole allowed transitions,

2p->ls and ls2p ! P° —> Is2 ! S the radiative decay rates, T

r

, of the order of 1013 - 1014 s

1

, approach

typical autoionization rates, ra

, of 1014 s

_1

. However, damping is negligible for all other ionization

stages where for the outer core transitions such as n = 3 -> 2, or n = 4 -> 3, F" is generally orders

of magnitude smaller than r°. Recently, employing the Breit-Pauli (BP) R-matrix method (BPRM)

[4] , the calculations of recombination have been extended to highly charged ions including the BP

relativistic effects and radiation damping [6]. We implement this new extension to C V, C VI, and

OVIII.

3 Results and Discussions

We have calculated the unified recombination cross sections of C V, C VI, and 0 VIII. Fig. 1 presents the detailed cjrc for e + C V —> C IV, obtained in three approximations, (a) in LS coupling

and (b) in BP approximations, and (c) in the BP approximation with damping of low-n

autoionizing states included. The (a) LS and the (b) BP(NRD) results are almost identical (except

that the resonances are better resolved due to a much finer energy mesh in the BP case),

indicating that the relativistic effects are negligible. The BP calculations involve considerably

more recombination channels than the LS calculations because of nearly twice as many fine

structure levels as LS terms, but the final results do not show a significant difference between the

two. The difference is less between LS coupling and BP approximation when damping is included.

The convoluted average of the two sets of BP results, with and without radiation damping, are shown in Fig. 1(d) - solid and dashed lines respectively. The BP(RD) results agree very well with

experiment, Fig. 1(e).

The total aR(T) is obtained for all ions in the isonuclear sequence of oxygen, 0 I - VIII. Calculations, such as abundances and ionization fractions, require the rates for all ionization

stages. The typical feature of aR(T) is similar to that of 0 IV as shown in Fig. 2 (solid curve)

where, starting with high recombination at very low temperatures, aR(T) decreases to a minimum

at logw(T) = 4.4 K for 0 IV, above which the DR dominates giving a "high T bump", such as the

bump around logw(T) = 5.2 K for 0 VI, beyond which the rate falls smoothly with T. Due to near-threshold autoionization, a small bump may be observed in the low-T region. There is often

considerable difference between the present and previously calculated values in the temperature

region of interest such as shown in Fig. 2(b) where the sum of RR (dashed), low-T DR (dotted), and

high-T DR (dot-dashed) rate curves [7] of Fig. 2(a) is compared with the present total

recombination rate coefficients (solid) curve.

4 Conclusion

Unified electron-ion recombination cross sections, <jrc, are obtained in the close coupling (CC)

approximation. We find (i) very good agreement with the experiments, (ii) relativistic effects are small for the second row of elements, and (hi) radiation damping is significant for H-like and

He-like ions only.

232 ICAMDATA 97 Proceedings
1 1

I I I I I I I 1

I I I 1 ' ' 1 ' ' ' I

' ' 220 240 260 280 300 320

Energy (eV)

Figure 1

3.2 Collisions 233
The total unified recombination rate coefficients, aR(T), for all oxygen ions, 0 I - 0 VIII, are

obtained. So far aR(T) have been calculated for 30 other ions including all carbon ions, nitrogen

ions, and carbon sequence ions C I, N II, 0 III, F IV, Ne V, Na VI, Mg VII, Al VIII, Si IX, and S XI,

and Si I, Si II, S II, S III, and iron ions, Fe I - Fe V.

Acknowledgements

The work was partially supported by grants from NSF (Iron Project at OSU, PHY-9421898) and

NASA. The computations were carried out on the Cray Y-MP at the Ohio Supercomputer center.

References

[1] M. J. Seaton, J. Phys. B 20, 6363 (1987); K.A. Berrington, P.G. Burke, K. Butler, M.J. Seaton,

P.J. Storey, K.T. Taylor, and Yu. Yan, J. Phys. B 20, 6379 (1987)

[2] R.H. Bell and M.J. Seaton, J. Phys. B 18, 1589 (1985)

[3] S.N. Nahar and A.K. Pradhan, Phys. Rev. A 49, 1816 (1994); S.N. Nahar and A.K. Pradhan,

Astrophys. J. 447, 966 (1995)

[4] N.S. Scott and K.T. Taylor, Comput. Phys. Commun. 25, 347 (1982); D.G. Hummer, K.A.

Berrington, W. Eissner, A.K. Pradhan, H.E. Saraph and J.A. Tully, Astron. Astrophys. 279,

[5] Wolf et al, Z. Phys. D Suppl. 21, 569 (1991); Kilgus et al, Phys. Rev. Lett. 64, 737 (1990);

Kilgus et al, Phys. Rev. A 47, 4859 (1993)

[6] H.L. Zhang and A.K. Pradhan, J. Phys. B 30, L571 (1997)

[7] Pequignot, D., Petitjean, P., & Boisson, C, Astron. Astrophys. 251, 680 (1991); Nussbaumer,

H. & Storey, P.J., Astron. Astrophys. 126, 75 (1983); Shull, J.M. & van Steenberg, M., ApJS

48, 95 (fitted from the works of Jacobs et al.) (1982a)

298 (1993)

1—1—

r

u I ' • ' '

I

1 1 1 1 L

-9

j L LL_l I 1 . . 2 5 6 3

-5 loKloT (K) loKloT (K)

Figure 2

234 ICAMDATA 97 Proceedings
K-matrix Correction of B, CB Cross-Sections

L. A. Vainshtein

P. N. Lebedev Physical Institute, Moscow, Russia

1 Introduction

There are two approaches in the calculations of excitation and ionization of atoms and ions by

electrons.

A. Sophisticated CC-type methods, such as R-matrix [1] and CCC [2]. They usually provide

sufficiently accurate results. However, there are some disagreements and questions in particular

cases.B. Rather simple Born-type (1. order) methods — B (Born), CB (Coulomb-Born) with possible

inclusion of exchange and normalization.

Generally, cross sections obtained by ^.-methods are preferable, but they are available for a

very limited number of transitions and atoms. Fast calculations for many transitions required for

atomic data in diagnostic code are in fact unreliable. Therefore, use of the 5-methods is necessary.

For example, using the code ATOM one can calculate as many cross sections and rate coefficients as necessary with minimal preparation.

Unfortunately, the accuracy of calculations by simple CB methods is often insufficient. To

create real databases it is important to understand the physical reasons for errors and to develop

sufficiently simple ways of correcting them. One very efficient way is the if-matrix method. It is based on a 1. order B (CB for ions) calculation of the matrix K for a given set of transitions

Km = (F \U\ V) , F = aelSTLT (1)

where a is a set of target quantum numbers, el are incident electron energy and orbital momentum,

and StLt are total angular momenta of the system. The Born if-matrix is used for the calculation

of S-matrix and cross section <r(ao — ai):

SW = T~iK{B) (2a)

a(a0 - ai \K)= J2 T^¥w l^o, rx |if) - i(r0 , r0| 2 (26)

lohSTLT

^L°i

where K,B in the argument denote if-matrix and B approximations. [SL]2 = (2S + 1)(2L + 1). The full if-matrix approach is released in the coupled programs ATOM-AKM. They can be

run on PC-486 and require about 10 minutes for 10 channels (transitions) in 10-20 energy points.

In the present report, we demonstrate two effects - normalization and channel interaction - which can be readily described by the if-matrix method.

3.2 Collisions 235
2 Normalization

The effect of normalization is related to the unitarity of the S'-matrix (conservation of incident

particle flux). It can considerably decrease cross sections of strong transitions, such as uIq — nl\.

Less evident is the similar decreasing effect for all other n/o — n'V transitions, in particular weak

ones.The pure normalization effect can be described by an approximate if-matrix in the one-row - one-column form : o r0 r' r0 r" ... K

r'r0 ooo ] r'T0

[

... o oo

In this case, Eq. 2 can be solved and we obtain:

(3)

a(ao-«i|JC)-.= £ £(r0 ) = E*2 (ror')

2

. (4)

IoIiStLt i l + ^(i o)J a'V One can see from Eq. 4 the influence of strong transitions on the weak ones due to the sum in

D. Moreover, for a given initial state, ao, the normalizing factor (1 + D)2is the same for all final states. From now on we call the approximation given by Eqs. 3-4 normalized Born BNm, where

m is the number of states a' in the sum for D.

One important consequence is the normalization effect for all transitions from the excited states. As an illustration, we show in Fig. 1-2 the excitation and ionization cross sections in He from the

2s l S state. B and BN8 (all nZ, n = 2,3,4) cross sections are obtained by the code ATOM.

CCC data are from [2]. BN8 results are considerably closer to CCC as compared to B. One can

see in Fig. 3 that the normalization effect for ionization is similar to that of excitation.

There is a large difference from experimental data for transitions from He metastables. As

a rule, measured cross sections (for example see [3]) are a few times (up to an order) larger than

calculated by any method . A typical example is shown in Fig. 4. The reason for such a discrepancy

is not clear. Maybe it is worthwhile noting that the presence of a rather small number of atoms in

the 2p3 P state (~10% of 2s3 S) might explain this disagreement (Fig. 4).

3 Interaction of Channels

The normalization effect decreases cross sections. Use of the full if-matrix in Eq. 2a yields more

complicated results. Besides normalization it provides channel interaction, which manifests itself by:

i. Transitions through intermediate levels; for example Is — 2p — 3d;

ii. Change of o~(E) due to the interaction of many levels. Is — 2p — 3d is a rather pure example of transitions through intermediate levels. Due to the

dipole interaction in both stages, <r(ls — 3d) is considerably larger than the one obtained by the B

method. The case of the 2s — 3d transition is more complicated: the effect of the two-stage dipole

transition is partly compensated by the normalization effect (which is absent for transitions from

Is state). This is manifested by the K36 curve in Fig. 3. Channel interactions of many levels leads

to a further decrease of the cross section (curve K74).

All these effects are even more pronounced in the case of the transition 2s — 4/, see Fig 4.

236 ICAMDATA 97 Proceedings
4 Conclusion

Born-type methods (CB for ions) together with the many-channel -matrix take into account

effects of normalization and channel interactions and provide reasonable cross sections. Use of

these methods in the code ATOM and complex ATOM-AKM give the possibility of a fast and

comparatively simple calculation of cross sections and rate coefficients for as many transitions as necessary.

References

[1] K. A. Berrington, P. G. Burke, J. J. Chang, A. T. Chivers, W. D. Robb, K. T. Taylor, Comp.

Phys. Commun. 8, 149 (1974)

K. A. Berrington, W. B. Eissner, P. H. Norrington, Comp. Phys. Commun. 92, 290 (1995)

[2] D. V. Fursa, I. Bray, Topical Rev. J. Phys B30, 757 (1997) and private communications

[3] M. E. Lagus, L. B. Boffard, L. W. Anderson, Ch. C. Lin, Ph. Rev. A53, 1505 (1996)

G. A. Piech, M. E. Lagus, L. W. Anderson, Ch. C. Lin, M. R. Flannery, Ph. Rev. A55, 2842

(1997)

3.2 Collisions 237
He2s-3p S=0

10

8

6

4

2

0

E ev

Figure 1: Excitation and ionization cross sections from He in the 2s 'S state. He2s-3d S=0 T— 1 1 1 1

. ^.4-Tr~tTr"——

U

i i

25

20

15

10

5

0

0 10 20 30 40 50

E ev Figure 2: Excitation and ionization cross sections from He in the 2s *S state.

He2s-3d S=l S=l

60

o B

K36. o

0

o -

o , i

i

i 1 0 20 40 60

E ev

80 100 120

Figure 3: Excitation and ionization cross sections from He in the 2s 3S state. He 2s-4f S=l S=l

E ev

Figure 4: Excitation and ionization cross sections from He in the 2s 3S state.

ICAMDATA 97 Proceedings
The Iron Project (OSU): Large-Scale Computations of

Atomic Data

H. L. Zhang, M. A. Bautista, S. N. Nahar, P. Romano, A. K. Pradhan

Department of Astronomy, The Ohio State University

Columbus, Ohio 43210, U.S.A.

1 Introduction

The Iron Project (IP) [1] is devoted to the study of radiative and collisional atomic processes and

the calculation of large-scale accurate atomic data, primarily for the iron-group elements for applications in astrophysical and laboratory plasmas. Among the processes of particular interest are: electron impact excitation (EIE), photoionization, unified electron- ion recombination,

and dipole allowed and forbidden transition probabilities. Calculations are carried out in

the close-coupling (CC) approximation using the R-matrix method. The computer codes developed

under the Opacity Project (OP) [2] were extended to include relativistic effects in the Breit-Pauli

(BP) approximation. The codes have been also adapted to massively parallel processors, the Cray

T3E and the IBM SP2. We report some sample results for one single astrophysically important

ion, Fe IV, calculated recently by the Ohio-State Atomic Astrophysics group.

2 Photoionization cross sections and oscillator strengths

Computations have been carried out for photoionization cross sections, o~pi, and oscillator strengths

(f- values) for dipole allowed transitions for Fe IV [3]. A 31-state eigenfunction expansion formed

from the configurations 3d4

, 3g?

3 4s, and 3d3 4p of Fe V is used. The results include 746 LS bound

states of sextet and quartet symmetries with n < 10, f- values for 34,635 LS transitions, and detailed

api with extensive resonance structures for all bound states. The new apj for the ground 6 5 state of Fe IV exhibits a large resonance near the threshold (Fig. 1) not found in previous calculations

for the OP and is likely to affect quantities such as the effective photoionization rate, the opacity,

and the recombination rate significantly. The resonance has been identified as the 3s2 3p5 3d6

( 6 P°)

state [3].

3 Excitation collision strengths and rate coefficients

Excitation collision strengths, £1{E), and maxwellian averaged rate coefficients, T(T), of Fe IV have

been calculated for 8,771 non-vanishing transitions among 140 fine structure levels, dominated by

the ground and excited configurations 3d5

, 3d4 As, and 3d4 Ap [4]. Calculations are carried out using a 49 term expansion in the CC approximation employing the R-matrx method. Q(E) is obtained

for electron energies up to 15 rydbergs, and T(T) is obtained at a wide range of temperatures.

Fig. 2 presents Sl(E) for transitions between levels within the ground configuration 3d5

.

3.2 Collisions 239
Fe IV + hu Fe V + e

. s 1 1 1 1 1 1 1 1 1 1 J 1 1 1 t I I I I L 1 1 1 1 L 1 1 1 i.

Photo Energy (Ry)

Figure 1

4 Electron-ion recombination

Calculations of the total electron-ion recombination rate coefficient, aft(T), of low charged iron ions,

such as Fe I - V, are being carried out [5] through large-scale computations employing the unified

treatment of Nahar and Pradhan [6]. The treatment subsumes the radiative recombination (RR)

and dielectronic recombination (DR) in a unified, self-consistent manner. This work represents

the first detailed study of electron-ion recombination for these iron ions. Previous results are from

much simpler approximations, such as central-field and hydrogenic approximations for RR at lower

temperatures and the Burgess general formula for DR at higher temperatures. Fig. 3(a) shows the

general shape of ocr(T) for Fe IV in a wide temperature region. Starting with a high recombination

rate, olr{T) decreases to a minimum at logio(T) = 4.8 K; above that the rate increases due to DR

peaking at logio(T) = 5.3 K, beyond which it falls monotonically. Fig. 3(b) presents a detailed

comparison of our total rate (solid curve) with the currently used ones [9] for the temperature

range of significant Fe IV abundance. The currently used rates are underestimated at lower T

because autoionizing resonances are not included in the RR rates and are overestimated at higher

T because interference effects with continuum and autoionization into lower states are not included

in the Burgess formula for DR.

5 Resonance Averaged Photoionization Cross Sections for Astrophysical Modeling

Under the OP and the IP, accurate photoionization cross sections, op/, have been calculated incorporating the complex autoionizing resonance structures. Owing to the complexity in the structures thousands of points are normally calculated to represent the detailed features for each bound state of the ion. While this is a great advance in terms of atomic physics and accuracy, the huge amount

and the inherent details of the data do present a serious practical problem for numerical modeling.

We present the resonance averaged apj for the ground state of atoms and ions, available from

the electronic OP database TOPbase [7] and the new data for the low ionization stages of iron

Fe I - V. The average is obtained by convolving the detailed apj with a Gaussian distribution over the autoionizing resonances. This preserves the overall resonant contribution to the cross sections in

240 ICAMDATA 97 Proceedings
Energies (Ky)

Figure 2

the important near- threshold regions. The effective cross sections are then represented by a small

number of points that can be readily interpolated linearly for practical applications. A Fortran

subroutine and data will be available electronically. Sample averaged cross sections along with the

detailed ones are presented in Fig. 4.

6 Conclusion

Large-scale a b initio calculations are carried out for atomic quantities of photoionization, oscilla- tor strengths, excitation collision strengths and total electron-ion recombination rate coefficients.

Resonance averaged photoionization cross sections are also presented for astrophysical models.

Acknowledgements: The work was partially supported by grants from NSF (Iron Project at OSU, PHY-9421898), and NASA. The computations were carried out on the Cray Y-MP at the

Ohio Supercomputer center.

References

[1] D. G. Hummer, K. A. Berrington, W. Eissner, A. K. Pradhan, H. E. Saraph, and J. A. Tully,

Astron. Astrophys. 279, 298 (1993)

[2] M. J. Seaton, J. Phys. B 20, 6363 (1987); K. A. Berrington, P. G. Burke, K. Butler, M. J. Seaton, P. J. Storey, K. T. Taylor, and Yu. Yan, J. Phys. B 20, 6379 (1987)

[3] M. A. Bautista and A. K. Pradhan, Astron. Astrophys. Suppl. (in press, 1997)

[4] H. L. Zhang and A. K. Pradhan, Astron. Astrophys. Suppl. (in press, 1997)

[5] S. N. Nahar, M. A. Bautista, and A. K. Pradhan, Astrophys. J. 479, 497 (1997) (Fe I); S. N.

Nahar, Phys. Rev. A 55, 1980 (1997) (Fe II); S. N. Nahar, Phys. Rev. A 53, 2417 (1996) (Fe

III); S. N. Nahar, M. A. Bautista, and A. K. Pradhan (Fe IV) (submitted, 1997)

3.2 Collisions 241
PSC X 1 .3

bio O

3 . 3x a o"

2.3x 1 O

1 .3x 1 OlogioT(K)

Figure 3

logioT(K)

[6] S. N. Nahar and A. K. Pradhan, Phys. Rev. A 49, 1816 (1994); S. N. Nahar and A. K. Pradhan,

Astrophys. J. 447, 966 (1995)

[7] W. Cunto, C. Mendoza, F. Ochsenbein, and C.J. Zeippen, Astron. Astrophys. 275, L5 (1993)

[8] N. S. Scott and K. T. Taylor, Comput. Phys. Commun. 25, 347 (1982); D. G. Hummer, K.

A. Berrington, W. Eissner, A. K. Pradhan, H. E. Saraph, and J.A. Tully, Astron. Astrophys.

279, 298 (1993)

[9] D. T. Woods, J. M. Shull and C. L. Sarazin, Astrophys. J. 249, 399 (1981)

r* SO —

0O

ao

+-> 1 o

o

Photon Energy (Ry)

Figure 4

242 ICAMDATA 97 Proceedings
3.3

Data

Production

Molecules

Ultraviolet Emission in the Dissociation of

N2 and O2 by K+ Impact

M. R. Gochitashvili, B. I. Kikiani, R. V. Kvizhinadze, and N. R. Jaliashvili

Physics Department, Tbilisi State University,

Tbilisi, 380028 Georgia

Ion-impact processes on molecular nitrogen and oxygen, N2 and O2, have been studied extensively

because of their importance in upper-atmosphere reactions and gas discharges. The excitation

function and absolute emission cross section of atomic lines of nitrogen and oxygen have been

measured in the vacuum ultraviolet (VUV) spectral region from 50 nm to 130 nm by K+ ionimpact dissociative excitation of N2 and O2 molecules in the K+ projectile energy range 3-8 KeV.

The experimental arrangement and calibration procedures of the light-recording system have

been described in more detail previously [1]. The uncertainties in the absolute values of the cross sections given here are estimated to be about 20%. Polarization of the radiation emitted in the

investigated processes is assumed to be negligible.

Fig. 1 shows examples of the emission spectrum obtained for the collision of K+ - ions with N2

and O2 at a laboratory energy of 4.0 keV for the K+ ion. Only the atomic lines of nitrogen and

oxygen are observed. These results indicate that direct dissociation plays an important role in the

formation of N* and 0*. There are many dissociative highly excited (Rydberg) molecular states that can produce a contribution to this inelastic channel. It is necessary to mention that the direct

excitation of dissociative molecular states by alkali metal ions is favored energetically. For

example, the minimum energies which are needed to produce the emission of dissociative products

of N I (at X = 120.0 nm) are AE = 20.1 eV, 30.2 eV, 34.6 eV in direct-dissociative, charge-exchange

dissociative and ionization-dissociative processes, respectively.

The energy dependence of the emission cross-sections of excited atomic products of N and O is presented in Fig. 2. It seems that the cross sections are independent of the energy of the K+ ion in

the investigated energy range. It appears that the "core" ion model [2] is adequate to interpret the

experimental results. This model predicts that dissociation is governed entirely by the core of the

ion and strongly depends on the form of the potential curves. Potential curves of the highly excited

molecule will be parallel to those of the core ion and lie lower in energy (electron binding energy).

The excited molecular states whose cores decay spontaneously in the Frank-Condon region give

rise to a major contribution of the formation of excited atomic products. After the decay of the

molecular ion core the weakly bound electron is moving to the atomic ions N+ or 0+ and captured

by them in excited states. In beginning to explain the dissociation mechanism we should remember that the spin

conservation rule is valid, because the spin-orbital interaction is ignored in our case. This implies

that during K+-N2 collisions the intermediate molecular state which is excited is a singlet.

Therefore, both fragments of atoms are left in the same state multiplicities. In the case of the

excitation of the more intense nitrogen atomic line at X = 120.0 nm (transition 3s 4P-2p3 4S) both

fragments of the dissociation must be formed in quartet states in the following way:

K+(3p6 iS)+N2(XiZg+

) -> K++N(3s4P)+N(2p3 4S).

3.3 Molecules 245
Similarly, the atomic line at A=124.3 A (transition 3s' 2 D -> 2p3 2D) can be emitted as a direct

result of the dissociation process of N2 when both fragments are formed in doublet states: K++N2 K++N(3s' 2 D)+N(2p3 2D).

In the framework of the core ion model the emission of the more intense nitrogen atomic line at A=120.0 nm may be caused by the excitation of an intermediate molecular singlet state of N2* in

which the ion core N2+

is in the states C2£u

+ or D2% (Fig. 3). The dissociation limit for these cores

is N(2p3 4 S)-N+(2p2 3P). For the C2SU state this dissociation limit is reached by predissociation

through the 4nu state. Formation of the nitrogen atomic line at A=123.4 nm can be due to the

decay of an excited intermediate molecular state of N2* with core N2+

(2 nu). The dissociation limit

for this core is N(2p3 2 D)+N+(2p2 3P). In both cases the excited atomic products are formed when

the weakly bonding molecular electron is attached to the N+(2p2 3P) ion. A high value of the cross section in the first case may be connected with a comparably small value of energy defects for the

inelastic process in this case.

110 115 120 \2S ^,nm 95 100 105 no Figure 1

115 120 125 130 135;?,TM

In the K+-02 collision the intermediate highly excited state of molecular oxygen must be a triplet

because the oxygen molecule in the ground state is in the triplet state, too. Following the spin

conservation rule the summed spin of the dissociative fragments should be equal to one. In the

framework of the core ion model the observation of the more intense oxygen atomic lines at /\=99.0

nm (transition 3s' 3D —> 2p4 3P) and at A=130.5 nm (transition 3s 3 S —> 2p4 3P) may be due to the

excitation of an intermediate molecular triplet state O2* with an ion core 02+ in the A2 nu or B4Ig states. The dissociation limit for these cores is 0+

(4 S)-0(3P). The triplet 3s' 3D and 3s 3 S states of

the oxygen atom can be formed as a result of the capture of an electron by the 0+

(4 S) ion and

hence these dissociative fragments must be correlated with the dissociative fragment 0(3P).

Similarly, the formation of the oxygen atomic lines at A=115.2 nm (transition 3s' 1 D° —» 2p4 *D)

and at A=121.8 nm (transition 3s" —» 2p4 X S) may be caused by the decay of the intermediate

molecular triplet state with the core 2nu (III). The dissociation limit for them is O(2D)-0(3P) when

a weakly bonded electron is attracted by 0+

(2D) ions and captured by them. The formation of

246 ICAMDATA 97 Proceedings
mm

singlet states 3s' X D° or 3s" iP0 takes place and hence these dissociative fragments should be

correlated with the fragment 0(3 P), too. In summary, it is necessary to mention that all core states N2+(C2 SU+

, D2 ng, 2 nu) and 02+(A2nu , B4Sg

-, 2 nu(III)) decay spontaneously in the Frank-Condon region.

10-10 cm*

6-

k

2

i

0.5

-17 o 10-10 cm

2

>o o o 0O °

i i i i ml 0.5

2

1

a m

6T 93.0nm)

rv q Q o O

*f 6 8l0Kev h S 8 lOKev "2

Figure 2

30 [c^ a nu n(

2 dW3

P)

OS 12 2.0 2.8 3.6 f$

Figure 3

References

[1] M. R. Gochitashvili, R. V. Kvizhinadze, N. R. Jaliashvili, and B. I. Kikiani, Zh. Tech. Fiz. 49

2338-43 (1993); see also the contributed paper by M. R. Gochitashvili, B. I. Kikiani, and

R. A. Lomsadze "Measurement of the absolute cross section of inelastic processes in slow

atomic collisions", in these proceedings

[2] K. C. Singlet, J. A. Schiavone, and R. S. Freund, J. Chem. Phys. 59, 5225-40 (1973)

3.3 Molecules 247
Electron Collision Cross Sections for the CF4 Molecule

by Electron Swarm Study

Yuichi Hayashi and Yoshiharu Nakamura

Faculty of Science and Technology, Keio University,

3-14-1 Hiyoshi, Yokohama 223, Japan

1 Introduction

Tetrafluoromethane(CF4) is widely used as working gas for gas discharge opening switches and in

etching plasmas for material processing [1]. Thus it is important to know an accurate electron

collision cross section set for the CF4 molecule in order to quantitatively understand the plasma

phenomena occurring in the above mentioned area. But the cross section data for CF4 in the low

energy region is not sufficiently reliable at present. Magnitudes and energy dependence of

vibrational excitation cross sections and the momentum transfer cross section, in particular, are considerably different according to various researchers [1,2]. We therefore have tried to determine

low energy electron collision cross sections for the CF4 molecule mainly from our own

experimental results for the electron transport coefficients.

2 Experimental Description

We used a double shutter drift tube with variable drift distance (1-10 cm) and measured the

arrival time spectra of electrons at each E/N value. From those spectra, the electron drift velocity,

W, and the product of the gas number density and the longitudinal diffusion coefficient, NDl,

were obtained [3] . The electron transport coefficients were measured in pure CF4 and two CF4-Ar

mixtures. All the measurements were carried out at room temperature, and at each E/N, the

measurements were repeated at three different pressures, at least. The advantages of using both

dilute molecular-rare gas mixtures and a pure molecular gas to determine the set of cross sections

for the molecular gas are mentioned in Ref. [4]

.

The mixing ratios of the gases and the range of the measurements are shown in Table 1.

Table 1: Mixing Ratios and the Range of the Measurements

E/N (Td) Gas Pressure (Torr)

pure CF4 (99.99%) 0.04-300 0.03-700

5.08% CF4-Ar 0.14-100 1.45-300

0.495 CF4-Ar 0.04-100 1.5-700

3 Results of the Measurements

Fig. 2 shows the electron drift velocity, W (solid squares), and NDl (solid circles) measured in pure

CF4. In this figure, the measured drift velocity (crosses) by Hunter [5] is also shown for

248 ICAMDATA 97 Proceedings
comparison. Figs. 3 and 4 show W and NDl with the same symbols as in Fig. 2 measured in the

5.08 % and 0.495% CF4-Ar mixtures, respectively.

4 Boltzmann Equation Analysis

A multi-term code of the Boltzmann equation analysis [6] and a Monte Carlo simulation (MCS)

were used, and an initial set of the cross sections for the CF4 molecule was modified by trial and

error until consistency between the electron transport coefficients and the experimental results

was obtained while applying the following steps:

Step 1 Modify inelastic cross sections (mainly vibrational excitation cross sections) until the

calculated W and NDl in the two mixtures agree with the experimental results in the

CF4-Ar-mixtures.

Step 2 Modify elastic momentum transfer cross sections so that the calculated W and NDl for

the pure CF4 molecule agree with the experimental results in pure CF4.

Step 3 Modify inelastic cross sections except vibrational excitation cross sections until the

calculated attachment and ionization coefficients agree with the experimental results for pure CF4.

The cross section set for the Ar atom determined by Nakamura and Kurachi [7] was used

throughout the study. The W and NDl calculated using the latest cross sections (Fig. 1) are shown

in Figs. 2-4 by solid lines. The calculated attachment and ionization coefficients are shown by

solid lines in Fig. 5, with the experimental results from [8-13].

As is seen in Figs. 2-5, the agreement between measurements and calculations is fairly good.

5 A Set of Cross Sections for the CF4 Molecule

The latest cross section set for the CF4 molecule is summarized in Fig. 1. This cross section set includes momentum transfer (Qm), vibrational excitation (Qv), electron attachment (Qa), neutral

dissociation (Qdn), and ionization (Qi). Also shown in this figure is the total scattering cross section

by L. G. Christophorou, J. K. Olthoff, and M. V. V. S. Rao [7]. In this cross section set, four vibrational excitation cross sections, v4 (degenerate deformation,

78meV), vl (symmetric stretch, 112meV), v3 (asymmetric stretch, 157meV), and 2v3 (the second

harmonics of v3) were considered in accordance with the energy loss spectra measured by an

electron beam experiment [14] at a resonance peak centered at 8eV, and the relative magnitude

was also maintained in the present vibrational cross sections.

The Ramsauer-Townsend minimum of the momentum transfer cross section is similar to that

of L. G. Christophorou, J. K. Olthoff, and M. V. V. S. Rao [15]. The present attachment cross section is about 20% smaller than given by them, but the neutral dissociation cross section is much larger.

3.3 Molecules 249
6 Conclusion

The drift velocity, W, and the product of the gas number density and the longitudinal diffusion

coefficient, NDl, were measured in pure CF4 and CF4-Ar mixtures over a wide E/N range.

A cross section set for the CF4 molecule being consistent with the measured electron transport

coefficients (drift velocity, longitudinal diffusion coefficient, attachment coefficients, ionization

coefficients) was obtained.

References

[I] A C.Bordage, P. Segur and A. Chouki, J. AppL Phys. 80 1325 (1996)

[2] H. Itoh et aL, Tech. Papers of Gas Disch. Committee IEE Japan ED-93-93 (1993)

[3] A Kurachi and Y. Nakamura, J. Phys. D 21 602 (1988)

[4] Y. Shishikura, K. Asano and Y. Nakamura, J. Phys. D 30 1610 (1997)

[5] S. R. Hunter, J. G. Carter, and L. G. Christophorou, Phys. Rev. A 38 58 (1988)

[6] R. E. Robson and K. F. Ness, Phys. Rev. A 33 2068 (1986)

[7] Y. Nakamura and M. Kurachi, J. Phys. D 21 718 (1988)

[8] I. M.Bortnik, and A. A. Panov, Sov. Phys. Tech. Phys. 16 571 (1986)

[9] M. S.Naidu,and A. N.Prasad, J. Phys. D 5 983 (1972)

[10] C. S. Lakshminarasimha, J. Lucas, and D. A. Price, Proc. IEE 120 1044 (1973)

[II] S. E. Bozin, and C. C. Goodyear, J. Phys. D 1 327 (1968)

[12] C. S. Lakshminarasimha, J. Lucas, and R. A. Snrlson, Proc. IEE 122 1162 (1975)

[13] S. R. Hunter, I G. Carter, and L. G. Christophorou, J. Chem. Phys. 86 693 (1986)

[14] L. Boesten, H. Tanaka, A. Kobayashi, A A. Dillon, and M. Kimura, J. Phys. B 25 1607 (1992)

100

0.001 0.01 0.1 1 10 100 Electron Energy [eV]

Figure 1: A set of electron collision cross sections for the CF4 molecule.

250 ICAMDATA 97 Proceedings
Solid lines BolUmau aiilyiii Symboli our mmifmail (circle,gquvc)

Huiiler[5](crosa) MCS (uiaiglc)

0 02 0 1 1 10 E/N [Td]

100 400

Figure 2: W and NDl in pure CF4 .

NIX

*• •

£^N* m

*

'— ^*VS

,

-

w

Solid UflM : BoMimirui «otJ> 01 Broken llnor. Put Af (our mtMuramcnt)

Syraboli : oor mnvunncnl

,

MCS (rrlnglc)

E/N [Td] Figure 3: W and NDl in the 5.08% CF4-Ar mixture.

100

0.1

0.01

c/U

[4| o [s] A [6]

[7]

[8J a 19] m [1] m (51

[el

17) T 181 B [9]

present

100 E/N [Td]

Figure 5: Attachment and ionization

coefficients in pure CF4.

Solid lira Bollsnm anirym

Broken lines rPure At (cur meafiuranaK) Symboli : cw measunnoii MCS unidgjej

E/N [Td] Figure 4: W and NDl in the 0.495% CF4-Ar mixture.

3.3 Molecules 251
Inelastic Cross Sections for the C3F8 Molecule from

Electron Transport Coefficients in

C3Fs-Ar Mixtures

Byoung-Hoon Jeon and Yoshiharu Nakamura

Department of Electrical Engineering, Faculty of Science and Technology,

Keio University, 3-14-1 Hiyoshi, Yokohama 223, Japan

1 Introduction

Perfluoropropane(C3F8) is frequently used as an effective etchant in semiconductor etching

processes, and it is also used as a gaseous medium in gas discharge switches and radiation

detectors [1]. Pirgov and Stefanov [2] derived a momentum transfer cross section and a total vibrationally

inelastic cross section for the molecule from electron swarm data measured by Hunter et al. [3] by

using a two-term approximation of the Boltzmann analysis, which may not be valid for molecules

with large vibrationally inelastic cross sections. There are also new measurements of the total

ionization cross sections including various positive ions of the molecules by Chantry and Chen [4]

.

In the present study, we measured the drift velocity and the longitudinal diffusion coefficient

of electrons in CsFs-Ar mixtures and derived a new set of electron collision cross sections for the

C3F8 molecule for applications in quantitative modeling of related plasmas.

2 Experiments

The apparatus and the data processing procedure used in the present measurement of the drift

velocity and the longitudinal diffusion coefficient were the same as those used in the works of

Nakamura [5] and Kurachi and Nakamura [6]. The special feature of the apparatus is that the

drift distance is variable (1-10 cm). This allows the application of the so-called differential method

which is very effective in reducing the effects of the electron energy relaxation, of the finite width

of the starting electron swarm, and of the non-uniform electric field around the electron shutters.

Measurements were repeated at least at three different gas densities at each E/N value. All

measurements were carried out at room temperature, 300 ± 2K.

The mixtures were composed of pure C3F8 gas (purity 99.99%) and argon (99.9999%), and the

actual mix ratio was determined by using a gas chromatography test.

3 Experimental Results

Electron transport coefficients, the drift velocity, W, and the product of the gas number density

and the longitudinal diffusion coefficient, NDl, of electrons, were measured in 0.526% and 5.05%

CaFs-Ar mixtures over the E/N range 0.03 to 100 Td and over the gas pressure range from 0.133 to 122 kPa (1 to 900 torr, 1 torr = 133.322 Pa). Typical scatter of the measured values at different

pressures at each E/N was less than 2% for the drift velocity and less than 10% for the NDl.

252 ICAMDATA 97 Proceedings
122 kPa (1 to 900 torr, 1 torr = 133.322 Pa). Typical scatter of the measured values at different

pressures at each E/N was less than 2% for the drift velocity and less than 10% for the NDl.

Fig. 1 shows the electron transport coefficients (W and NDl) measured in the 0.526% CsFs-Ar

mixture (solid squares), and Fig. 2 shows those in the 5.05% CsFs-Ar mixture with the same

symbols as in Fig. 1. Both figures also show the respective transport coefficients in pure argon [7], by solid triangles, for comparison.

The drift velocity measured in each mixture was enhanced by more than an order of

magnitude from that in pure argon by adding only a small fraction of the C3F8 molecule and

showed clearly the so-called negative differential conductivity (NDC) over the E/N range from 0.4

to 10 Td in the 0.526% mixture and from 2 to 35 Td in the 5.05% mixture. The NDl in each

mixture showed a similar but pronounced structure over the measured E/N range.

For higher E/N values each transport coefficient approached that of pure argon. This can be

explained by the shift of the dominant inelastic collision processes in the swarm from those with

C3F8 molecules to electronic excitations of the majority of argon atoms.

4 Boltzmann equation analysis

The electron transport coefficients (W and NDl) were calculated using a multi-term

approximation of the Boltzmann equation analysis [8]

.

The cross section set for Ar atoms determined by Nakamura and Kurachi [7] was used

throughout the present study. The initial cross section set for the C3F8 molecule consisted of those

for elastic momentum transfer (Qm) cross sections by Pirgov and Stefanov [2], total attachment

including various negative ions (Qatt) by Hunter and Christophorou [9], total ionization including

various positive ions (Qi ) by Chantry and Chen [4] , and vibrational excitations (Qv) by Pirgov and

Stefanov [2]. A trial calculation showed the need for inclusion of additional vibrational cross

sections, and we also tentatively included the set of vibrational cross sections for C2F6 proposed by

Hayashi and Niwa [10] because of insufficient information on the vibrational threshold energies of

the C3F8 molecule.

According to a comparison of the present transport coefficients in the CsFs-Ar mixtures with

those in C2F6-Ar mixtures [11], the E/N dependence of the measured transport coefficients for the

two mixtures are similar, and we may assume the threshold and the energy dependence of

vibrational cross sections of the C3F8 molecule to be similar to those of the C2F6 molecule, possibly

with lower resonance energy.

Electron transport coefficients, W and NDl, calculated using this initial cross section set, are shown by solid and dashed lines in Figs. 1 and 2. In Fig. 1, the maximum differences in W and NDl between the measurements and

calculations, shown by solid lines, are 57% and 83%, and those by dashed lines are 21% and 48%,

respectively, over the E/N range from 0.03 to 0.2 Td. In Figs. 2 and 3, those differences are 47.6%

and 86%, and 16.7% and 56%, respectively, over the E/N range from 0.03 to 1.2 Td. The

corresponding mean electron energies for these E/N ranges were 0.09-0.3 eV, and the magnitudes

of the vibrational excitation cross sections in this electron energy range were amended so that the

calculated results agreed with the experimental results.

The magnitude of the vibrational excitation cross section of about 0.09 eV threshold energy

was multiplied by a factor of 5 in the energy range 0.09-0.2 eV. That of about 0.13 eV threshold

energy was multiplied by a factor of 3.4 in the energy range 0.13-0.3 eV, and the threshold energy

of this cross section was changed by 0.113 eV after numerous trials. The new set of electron collision cross sections for the C3F8 molecule is shown in Fig. 3.

3.3 Molecules 253
5 Conclusion

We measured electron transport coefficients for 0.526% and 5.05% CsFs-Ar mixtures over the E/N

range from 0.03 to 100 Td. The measured transport coefficients were compared with those

measured in the CnF2n+2(n=i,2)-Ar mixtures with similar mixing ratios.

The E/N dependence of the measured transport coefficients clearly indicates possible

directions for changes of the vibrational excitation cross sections. We have determined the

inelastic cross sections for the C3F8 molecule. We started the measurement of transport

coefficients in pure C3F8 and are going to determine the elastic momentum cross section for the

C3F8 molecule, after completion of the measurements, by using the present vibrational cross

sections.

References

[I] M. Hayashi, Proc. "4th Symp. Inelastic Electron-Molecule Collisions", Springer, New York

1985

[2] P. Pirgov and B. Stefanov, J. Phys. B 23, 2879 (1990)

[3] S. R. Hunter, J. Carter and L. J. Christophorou, J. Appl. Phys. 58, 3001 (1985)

[4] P. J. Chantry and C. L. Chen, J. Chem. Phys. 90, 2585 (1989)

[5] Y. Nakamura, J. Phys. D 20, 933 (1987)

[6] M. Kurachi and Y. Nakamura, J. Phys. D 21, 602 (1988)

[7] Y. Nakamura and M. Kurachi, J. Phys. D 21, 718 (1988)

[8] K. F. Ness and R. E. Robson, Phys. Rev. A 33, 2068 (1986)

[9] S. R. Hunter and L. J. Christophorou, J. Chem. Phys. 80, 3001 (1984)

[10] M. Hayashi and A. Niwa, in Gaseous Dielectrics V, Proc. of the 5th International Symposium

on Gaseous Dielectrics (1987)

[II] H. Okumo and Y. Nakamura, in these proceedings

0.02 0.1 1 10 100 E/N (Td)

Figure 1: The electron drift velocity, W, and the product of the longitudinal diffusion coefficient

and the gas number density, NDl, as a function of E/N in a 0.526% CsFs-Ar mixture. The broken

curves show the analysis using the initial cross section for C3F8 molecule. • - Experimental

results; A - Calculated values using the present cross section set; - Ar. (Nakamura and Kurachi

1988)

254 ICAMDATA 97 Proceedings
200

0.01 0.1 1 10 100 E/N (Td)

Figure 2: The electron drift velocity, W, and the product of the longitudinal diffusion coefficient

and the gas number density, NDl, as a function of E/N in a 5.05% CaFs-Ar mixture. The broken

curves show the analysis using the initial cross section for C3F8 molecule. • - Experimental

results; A - Calculated values using the present cross section set; A - Ar. (Nakamura and Kurachi

1988).

0.002 0.01 0.1 1 10 100 Electron Energy (eV)

Figure 3: The present set of electron collision cross sections for the C3F8 molecule. The solid curves show the present cross section set for the C3F8 molecule. The dotted curves show initial cross section for the C3F8 molecule.

3.3 Molecules 255
Accurate Ab Initio Calculation of

Molecular Constants*

S. Kotochigova and I. Tupitsyn1 National Institute of Standards and Technology, Gaithersburg, MD 20899

1 Chemistry Institute, St. Petersburg University, Russia, 198904

1 Introduction

We present a new version of the valence-bond ( VB) method, which is able to calculate the electronic

structure of diatomic molecules. The first version of this ab initio method was developed by Heitler

and London [1] and applied to the H2 molecule. The main idea of the method is to describe the

molecular wave function as a linear combination of localized atomic wave functions. The new version

of the method is oriented toward the calculation of many-electron molecules [2]. The self-consistent wave functions of the constituent atoms are constructed from determinants by using the HartreeFock (HF) method for non-relativistic atoms or the Dirac-Fock (DF) method for relativistic atoms.

The construction of molecular wave functions from the many-electron atomic wave functions leads

to the proper dissociation behavior. The total energy of the molecule as a function of inter-nuclear

separation is presented as a power series in overlap integrals. This series converges quickly with

atomic HF and DF functions.

The molecular basis set contains both occupied and unoccupied atomic HF or DF orbitals.

Since the excited orbitals have a large radius and are not effective in describing the correlation and

polarization in the molecule, we create additional basis functions made of localized orbitals, i.e., the Sturm's wave functions [3]. This way of constructing the molecular wave functions avoids the

need for large basis sets and ensures much shorter computation times as well as smaller errors in

the calculation of the correlation expansion. The configuration interaction (CI) procedure, which

takes into account the most important inner and outer shell correlation, simplifies and converges

quickly as well, due to presence of HF or DF occupied orbitals.

The important advantage of this method is that the atomic core orbitals are not introduced by a

pseudo-potential but calculated exactly. Although the inner-core orbitals do not affect significantly

the molecular formation, the exact representation of the core orbitals is important for properties

of molecules that depend on the inner core wave functions such as, for example, the hyperfine

interactions. These core effects are especially pronounced for molecules with heavy atoms. In

principle the Coulomb and exchange interactions can be calculated between all atomic orbitals,

but this procedure can be limited to the most important orbitals to simplify the diagonalization

procedure and save computer memory for the CI. The remaining orbitals will then form the core. A crucial step in the method is the calculation of many-center integrals using the sophisticated

HF and DF functions. For the dimers the evaluation of the two-center integrals is simplified by

using a reexpansion procedure [4]. In this procedure each of the two-center integrals is expanded

"This paper was inadvertently published in the NIST Journal of Research. In order to have a complete set of poster papers of ICAMDATA 97 in this Special Publication, it is reprinted here again.

256 ICAMDATA 97 Proceedings
in terms of one-center integrals located on the atomic centers. We have found that convergence

of this expansion is accelerated by dividing the range of integration in two and considering only a reexpansion of the slowly varying part of the atomic wave function away from its nuclear center. The formalism of the VB method is described in more detail in Ref. [2]. Here we discuss the

computational details of a calculation of the molecular constants of the monohydrides OH and

AgH+. The OH molecule is chosen because precise experimental data [5, 6, 7] as well as theoretical

data [8] are available. To our knowledge no experimental data exist for the AgH+ molecule. However

due to the fact that the hydrogen atom is slightly polarized by the Ag+ core, the bond is weak

and an accurate determination of binding energy and bond length requires high precision of the

theoretical method. Our AgH+ result is compared to the pseudo-potential calculation of Ref. [10].

2 Computational Details and Results

The first step of the calculation is related to computing the atomic wave functions. The HF functions

are obtained with the one-electron center of gravity approximation and calculated for each atom

of the molecule. Instead of taking large-radius unoccupied orbitals in building CI wave functions,

we have added the Sturm's orbitals. They are localized and create a nearly complete basis set. A multi-configuration (CI) technique is employed to calculate correlation corrections. For the OH

molecule two CI basis sets were considered. The first has 38 configurations. The configurations

are built from the 2p4 valence shell of oxygen, with additional single and double excitations of

the 2p electrons into the 3s, 3p, 3d, 4s, 4p, and 4d orbitals, and the Is orbital of hydrogen with

excitation in the 2s, 2p, 3s, 3p, and 3d orbitals. The excited states in both atoms are described by

Sturm's wave functions. The ls2 2s2 shells of the O atom are treated as a core. The second basis

has 262 configurations. The CI configurations include single-excitations of Is2

, 2s2

, and 2p4 shells as well as double-excitation of the 2p4 shell where again these excitations are represented in terms

of Sturm's orbitals. Moreover both basis sets have configurations that represent the ionic states 0

+ H

_

, and 0~H+ . The inclusion of excitation from the Is and 2s orbitals of the oxygen atom

in the second basis set leads to a better treatment of the core polarization. Table 1 shows that

this substantially improves the agreement with experiment. The table includes the spectroscopical

constants of the ground state of OH. Our best results disagree with experiment by 0.2 % for the

equilibrium internuclear distance i?e , 2.7 % for the vibrational constant we , 0.4 % for the rotational

constant Be , and 4 % for the dissociation energy De

. We want to point out that even with a very

small basis set (38 configurations) we reached good agreement with experiment for the and Be parameters. Another theoretical result [8] obtained by a Hartree-Fock method using a if-functional

treatment of correlation effects has a larger difference from the experimental values than ours. The

origin of the disagreement in the dissociation energy of the VB and HF method seems to be related

to the fundamental difference in constructing the molecular wave function. In the VB method

the molecular wave function is constructed directly from many-electron atomic determinants with

singly occupied atomic orbitals. For large internuclear separation this molecular wave function has

the correct asymptotic behaviour and reduces to a product of the wave functions of the individual

atoms. The HF method makes use of molecular orbital (MO) wave functions, which contain two

electrons at all internuclear separations. In general, the one-determinant form of the HF method

is a very poor approximation for large internuclear distances. As it is described in Ref. [9] the

molecular wave function in Ref. [8] is introduced in a two-determinant form, which enables them

to improve the asymptotic behavior of the energy. However, this modification is still insufficient to get a fair agreement of De with the experimental value [7]. The molecular constant, Re , from Ref. [8] and our value (Table 1), lie on the opposite sides

3.3 Molecules 257
Table 1: Constants of the X

2 II OH molecule (1 A= 0.1 nm; the energy equivalent 1 cm-1

is 29.979 245 8 GHz; HF: the Hartree-Fock method).

Ref.

Basis set (number of conf.) Re (k) o;e (cm *) B (cm" 1 ) De (eV)

This work 38

262

0.972

0.967

7297.25

3638.39

18.782

18.834

-3.1701

-4.4302

HF+K-functional [8] 0.947 -4.4082

Experiment [7] 0.969 3737.76 18.910 -4.6259

of the experimental value [7]. This can be related to the difference in the treatment of correlation

in the two approaches. In our study we apply Sturm's wave functions in the CI expansion. This

is a very efficient treatment of correlation effects in atoms and molecules, because the purely

discrete spectrum of Sturm's eigenvalues contains the continuum spectrum as well and hence the

CI expansion converges quickly. On the other hand, the K- functional technique of Ref. [8], makes

use of an effective potential obtained by modifying the exchange operator in the Hamiltonian. This

modification does not effect the closed shells of the interacting atoms, therefore the polarization

and correlation effects of the core are not taken into account. Finaly, we conclude that the use of

Sturm's CI expansions for all orbitals of the OH molecule gives us an advantage in calculating the

equilibrium internuclear distance Re

. The CI treatment of the AgH+ molecule excludes all closed orbitals of the Ag+ ion with the

exception of the 4p6 4d10 shells. Single- and double-excitations of the 4p6 and 4d10 shells are considered. Additional Sturm's functions for 5s, 5p, 5d, 6s, and 6p orbitals were constructed for

the CI expansion. The number of configurations is 150. Our calculated values for the molecular

constants of AgH+ are given in Table 2. The other theoretical results [10] are obtained by using a DF pseudopotential and a density functional approach to describe the valence correlation and

polarization energies of the molecule. Due to the fact that AgH+ is a "single" electron molecule, the

correlation effects are not very important. However, the presence of the hydrogen atom polarizes

the Ag+ ion orbitals and the CI treatment is still required. The comparison with other theoretical

results [10] shows that we agree very well in the calculation of dissociation energies and mostly

disagree in the computation of the rotational constant u>e

.

3 Conclusions

In this paper we have shown that a quite accurate determination of molecular constants of molecules

with open shells using our version of the valence-bond method is possible. We treated O and Ag as many-electron atoms, where core polarization must be properly accounted for. The disagreement

with experiment varies from 0.2 % to 4 % for the molecular parameters of OH. In addition the

calculation of OH with a small number of configurations (38), which requires a few seconds of

258 ICAMDATA 97 Proceedings
Table 2: Constants of the X

2 S AgH+ molecule (DF: the Dirac-Fock method).

Ref.

Basis set (number of conf.) MA) we (cm-1

) B (cm-1

) De (eV)

This work 150 2.19 366.14 3.5172 -0.145

DF [10] 2.37 515 -0.15

DF+core [10] 2.41 519 -0.14

computer time for each internuclear separation, has less than a 1 % discrepancy for the Re and Be parameters. The difference between our values and other theoretical values for the AgH+ molecule

does not exceed 7 %, except for u;e , which also serves as a further test of our method.

References

[1] W. Heitler and F. London, Z. Phys. 44, 455 (1927)

[2] S. Kotochigova and I. Tupitsyn, Int. J. Quant. Chem. 29, 307 (1995)

[3] A. I. Sherstyk and P. F. Gruzdev, Opt. Spectrosc. (USSR) 42, 690 (1977)

[4] R O. Lovdin, Advances in Physics 5, 1 (1956)

[5] J. A. Coxon and S. C. Foster, Can. J. Phys. 60, 41 (1982)

[6] J. A. Coxon and S. C. Foster, J. Mol. Spectrosc. 93, 117 (1982)

[7] K. Huber and G. Herzberg, "Molecular Spectra and Molecular Structure 4. Constants of Diatomic Molecules", Van Nostrand, Princeton 1979

[8] L. Pisani and E. Clementi, J. Chem. Phys. 103, 9321 (1995)

[9] L. Pizani, L. de Windt, and E. Clementi, Int. J. Quant. Chem. 58, 219 (1996)

[10] H. Stoll, P. Fuentealba, M. Dolg, J. Flad, L. V. Szentpaly, and H. Preuss, J. Chem. Phys. 79,

5532 (1983)

3.3 Molecules 259
Electron Collisions with Small Molecules

B. M. McLaughlin, C. P. Ballance, D. G. Thompson, K. A. Berrington, and P. G. Burke

Department of Applied Mathematics & Theoretical Physics

The Queen's University of Belfast, Belfast BT7 INN, UK

1 Introduction

Ab initio methods in electron collisions with molecules provide accurate data for use in the modelling

of many astrophysical phenomena. Molecules are found in shock waves, dense interstellar clouds,

circumstellar outflows, supernova remnants and accretion disks. Molecular species such a water,

hydrogen, oxygen, and carbon monoxide and triatomic hydrogen ions are of interest at temperatures

below 4000 K. Developments in techniques using R-matrix methodology [1] by the UK group over many years, based around the ALCHEMY [2] and more recently the SWEDEN-MOLECULE [3] quantum chemistry programs are providing information on a variety of systems [4]. Species such as molecular oxygen and nitrogen and their ions are of great interest in understanding the ionospheric

and auroral phenomena and in many gaseous discharges. A vast amount of R-matrix work has

been done on the molecular oxygen complex, providing electronic and vibrational excitation cross sections together with dissociation [4]. Hydrocarbons and many impurities such as water and carbon

monoxide are of interest in tokamak plasmas. Many of the sought after observables, cross sections

and rates, for electronic and vibrationally elastic and inelastic processes are of great importance

for applications.

2 Diatomics

Electron and photon collisions with nitrogen molecules are of fundamental interest in understanding

ionospheric and auroral phenomena in the Earth's upper atmosphere, in the modelling of re-entry

flow fields around high velocity projectiles and in many gaseous discharge processes. Quite a number of calculations have been reported on electronically elastic, low energy, electron collisions

with N2 molecules but there are relatively fewer studies in which the target is itself excited [5, 6, 8]. Although, experiments exist they are frequently limited in scope, in energy range and in the range of

angles for which differential cross sections are reported. Recently, R-matrix theoretical studies on e~

- N2 collisions [7] have been extended to study electronic excitation of the target, with a comparison

of the integrated and differential cross sections being made with the available experimental data

[8]. Extensive calculations of angular distributions in e~ - N2 collisions were then performed to provide a comprehensive set of differential cross section data on several low lying optically forbidden

transitions, from each of their thresholds to 17 eV [9]. The applications of cross sections and rates obtained from ab initio studies on electron impact

excitation of CH molecules are multi-fold. CH molecules are of particular interest due to recent speculation of their presence in the Red Rectangle nebula at wavelengths longer than 3000 A[10].

The use of carbon fibre composites as a plasma facing material give rise to a range of CnHn (n > 1) hydrocarbon impurities in tokamak plasmas and molecular constituents such as BeD,

CD, H2O and CO are additional species of interest. Therefore electronic and vibronic excitation

260 ICAMDATA 97 Proceedings
of the CH molecule by electrons are of fundamental importance in fusion plasmas edges and for

astrophysical applications. Furthermore, the excited Rydberg states of the CH molecule are thought

to play a vital role in the dissociative recombination process, that occurs in interstellar shocks and

diffuse molecular clouds. The chemistry of the interstellar medium is influenced by hydrocarbon

molecules and their cyclic partners which are important constituents that play an active role in

the astrochemistry. Cross section calculations for electronic excitation were performed on the e~ - CH complex, for a range of low electron impact energies, using the R-matrix technique. The X

2 U

ground state and the lowest four valence excited states (A 2 A, B

2 E~, C2 S+ and a

4 E~), of CH are included in the close coupling expansion with each state being represented by a multi-configuration

interaction wave function. Cross section calculations for electronic excitation of the CH molecule by

electron impact were then made for the, A

2 A - X

2n, B2 E~ - X

2 n and C

2 E+ - X

2 n transitions.

A Morse potential was fitted to the ab initio values and the adiabatic approximation invoked to determine the vibronic excitation cross sections for the X-A transition in both the CH and CD

molecules [11, 12].

For R-matrix studies on the molecular nitrogen cation the lowest three electronic target states; X 2 E+: Ia2

g lal2a2

g 2al3ag lirl A

2 UU : la2g la2u

2<j

2

g 2a2u Sa2

g

l7r3u and the B

2 E+: Ia|laj2^2er0 3ojl7rl, were included in the close coupling expansion of the inner region wave-function with each state represented by the valence CI model. The molecular cation belongs to the Abelian point

group, so the Slater basis from the work of Ermler and co-workers [13] is a natural choice to use

to represent the target states. Initially an SCF calculation was performed on the ground state of

• In order to provide a suitable representation of the excited states of the molecular cation at the equilibrium separation, this was extended to a valence CI and an elaborate CI model. Closed

channel bound state calculations were performed for several symmetries of the neutral nitrogen

molecule within both approximations. In Table 2, the Rydberg bound state results for the N2

molecule close to equilibrium separation for the 1,3 E+ symmetries in both approximations are given.

Electronic excitation cross sections for the X-A and X-B states of the cation were investigated

and vibronic excitation calculated for the same transitions in both the adiabatic and non-adiabatic

approximations [14]. In our R-matrix work on the molecular oxygen cation, the lowest five electronic target states; X 2 Il

g

, a

4 nu , A2 nu , b4 E~ and the B2 E~ were included in the close coupling expansion with

each target state represented by the valence CI model. There has been recent photon impact

experimental studies on the oxygen molecule [15] and many of the resonant characteristics evident

in the corresponding photoabsorption cross sections may be identified from electron scattering by

the molecular oxygen cation. The possible channels open within our five-state valence CI model

would therefore feature the following;

hu + o2 -> o*2

* -> of(x 2 ng ,a

4 nu ,A 2 nu ,&

4 s;,£ 2 E;) + e

-. (i)

We note that the lowest five states of the molecular cation are denoted by; X 2 ns

, A

4 nu , a2 nu , b

4 E~ and B

2 E". In the SCF representation these are; X

2 Ug

: 1 a

2

1 cr2 2a2

2cr

2 3a2

l7r

4 l7r

s

, a

4nu and A

2 nu : loJlo^J&TjaflrJluJlirJ, b

4 E~ and B

2 Xg

: la2 lapa2g 2a2u 3a lg l7r*lir2

g

. In order to improve upon the SCF representation of the target states one has either to use, the valence CI, an

elaborate CI, the MCSCF approach or a combination of them. In order to highlight the resonant

features we have chosen the 3 E~ scattering symmetry. Table 3 gives a comparison of our 5-state

VCI results for the ndng resonances in the 3 E~ scattering symmetry with recent 3-state VCI work

[17]. The ndirg resonances in this scattering symmetry represent a transitory state of a Rydberg

electron interacting with the core on the fringes of the molecular charge cloud. This activity

manifests itself in the form of Rydberg resonance series in the 3 E~ symmetry denoted by nd-Kg and

3.3 Molecules 261
ng-Kg which approach the a

4Ilu and A

2 UU thresholds of the molecular oxygen cation. In this half

collision process for the 3 S~ scattering symmetry, we note that the following resonant processes

may occur; hu + 02 (X%) 02*(la2 la2

. . . 3aJl7rJl7rJ : a

4 IIU , A2 Hu]ndng , ngng

3 E~)

I

02+ (la,2 l(j2...3a2l7rJl7r

g

2

: a

4 Uu ,A 2 Uu ) + e~

(2)

As noted by Noble [17] the ng-Kg resonances are three orders of magnitude narrower than those of

the corresponding ndiTg series. The lower members of the ndixg series are sufficiently broad and

isolated that the resonance parameters may be obtained by fitting the eigenphase sum. Higher

members of the ndixg series become narrow and so reliable results require the use of the complex

energy technique or variant theories that calculate the parameters directly. For the 3

IIU scattering

symmetry there is more elaborate resonance structure, due to the target states being able to couple

to both a and 5 continuum. Rydberg series of the form nsa, nda, nsS and nd8 will therefore be

associated with the respective a

A Hu and A2 HU thresholds of the molecular oxygen cation.

3 Polyatomics

Electron collisions with polyatomic systems within the R-matrix methodology [4] is currently being

undertaken as a part of a UK wide collaborative project based around the SWEDEN-MOLECULE

Gaussian code [3]. Integral and differential cross sections results have been performed on N2 0 [18] at the static-exchange plus polarization (SEP) level and compared with experiment and previous

theoretical work [19]. Presently the UK group are working on several systems such as; H2O, O3,

CO2, CH4 and CH2 . Table 1 gives the SCF energies of the lowest l A\ state for the three polyatomic

systems; CH2 , CH4 and H2 0 obtained using the SWEDEN-MOLECULE code with their respective

contracted Gaussian type orbital (CGTO) basis. Detailed scattering results for these and several

other systems will be forthcoming in the near future.

Table 1: Electronic energies of the polyatomic molecular systems; CH2 , CH4 and H2 0 at the SCF

level in the Abelian point group C2v from the SWEDEN-MOLECULE Gaussian code. The bond

angle G and the bond distance r are given in their appropriate units.

CGTO Basis Species Escf (ao) r (ao) r(A) 6 (Deg) Molecular State

[4s 2p ld/2s lp] [8s bp 2d/5s 2p]

[5s 3p 2d/2s lp]

CH2 CH4 H2 0-38.8677980686

-40.2148093594

-76.0440308704

2.110

2.066

1.800

1.11656

1.09328 0.95252

102.4° 109.47°

105.0°

la\2a\lbl?,ai 1 A\

la\2a\lb2

2 ?,a\lb\ l Ax

la\ 2a\ l&23di lb\ 1 Ai

4 Acknowledgments

This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC),

the Collaborative Computational Project Two (CCP2), the US National Science Foundation and

NIDevR/ESF. Mr. C P Ballance thanks NIDevR/ESF for financial support during the course of

this work.

262 ICAMDATA 97 Proceedings
Table 2: The lowest ten X E+ states of the N2 molecule at the fixed internuclear distance of 2.1 ao from the basic valence and the extended CI scattering models. All energies are given in Hartrees. The effective quantum numbers and defects, respectively v and \i of these states are presented for

both scattering approximations.

VALENCE - CI (VCI) EXTENDED - CI (EX-CI)

State Energy (Ry) V Energy (Ry) V

-109.083784 0.950793 0.049207 -109.087911 0.949250 0.050750

2 -108.644130 2.099451 -0.099451 -108.648555 2.080286 -0.080286 3 -108.589836 2.907556 0.092444 -108.592441 2.900719 0.099281 4 -108.582016 3.121228 -0.121228 -108.584833 3.106394 -0.106394 5 -108.570430 3.547164 0.452836 -108.570982 3.629105 0.370895

6 -108.563275 3.917315 0.082685 -108.565722 3.910057 0.089943

7 -108.559335 4.178071 -0.178071 -108.561758 4.170959 -0.170959

8 -108.551443 4.908630 0.091370 -108.553849 4.899187 0.100813

9 -108.550750 4.992768 0.007232 -108.553073 4.993064 0.006936

10 -108.549396 5.170251 -0.170251 -108.551823 5.156397 -0.156397

Table 3: The ndirg resonance positions (er ) and autoionization widths (r) for e_ - O2 scattering in

the 3 E~ symmetry at the fixed bond length of 2.30 ao- The effective quantum number u, the real and imaginary parts, a and (3 respectively of the complex quantum defect /i = a + ifi for several

members of the ndirg series are included for completeness. The ndirg resonance parameters from

our work for the 3 £~ symmetry were obtained by fitting the eigenphase sum of the 5-state valence

configuration interaction (VCI) scattering model to a Breit-Wigner form. The 3-state valence CI

results obtained using a similar approach for the molecular oxygen Rydberg resonance states; O2

(l<7gl(7„ . . . (a4 IIu ) nd-Kg 3 S~) are included for comparison purposes.

Resonance 4 (Ry) 4 (Ry) T° (Ry) T" (Ry) V P

3d7T9 0.2151 0.2103 0.1060(-2) 0.1085(-2) 3.0088 0.0088 0.7390(- 2) 0.029 0.2610 0.2583 0.4270(-3) 0.2102(-3) 4.0019 0.0019 0.3367(-2) 0.048 5dng 0.2822 0.2796 0.1990(-3) 0.2185(-3) 4.9264 0.0736 0.6531(-2) 0.026

Qd-Kg 0.2937 0.2918 0.0822(-3) 0.1172(-3) 5.8724 0.1736 0.3811(-2) 0.015

Id-Kg 0.2998 0.1414(-3) 6.9176 0.0824 0.1170(-1) 0.039

Zd-Kg 0.3047 0.7934(-4) 7.8934 0.1066 0.9756(-2) 0.037

9dlVg 0.3081 0.5237(-4) 8.8840 0.1160 0.9182(-2) 0.036

lOdlTg 0.3105 0.3688(-4) 9.8778 0.1222 0.8883(-•2) 0.035

lldltg 0.3123 0.2704(-4) 10.8744 0.1256 0.8667(--2) 0.034 I2dng 0.3137 0.2044(-4) 11.8717 0.1283 0.8551(--2) 0.034

a 3-state valence CI

b 5-state valence CI

3.3 Molecules 263
References

[1] C. J. Gillan, J. Tennyson and P. G. Burke, Computational Methods in Electron-Molecule Collisions, Edited by W. M. Huo and F. Gianturco, (Plenum: New York and London, 1995) 239

and references therein

[2] The ALCHEMY I and II suite of programs were originally developed by P. S. Bagus, B. Liu,

A. D. McLean, M. Yoshimine and B. Lengsfield III

[3] J. Almlof and P. R. Taylor, Advanced Theories and Computational Approaches to the Electronic

Structure of Molecules, Edited by C. E. Dykstra (Dordrecht: Reidel, 1984)

[4] L. A. Morgan, Photon and Electron Collisions with Atoms and Molecules, Edited by P. G.

Burke and C. J. Joachain, (Plenum: New York and London, 1997) 57 and references therein

[5] C. J. Gillan, C. J. Noble and P. G. Burke, J. Phys. B: At. Mol. Phys. 23, L407 (1990)

[6] W. M. Huo, Nonequilibrium Processes in Partially Ionized Gases, Edited by M Capitelli and

J N Bardsley, NATO ASI Series (Plenum: New York and London) 341 (1990)

[7] C. J. Gillan, O. Nagy, P. G. Burke, L. A. Morgan and C. J. Noble, J. Phys. B: At. Mol. Phys.

20, 4585 (1987)

[8] C. J. Gillan, J. Tennyson, B. M. McLaughlin, and P. G. Burke, J. Phys. B: At. Mol. & Opt.

Phys. 29, 1531 (1996)

[9] C. J. Gillan, B. M. McLaughlin and J. Tennyson, At. Data and Nucl. Data Tables, submitted

for publication

[10] R. J. Glinski, J. A. Nuth III, M. D. Reese and M. L. Sitko, Astrophys. J. 467, L109 (1996)

[11] K. A. Berrington, P. G. Burke, W. G. V. Darlington, W. C. Fon, C. J. Gillan, B. M. McLaughlin, J. Pelan, R. H. G. Reid and J. H. Tait, Atomic Data for Spectroscopic Studies on JET,

JET Report JP5/ 10061 (1997)

[12] B. M. McLaughlin, C. J. Gillan and P. G. Burke, J. Phys. B: At. Mol. & Opt. Phys., in

preparation

[13] W. C. Ermler, A. D. McLean and P. S. Bagus, IBM Res. Rep. RJ3243, 1 (1981)

[14] O. Nagy, B. M. McLaughlin, C. P. Ballance and P. G. Burke, J. Phys. B: At. Mol. & Opt.

Phys. in preparation

[15] D. M. P. Holland, private communication.

[16] C. P. Ballance, B. M. McLaughlin and K. A. Berington, J. Phys. B: At. Mol. & Opt. Phys. in

preparation

[17] C. J. Noble, in Computational Methods for Electron Molecule Collisions, Edited by W. M.

Huo and F. Gianturco (Plenum: New York and London, 1995) 324

[18] L. A. Morgan, C. J. Gillan, J. Tennyson and X. Chen, J. Phys. B: At. Mol. & Opt. Phys. 30,

4087 (1997)

[19] B. K. Sarpal, K. P. Pfingst, B. M. Nestmann and S. D. Peyerimhoff J. Phys. B: At. Mol. &

Opt. Phys. 28, 3045 (1996)

264 ICAMDATA 97 Proceedings
Electron Transport Coefficients in C2 F6 -Ar Mixtures

and Inelastic Cross Sections for the C2 F6 Molecule

Hiromichi Okumo and Yoshiharu Nakamura

Faculty of Science and Technology, Keio University,

3-14-1 Hiyoshi, Yokohama 223, Japan

1 Introduction

Hexafluoroethane(C2F6) is used as a working gas for diffuse discharge switches and etching plasmas

for materials processing and also as a gaseous insulator in high voltage equipment. But the present

state of cross section data for the molecule is not reliable enough for numerical simulations. We have

been studying electron collision cross sections of molecules by the measurement of electron swarm

parameters in dilute molecular gas-rare gas mixtures and in the pure molecular gas. Electron swarm

parameters in the mixtures are very sensitive to the vibrational cross sections of the molecule and

the elastic cross section of the rare gas atom and are nearly insensitive to the elastic cross section

of the molecule. We, therefore, were able to derive detailed information on the vibrational cross sections of the molecule from the electron swarm parameters, measured in the dilute molecular

gas-rare gas mixtures exclusively. The swarm parameters in the pure molecular gas, on the other

hand, depend on the elastic and inelastic cross sections of the molecule, and, once the inelastic cross sections were known, we were able to derive the elastic cross section for the molecule from

the measured swarm parameters measured in the pure molecular gas. Presented in this report are the experimental results for the drift velocity and longitudinal

diffusion coefficient of electrons in dilute C2Fe-Ar mixtures and the derived vibrational excitation

cross sections which are consistent with the measured swarm parameters.

We are now measuring the swarm parameters in the pure C2F6 gas and we are going to derive

the elastic cross section for C2F6 using the present vibrational cross sections after completion of

the measurements.

2 Measurements

We used the double shutter drift tube [1] with variable drift distances (1-10 cm) for the measurements of the electron drift velocity, W, and the product of the gas number density and the

longitudinal diffusion coefficient, NDL , in 0.524% and 5.47% C2 F6-Ar mixtures. The ranges of the

measurements are shown in Table 1. The measured electron drift velocities in the mixtures show the Negative Differential Conductivity (NDC) indicating a strong contribution from the vibrational inelastic processes of the C2F6 molecule over the E/N range 2 - 25 Td in the 5.47% mixture, and 0.35 - 20 Td in the 0.524%

mixture.

The measured products NDL in mixtures also show clearly the contributions of the molecular

additive in argon. The peaks of the measured NDL over the E/N range 5 - 20 Td in the 5.47%

3.3 Molecules 265
Table 1 : The ranges of the measurements

Mix Ratio (%) E/N Range (Td) Gas Pressure Range (Torr)

5.47

0.524

0.04 - 100

0.04 - 70

1 - 560

1 - 700

mixture and 1.4 - 7 Td in the 0.524% mixture show the characteristic of perfluoroalkanes, CnF2n+2

(n=l,2,3).

Fig. 1 compares the results of the present measurements of W and ND^in the 5% and 0.5%

C2F6-Ar mixtures [2], and of the electron drift velocity W in pure Ar [3].

3 Analysis

The cross sections are shown in Fig. 2. The initial set of cross sections for the C2F6 molecule by

Hayashi [4] was modified by using a multi-term Boltzmann analysis [5]. We modified the vibrational excitation cross sections for the C2F6 molecule until consistent

values for W and NDl were obtained from the measurements. The thresholds of the vibrational

excitation cross sections for the C2F6 molecule by Hayashi are shown in Table 2.

Table 2: Thresholds of the vibrational excitation cross sections for the C2F6 molecule

vibrational cross sections thresholds (eV)

qv6 0.089

qv5 0.138

qv7 0.155

The results are shown in Fig. 3 and Fig. 4. The measured drift velocities in the two mixtures

agree with the calculated ones over the E/N range 0.04 - 10 Td in the 5.47% mixture, and 0.04 - 4

Td in the 0.524% mixture.

4 Conclusion

We measured two electron swarm parameters, drift velocities and longitudinal diffusion coefficients

in 0.524% and 5.47% C2 F6-Ar mixtures over the E/N range from 0.04 to 100 Td. The measured

swarm parameters were compared with those measured in CF4-Ar and CaFg-Ar mixtures with

similar mixing ratios. The E/N dependence of the measured swarm parameters clearly indicates

possible direction for refinement of the vibrational cross sections.

5 Future work

We will determine the best consistent vibrational cross sections for C2F6 from the present measure- ment in the mixtures. And after that, we will determine the momentum transfer cross section for C2F6 from our new measurement of swarm parameters in pure C2F6, which has just been started.

266 ICAMDATA 97 Proceedings
References

[1] Y. Nakamura, J. Phys. D 20, 933 (1987)

[2] S.R. Hunter, J.G. Carter, and L.G. Christophorou, J. Appl. Phys. 58, 3001 (1985)

[3] Y. Nakamura and M. Kurachi, J. Phys. D 21, 718 (1988)

[4] M. Hayashi and A. Niwa, in Gaseous dielectrics V, Proceedings of the 5th international symposium on gaseous dielectrics (1987)

[5] R.E. Robson and K.F. Ness, Phys. Rev A 33, 2068 (1986) : James Cook University multi-term

Boltzmann code

Plots : present measurements

Lines references

a Closed symbols : 5.47% C2Fs-Ar mixture

a

a Open symbols : 0.524% C2F6-Ar mixture

a

> A* 4

a

o ooo.-fl'J „ 5K [2] .... , . ..8 5

i°°o 0 o/^ 0. 5X[2] c ° o 0 oo oooo o°5^

0?

W o..-- <?• • o .

0 .*

•

pure Ar[3]

0.04 0.1 1 10 100 E/NCTd)

Fig.l W and NDl as a function of E/N in C2F6-Ar mixtures

0.001 0.01 0.1 1 10 100 1000 Electron energy (eV)

Fig.2 Electron collision cross sections for C2F6

3.3 Molecules 267
^ 10 o

_ T___^-

N Ul

~**y J T

-

• MP W

• lip ND

Hayaahi

:

W

Hayashi

;

NO / w

T

prosont :W

- present:

NO

5. 47% C 2 F 6 -Ar m xture

== 0.04 0.1 1 10 100 E/N (Td)

Fig. 3: W and NDl in the 5.47% C2F6-Ar Mixture

T 200

E/N (Td)

Fig. 4: W and NDL in the 0.524% C2F6-Ar Mixture

268 ICAMDATA 97 Proceedings
Validation of Ozone Infrared Line Intensities

M. A. H. Smith

NASA Langley Research Center

Hampton, Virginia

1 Introduction

Measurements of infrared absorption or emission are used to determine the concentrations and

distributions of atmospheric gases on global, regional, and local scales. The accuracy of these remote

measurements depends significantly on the accuracy of our knowledge of the molecular spectra of ozone and other infrared-active atmospheric species. Several recent high-resolution spectroscopic

studies [1, 2, 3, 4] have determined absolute intensities of ozone infrared absorption lines in the

9-11 (Urn region, using as a reference standard the UV absorption cross-section of ozone at 254 nm.

This paper reviews the various measurements and compares them to each other and to the current

HITRAN line parameters compilation [5].

2 Review of Measurements

The first study reporting measurements of ozone 10- //m line intensities referenced to a 254-nm UV

absorption standard was that of Pickett et al. [1]. They used a high-resolution Fourier transform

spectrometer (FTS) to measure intensities of 47 lines in the P branch of the v% fundamental band.

Ozone partial pressures in the sample cell were determined through measurements of UV absorption

at 254 nm, using as a reference standard the cross-section measurements of Hearn [6]. The results are based on individual measurements in two spectra fitted separately. Taking an arithmetic average

of all the intensity measurements, the mean difference from HITRAN is +8.3 %. However, if the

most well-determined intensities are given greater weight, the mean difference from HITRAN is +5.1 %. The reported absolute accuracy of these measurements is 1 %; however, we note that the

reference UV standard [6] has an accuracy of only 2 %.

Measurements of the intensity of the single (10 5 6)«-(9 5 5) line at 1048.6736 cm-1

, made

using both tunable diode laser (TDL) and laser heterodyne spectrometers, were reported by DeBacker et al. [2]. Ozone concentrations in these experiments were determined by continuously

monitoring the total pressure in a closed system. The accuracy of this technique has been veri- fied [7] by measuring the UV absorption at 254 nm, using the more recent reference standard of

Mauersberger et al. [8]. The line intensity resulting from the TDL measurements agrees exactly

with the HITRAN value, while the laser heterodyne result is approximately 1 % larger. These

small differences are consistent with the 1 % precision reported for the measurements.

In addition to the (10 5 6)«-(9 5 5) line, DeBacker-Barilly and Courtois [3] used their TDL

system to measure intensities of 46 other lines in the R branch of the v% band. The reported

accuracy of the intensities for these lines is 4 % and their weighted-mean difference from HITRAN

is —5 %. However, there is considerable scatter among the individual differences from HITRAN,

and their arithmetic average is —7.5 %.

3.3 Molecules 269
Recently Smith et al. [4] have determined absolute intensities of numerous 16 O3 lines in the

9-11 /im region from spectra recorded using the 1-m FTS at Kitt Peak. Ozone concentrations in the

sample cell were determined using a 254 nm UV-absorption monitor of the same design as Pickett et

al. [1]. However, the more accurate (±0.5 %) UV cross-section value of Mauersberger et al. [8] was

used as the reference standard for these measurements. Four spectra for which the ozone partial

pressure varied by < 1.0 % during the recording were fit simultaneously using a multispectrum

nonlinear least-squares procedure [9]. Line positions and intensities were determined for over 270

lines in the P, Q, and R branches of the z/3 fundamental band and 10 lines in the R branch of

the v\ band. Absolute accuracies of these intensity values range from 2 % for the strongest, most

well-isolated lines to over 4 % for the weakest lines measured. For both arithmetic and weighted

averages, the mean difference from HITRAN is +1 % in the 1/3 band and —0.2 % in the v\ band.

3 Intercomparison

On average, taking all the measurements [1, 2, 3, 4] together, the line intensities are about 1 %

larger than the values on the current HITRAN compilation [5]. However, a few individual measured

intensities differ from the HITRAN values by as much as 9 to 15 %. Only 44 lines were measured

in more than one experimental study, and only one of these lines has more than two independent

measurements. Comparison of the various intensity measurements shows excellent agreement for a few lines but considerable discrepancies (greater than the stated uncertainties) for others.

The (10 5 6)-f-(9 5 5) line at 1048.6736 cm-1 was measured by three different techniques: TDL

[2, 3], laser heterodyne spectrometer [2], and FTS [4]; all three intensities are within 1.1 % of the

HITRAN value. For the 44 z/3 band transitions with at least two measurements, the intensities

of Smith et al. [4], obtained for both P— and R—branch transitions, average 1.4 % larger than

the values on the HITRAN compilation [5] . This result appears to split the difference between the

FTS measurements of Pickett et al. [1] in the P branch and the tunable diode laser (TDL) results

reported by DeBacker-Barilly and Courtois [3] in the R branch. However, for these two earlier sets of

measurements [1, 3] the intensity differences from HITRAN appear to become larger for increasing

rotational quantum number J". There may be a contribution to these trends from experimental

temperature uncertainties; further investigation is needed to determine the exact cause. The study

of Smith et al. [4], which covered a wide range of rotational quantum numbers in the P, Q, and

R branches of the v-$ band, found no obvious ./"-dependence of the intensity differences from the

HITRAN compilation.

In summary, the recent experimental studies in the 9-11 fim region appear to have verified that

the intensities of L6 03 transitions given in the HITRAN line parameters compilation [5] in this

region have an absolute accuracy of 2 % at best. The HITRAN ozone intensities in the infrared

also are quite consistent (1 % precision) with the ultraviolet absorption cross-section standard at 254 nm [8].

References

[1] H. M. Pickett, D. B. Peterson, and J. S. Margolis, J. Geophys. Res. 97, 20,787-20,793 (1992)

[2] M. R. DeBacker, B. Parvitte, V. Zeninari, and D. Courtois, J. Quant. Spectrosc. Radiat. Transfer 54, 1009-1018 (1995)

[3] M. R. DeBacker-Barilly and D. Courtois, Appl. Phys. B 64, 607-611 (1997)

270 ICAMDATA 97 Proceedings
[4] M. A. H. Smith, C. P. Rinsland, V. Malathy Devi, and D. Chris Benner, 52nd International

Symposium on Molecular Spectroscopy, Ohio State University, Paper RF03 (1997); manuscript

in preparation (1997)

[5] L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie,

L. R. Brown, and R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 48, 469-507 (1992);

L. S. Rothman et al., manuscript in preparation, (1997)

[6] A. G. Hearn, Proc. Phys. Soc. 78, 932-940 (1961)

[7] M. R. DeBacker, Ph.D. Thesis, Universite de Reims Champagne-Ardenne, 1995

[8] K. Mauersberger, D. Hanson, J. Barnes, and J. Morton, J. Geophys. Res. 92, 8480-8482 (1987)

[9] D. Chris Benner, C. P. Rinsland, V. Malathy Devi, M. A. H. Smith, and D. Atkins,

J. Quant. Spectrosc. Radiat. Transfer 53, 705-721 (1995)

3.3 Molecules 271
Hyperfine Structure Constants for Diatomic Molecules*

I. Tupitsyn and S. Kotochigova1 Physics Department, St. Petersburg University, Russia, 198904

1 National Institute of Standards and Technology, Gaithersburg, MD 20899

1 Introduction

The hyperfine Fermi contact term as a function of internuclear distance R is computed for the X

2 TI state of OH and the X

2 E state of AgH+ . The all electron ab initio valence-bond method [1] with

Hartree-Fock (HF) and Sturm's [2] basis sets is used to calculate the electron spin density near the

nuclei correctly This leads to an accurate determination of the molecular magnetic dipole coupling

constants and in particular the molecular Fermi contact term, Az

. The method uses many-electron

atomic wave functions to construct the molecular wave function and yields the correct asymptotic

properties for the molecule, one of which is the convergence of the molecular hyperfine interaction

parameters to the atomic values for large internuclear separations.

Magnetic hyperfine parameters are very sensitive to the quality of the molecular wave function

in general and to the spin polarization of atomic cores in particular. One of these parameters, the

Fermi contact term, is proportional to the electron spin density at the position of the nuclei that

have nonzero spin. When a molecule has electrons in open shells, it leads to one or more unpaired

spins in valence orbitals and gives an unbalanced spin density at the nuclei. Computationally it implies different exchange potentials for electrons with spin up and spin down. The contact term,

Ac , is proportional to the difference in the spin densities of electrons with the opposite direction

of spin. The accurate determination of this parameter requires both correlation and polarization

interactions in the model. The configuration interaction (CI) approach is used to treat these effects. We build the CI on the basis of the non-orthogonal many-electron atomic HF and Sturm's functions.

Hyperfine splittings have been observed in the optical spectra of diatomic molecules with very

high accuracy. Very precise theoretical calculations are required for comparison. One of these

calculations was performed by Kristiansen and Veseth [3] for the OH molecule. A many-body

perturbation theory was used to compute magnetic hyperfine parameters for the lowest vibrational

levels of the 2 U ground state. Their disagreement with experiment does not exceed 2 % near the

equilibrium distance i?e =1.8342 a.u. (1 a.u. = 0.0529177 nm).

In our calculations the Fermi contact term is determined over a wide range of R (1.5 a.u. to 8 a.u.). The asymptotic value of Ac can be compared with our value at the largest internuclear

separations.

The only previous study of the molecular potentials of the AgH+ molecule [4] was performed

using a pseudopotential approach with its inherent integrated treatment of the core orbitals, and

therefore does not give theoretical information about the AgH+ hyperfine coupling constants. Our

AC (R) values were obtained for R between 2 a.u. and 18 a.u. and converge for large R to the

atomic values.

'This paper was inadvertently published in the NIST Journal of Research. In order to have a complete set of poster papers of ICAMDATA 97 in this Special Publication, it is reprinted here again.

272 ICAMDATA 97 Proceedings
2 Theoretical and computational details.

The total electronic wave function v&ab of the molecule is introduced as a linear combination of

Slater's determinants deta , corresponding to various configurations a of atoms A and B. That is

^AB = ^2Ca detQ , (1) a

where the Ca are obtained by solving a generalized eigenvalue matrix problem, described by the

equation

HabC — SabC, (2)

where Hab is the Hamiltonian of the molecule AB. The right-hand-side of (2) includes the nonorthogonality matrix Sab-, which describes an overlap between determinants < deta \detp > and it is given

as (Sab)o0 = < deta I det0 > = {DaaDmy

l,2 Da0 , (3)

Dap = det\ < a\\Pi > ... < on\f3j > ... < cxnIPn > \, and N is the total number of electrons in the

molecule. For the particular one-electron orbitals on and j3j, the overlap matrix elements S?j are used to describe the one-electron density matrix p"'^(x,x') of the molecule as

Pl'

PM= (D^D^y^D^ (4)

id

where the <f>(x) are the one-electron wave functions and x denotes both coordinates and spin of the

electron.

Moreover, the two-electron density matrix is

p^(xu x2 \x[,x'2) = (I3aQ%)-1/2 -^tEi3iir (5)

id k,l

<t>i (Xi ) 4>* (x[ )

<j) k {x2 ) 4>* (x'2 )

,

where = D«e ^s

~ l)if (s-rk f(s-xf (s-rk f] (6)

Finally, the Fermi contact term can be expressed in terms of the total spin densities p

Q

'^(t)

and p

a

'^(i) at each nuclear site for the electrons with spin pointed up (t) and down (I). The (CI)

form of Ac is introduced as Ac = 2 p0 9I pN ^ca c0 (pa>P(V - p^U)), (7)

where g/ denotes the nuclear g- factor, pn is the nuclear magneton, and po is the Bohr magneton.

3.3 Molecules 273
1500

OH molecule

-50

0 H

.

1

, 1,

1

,

1

, h -225

1.0 2.4 3.8 5.2 6.6 8.0 R (a. u.) Figure 1: Fermi contact term Ac of the OH molecule as a function of the internuclear separation.

In our model the CI expansion for OH includes configurations obtained from the occupied Is

2

, 2s2

, and 2p4 shells of oxygen and the Is shell of hydrogen, as well as configurations created by

excitations of these electrons into the 3s, 3p, 3d and 4s states of O and the 2s, 2p, 3s, 3p and 3d

states of H. The total number of configurations was equal to 238. To describe the virtual excited

states we use localized Sturm's functions. The result of our computation of the -AC (R) for the oxygen

and hydrogen atom in the 17 OH molecule is shown in Fig. 1. The agreement of the calculation over the wide range of internuclear separations R (1.5 a.u. to 8 a.u.) is better than 1 % in comparison

with precise experimental values, which are for the equilibrium distance Re — 1.8342 a.u., Ac =

-73.1258 MHz [5], and for the asymptotic values A{0)= -219.6 MHz and ,4(H)= 1420.40575 MHz

[6, 7]. The CI treatment of the AgH+ molecule was based on the occupied 4p6 4d 10 shells for the Ag+

ion and the Is shell for the H atom as well as the 5s, 5p, 5d, 6s and 2s, 2p, 3s, 3p, 3d virtual

Sturm's orbitals for Ag+ and H, respectively. Computed values of the Fermi contact term of the

107 AgH+ molecule are presented in Fig.2. The asymptotic values of Ac for H and Ag+ fit, within

about 1 %, the well known experimental value of the hyperfine coupling constant for the H atom,

and the expected zero value for the closed shell ion Ag+ .

274 ICAMDATA 97 Proceedings
AgH+ molecule 1500-1

-1000 -

0 4 8 12 16 20 R (a.u.) Figure 2: Fermi contact term Ac of the AgH+ molecule as a function of the internuclear separation.

References

[1] S. Kotochigova and I. Tupitsyn, Int. J. Quant. Chem. 29, 307 (1995)

[2] A. I. Sherstyk and P. F. Gruzdev, Opt. Spectrosc. (USSR) 42, 690 (1977)

[3] P. Kristiansen and L. Veseth, J. Chem. Phys. 84, 2711 (1986).

[4] H. Stoll, P. Fuentealba, M. Dolg, J. Flad, L. V. Szentpaly, and H. Preuss, J. Chem. Phys. 79,

5532 (1983)

[5] J. A. Coxon, K. V. L. N. Sastry, J. A. Austin, and D. H. Levy, Can. J. Phys. 57, 619 (1964)

[6] G. H. Fuller, J. Phys. Chem. Re}. Data. 5, 835 (1976)

[7] E. Arimondo, M. Inguscio, and P. Violino, Rev. Mod. Phys. 49, 31 (1977)

^U.S. GOVERNMENT PRINTING OFFICE:1998-43 3-235/93226 3.3 Molecules 275

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