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U.S.

DEPARTMENT

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National

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of

Standards

Resonances in Electron Impact on

Atoms and Diatomic Molecules
NATIONAL BUREAU OF STANDARDS

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national Bureau of Standards

1374

Resonances in Electron Impact on

Atoms and Diatomic Molecules

George J. Schulz

Department of Engineering and Applied Science

Yale University

New Haven, Connecticut 06520

Reprinted from

Reviews of Modern Physics

Yol. 45, No. 3, pp. 378-486, July 1973

NSRDS

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued October 1973
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Foreword

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Richard W. Roberts, Director

iii
Preface

The publication philosophy of the National Standard Reference Data System recognizes that

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Reference Data System-National Bureau of Standards series.

IV
Contents

Page

Foreword iii

Preface iv

Resonances in Electron Impact on Atoms

George J. Schulz 1

Resonances in Electron Impact on Diatomic Molecules

George J. Schulz 47

v

Resonances in Electron Impact on Atoms*

George J. Schulz

Department ofEngineering and Applied Science, Mason Laboratory, Yale University, New Haven, Connecticut 06520

Electrons colliding with atoms can form, at well-defined energies, compound states consisting of the target atom plus the incident electron. The compound states, which are also called “resonances” or “temporary

negative ions,” often dominate electron collision processes. In this review we discuss the experimental

methods which are useful for studying these resonances, and review the results obtained by various

investigators. We list the energies and the widths of resonances for H, He, Ne, Ar, Kr, Xe, Li, Na, Hg, and

O. The configurations and other properties of resonances in atoms are discussed. Whenever applicable,

results are presented in the form of tables and energy level diagrams.

Key words: Atoms, H, He, Ne, Ar, Kr, Xe, Li, Na, Hg, 0; compound states; cross-sections; electron impact; energy levels; resonances; temporary negative ions. CONTENTS

I. Introduction 1 A. Theory 2

B. Relationship of Theory to Experiment 3 C. Isoelectronic and Isostate Comparisons 5 D. Experimental Techniques 5

II. Hydrogen 11 A. Resonances in the Elastic Cross Sections 12 B. Resonances in the Inelastic Cross Sections 14 C. A Resonance Involving H“ “ 15 m. Helium . , 17 A. Classification of Energy Levels in He 18 B. Resonances from 19.3 eV to the Ionization Potential 20

1. 19.34 eV (ls2s2

, 2S) 20

2. 19.45 eV (?) 21

3. 19.5-20.3 eV (?) 21

4. 20.3-20.45 eV (22P) 22

5. Effects near the Thresholds of the 2

35 and 2

lS

Excitation Cross Section 22

6. Structure in the Elastic Cross Section near the

2

3S and 2

1 S Thresholds (Wigner Cusps) 26

7. 21.0 eV (22D) 26

8 . 22.42-24 eV (325, 3

2P etc.) Optical Excitation Functions 27 C. Resonances Above the Ionization Potential:

{2s22p) 2P and (2s2pP) 2D 28

IV. Neon, Argon, Krypton, and Xenon 30 A. Resonances below the Ionization Potential 30

B. Resonances above the Ionization Potential 32

V. Lithium and Sodium 32

VI. Mercury 34 VH. Oxygen (O) 35

Appendixes

I. Resonances in H 37 H. Values for the Is (2s)

2 2S Resonance in Helium 38 HI. Position of Resonances below Ionization in Helium . 38 IHa. Larger Structures in the Optical Excitation Functions

of He 39

IV. Position of Resonances above the Ionization Potential

in He 39 V. Position of Resonances in Neon 40

VI. Position of Resonances in Argon 40 VH. Position of Resonances in Krypton 41 ViLL Position of Resonances in Xenon 41 IX. Suggested Resonances in Ne and Ar 42 X. Position of Resonances in Mercury 43 References 43

I. INTRODUCTION

This paper and the paper following deal with a

special topic in the field of electron impact on atoms and

molecules. The object of interest are “resonances,”

also called “compound states” or “temporary negative

ions.” These three terms are synonyms and will be

used interchangeably. “Resonances” occur at more or less well-defined energies when electrons scatter from atoms

or molecules. The object can be considered as a “compound state,” in that the incident electron attaches

itself to the target atom (or molecule) for times which

are longer than the normal transit time through the

atom or molecule. Since the projectile is always a negatively charged electron, the “compound state” has a negative charge. Hence the term “temporary

negative ion.”

The “resonances” can be viewed as nonstationary

(short-lived) states of an atom or molecule. In sharp

contrast to stationary states of atoms, “resonances”

decay by the emission of electrons, not by photons. Our

definition of “resonances” in the present context

excludes some types of nonstationary states which also can be viewed as resonances. For example, doubly

excited states of atoms (e.g., the 2

2 and 2s2p states in

helium) are nonstationary states which decay by

electron emission, yielding positive ions. Nevertheless,

such states are excited states of the neutral atom, and

therefore do not meet our definition, namely that the

states be temporary negative ions. This limitation of

the review is rather arbitrary.

Resonances were discovered almost simultaneously

by experiment and theory about 10 years ago, and great

progress has been made in our understanding of these

phenomena in the past decade. These two review papers

represent an effort to discuss the spectroscopy of resonances in a more or less systematic fashion. The

review is divided into two parts: In the present paper, we discuss resonances associated with atoms; in the

second paper we discuss resonances associated with

diatomic molecules. Resonances associated with more

complex molecules also exist, but too little is known

about them to justify inclusion in the present work.

1
In both parts of this review we present a concise

discussion of the energy levels, the classification of resonances, and their decay. Comparison with theory is presented whenever such comparison is meaningful,

but a full exposition of theory is not attempted. Energy

level diagrams for resonances are constructed to aid

the overview and the tables of values can be found in the

appendixes. The discussion is organized by species. A. Theory

In atoms, resonances are mostly associated with excited states (“core-excited resonances”) . Resonances as- sociated with the ground states of atoms have been

established only for the alkalis. One can distinguish

between two distinct types of resonances, namely those

that lie energetically below the state from which they

derive (i.e., below the “parent”) and those that lie above. Thus we introduce what may be called the

geneology of resonances, a concept actually introduced

for a better understanding of resonances in molecules

and discussed in more detail in the second paper of this

review. A positive ion with a particular configuration of

electrons is considered the grandparent. Adding a single

electron to this positive ion configuration gives a Rydberg state of the neutral atom or molecule: this is the parent. Adding an extra electron to the parent, we

have a particular “resonance.”

Resonances which lie below their parent are interchangeably called “closed-channel resonances,” “Feshbach resonances,” or “Type I resonances” (Taylor

et al., 1966, Taylor, 1970) . They arise when the interaction potential between the incident particle and the

excited state of the target is strong enough to support a bound state. They usually lie approximately 0-0.5 eV

below the parent. When the excitation takes place near

the center of the resonance, decay into the parent is energetically forbidden, but decay into some other

states (nonparents) is allowed. Because decay into nonparents involves a change in configuration of the

atoms, Feshbach-type resonances are usually long-lived

and their widths are narrow. When such resonances are

excited in the high-energy wing, decay into the parent

may become energetically possible (Taylor, 1970),

and such decay is favored. The end-result of such a decay is often a sharp peak near threshold in the excitation function of the parent state. Such effects are known

in both atoms and in molecules.

A special case of a Feshbach-type resonance occurs when the energy level lies near the very top of the

potential well. Such a state is called “virtual” and an

example is discussed in connection with the 2

1 S state

of helium in Sec. IIIB5.

Resonances which lie above their parents are called

‘shape resonances” or “open-channel resonances,” or ‘Type II” (Taylor et al., 1966). In this case, the

potential forms a penetrable barrier which traps the

incident particle near the target. The barrier is formed

by the angular momentum of the electron. Thus, we

expect p-, d-, /-wave resonances but generally not

j-wave resonances, since the latter have /=0 and thus

produce no barrier.

Shape resonances show a preference for decay into

their parents and very often dominate the excitation

cross section of their parent. Thus shape resonances

usually have a shorter lifetime (i.e., larger width)

compared to Feshbach resonances. An exception occurs when a shape resonance exists barely above an inelastic

threshold (Macek and Burke, 1967). In this case the

barrier can be viewed as being very thick (Taylor,

1970) and the resonance becomes long-lived, i.e., the

width is narrow; such a case exists in atomic hydrogen.

The presence of resonances is ascertained experimentally by measuring structure in the energy dependence of elastic or inelastic cross sections. Because

the structure is often very sharp, monochromatic

beams of electrons are needed for such studies and the

techniques generally employed are briefly reviewed

below. These techniques are also useful for the study of resonances in molecules.

A particular resonance can decay, by the emission

of an electron, into many final states. We thus may

speak of “channels of decay” for a given resonance. Therefore the existence of a resonance may be detected

by measuring the structure in the energy dependence of

the cross section of any state which lies energetically

below or near the resonance. In fact, sometimes it is possible to detect the existence of a resonance even in a

state which lies energetically above the center of resonance. This effect is caused by the “wings” or

“tails” of the resonance (Taylor, 1970) . Not all decay

channels are equally useful for detecting a particular resonance. Often, the branching ratio favors a particular

decay and then it is easier to detect structure in the

final state which is favored, provided that the nonresonant portion of the cross section is of the same order

in the two states. Such phenomena are particularly

important in molecules.

The energy dependence of the elastic cross section in

the neighborhood of an isolated resonance in the s wave

with a single decay channel can be expressed by the

Breit-Wigner formula (Blatt and Weisskopf, 1952),

*(E)~TrX2

I A+{ r/[(£-£o) + (¥) r]} I 2

. Here, A

represents direct “potential” scattering which varies

only slowly with energy; T is the “width” of the state,

i.e., the range of energies over which the resonance has a

large effect on scattering; E0 determines the location of

the resonance; E is the energy; and X is the reduced

wavelength of the electron. The cross section off resonance becomes 7rX2

1 A | 2

. When direct scattering is small, the cross section near a resonance becomes

7rX2 [r2/(£— E0) 2 +(^r) 2]. The maximum cross section

then occurs at the resonance energy E0 and the half- width is T. In general, however, interference occurs between direct scattering and resonance scattering so that the shape of the cross section becomes more complicated, leading to destructive and constructive inter2
Fig. 1. Partial wave phase shift near a resonance (top portion)

and resulting shape of the cross section near a resonance (bottom

portion) . The figure illustrates the interference between potential

and resonance scattering. [After Smith (1966).]]

to Fano and Cooper (1965a)

<t{E) =cra [(g+€) 2/(l+€2 )]+o-6.

Here, cr0 and cr6 are the resonant and nonresonant

portions of the cross section, e= (E—

0)/%T, and q

is the “line profile index.” Simpson et al. (1966) describe

how one can evaluate the parameter q from experimental measurements. In fact, many authors extract

this parameter from their experimentally observed line

profiles. Figure 2 shows the line profiles plotted for various values of the parameter q. If one wishes to analyze the line profile in terms of a symmetric and an asymmetric component, one can

write (Shore, 1967) a (E) = C (E) +hTBl (E-Eo) 2 + ( r/2)

^

+D(E

0) [ (£-E0yH- ( r/2) 2 ]-h

The parameters B and D, specifying the symmetric and

asymmetric components of the line, are constants. They

are related to the Fano formula by the equation B/D=

(g

2 — 1)/(2q)

Comer and Read (1972) have developed

a simple method for obtaining resonance energies from

broadened profiles using the formulation of Shore.

Recent reviews of the theory have been assembled by

Smith (1966) and by Burke (1968).

ference. The phase shift -t] which always enters the ex- pression for the elastic cross section [for 5-wave scat- tering we can write o{E) = 47rX2 sin2

77 ], increases by r

radians as the energy traverses each resonance. This can be seen from the expression for the resonant contribution to the phase shift, r) Tes = — cot-1 [ (E—

0) /\Y~\.

The smaller the width T, the more rapidly occurs the

traversal of the phase shift by 7r radians. In Fig. 1 we

plot the phase shift as a function of energy near a resonance for four arbitrary cases. The phase shift for potential scattering is different for each case, but in

each case it increases by 7r radians as the energy

traverses the resonant energy E0 . The shape of the

resulting cross section, shown on the bottom of Fig. 1, shows the expected interference structure. The position

of E0 is defined to be the energy at which the resonant

portion of the phase shift has increased by r; i.e.,

’

7res=!( 2w+l) 7r. That is the position where the total phase shift (consisting of the sum of the phase shifts due to potential and resonant scattering) has increased

by 7r/2 radians above the phase shift due to potential

scattering which prevails just below the resonance. When we are dealing with inelastic scattering, decay

can take place to a state other than the ground state, and the resonant portion of the cross section becomes

7rX2 [rinrout/[(£-£o) 2 + (£r) 2]. Here rin is the width

for decay into the ground state plus a free electron and

rout is the partial width for decay into the excited state plus a free electron. Then we have T= rin +r0ut- It is often desirable to evaluate line profiles of resonances using the formula due to Fano (1961) and

B. Relationship of Theory to Experiment

The search for resonances in atoms by experimental

methods consists of a search for structures in various

cross sections. In circumstances when this structure is relatively narrow ( <300 meV) and far removed from

neighboring resonances, little ambiguity exists. In

cases when the structure is broad, further verification is needed. Often, the angular distribution of scattered

electrons can elucidate the process involved. In molecules, dissociative attachment and vibrational excitation provide extra evidence. This multiplicity of decay

channels often makes the identification of resonances

easier in molecules than it is in atoms.

There are many theoretical approaches to the cal- culation of resonances but a thorough review is beyond

the scope of this paper. Nicolaides (1972), in reviewing

the field recently, lists many of the pertinent theoretical

references. One may rather arbitrarily divide the

theories into the following classifications

(a) Theories using the “scattering viewpoint. ,, (b) Theories treating resonances as a “decaying

state.”

(c) Theories treating resonances as special types of

bound states using projection operators.

(d) Theories treating resonances as special types of

bound states without use of projection operators.

The theories which use the scattering viewpoint, as exemplified by the close-coupling method, essentially

simulate a scattering experiment and they calculate

cross sections for various processes from the phase

3
Fig. 2. Natural line shapes for

different values of q. Reverse the

scale of the abscissa for negative q. [From Fano (1961) .]]

C

shifts. When the phase shift rises rapidly by 7r radians,

the resonance is located. The width is determined from

the energy range over which the phase shift rises through 7r radians. This method appears to be very

general and gives, in addition to the location and positions of resonances, cross sections for various processes. However, in all but the simplest systems, the computational needs become enormous. Therefore, considerable a priori judgement must be exercised as to which states to include to make a particular cross section meaningful.

A great deal of relevant insight has been gained by the

close-coupling calculations for various atoms and molecules. The frame-transformation theory also belongs in

category (a). Here, an expansion is performed in the

molecular frame of reference and the region around the

molecule is divided into a “core region,” and an outer

region in which electron correlations are disregarded.

This method has had good successes in recent years. Theories treating resonances as decaying states (which they are) are based on the Kapur-Peierls

theory. Here, a stationary value for a complex energy is obtained, which gives both the width and the energy of

the resonance. Problems are the need for good wave

functions and the need to define a definite radius of

interaction. Both shape and Feshbach resonances can be

treated in this manner.

Theories treating resonances by the use of projection

operator techniques solve directly for the expectation

value of the Hamiltonian, with the decay of the state ignored. The decay can be later introduced to give an

estimate of the width of the state, but this is usually a

difficult step. Only Feshbach-type resonances can be

calculated in this manner.

Similar to the latter category are the techniques which

search for locally stationary points of the expectation

value of the Hamiltonian. A foremost example is the

“stabilization method.” Here, One takes a trial function

which contains all the knowledge one has about the

resonance. Both shape and Feshbach resonances can be

calculated in this manner, but the width is again a

difficult quantity to extricate.

When scattering amplitudes are calculated, struc- tures in the cross section can be caused by poles, zeros, and branch points in the scattering amplitude. Only

the poles should be associated with resonances. The

zeros in the scattering amplitude for a single partial wave are associated with Ramsauer minima.

For simplicity of interpretation we assume in this

4
review that every resonance is characterized by a well- defined energy and width. Also, an attempt is made to

associate resonances with one or two molecular orbitals

of a negative ion state of the atom or molecule. Actually, a superposition of a few molecular orbitals must always

be considered in order to describe a resonance properly.

When only a single term is given, it is understood that

this is the leading, i.e., dominant, term. Despite the

fact that these assumptions oversimplify the problem,

they seem to be applicable for most resonances discussed

in this review. Exceptions are pointed out in the text. Thus, it is sometimes necessary to invoke the energy

dependence of the resonance width and in other cases the resonance center cannot be located precisely from

experimental information alone. Sometimes it does not

appear to be possible to associate a dominant molecular

orbital configuration with a particular resonance.

C. Isoelectronic and Isostate Comparisons

It is sometimes desirable to deduce the energy levels of resonances, especially those of the Feshbach type,

from known energy levels of other atoms which exhibit some similarities with the resonances. This approach is of course only approximate but often the sequence of

resonant states and the physical picture can be deduced

from such comparisons.

A simple example is discussed by Herzenberg (1971)

The lithium atom in its ground state has the approximate electronic structure \s2 2s, and is known to be able

to attach an electron with a binding energy of 0.6 eV to form a stable Liion with the approximate structure

ls22s2

. The nucleus and the two Is electrons in the ion

form a small tightly bound core of charge + 1 e l which

provides an attractive potential to hold the two 2s

electrons, whose wave functions extend far outside the

core. A He+ ion with its single Is electron also constitutes a small tight core of charge + [ e | to which two

electrons can be bound in an approximate configuration

2s2

, as in Li-

. However, the resultant configuration

ls2s2 of Helies now nearly 20 eV above the configuration Is2

, and can therefore autoionize. It is the state

ls2s2 which shows up as a Feshbach resonance, with a binding energy of about 0.47 eV with respect to the

(ls2s) 3 5‘ state of He. This binding energy is somewhat

smaller than the binding energy of 0.6 eV of the ls2 2s

state of lithium. Using such an approach, one can apply

this kind of numerology to other twinned atomic

systems.

Kuyatt, Simpson, and Mielczarek (1965) use a somewhat different method of comparison: They consider the known energy levels of doubly excited states

in helium (2s2

, 2s2p, 2p2

, 3s3p, etc.). The two excited

electrons are moving in a Z= 2 field, whereas the two

electrons in He-

(ls2s2

, Is2s2p, etc.) are moving in the

Z— 1 field of He+. Kuyatt et al. take the energies

of the doubly excited states of helium relative to the

energy of He++ and divide this energy difference by

Z2 =4 in order to obtain the corresponding energies of

the Hestates relative to He+. There is a fair resemblance between the Hestates thus obtained and the

measured values.

Still another comparative method is used by Swanson,

Cooper, and Kuyatt (1973). In order to interpret resonances in krypton, they compare the spectrum of resonances, i.e., Kr-

, with the isoelectronic atom, Rbl.

It appears that a fair comparison between these two

sets of energy levels can be made if an arbitrary scaling

constant is used.

D. Experimental Techniques

In this section we review briefly the particular ex- perimental techniques which made possible the dis- covery and the analysis of resonances. The developments described here span a period of about ten years, but they are based on principles which have been known

for a much longer period. Actually we are dealing here

with a combination of methods which were brought to bear on the problem of resonances in electron collisions with atoms and molecules. Some of the techniques were borrowed from other fields of physics : ultra-high

vacuum technology, low-current measurements, particle counting, and signal averaging. Also, progress was partially facilitated by the commercial availability

of many of the necessary components. Parallel with

these developments was an improved understanding of

electron optics (see, e.g., Heddle, 1970; Read, 1970,

1971; Adams and Read, 1972) and the development of

new types of electron monochromators (see, e.g., Kuyatt and Simpson, 1967 ; Klemperer, 1965 ; Kuyatt,

1968). Good electron monochromators and electron

analyzers are a necessary prerequisite for the experimental studies described in this and the following

review, since many of the phenomena of interest occur

in a very narrow range of energies and thus the use of

electron beams with a narrow energy resolution is a

sine qua non.

Since all of the techniques have been described in the

recent literature, in reviews (see, e.g., Bederson, 1968;

Kuyatt, 1968) and in books (Hasted, 1964; McDaniel,

1964; Massey and Burhop, 1969) only a very brief

outline of the techniques is given here. For details,

the reader is referred to the above reviews.

Many combinations of electric and magnetic fields,

using appropriate geometrical arrangements and suit- able holes or slits, can give chromatic dispersion of

electrons and can thus be used for producing monochromatic electron beams. Equally important is the use of metals with desirable surface properties. One

wishes to have a surface with a uniform potential and

high conductivity. The surface should not be affected

by the gas which is being studied. Although many

surfaces have been tried by different groups (e.g., gold,

Advance, stainless steel, copper) it appears that

molybdenum is a most desirable surface.

A variety of geometries are useful for producing

monochromatic electrons: The parallel plate and the

5
MEASURED

CROSS SECTION I

Fig. 3. Schematic overview of experiments which are useful for the study of resonances in atoms and molecules.

coaxial cylindrical “mirror” configurations, the 127°

cylindrical electrostatic, and the 180° concentric

spherical configurations. For production of very slow

(<1 eV) monochromatic electrons, one can use the

time-of-flight spectrometer. Monochromatic electrons can also be produced by ionization, using monochromatic photons. Electron monochromators- can also be

used in series to further improve the energy resolution.

It appears that, at the present time, the most widely

used monochromators for experiments in which a

magnetically field-free region is desired are the 127°

cylindrical and 180° concentric electrostatic configurations. When an axial magnetic field is desired, one can use

the retarding-potential difference method. The

retarding-potential-difference method relies on the

chopping of the electron distribution and thus is not a

true monochromator. Although important advances

have been made by use of this method, it has been made

obsolete by the trochoidal monochromator. Also note- worthy are the 180° magnetic selector and the crossed

electric and magnetic selector (Wien filter).

Figure 3 gives an overview of the experiments which

are used for the measurement of resonances. The elec- tron monochromator and the collision chamber are common to all experimental arrangements. The detection methods, however, differ widely, and are listed in

Fig. 3. Below we discuss the various methods in slightly more detail, without giving credit to the inventors and

users of the methods. Such credit would only duplicate

the much more detailed credit given in the subsequent

chapters (and in the following paper) when the actual

accomplishments are .discussed.

Differential Cross Section Measurements using

Electrostatic Monochromators and Analyzers

A typical arrangement used for the measurement of structure in the differential elastic or inelastic cross section is shown in Fig. 4. This type of apparatus is typical of many instruments used in various laboratories to obtain the results discussed in subsequent

sections. It is capable of measuring differential elastic or inelastic cross sections and usually it is possible to

alter the angle between the monochromator and the

analyzer, so that angular distributions of the scattered

electrons can be obtained.

Electrons emitted from the filament are focussed,

using electrostatic lenses (1-6) on a hole in plate 7, which serves as the input aperture for the monochromator. The monochromator itself may consist either

of coaxial cylinders (127°) or concentric hemispheres

(180°). Either of these devices should give an energy

distribution with a full width at half-maximum of

0.02-0.06 eV. The electrons are focussed onto a molecular beam by the three-element lens system (10, 11, 12).

Electrons scattered from the molecular beam pass

through the electron optics of the analyzer, through the

analyzer proper, and finally impinge on a multiplier and

6
Collector

Fig. 4. Schematic diagram of a typical electrostatic monochromator with electrostatic analyzer. Angular distribution can be ob- tained by rotating the analyzer with respect to the monochromator. Elastic and inelastic differential cross sections can be obtained

with such an instrument. QFrom Pavlovic, Boness, Herzenberg, and Schulz (1972).]

are counted. Use of a well-collimated molecular beam

reduces Doppler broadening of the resonances. The

electron optics is designed to maintain constant trans- mission characteristics throughout the spectrometer.

Many shields are usually necessary (S1-S5) to restrict

stray electrons from reaching the multiplier. One

usually eliminates magnetic fields from the collision region, either by using a magnetic shield or by using

Helmholtz coils. Double electrostatic analyzers of the type shown in

Fig. 4 have given a wealth of information on resonances.

Usually, one obtains the energy dependence of the

elastic or the specific inelastic cross section at a fixed

angle of observation. Structure in such curves is analyzed and the position and the width of resonances can be deduced. Alternatively, one can obtain at a

given incident energy the angular distribution of elec- trons. Such information is valuable for determining the

configuration of particular resonances. The inelastic cross sections that have been studied are the vibrational

and the electronic cross sections. Rotational cross sections have been studied only in the single case of H2 . Measurement of Resonances in the Total Cross Section

The Transmission Method

The transmission method can also be used for

studying resonances. In the appropriate geometry, the

transmitted current It through a gas-filled chamber is related to the incident current 70 by the relation

It=h exp (—NQtL), where N is the gas density, Qt is

the total cross section, and L is the length of the colli- sion chamber. Small excursions in the cross section Qt which often indicate the existence of resonances are exhibited by structures in the transmitted current. In

fact, when NQtL> 1, then some amplification of the

structure takes place; i.e., the percentage change in the

transmitted current is larger than the percentage

excursion in the cross section. This fact can be utilized

for a very sensitive measurement of resonances. A

further refinement can be introduced by modulating the

energy in the collision chamber and by observing

essentially the derivative of the transmitted current. An example of the arrangement for a transmission

experiment is shown in Fig. 5. Here, a trochoidal

monochromator is used for creating a monochromatic

beam in an axial magnetic field. The electrons then

enter the collision chamber region, maintained at a

pressure of about 10-2 Torr, in which a cylindrical

electrode M is mounted. A small modulation voltage

(0.005-0.06 V) is applied to electrode M so that the

electron energy in the collision chamber is modulated.

The modulated transmitted signal is detected on the

collector C. The retarding electrodes R are used to cut

off all those electrons which have made collisions in the

collision chamber, so that only the unscattered electrons are transmitted to the collector C. Only under such

circumstances is the exponential relationship between

the transmitted and the incident current valid.

Copious examples are given in the text showing the

sensitivity of this method of measurement, both for

7
Fig. 5. Schematic diagram of a transmission experiment (top) and

the details of the trochoidal monochromator (bottom). [From

Sanche and Schulz (1972) and

Stamatovic and Schulz (1970) .]

TROCHOIDAL COLLISION

—~ V

B R

atoms and for molecules. The high sensitivity for detecting resonances is thus established. However,

since one cannot obtain information on the angular

distribution of the electrons, one has great difficulty

in establishing the configuration of the resonances.

Also, it is difficult in this method to establish the final state to which a resonance has decayed. Thus, if one

wishes to obtain more detailed information regarding

the configuration and the channels of decay, one has to revert to the less sensitive but much more versatile

double electrostatic analyzers.

It should be noted that the transmission method for

detecting resonances need not use an axial magnetic

field. Instead of a retarding electrode (R), one then can use a simple hole or slit for limiting the exit angle.

Either method, with or without a magnetic field, should

lead to an exponential dependence of the transmitted

current with NQL. Optical focussing effects, i.e., the

energy dependence of the transmitted current in the

absence of gas, are inherently different in these two

systems of measurement, but the optical focussing

effects are probably easier to overcome in the presence

of an axial magnetic field. And when one wishes to study

resonances in a wide energy range, it is essential that

optical focussing effects be small.

Total Cross Section Measurements using the Ramsauer

Method

The measurement of resonances using the Ramsauer

technique is a modem application of possibly the oldest

quantitative approach to the measurement of cross

sections, originated by Ramsauer and Kollath in the

1920’s and 1930’s. A review of the early work can be ; found, e.g., in Massey and Burhop (1969). A modern ! version of the apparatus is shown in Fig. 6. It is very

similar to that used by Ramsauer and Kollath, the

major modification being the provision here for differen- ! tial pumping. Briefly, the electrons from an oxidecoated cathode, or a thoriated iridium filament, are , momentum selected by the combination of the three ; slits, Si, S2 , S3, and a uniform magnetic field is applied i perpendicular to the plane of the drawing. The electrons are then allowed to interact with the gas to be studied in

the scattering cell, and the transmitted electron signal

is studied as a function of gas density in the scattering

region at a particular value of electron energy. If it is assumed that a current of electrons 7co+7go=7o enters j the scattering region, the current reaching the collector

is given by 7C (£) =Ic0 (E) exp [— <r t (E)Nx~\, where

7c0 is that part of the current entering the scattering

region which would reach the collector in the absence

'

of scattering, <J t (E) is the total cross section, N is the

gas density, x is the path length of the electron beam

through the scattering chamber, and E is the electron

energy. The current reaching the scattering chamber

walls is given by 7g =7g0 +7c(£l — exp( —<r (iV:r)], where

7g0 is that part of the current entering the scattering!

chamber which would reach the scattering chamber

walls in the absence of scattering. Then we have

In [(7C +

7

g )/7c]= In £(7co+7go)/7co^d-0'tA

r £. The total cross section is directly determined by measuring thej

slope of a plot of the left-hand side of this equation vs N,

8
Fig. 6. Schematic arrangement of a modified Ramsauer ap- paratus for the measurement of total scattering cross section. [From Golden and Bandel (1965) .]

at a constant energy. In this kind of selector, two

parameters define the electron energy. One is the

magnetic field strength and the other is the accelerating

voltage. This coupling of the energy to two experimental

parameters leads to the fact that the electron energy is usually not continuously variable. Since the energy

spread is a function of the electron energy, the study of resonance effects is quite tedious, but resonances have

been measured using this method. The advantage of this

method lies in the fact that it yields the absolute magnitude of the total cross section at and near the resonance.

Inelastic Cross Section Measurements using the Trapped-Electron Method

The trapped-electron method has been used for the

past 15 years for the measurement of inelastic cross

sections, particularly near the threshold of excitation.

Basically, the method consists of establishing an

electrostatic potential well in which low-energy elec- trons, resulting from inelastic collisions, are trapped and

subsequently collected with a very high efficiency.

Figure 7 shows a schematic diagram of the tube and

the variation of potential along the axis. An electron

beam collimated by a magnetic field is accelerated into

the collision chamber with voltage Va- The collision chamber consists of two end plates and a grid. A

cylindrical (or parallel plane) outer collector surrounds

the collision chamber. By applying a positive voltage to

this collector, with respect to the collision chamber, an

electrostatic well, having a depth W (in volts) , can be

produced along the axis of the tube.

An electron making an inelastic collision just above

the threshold for an inelastic process loses most of its energy and is trapped in the well. It spirals back and

forth following the magnetic field lines and eventually

makes enough elastic collisions to diffuse across the

magnetic field to the trapped-electron collector. At an

electron energy that exceeds the threshold of an inelastic process by the amount W, the electrons have

enough energy remaining to escape over the potential

barrier at the end of the collision chamber, and the

trapped-electron current vanishes. Therefore, as a

function of accelerating voltage, the trapped-electron current is zero below an inelastic threshold, and then

grows to a peak which is proportional to the magnitude

of the cross section at an electron energy that exceeds

the threshold by W.

The well depth can be determined by applying a negative voltage to the trapped-electron collector relative to the collision chamber, thus creating a

potential barrier in the path of the electron beam.

The shift in the electron-beam retarding curve for different values of the applied voltage measures the

size of the barrier, which is the well depth with reversed

polarity. Other methods for establishing the well depth

also exist. Using the trapped-electron method, sometimes in

conjunction with a modulation of the well depth, it is possible to measure an excitation function for several eV

above the onset. A method very similar in concept to the trappedelectron method is the “SF6 scavenger technique.”

This technique takes advantage of the fact that SF6 has a very large attachment cross section for zero- energy electrons, and a very small cross section for all other energies. Thus one admixes a small amount of

SF6 to the gas under study and whenever an inelastic

collision takes place, it leads, near threshold, to zero- energy electrons which promptly attach to SF6

. By

Fig. 7. Schematic diagram of a trapped-electron experiment

and potential distribution at the axis of the tube. F is the filament,

P2 is the retarding electrode, G is the cylindrical grid forming

the collision chamber, M is the cylinder for collection of trapped

electrons, E is the electron beam collector, Va is the accelerating

voltage, and W is the depth of the well. The double line in (b) indicates the energy of the electron beam and the arrow indicates the energy lost by an electron in an inelastic collision. The electron energy in the collision chamber is (Va+W). [From Schulz

(1959).]

9
observing the SF6“ current using a mass spectrometer, one can obtain information regarding the threshold

behavior of inelastic cross sections. Often, the threshold

region of inelastic cross sections shows resonance

structures. Measurement of Cross Sections for Metastable States using Surface Ejection

Measurements of the cross section for production of

metastable states can be accomplished with high

efficiency if the metastable state to be measured has an

internal energy higher than about 10 eV. In this case, one can use for signal detection the ejection of electrons

resulting from metastables impinging on a metal

surface. Any kind of electron monochromator, magnetic or electrostatic, can be used for producing the

monochromatic electron beam. Figure 8 shows a

sketch of such an apparatus. If a single metastable state

is involved, the current measured on the metastable

detector iu is given by iM=ioNQLya, where N is the gas

density, i0 is the current incident on the collision chamber, L is the path length, y is the number of elec- trons ejected per metastable incident, a is the solid

angle subtended by the metastable detector, and Q is the

cross section for the particular metastable state. Since

atoms may have more than one metastable state (e.g., 2

3 S and 2

l S states for He), and since each metastable

state leads to a different 7, the total curve is not easy to

interpret. However, structure in the total metastable

cross section is often very pronounced. Examples of

such curves are shown in the text.

Measurement of Optical Excitation Cross Sections

Since resonances can be detected in any decay channel

it is obvious that the excitation cross sections to any

of the radiating states of atoms should also exhibit structure resulting from resonances. Any kind of

monochromator which gives a sufficiently narrow

electron energy distribution in conjunction with a

sufficiently high electron current is acceptable for such

experiments. This type of measurement is particularly

suitable for detecting resonances at higher energies, e.g., a few eV below the ionization potential.

Measurements of the optical excitation functions

using narrow electron energy distributions are just now

receiving attention and a complete analysis of the

observed structures is not yet available. Thus this review cannot do justice to this interesting experimental

field, but one can anticipate interesting results in the near future.

Measurement of Positive Ions

Resonances can lie above the ionization potential of

the atom. Such resonances can be studied by the

methods previously outlined. However, it is now known

that such resonances can decay by two-electron emission, yielding a positive ion. It was actually the use of

COLLISION

CHAMBER

Fig. 8. Schematic diagram of an apparatus for study of metastable excitation by surface ejection of electrons.

the trapped-electron method which established this

type of decay (see Sec. IIIC). If one examines the

positive ion cross section very carefully, one can observe

the resonances lying above the ionization threshold. As

described in Sec. IIIC, such measurement must use

sophisticated signal accumulation techniques, since the

structure in the positive ion cross section is superimposed on a large monotonically varying background

resulting from “direct” ionization. This background

signal can be subtracted by use of electronic methods.

When measuring structure in positive ion cross

sections, one must be careful to distinguish between

“resonances”, i.e., temporary negative ions and states

of the neutral atom which lie above the ionization

potential (“autoionizing states”). Both of these types

of states can cause structure in the positive ion cross

section.

Electron-Energy Distributions in Fast Neutral-Neutral

Collisions

It has been pointed out by Barker and Berry (1966)

that the electron energy distribution of the electrons

resulting from collisions of fast neutral atoms could be

used for detecting “resonances.” The reaction leading

to the detection of resonances is of the type

He ( Is2

) +He( Is2

) -+He“( ls2s*) +He+ ( Is) —>He ( Is2

) +He+ ( Is) +e. The electrons in the above reaction result from the

decay of the l$2s2 resonance and cause interference with

electrons produced directly. Thus, structure in the

electron energy distribution can be observed.

Actually, pronounced peaks consistent with the above

reaction have been observed by Barker and Berry

(1966) and by Schowengerdt, Smart, and Rudd (1973),

in the energy range up to 150 keV.

However, no new information regarding the location or width of resonances has been generated with this method up to the present time, and thus no further use

10
can yet be made of this phenomenon. Nevertheless, the

reaction itself appears to be of interest to the understanding of electron exchange in neutral-neutral collisions.

Electron-Energy Distribution in Fast Ion-Neutral

Collisions

Fast ion-neutral collisions also lead to electron

ejection which can be associated with resonances. When a stable negative ion collides with a neutral

atom, the outer electron in the negative ion can be

promoted to a resonance state. A peak in the energy

distribution of ejected electrons occurs at the energy of

the resonance. The results of such an experiment,

involving O

-

ions, are discussed in Sec. VII.

It is conceivable that the impact of fast positive ions on neutral atoms also could yield electrons associated

with resonances. This process would involve electronexchange, similar to that in neutral-neutral collisions.

Calibration of Energy Scales

Any discussion of new methods of measurement in

the field of electron impact on atoms and molecules

must point out the really significant progress which has

been made in the past ten years or so in our ability to

calibrate the electron energy scale accurately. Usually,

the “primary” standard is a known ionization potential

or an excitation potential. Important resonances are calibrated against such a standard. The resonances, in

turn, can be used as “secondary” standards if they have

a natural width which is narrow compared to the elec- tron energy spread. Such a calibration can be performed

to an accuracy of ±0.03 or ±0.05 eV, although in some cases even lower values are quoted. n. HYDROGEN

From the theoretical viewpoint atomic hydrogen is obviously the simplest system for the calculation of resonances, but measurements in atomic hydrogen are

difficult. The combination of establishing a monochromatic electron beam and a source of atomic hydrogen in an experiment proved to be elusive for many

years. Thus, it is not surprising that the first indication

of resonances in the scattering of electrons by atomic

hydrogen came from theoretical work (Burke and

Schey, 1962) and the lowest state was identified as

x 5,

lying about 0.6 eV below the n— 2 state of hydrogen.

Since that discovery many determinations using a

variety of theoretical methods have been made of the

resonant energies.

The position of resonant energies can be evaluated

by variational methods as eigenvalues of the Hamiltonian with the open channel projected out. The

results thus obtained are approximations to the actual

physical resonances in that the shift resulting from the

coupling to the neighboring continuum is not included,

and the finite width of the state is not considered.

It turns out, however, that the actual shifts are small

so that the variational calculations give a close indication of the position of the compound-state energy

levels. This can be ascertained from Appendix I, where

the results of the variational calculations are indicated

by the appropriate symbol.

The position of resonant energies can also be determined by calculating the elastic or inelastic cross section

for scattering of electrons with a very fine mesh of

incident energies. In such a calculation, the existence of

the resonance is exhibited by rapid transit of the phase

shift through tv radians in the vicinity of the compound

state. From the variation of the phase shift, one can

determine the position and width of the resonance and

thus obtain a more complete description of the resonant

behavior. The rapid transit of the phase shift through

7r radians is reflected in the behavior of the cross section

by the appearance of sharp structure. To calculate the

cross section, one must include several states of the

target atom. For low-lying levels in hydrogen, it has

been shown that it is sufficient to include the three

lowest states of the atom in the close-coupling calculation (cc). As a next step, one can do close-coupling

calculations with correlations included (ccc). For some

calculations it has been found desirable to include six states of the target atom in the calculations (6-state)

Appendix I lists the results of various calculations

for the energy and the width of resonances below the

n= 2 threshold. An energy level diagram is shown in

Fig. 9. Here, only a single set of energy levels is shown,

extending up to the n—3 threshold. Of the values listed in Appendix I, it is expected that the most accurate ones are those using an expansion of the wave function

in terms of th,e Is, 2s, 2p states of the target, together

with up to 20 correlation terms. The results thus obtained are marked (ccc) in Appendix I, following the

notation of Burke (1968). The values marked (cc) in

Appendix I are obtained by Burke using the 15, 25, 2P

states of the target atom in a close coupling expansion.

The agreement between the values obtained (cc and

ccc) gives confidence that the three-state close-coupling

results are reliable. In fact, the good agreement between

Burke’s values and the values obtained by other

investigators is remarkable.

Alternately, one can use the pseudo-state method

(ps. st.) developed by Burke, Gallaher, and Geltman

(1969) in which the first few states included are atomic

eigenstates while higher bound and continuum states are represented by pseudo-states chosen to be orthogonal. The results of these calculations are marked

(ps. st.) in Appendix I. The theoretical values shown in Fig. 9 are those

obtained by Burke using the close coupling plus correla- tion method (ccc) . Above the lowest two levels, l S and

IP, and below the n= 2 threshold of H, there are shown

a number of states which converge to the n= 2 limit. It has been pointed out by Gailitis and Damburg (1963)

that the degenerate dipole coupling between the 25 and

11
Fig. 9. Energy level dia- gram for compound states

in atomic hydrogen, con- structed from the results of theory and experiment. The

theoretical values are taken

from Burke (1968). Values

below the n = 2 level are also

listed in Appendix I (marked ccc) in comparison

with other results. The

experimental values listed in the figure are those of Sanche and Burrow (1972)

for the lowest three reso- nances and of McGowan

et al. (1965, 1969) for the remainder.

13.0

>

<D6

p

4/> "OI

>2.0

0

1

o

>o

_Q

<

X

O)

i_0)c

11.0

10.0

H

's c ii

c II 00 12.037

11.733

c II CM 10.178 10.204

9.56

2

states of hydrogen produces, at large distances, an

r~2 potential. This potential is sufficiently attractive to support an infinite number of bound states (S, P, D) in the absence of coupling to the ground state of

hydrogen.

The state marked (2p)

2 in Fig. 9 is a3P state, but

with even parity whereas all the other states in the 3P

column are of odd parity. If LS coupling is a good

approximation, the (2p)

2 state does not participate in

elastic scattering, nor does it decay to the ground state. The value quoted for the (2p) 2 state has been calculated

by Drake (1970) by Holjfien (1960).

Just above the n= 2 state of hydrogen, Taylor and

Burke (1967) find a core-excited shape resonance lP.

Using a three-state plus twenty correlation term

approximation, the energy is found to be 10.22204 eV

and the width T = 0.0151 eV. This width is unusually narrow for a shape resonance. As is common for shape

resonances, the mechanism for the l P resonance is provided by the angular momentum barrier, together

with the short-range nuclear attraction. Because the resonance lies so close to the n= 2 state, the barrier is very thick, and the penetrability very low. As pointed

out in Sec. I, such circumstances lead to a narrow

width. The existence of such a resonance close to the

threshold of an inelastic process dominates the behavior

of the inelastic cross section near threshold.

The tabulated data of Taylor and Burke (1967)

Theory: H Experiment

H

11.915

12.048

11.764

11.819

12.35

12.23

12.16 12.06

11.89

11.77 1165 ( *S)

SHAPE RES.

(2p)

2

f i 10202 >0 222 10. 200

10.150 10.177 10.190

10.125

10.65 (?)

10.45

10.29 ('p) 10.128 (

] D)

9.74

Energy Levels of H

9.738 ( 3

P) 9.558 (

] S)

show that the lP resonance exhibits itself by a peak in

the elastic cross section near 10.222 eV. This peak,

being only 1.3% of the elastic cross section would be

difficult to observe experimentally. Nevertheless, this peak in the elastic cross section provides an example of

the decay of a core-excited shape resonance into the

elastic decay channel.

The six higher states of H

-

(near n=3) shown in Fig. 9 are the result of a close-coupling calculation in- volving the Is, 2s, 2p, 3s, 3p, and 3d states (Burke

et al., 1966, 1967) . The energies and the widths for these

states have been obtained by Macek and Burke (1967)

and are also discussed by Burke ( 1968)

.

A. Resonances in the Elastic Cross Section

As previously mentioned, experiments with monochromatic electrons in atomic hydrogen are among the

most difficult. The first confirmation of the theoretical

considerations was the experiment of Schulz (1964a)

who found a peak in the unscattered electron current transmitted through atomic hydrogen at an electron

energy of 9.70=b0.15 eV. For various technical reasons, the electron energy distribution in this early experiment was insufficient to resolve the l S and the 3P i resonances. Very recently, Sanche and Burrow (1972)

succeeded in resolving these states in a transmission

experiment which uses many improvements developed

12
Fig. 10. Derivative of the transmitted current vs electron energy in atomic hydrogen. The experimental results are shown

by the solid line. The points are the best fit that can be obtained

from the theoretical shape of the cross section, but leaving the

energies and the widths of the resonances as parameters. The

computer program which is used for obtaining these points in- cludes Doppler broadening and approximates the electron energy

distribution by a Gaussian function with a half-width of 70 meV.

The energies and widths which give the best fit to the experiment are listed in Appendix I. The arrows point to the energies

of the major resonances obtained using close coupling plus correlation. [From Sanche and Burrow (1972).]

over the past few years : A trochoidal monochromator is used and the electron energy in the collision chamber

modulated in a manner similar to that introduced by

Sanche and Schulz (1972). A plot of the derivative of

the transmitted current (which is the primary measure- ment in this type of experiment) vs electron energy is shown by the solid line in Fig. 10. The energies of several

compound states (taken from the theoretical calculations cited in Fig. 9) are also shown in Fig. 10. The

points in Fig. 10 are calculated from theory in the

following manner: Sanche and Burrow (1972) take the

theoretical values of the nonresonant phase shifts which

are believed to be “exact” and use the energies and

widths of the resonances in single-level Breit-Wigner

formulas as parameters. They fold these results with a Gaussian electron energy distribution of appropriate

width (70 meV), and include Doppler broadening.

Then they calculate the derivative of the transmitted

current. The values for energies and widths of the

resonances which give the best agreement with experiment are listed in Appendix I and the derivative of the

transmitted current vs electron energy which is obtained when these optimum values are used is shown by

the points in Fig. 10. This experiment therefore shows

that the theory using close-coupling plus correlation

(ccc) is in agreement with experiment.

Kleinpoppen and Raible (1965) performed a crossedbeam experiment and found a decrease in the cross section (which corresponds to an increase in transmitted

current) at an electron energy of 9.73±0.12 eV, as shown in Fig. 11. In addition, less pronounced structure around 10.1 eV was observed by Kleinpoppen and

Raible, but was not discussed in their paper, probably

because the authors did not consider it a sufficiently

reliable observation. However, it is clear from Fig. 10

that such structure around 10.1 eV is expected to be

visible. The third experiment bearing on the subject of ex- perimental observation of resonances below the n= 2 threshold of hydrogen was performed by McGowan,

Clarke, and Curley (1965) and their results are shown

in Fig. 12. At first sight, this experiment shows little resemblance to the results of Kleinpoppen and Raible.

However, McGowan (1966, 1967) points out that there

is a strong variation of the differential cross section

with angle: The interference between the potential and

the resonant scattering causes the structure of the

differential elastic cross section to depend strongly on

the angle of observation. In order to demonstrate this

effect, McGowan (1966) calculated the differential

elastic scattering cross section in the region of the

resonances, at selected angles of observation. Figure 13

shows the results of these calculations in comparison

with some experiments. The experimental results of

Kleinpoppen and Raible (taken at 94°) resemble the

shape of the theoretical curve for 0= 100°. The experimental data of McGowan, Clarke, and Curley resemble

the theoretical curve at 90°, as shown on the bottom

left-hand portion of Fig. 13. A more detailed comparison

is shown in Fig. 14. Here, the width of the X S resonance

is left as a parameter. The best fit to experiment is obtained when the width of the 1 S resonance is taken to be

0.043 ±0.006 eV, in good agreement with the value of

0.0475 eV given by Burke.

The sharp hump observed just below the n—2 level of hydrogen in Fig. 12 can be ascribed to the effect of

the lD state (Ormonde, McEwen, and McGowan,

1969) . Figure 15 shows a detailed comparison between

theory and experiment in the region 9.9-10.2 eV,

91 9.3 9.5 97 9.9 10.1 eV

Electron Energy

Fig. 11. Elastic cross section for electrons on atomic hydrogen.

The angle of observation was 94°, and the width of the energy

distribution about 0.1 eV. [From Kleinpoppen and Raible

(1965).]

13
Fig. 12. Differential scattering cross section in hydrogen. The angle of observation is 90° with respect to the bombarding electrons. The position of the three lowest resonances, 1 S, 3 P, and

1 D, are shown. [From McGowan, Clarke,

and Curley (1965) and McGowan

(1970).]

ELECTRON ENERGY (eV) Fig. 13. The experimental results of Schulz (S), Kleinpoppen

and Raible (KR), and McGowan, Clarke, and Curley (MCC)

compared with the differential scattering calculations of McGowan

(1966, 1967) for different scattering angles 0. The dashed line corresponds to the calculated cross section for an angular window

of 15°. The position of the l S resonance is taken to be 9.56 eV

and its width 0.04 eV. The 3 P resonance is taken to be at 9.73 eV

with a width of 0.01 eV. The solid line represents the same cal- culation with the experimental value of the electron energy

distribution (0.06 eV) folded in. [From McGowan (1966).]

when the lD state alone is considered. The agreement in

Fig. 15 must be, presumably, considered fortuitous

because a valid comparison between theory and experiment must also include the S, P, and ZD contributions.

For a comparison at 90°, such as is the case for

McGowan’s experiment, the P-wave contribution to the cross section should be zero. Figure 16 shows the

valid comparison between theory and experiment. The

lD compound state of H~ seems to be the dominant

contribution near 10.1 eV.

It is clear from the work of McGowan that experiments on the angular distribution of electrons in the

neighborhood of the l S and 3P resonances in hydrogen

are strongly dependent on the angle of observation and

on the acceptance angle of the apparatus. Further work

with much better angular resolution will be necessary

before a really satisfactory check of the very elaborate

theory can be made.

B. Resonances in the Inelastic Cross Sections

Resonances lying above the n= 2 state of hydrogen seem to be most pronounced in the inelastic cross

section. Figure 17 shows the cross section in the 2p

excitation from threshold to about 3 eV above threshold.

Structure in the cross section is evident and the location

of this structure is transposed onto the energy level diagram, Fig. 9. Also shown in Fig. 17 are the theoretical curves. The sharp onset of the 2p

excitation

cross section results from the proximity of the lP shape

resonance, which is almost coincident with the n= 2

!

level. This sharp peak near threshold seems to be consistent with the earlier experimental results of Chamberlain, Smith, and Heddle (1964) which were obtained

14
Fig. 14. Comparison between experimental and calculated cross sections in the region of the 1 S and 3P resonances in hydrogen.

The positions of the two resonances are fixed at 9.56 and 9.73 eV, respectively, and the width, To+ of the X S resonance is varied from

0.01 to 0.110 eV. The best fit to the experimental data, indicated by the circles, is obtained when ro+ =0.043±0.006 eV. [Trom McGowan

(1967).]

with a broader electron energy spread. Also, the sharp

peak near threshold is consistent with theory.

Two subsidiary peaks in the experimental curve shown in Fig. 17 occur at 10.45±0.03 eV and at 10.65±

0.03 eV, i.e., just above the n— 2 state of hydrogen.

According to McGowan et al. (1969), the first of these

is statistically real and the second is not. McGowan

et al. argue that the 10.45-eV peak may be an interference effect of the first resonance, as calculated by

Marriott and Rotenberg (1968), or another shape

resonance. Geltman and Burke (1970) used the pseudostate expansion theory in an attempt to confirm the

experimental structure near 10.45 and 10.65 eV. Their

theory, however, shows no signs of the experimental

structures and shows a smooth behavior in this energy

range. It should be remarked that the pseudo-state

expansion theory has achieved measures of success, notably in calculating the ratio of excitation cross

sections <r(ls— 2s) /a (Is— 2p) in remarkably good

agreement with the experiment of Ott, Kauppila, and

Fite (1970).

Below the n=3 state of hydrogen, a number of resonances appear in both the experimental and theoretical curves of Fig. 17. For the lowest 1 S resonance, agreement exists between theory and experiment as to position and width. The dominant feature of the theory

below the n=3 threshold is the 1D resonance near

11.8 eV, but the dominant feature of the experimental curve appears about 0.1 eV higher. McGowan et al. (1969) argue that the theory is insufficient to predict

the position of the 1D resonance accurately and that more states need to be included in the theory to give the

proper position for the lD resonance. Thus it may be more desirable to correlate the “dominant” features of

experiment and theory.

The broad maximum in Fig. 17 just above the n=3

threshold appears to be a core-excited shape resonance (McGowan et al., 1969).

C. A Resonance Involving H

Electron impact experiments on neutral atoms cannot

give information on the possibility of the existence of resonances which involve doubly charged negative

ions, e.g., H—. In order to gain such evidence, one has

to perform experiments in which electrons collide with

negative ions. Such an experiment has recently been

reported by Walton, Peart, and Dolder (1970). They

studied the reaction e+H-—>H+2e in a beam experiment; their results are shown in Fig. 18. Noteworthy

is the sharp structure appearing near 14.5 eV, which

Walton et al. (1970) attribute to a state of H , with a

lifetime of about 10~15 sec.

15
Taylor and Thomas (1972) calculated the position

and designation of the state responsible for the experimental structure, using the stabilization method which

is described in detail by Taylor (1970) and by Hazi and

Taylor (1970). Taylor and Thomas (1972) find that a

short-lived resonant state, H—, with a configuration

principally ( 2s) 2 2p 2P° and an admixture of (2p)

z

, exists at an energy of 14.8 eV and that its width can be

estimated to be about 1 eV. The calculated energy and

the lifetime are in good agreement with the experiment

of Walton et al. (1970). Taylor and Thomas further

point out that they find another resonance with a

largely (2p)

z wave function at some higher, unspecified

energy.

The geometric structure of the H~~ ion has been

studied by Herzenberg and Ton-That (1973). They

suggest that the only geometry which can lead to a

quasistationary state must have all three electrons lo- cated at about the same distance from the proton, near

the comers of an equilateral triangle. Then all three

electrons comprising the H~ “* ion are attracted to the

proton. By minimizing the expectation value of the

Hamiltonian with respect to parameter controlling the

Fig. 15. (a) Close-coupling l D cross sections over the resonance

region, (b) l D cross sections folded with the resolution of the experimental electron beam. The theoretical calculations cor- respond to the left-most scale, and the experimental points to the scale on the right. Because the measurements are relative, the results are displayed as shown in order to emphasize the agree- ment in shape between theory and experiment. [From Ormonde,

McEwen, and McGowan (1969).]

«p.090

Z

<

o

<

tr£ .089

(/> \z

O

I-O

id

</> V) .080-

V)o

<ro

.079-

o /

EXPERIMENTAL

6 STATE

9.9 10.0 ELECTRON

l O.l ENERGY10.2 (eV)

Fig. 16. Comparison of experimental and theoretical cross sections in the energy range 10.0-10.2 eV, for 90° scattering in atomic hydrogen. The theory (close-coupling) includes the 1 D

and X S resonances as well as the li3 S and li3 Z) background phase

shifts. The theoretical results are averaged over a 15° cone and

folded with the experimental beam width. The absolute scale for the experimental points is obtained by normalizing the measured

differential cross section in the region below the lowest 1 S res- onance to the calculated cross section in that region. [From

Ormonde, McEwen, and McGowan (1969).]

radial distance of the electrons from the proton and

the angles between the electrons, they find a quasistationary state. Their value for the energy of this state is 11.9 eV (compared to 14.5 eV for the experimental value quoted above) and a lower limit for the

width is r>0.3 eV. The contribution of the s

2p configuration is 87%, that of the p

z configuration is 10%.

Herzenberg and Ton-That also find an analogous

state in He“, at an energy of 45.9 eV, with all three

electrons equidistant from the nucleus. This state could

provide an interpretation for the broad resonance around 50 eV (see Sec. IIIC) observed in helium by

Crooks et al. (1972)

.

Other doubly charged negatives have recently been

observed using mass spectrometry (Baumann et al., 1971) . In this experiment, negative ions are formed in a Penning source. Electric and magnetic deflection ex- periments confirm that doubly charged negative ions are present in the beam. The ions which have been

identified are O , Te , Bi , F , Cl , Br , and

I—. The lifetime of the above ions must be relatively

long in order for them to survive their trip through the mass spectrometer (^lO^-lO-7 sec) . This is in contrast

to H—, for which the lifetime is about 10-15 sec. Fano

(private communication) suggests that a plausible

16
ELECTRON ENERGY (eV)

Fig. 17. Total 2p excitation cross section in hydrogen. The high-resolution experimental data indicated by the closed points were

obtained with an energy spread of 70 meV and the low-resolution data, indicated by the open circles, were obtained with an energy

spread of 180 meV. The experimental data are from McGowan, Williams, and Curley (1969). The cross section is plotted on an absolute scale, referenced to the values of Long, Cox, and Smith (1968). Also shown is the “six-state close-coupling” theory of Burke

et al. (1967) and the “three-state close- coupling plus electron correlation” theory of Taylor and Burke (1967), into which the experimental resolution (70 meV) has been folded. [From McGowan, Williams, and Curley (1969).

explanation for these long-lived negative ions could be a

sextet of the type 3^4

(

3P)4s4_p2 for Cl and a configuration 2

p

z

(AS)3s3p2 for 0 . The energy of these levels

is not known.

m. HELIUM

As we review the field of resonances and go from

atomic hydrogen to helium, the most striking effect is the decrease in theoretical effort and the increase in

experimental effort. Thus the guidance for classifying

the structures found by experimentalists is not too

extensive, and experiments usually precede theory. In

fact, much of the classification has been obtained

Tom experimentally measured angular distribution. The

experiments performed to date have analyzed struc- tures in the 2

3 5, 2X S, 2

3P, and 2lP cross sections as well

as in the total elastic and total metastable cross section.

The discovery of resonances in atoms came from

measurements of the structure in the elastic cross

section, as shown in Fig. 19. This type of experiment,

especially when it is coupled with a measurement of

angular distributions (Fig. 20), gives a great deal of

information regarding the width, symmetry, and shape

of the resonance, especially for resonances lying below

the first electronically excited state of the atom.

For resonances lying above the first electronically

excited state, as in the case of core-excited shape

resonances associated with n= 2 and higher-lying

states, it is advantageous to study structures in the

electronically excited states, such as 2

3 S, 2

1 S, 2

3P, 2

1P,

etc. The decay into these final states is usually preferred. For an overview of all the sharp resonances occurring

by electron impact, it is advantageous to use a trans- mission experiment. These types of experiments,

pioneered by Kuyatt, Simpson, and Mielczarek (1965), can be made very sensitive to sharp structures in the

cross section by modulating the electron energy and

thus performing a differentiation of the transmitted

electron current with respect to energy. Such experiments have been performed for all rare gases by

Sanche and Schulz (1972). A sample of their data for helium is shown in Fig. 21. The advantage of this type

of experiment is the overview of the location of reso- nances on the energy scale. The disadvantage lies in the limited information: One generally cannot

deduce the symmetry, the width, or the exact shape.

Nor is it possible to observe broad resonances (e.g.,

shape resonances) very clearly. Various elastic and

inelastic cross sections must be measured at different

angles of observation to fill out the picture.

As an aid to the subsequent discussion, Fig. 22 shows an energy level diagram of the lowest states of neutral

He and the position of resonances, as observed by

17
various investigators, both experimentally and theoretically. The solid horizontal lines indicate those resonances which seem well established at the present

time.

A. Classification of Energy Levels in He

It has already been pointed out that the levels of the

compound states in helium and other gases arise from

the addition of an electron to a particular excited state

Interaction energy (eV)

Fig. 18. Cross sections for detachment from H

- by electron impact. The symbols #, and A; respectively, refer to measure- ments with inclined beams in which the ion beam laboratory

energies were 7, 8, and 10 keV. The open circles denote earlier measurements by Peart et at. (1970). Estimates of energy resolu- tion and 90% confidence limits of random error are shown for each point. [From Walton, Peart, and Dolder (1970).]

Fig. 19. The original observation of the (ls2s2

) 2 S resonance

in helium. The ingle of observation is 72° and the elastic cross section is measured. The decrease in the cross section near 19.3 eV

is approximately 14%. [From Schulz (1963).]

Table I. The superscripts designate states of odd and

even parity. The 2s2p configuration can lead to 3P and

l P states. The addition of a Is electron to this term

results in two distinct 2P states of different energy for

the Is2s2p configuration. One of these states has spins

of the outer electrons parallel (

2Ptt ), the other antiparallel (

2Pfl)- The “parents” of these two states are the (2s2p) 3P and (2s2p) 1P states, respectively.

The (2p)

2 configuration, being composed of two

equivalent electrons, results in l S, 3P, and lD states.

of the atom. The resulting state lies, for the case of

Feshbach resonances (also called “closed channel”

and core-excited resonances), below the energy level of the parent. Thus one can think of these states as negative ions with a definite electron affinity, in the

range of about 1/2 eV. It is also possible for the com- pound state to lie at the energy of the parent state (“virtual states”) or above the parent state, by up to

3 eV. Thus one can list all the relevant configurations

which can be derived from an excited state of helium,

plus an additional electron. From the lowest states of

helium, ls2.y and \s2p, we can write the states listed in

Table I. Possible states of He-

.

Outer electrons equivalent

Additional states for nonequivalent

electrons

(unlikely)

1s252 2S*U

\s2s2p 2P°n, 2P°t W ...

ls2p2 2Se tt,

2Pe

, 2 De )]

18
DERIVATIVE

OF

TRANSMITTED

CURRENT

(ARBITRARY

UNITS)

and Ehrhardt (1966).]

Adding a Is electron, we obtain 2 6*, 2P, 4P, and 2D

states. These are the only allowed states within the LS

coupling scheme, which is expected to be applicable

for the case of He-

. It was first pointed out by Fano and Cooper (1965)

that there are restrictions on the quantum numbers of

the compound states that can be reached by the

collision of an electron with a ground-state helium

atom (

1 5) . The parity and the total angular momentum

quantum number J of the input channel must be in- variant in the collision. They must be conserved for the

system e+He(1 5) and for the system He-. The spin

quantum number £ and the orbital angular momentum

quantum number are each individually conserved only

insofar as LS coupling is applicable. This should be the

case for helium.

We can eliminate all the quartet states in Table I because these would require a spin-flip. Also, we can

eliminate, as pointed out by Kuyatt et al. (1965) the

state 2Pe resulting from the ls(2p) 2 configuration. The

parity of this state is necessarily even. In order to produce this state from 1 S state of helium (parity

even) , the electron must have a parity (— 1 )

l

, where l is the orbital angular momentum. In order to produce a P state from an S state, we must have 1=1, e.g., odd

parity. Thus we cannot conserve parity and must

I i 1 i I I I I I I 1 19 20 21 22 23 24 25

ELECTRON ENERGY, (eV)

Fig. 21. Derivative of transmitted

current vs electron energy in helium,

below ionization. The gain of the

amplifier is increased by a factor of 25 for the lower portion of the curve and by a factor of 100 for the inset in the upper right, compared to the

region around 19.3 eV. The excursion around 19.3 eV corresponds to a change in transmitted current of about

10%. The smaller excursions (e.g., # 12) thus correspond to a change in transmitted current of about 0.01%,

which is the limit of this transmission experiment. [From Sanche and Schulz

(1972).]

19
Fig. 22. Survey of energy values for resonances in helium. On the left-hand

side of the diagram we show the lowest energy levels in He. The names of the authors are indicated above; just

below the names we indicate the decay

channels in which the resonances are observed. The dots indicate the posi- tion at which structures have been

observed. Two theoretical columns

are also included. Burke et al. (1969)

calculate the widths of the 2 P, 2D, and

2 F resonances and these are indicated by the vertical lines. The full horizontal lines indicate those res- onances which seem firmly established. The many extra resonances found by Golden et al. (1970), as well

as the resonance at 19.45 eV (dashed

horizontal line), have been put in doubt by the results of Sanche and

Schulz (1972) and must be seriously

questioned at the present time. [From Sanche and Schulz (1972).]

>

©

£

2

> ©

cross out the 2Pe state in Table I. This leaves us with one

state from the ls2s2 configuration, 2 S

e

, two states from

the ls2s2p(2P°) configuration (one with spins in the

outer shell parallel, one antiparallel), and two states from the ls2p2 configuration 2 S and 2D. The total

number is 5. If the electrons in the outer shell are not equivalent,

then we have to write Is2p2p', where 2p’ stands for

electrons in an np orbital (n= 2—>oo) and additional

states are possible, as postulated by Golden and Zecca

(1970). These additional states are also listed in

Table I, although they may not be real possibilities.

B. Resonances from 19.3 eV to the

Ionization Potential

In this section we discuss resonances above the

lowest 2

2 S at 19.34 eV, and list them in a sequence of

increasing energy. An attempt is made to establish the

reliability of each determination. At the outset it must

be stressed that differences in energy which are less than

the observed width of these resonances (i.e., about

0.05 eV) must be ignored. Resonances can exhibit a

different shape, depending on the angle of observation,

or the acceptance angle at a fixed angle, or depending on

the decay channel in which they are observed. Only a complete analysis involving phase shifts could establish a reliable guide to such differences.

1. 19.34 eV ( ls2s2

, 2S) The resonance occurring near 19.3 eV was the first to be measured experimentally for an atomic system.

Although some discrepancies as to the exact energy and

width emerged initially, all the experimental values

have converged to the region 19.30-19.35 eV. Appendix

II lists some of the recent values obtained by experiment and by theory. Figure 19 reproduces the original

measurement of this resonance obtained by observation

of elastic scattering at an angle of 72 degrees, in a double electrostatic analyzer. Simpson and Fano (1963)

confirmed the existence of this resonance and classified

it as the Is (2s) 2 2 S state. Further experimental confirmation came from a Maier-Leibnitz type experiment

of Fleming and Higginson (1963). Andrick and Ehrhardt (1966) obtained the angular dependence in the

region of 19.3 eV and confirmed that the resonance appears in the 5-wave. Figure 20 shows that the

20
Fig. 23. Comparison of cross sections for production of metastables in helium, (experiments) a—resonance at 19.3 eV

observed in a transmission experiment; b—total metastable cross section (Pichanick and Simpson, 1968) ; c—total metastable

cross section (Schulz and Fox, 1957) ; d

2

3 S differential cross section at 72° (Schulz and Philbrick, 1964) ; e—

X S differential cross section at 0° (Chamberlain, 1967) ; f

2?S differential cross section at 0° (Chamberlain, 1967) . [From Pichanick and Simpson

(1968).]

resonance can be clearly observed at 90°, at which

angle the p wave disappears. An analysis of the phase

shift shows that the phase shift of the 5 wave for

potential scattering is 100 degrees, for the p wave 25

degrees, and for the d wave 4 degrees. These phase

shifts can be compared with a subsequent study of

Gibson and Dolder (1969) who obtained 770 = 110°,

771 = 17°, and 772 = 3°. The agreement with the theory of

LaBahn and Callaway (1964) is satisfactory. The

variation of the resonance shape with angle is attributed

to the interference of the s-wave with the other partial curves. Whereas the width of the resonance was

estimated by Andrick and Ehrhardt (1966) to be

15-20 meV, more detailed analysis by Gibson and

Dolder gives a value of 8 meV for the natural width at

half-height, in good agreement with previous estimates.

The value of 8 meV for the width of the resonance at

19.3 eV is probably the best experimental value

available at this time. Appendix II compares the

widths deduced from experiment and from theory. The

latest calculations of this width, due to Temkin et al. (1972) and Sinfailam et al. (1972) give values of 14

and 15 meV, respectively.

2. 19.45 eV (?)

A small structure was observed by Gibson and Dolder

(1969) in the differential elastic cross section just above

the 2

2 S resonance. This structure is most pronounced at an angle of observation of 54.5° and disappears at 90°. The angular distribution is indicative of a resonance in

the p wave and we would deduce that the designation of

the state is ( Is2s2p) 2P°. The signal-to-noise ratio with

which the 19.45 resonance was observed at 54.5° was only unity, and thus this observation alone cannot

be considered to be conclusive. However, this resonance was observed at the identical energy in the transmission

experiment of Kuyatt, Simpson, and Mielczarek

(“peak” at 19.43±0.01 eV, “dip” at 19.47±0.01 eV),

but was visible only on the runs with the highest energy

resolution. Also, Golden and Zecca (1970) observed

structure in their transmission experiment (“peak”

at 19.47 eV, “dip” at 19.52 eV) . Andrick and Ehrhardt

(1966), whose experiment is similar to the experiment

of Gibson and Dolder, did not observe the structure at

19.45 eV. Neither did Pavlovic (private communication) observe this resonance in an experiment which was specifically performed to study this resonance. Sanche and Schulz (1972) consider the 19.45 eV reso- nance a spurious effect resulting from the replication of the ( ls2s2 ) 2S resonance by electrons which have

lost energy on collision with slits. In their theoretical study, Eliezer and Pan (1970)

found a

2P root at 19.6 eV, but it “stabilized rather

poorly.” The latter authors consider the evidence unconvincing. Burke did not obtain such a state. Neither

did Temkin, Bhatia, and Bardsley (1972), who made a purposeful attempt, using their quasi-projection theory, to find states below 19.8 eV. Similarly, Sinfailam and

Nesbet (1972) searched for resonances below the 2

3 S

state with a fine mesh using a variational technique

which takes polarization and correlation effects into account. They, too, find no evidence for resonances apart from the 2 S resonance. Thus we must conclude

that the existence of a resonance at 19.45 eV is uncertain

and in serious doubt.

3. 19.5-20.3 eV

Between 19.5 and 20.3 eV only Golden and Zecca

(1970) have observed resonances. These authors observe 4 structures, each exhibiting a peak and a dip.

The assignment given to these structures and the

energies (in eV) of the peak and the dip are : ( \s2p2

)

2Dt t

: 19.58/19.62; (ls2p2

) 2Du : 20.04/20.10; (ls2s2p) 2Pu

°: 20.17/20.21; (1s2p2

)

2 S^: 20.3/20.35. No one else has

observed structure attributable to resonances in this

energy range (19.5-20.35 eV), although other trans- mission experiments in fact had a higher sensitivity for observing resonant structures. One would have to invoke some special features of Golden and Zecca’s apparatus which would make this particular apparatus more sensitive to the particular resonances in the energy

range under discussion. The angular acceptance angle

for forward-scattered electrons could possibly be such a

feature, but up to now very little attention has been

given to such considerations.

Until the structure in this energy range is reproduced

by other experiments, one must retain a skeptical

attitude regarding the reality of the 4 structures in the

21
Fig. 24. Energy dependence of 2

3 S

cross section at 0° and 72°. The solid

lines are from the close-coupling

theory of Burke, Cooper, and

Ormonde (1966). The dashed curves

are experimental: The 72° data are from Schulz and Philbrick (1964) and

the 0° data from Chamberlain and

Heideman (1965). The first peak in the cross section curves is attributed

to the 2P resonance and the second to the 2D resonance. [From Burke,

Cooper, and Ormonde (1966).]]

ELECTRON ENERGY (eVl

energy range 19.5-20.3 eV. We should note that the

last of these structures coincides in energy with the

broad 2

2P shape resonance discussed in the following

section.

4. 20.3-20.45 eV ( 2

2P) The total cross section for excitation of the 2

3S state

exhibits a maximum at about 0.5 eV above threshold as shown in Fig. 23. It has been pointed out by Baranger

and Gerjuoy (1957) that such behavior can best be

explained by considering that the inelastic process

proceeds via a compound state. By fitting the total 2

3 S

cross section with a Breit-Wigner one-level formula,

they obtained a very good fit to the experimental

cross section for metastable production (23 5+211S)

of Schulz and Fox (1957) . The parameters that resulted

in the best fit located the position of the resonance

at 20.2 eV with a width of about 1.0 eV. More detailed

theoretical considerations by Burke, Cooper, and

Ormonde (1966), using the close-coupling approach,

confirmed these ideas. Burke et al. found that the

major peak of the 2

3 S cross section occurs within the

range of the p-wave resonance, which they calculate to occur at 20.2 eV with a width of 0.52 eV. Another

smaller peak at the 2D resonance (21.0 eV) is also

found in this calculation. These considerations then lead us to associate experimentally determined maxima of

the 2

ZS cross section with the existence of compound

states.

If the width of the p-wave resonance is anywhere near

the value quoted by Burke et al. (0.52 eV), it is not

surprising that the observed location of this maximum

varies depending on angle and the mode of observation.

Whereas the total 2

3 S cross section peaks at 20.3-20.35

eV, (see, for example, Schulz and Fox, 1957; Pichanick

and Simpson, 1968) the differential cross section peaks

near 20.45 eV (Chamberlain, 1967; Ehrhardt and

Willmann, 1967; Ehrhardt, Langhans, and Linder,

1968) . It is doubtful that this discrepancy, of the order

of 100 meV, is instrumental. In fact, the “shifting” of

the peak is dramatically demonstrated in Fig. 24, due

to Burke et al., which shows a shift in the location of the

peak in the 2

Z S cross section by almost 200 meV

between an angle of observation of 0° and 72°. Thus it is impossible to define, without a detailed analysis, the

exact center of this resonance. Ehrhardt and Willmann (1967) find that the

angular distribution of the scattered electrons which

have excited the 2

3 S state around 20.45 eV (see Fig. 25)

exhibits a p-wave character, so that the designation of

this resonance as 2

2P seems established.

5. Effects near the Thresholds of the 2

3 S and 2

1 S

Excitation Cross Section

The differential cross sections for both the 2

3

-S' and the

2

1 5' states exhibit a small peak within 150 meV of

threshold. This behavior has been observed in two

independent experiments, one performed by Chamberlain and Heideman (1965), who analyzed the inelastically scattered electrons in the forward direction, and

the other by Ehrhardt and Willmann (1967) and by

Ehrhardt, Langhans, and Linder (1968), who observed

inelastically scattered electrons at 10-90°. The latter experiments show that the angular dependences of the

structures near both the 2

36' and the 2

l S thresholds are

isotropic, indicating an s wave. The peaks occur at

19.95 eV (140 meV above the 2

3 .S threshold) and just

above 20.6 eV, respectively.

The results of Ehrhardt et al. (1968) are shown in

22
Fig. 25. Angular distribution of electrons having excited the

2

3 S state in helium. The incident electron energy E, is indicated. The angular dependence at 19.95 eV corresponds to an 5 wave,

at 20.45 eV to a p wave and at 21.00 eV to a d wave. All curves

are experimental. [From Ehrhardt and WilJmann (1967).]]

Fig. 26. However, it seems that a note of caution is appropriate in analyzing the behavior of these excitation curves within the first 0.5 eV of threshold. This regime

involves electrons which possess only 0-0.5 eV of

energy after the collisions and which must be accepted

by the electron analyzer. For the curves of Fig. 26 to be

meaningful, it is desirable that no energy discrimination

be present in this energy range. This requirement

imposes a very severe demand on the electron optics

which must exhibit a complete absence of chromatic

aberration in the range 0-0.5 eV. This problem has not

yet been solved. Also, there should be a complete

absence of stray electric and magnetic fields, which

could cause severe discrimination problems. It is probable that the curves of Fig. 26 are afflicted, within

0.5 eV of their thresholds, by an error of unknown

magnitude, i.e., a correction factor of unknown shape

should be applied to these curves. One can obtain an indication of the seriousness of the

problem outlined in the previous paragraph by taking

the ratio of cross sections for the 2

3 S excitation at two

different energies, e.g., the ratio o-(20.45 eV)/cr(19.95

eV) . This is the ratio of cross sections near the center of

the 2P resonance to the peak near threshold. For the curve of Fig. 26, this ratio is about unity (at 70°),

whereas it is about three (at 60°) in the older work of

Ehrhardt and Willmann (1967). One should prefer, at

the present time, the data shown in Fig. 26, due to Ehrhardt, Langhans, and Linder (1968) in preference

to the older data of Ehrhardt and Willmann since the

former authors have made a study of the energy

discrimination in their apparatus and have come to the

conclusion that the error is less than 50% in the energy

range within 300 meV of the 2

3 S threshold.

The experimentally measured width of the threshold

structure near the onset of the 2

3 S state is about 150

meV and thus should have been noticed in measure- ments of the total cross section for the 2

3 S state. Although the resolution of many of the experiments on

the total excitation of the 2

3 S state had sufficient resolution, such a structure was not observed (see,

e.g., Schulz and Fox, 1957) and the total 2

3 S cross section rises to a broad maximum near 20.3 eV. Pichanick and Simpson (1968) made a careful examination of the threshold region with the purpose of

examining the threshold structure (see Fig. 23), but

failed to find any indication of its existence. If one

integrates the theoretical differential cross section over

all angles to obtain the total cross section, the threshold

structure becomes almost invisible [Burke et al. (1967)

and Linder, private communication] and thus the

threshold structure near 19.95 eV cannot be observed

in the total cross section for exciting the 2

3 S state.

Fig. 26. Energy dependence of the differential cross sections

for the excitation of 2

3 S, 21 S, 2

3 P, and 2l P levels of helium near

threshold, at selected angles of scattering. The angle of observation is indicated, for each curve, on the left-hand side. The number

following the designation of angle indicates the enlargement of the particular curve with respect to the 2

l S curve at 20°. Experimental. [From Ehrhardt, Langhans, and Linder (1968).]

23
Although the structures near the thresholds of the

2

ZS and 2

1 5 states have a similar appearance, the

interpretation advanced by Ehrhardt (1969) for the

two effects is very different.

Ehrhardt and Willmann (1967) find that the threshold

peak at 19.95 eV in the 2

3 S differential excitation cross section is independent of angle. Thus they deduce that

the threshold peak appears in the j-wave. In a number of

publications, Ehrhardt et al. (1967, 1968, 1969) point

out that the threshold effect is caused by the tail

(i.e., the wings) of the 2

2 S resonance, whose center is located at 19.34 eV. This conclusion relies heavily on

the fact that the theoretical work of Burke and of

Taylor could not account for other 2S resonances in this

energy range. In his review, Taylor (1970) further dis- cusses the qualitative aspects of threshold peaks in

inelastic cross sections caused by core-excited reso- nances lying below the inelastic threshold.

It is pointed out by Herzenberg (private communication), that very sharp peaks in inelastic cross sec- tions near threshold can not be explained quantitatively

in such a simple fashion. Rather, one has to realize

that the decay width for a Feshbach resonance (e.g.,

2

2S in helium) shows an abrupt increase in a narrow

energy range starting at the inelastic threshold. Thus,

in the case of helium, one can understand how a narrow

width (~8 meV) below the threshold of the 2

3S state can be reconciled with a width considerably broader

(^1 eV) above the 2

3 S state. This argument should

Fig. 27. An expanded view of the derivative of the transmitted

current in the neighborhood of the lowest inelastic thresholds in helium. The solid line shows the experiment of Sanche and

Schulz (1972) and the dashed line is obtained from the total metastable cross section. The two curves are normalized to each

other in the region of the 2

1 5 excitation. The rise in the transmission curve just below the threshold for the 2

3 S and 2

1 S states is interpreted as a Wigner cusp in the elastic cross section. [From

Sanche and Schulz (1972).]

Fig. 28. Differential inelastic cross sections in the energy range

22.4-23.5 eV for helium. The structures are due to the n—3 compound states. The final state and the angle of observation are

indicated for each curve. [From Andrick, Ehrhardt, and Eyb

(1968).]

be applicable generally to the threshold excitation of

those states which are parents of Feshbach resonances.

It would be satisfying if the threshold structure in the

2

1 S state could be explained along similar lines. However, there seem to be good reasons to invoke a different

explanation. This explanation is based on the work of

Burke et al. (1967) and of Burke, Cooper, and Ormonde

(1969) who calculated, using close-coupling methods,

the cross section for the transition e+He(235)-^

He(21 5')+e. They found a sharp peak at the threshold

of the 2

1 S state, which they attributed to a2S resonance

close to the threshold of the 2

l S state. The existence of

such a resonance would, of course, also affect the cross section e+He(l1 S)-^Ke(21 S)-\-e.

The elastic cross section for scattering of electrons

from the 2

1 5' state has a very large value (143O7ra02

) near the 2

1

,S' threshold, in the /=0 partial wave, again

indicating the existence of a

2 S resonance near the 2

1 5

state. The threshold behavior of the elastic cross section

for scattering from the 2

3 S state is markedly different.

Thus Ehrhardt et al. (1968) attribute the threshold

structure near the 2

l S onset to a2S state existing near

the 2

1 5 state and designate the 2 S resonance as a

“virtual” state. On this model, the electron is captured

just at the upper plateau of the potential well and

experiences a phase shift. Taylor (1970) describes this

24
TOTAL

COUNT

xIO'"

TOTAL

COUNT x

10

Fig. 29. (a) Optical excita- tion functions of the 41 5' and 43 S states of He (5047 A and

4713 A) after averaging for 180 h. The energy scale is deter- mined by setting the second

prominent peak of the 41 6’ excitation function at 23.937 eV and for the 4s S excitation function at 23.939 eV. These

energy values were determined

in a previous run. [From

Heddle, Keesing, and Kurepa

(1973).] (b) Optical excita- tion functions for the 33D and 43D levels in helium (5876 A

and 4472 A). [From Heddle

(private communication) .] (c) Optical excitation functions for the 33 P (3889 A), 43P (3188

A), and 53 P (2945 A) levels of helium. [From Kisker

(1972b).]

25
virtual state as a “bound” state that just slipped out of

the potential well. Taylor (private communication) describes the

formation of the two 2

2 S states as follows: The 2

3,5' state mixes with the 2

ZP state, thus forming a polarization potential which combines with the low screening

in excited states to form a well. The electron binds in

this well and we get a resonance below the 2

3 S state. Similarly, the 2

1 6' and 2

1P states mix to give a resonance below the 2

1 5' state. Both resonances have a

2 S character. As the two 2 S channels mix, the two states split

apart. The lower 2 S state moves down to 19.3 eV and the

upper 2 S moves up and slips out of the well, to become

virtual. This approach, if substantiated by calculations,

provides a very picturesque way to visualize the two

low-lying 5-wave resonances in He. In fact, experiments

in other rare gases seem to indicate that such a picture

is applicable there too. The designation of the virtual state in terms of

orbitals is by no means clear. Table I indicates that the

only 2S state which is not accounted for has the ls2p2 configuration. However it is not suggested that this is the proper answer, since the ls2p2 may have a very

large width, and may lie at higher energies.

The resonance near the 2

1 6' threshold also strongly

influences the superelastic cross section e-\- He(21

1S)—» He(23 ,S')+e. This cross section exhibits a strong peak

near zero energy. A very large average cross section for

this process (^3X10~14 cm2 ) for 300°K electrons had

been previously measured by Phelps (1955) and the

theory of Burke et al. (1969) shows agreement with this

large value, which was not completely understood until

the resonance process was invoked.

6. Structure in the Elastic Cross Section near the 2

ZS and

2*S Thresholds ( Wigner Cusps)

The opening of an inelastic channel should be accompanied by the appearance of a cusp in the elastic cross

Fig. 30. Derivative of the transmitted current in he- lium in the region of doubly

excited states. The vertical

lines show the positions of the 2s2 and 2s2p excited

states of helium. [From

Sanche and Schulz (1972) .]

57 58 59

ELECTRON ENERGY, (eV)

26

60

>

<x>

LlI <

CO 59

3

O

ceo

LlI >

O

CD<

>-CD

OC

LlI

58

UJ

57 -

DOUBLY EXCITED

STATES, He

RESONANCES,

He"

(2p2 ) 'D

(2p2

) 3 P

(2s 2

) 'S

59.95

59.64

( 2s 2 p) 3 P 58.34

(2s2p 2 \ 2 ,

57.82

(2s 2 2p) 2 P 57.16

58.25

Fig. 31. Energy level diagram for the lowest doubly excited states of helium and the two associated compound states, He-

.

is section (Wigner, 1948; Baz 1958) . Such a cusp has been is observed recently in a transmission experiment in J helium (Sanche and Schulz, 1972) as a sharp in- crease in the transmitted current and its derivative ^ just below the threshold for the 2

3S and 2

1 S states. The ^ results are shown in Fig. 27. In the differential elastic 1 cross section at 90°, the Wigner threshold cusp appears

e as a downward step which causes the cross section to I decrease by about 1% (Cvejanovic, Comer, and Read, ’ 1973). !

7. 21.0 eV (22D)

The experimental determination of the location of the 1 2

2D resonance comes from the observation of a well- i pronounced peak in the 2

ZS and 2

1 5' cross sections at i various angles of observation as shown in Fig. 26. The decay into the elastic channel has not yet been

observed. The designation as

2D comes from the angular

distribution and from theoretical considerations. The

experimental observations are as follows:

2

Z S excitation: Schulz and Philbrick (1964) observed a peak, at 21.0 eV with a width of about 0.4 eV, at an

angle of 72°. Ehrhardt and Willmann (1967) extended

the angle of observation to include the range 7-110°.

The angular distribution at 21.0 eV is found to be

characteristic of a d wave, as can be seen in Fig. 25. Chamberlain (1967) studied forward-scattered elec- trons having excited the 2

Z S state and finds structure at
ELECTRON ENERGY (eV)

s Fig. 32. Typical line shapes of the 57.1- and 58.2-eV resonances

(2s?2p and 2s2p2

)

as observed in *S, 1 S, and inelastic channels. The angles of observation are indicated on the figure. The ordinate

is in arbitrary units and the zeros are displaced. The energy scale

l is accurate to about 0.2 eV. [From Simpson, Menendez, and

I Mielczarek (1966).]

, 20.7 eV, which probably results from the 2D resonance. The position of the peak resulting from the 2D reso- nance shifts to lower energies (i.e., from 21.0 eV to 20.7

eV) as the angle of observation is decreased (Linder,

private communication) . In view of the large width of

this resonance and the possibility for interference,

such a shift is not unusual.

2

X S excitation: The 2D resonance at 21.0 eV is also

prominent in the 2

1 S excitation, as reported by Ehrhardt, Langhans, and Linder (1968) particularly at small angles of observation (10°~50°) and in forward

scattering (Chamberlain, 1967).

In the total metastable excitation, which measures

the sum of the 2

3 5 and 21 S excitation, a peak occurs

at 21.0 eV. This peak can be attributed, in retrospect, to the 2D state. The theoretical work on the 2D state appears fairly

consistent. Burke et al. place the 2D state at 21.0 eV,

and ascribe to it a width of 0.4 eV. The stabilization

technique of Taylor gives a value of 20.3 eV (Eliezer

and Pan, 1970) . Also, the 2D state is prominent in the

calculated cross section for electron excitation of the

2

l S state from the 2

3 S state (Burke et al., 1967). The

theory of Burke et al. (1969) shows that both the elastic

and inelastic cross sections for electron impact on the

low-lying metastable states in helium are dominated by

the presence of the 2P and 2D resonances.

8. 22.42-24 eV (3*5, PP, etc.) Optical

Excitation Functions

The data of Fig. 21 show many partially overlapping

structures starting near 22.42 eV and extending to the

ionization potential of helium. The lowest of these

structures have been studied in the differential inelastic cross sections and are shown in Fig. 28. The values of

the energies are listed, together with the suggested

designations, in Appendix Ilia.

Very recently optical excitation functions have been

studied using monochromatic electrons. Kurepa and

Heddle (1972) have studied the following excitation

functions: 4

3,S-*23P (4713 A); 4

1 S-21P (5047 A);

3

3 S-23P (7065 A); 4

1P-21P (4922 1); 43D-23P

(4472 A); 3

3D— 23P (5876 A). Heddle, Keesing, and

Kurepa (1973) have further analyzed the 4

1 S and 4

3 S

excitations. Kisker (1972) has reported data on the

3

3P-^23 S (3889 A) and the 4

3P->23 S (3188 A) lines. Kurepa and Heddle (1972) detected seventeen

structures, many of which appeared rather small, in the

energy range 22.80-24.08 eV. Appendix Ilia lists the more prominent structures observed in this work. Also,

Appendix Ilia lists large structures observed by Kisker

(1972) in the 3

3P excitation and 4

3P excitation functions.

Most of the observations on structures in the optical

excitation functions have not yet been analyzed in

sufficient detail, so that any assignment is preliminary.

ELECTRON ENERGY (eV

Fig. 33. Formation of He+ by electron impact on He. The

background ion formation is subtracted so that only the structure remains, representing ~0.8% of the total He+ signal. The count

rate is indicated. The structure results from the decay of the

(2s*2p) and (2s2p2

) resonances by two-electron emission. [From

Quemener, Paquet, and Marmet (1971).]

27
I I I

I I I I—I 1 1 1 1 16 17 18 19 20 21 22 s ELECTRON ENERGY, (eV) 1

Nevertheless, Kurepa and Heddle (1972) propose that

the large feature at 22.95±0.02 eV which appears in

many of the excitation functions, be assigned to the

ls4.?2 state of He-

. Similarly, the feature at 23.94dz0.02

eV is assigned to the 5s2 configuration. It is, of course, understood that the above orbitals represent the dominant wavefunctions and that admixtures of other states are expected to contribute.

Figure 29(a) shows the results of Kurepa and Heddle

(1972), as analyzed by Heddle et al. (1973) who have

added all data from all their runs to aid in the distinction

of real features from small fluctuations. The peak near 23.94±0.02 eV is very clearly exhibited in Fig. 29(a).

Figure 29(b) shows the optical excitation functions

to two D states, and Fig. 29(c) the excitation functions

to three P states, obtained by observing the wavelength

indicated in the appropriate figure caption.

C. Resonances above the Ionization Potential

Table II. Values of the splitting between the 2P3/ 2 and 2Pm

levels in the positive ion and in the compound state for Ne, Ar, Kr, and Xe.

Gas

Compound state

Positive

ion

Sanche and Schulz

(1972)

Kuyatt, Simpson,

Mielczarek (1965)

Ne 0.095 0.095 0.097 Ar 0.172 0.172 0.177

Kr 0.66 0.64 0.666

Xe •—'1 .1.25 1.306

(:2s22pYP and ( 2s2p^D

The lowest doubly excited states of helium are the

(252

)

x 5 state at 57.82 eV, and the ( 2s2p) zP state at 58.34 eV (Rudd, 1964, 1965). Kuyatt, Simpson, and

Mielczarek (1965) discovered, using a transmission

experiment, that resonances of the Feshbach type are associated with these states. Golden and Zecca (1970),

as well as Sanche and Schulz (1972), confirmed the

position of these resonances using the transmission

method (Fig. 30). Appendix IV lists the values for

these resonances, as found by different experiments.

Fano and Cooper (1965) classified these resonances as

( 2s22p) 2P for the lowest (^57.16 eV) and ( 2s2p2

)

2D

for the second (^58.25 eV). Various theoretical

28
J

Fig. 35. Total metastable cross section for neon vs electron energy. Curve (a) is from Pichanick and Simpson (1968) with 50-meV resolution; curve (b) is the detail in the 18-19-eV

range by the same authors, with 35- meV resolution; curve (c) is from

Olmsted et al. (1965). [From

Pichanick and Simpson (1968) J

16.0 17.0 18.0 19.0 20.0 21.0

Impact Energy (eV)

approaches confirm the above assignment. Eliezer and

Pan (1970) use the stabilization method to calculate

the position of the 2s22p and 2s2p2 states and Nicolaides

(1972) uses a variational principle applied to the

projection method with correlation included. Both

theoretical methods give good agreement with the

energies observed experimentally (see Appendix IV)

and thus the assignment of the leading term ( 2s22p

and 2s2p2

) for the two resonances seems well established. In fact, Nicolaides (private communication)

finds that the 2s22p configuration contributes 73% to the square of the wave function of the 2P resonance, with the remainder in terms like 2p

z and 2s2pnd. For

the 2D resonance, the leading term, 2s2p2

, contributes

83%, with the remainder in terms such as 2s

2nd and

2p?nd.

Figure 31 shows an energy level diagram in the

region 57-60 eV. The 2P and 2D resonances can decay

by the emission of a single electron into various excited

states of helium. Decay into the 2

3 <S, 21 S, and 2lP

states has been studied by Simpson, Menendez, and

Mielczarek (1966) whose data are shown in Fig. 32. The same resonances can also decay by the emission of two electrons, yielding He++2e. This type of decay has

been found by Burrow and Schulz (1969) by studying

the interference of zero-energy electrons produced in

the two-electron decay. The trapped-electron method

was used for these studies. This two-electron decay

also causes structure when one observes the energy

dependence of the formation of He+

, as was done by

Grissom, Compton, and Garrett (1969). Quemener,

Paquet, and Marmet (1971) have improved the sensitivity for the detection of structure in positive ion curves by several orders of magnitude. Their results are shown in Fig. 33. An analysis of the peak shapes

yields, for the 2P state, T = 0.045 ±0.007 eV ( q= — 0.75±0.12) and, for the 2D state, r = 0.025±0.010 eV

( q= —0.95 ±0.25) . Here, T is the width of the state and

q

is the “line profile index” (see Sec. I)

An unusual feature has been recently observed in the

2

3 S excitation cross section near 50 eV by Crooks et al. (1972) . When the energy dependence of the differential cross section for the electrons having excited the 2

3S

state is examined around 90 degrees, a precipitous dip in

the cross section is observed near 50 eV. Such behavior is reminiscent of interference phenomena, and calculations

show (Macek and Wooten, unpublished) that the

5 and d waves exhibit interference. When the differential cross sections for excitation to the 2

3 S state are

integrated, the resulting total cross section exhibits a peak near 50 eV, which is 15 eV wide. Crooks et al. interpret this peak in terms of a p-wave resonance. It therefore appears that near 50 eV in helium, there is interference of partial waves and, in addition, a broad

resonance. The resonance itself could be understood by con- 29
sidering a state of Hein which the three electrons

comprising Heare equidistant from the nucleus. Such

a quasistationary state was calculated by Herzenberg

and Ton-That (1973) to exist around 45.9 eV. It is of a simil ar nature as the state of H discussed in Sec. IIC, with the wave function having no radial nodes.

The 2s22p state at 57.16 eV, which has the same 2P

symmetry, has a radial node in each of the 2s factors.

Neon

0.095 eV

16.04 eV !35eV

75°

I

NEON

Fig. 37. Energy level diagram for neon, showing states of neon and the associated resonances. The values for the resonances

are taken from Sanche and Schulz (1972) and a comparison with

other values is shown in Appendix V. Metastable states are denoted by the letter M.

of the ion core, as shown in Table II, where comparison

is made between the two available experiments on

resonances and the known splitting of the ion core. The

agreement between the splitting of the resonances and

the positive ion core assures that the designations

advanced by Simpson and Fano (1963) are correct. Thus, the lowest resonances in Ne, Ar, Kr, and Xe have

90°

1 ARGON

j 1 1 1

15.0 15.5 16.0 16.5 17.0 ELECTRON ENERGY (eV)

Fig. 36. Elastic cross section vs electron energy at designated

angles of observation in neon. The vertical bars designate a 10%

change in cross sections. The angular dependence of the resonances

is characteristic of the p wave. [From Andrick and Ehrhardt

(1966).]

IV. NEON, ARGON, KRYPTON, AND XENON

The rare gases Ne, Ar, Kr, and Xe exhibit marked

similarities in terms of their resonances so that it is appropriate to consider them under a single heading.

A. Resonances Below the Ionization Potential

The first resonances in all the rare gases discussed in

this section consist of two s electrons attached to the

positive ion core (Simpson and Fano, 1963). Since the

positive ion core is a doublet (/ =\ and /=§), the resonances are also split. In fact, the splitting of the resonances is in very good agreement with the splitting

3p 5 (2p 3/2 ) 3p 5 (2p |/2 ) ^ * s / *

S LlI

13.4

-— 1 3.3 — 13.2 ^1 3.06 ^ 1 2.90

1 1.91 11.71 11.28

II. II

Fig. 38. Energy level diagram for argon. Numerical values arf listed in Appendix VI. 30
KRYPTON Li Li"

4p 5

( 2 P 3 /2) 4p 5

( 2

P, /2 )

iuG. 39. Energy level diagram for krypton. Numerical values are

listed in Appendix VII.

:he form (2p

5Ss2

)( Sp54:s

2 ), (4/>

55^2 ) , and (5p56s2), •espectively, each resonance being split by the amount

ndicated in Table II into a

2Ps/2 and a2Pi/2 component.

Just as in the case of helium, our knowledge of resonances in Ne, Ar, Kr, and Xe comes from trans- mission experiments (Kuyatt et al., 1965; Sanche and

Schulz, 1972), from experiments on total metastable

production (Olmsted et al., 1965; Pichanick and Simpson, 1968) and from differential elastic scattering ex5.37

Li +

( Is 2

) 'S

3.88^ t |s2:5d ) 2p

3 - 84 "

( ls 2 3p) 2 P

3.36 —

( I s 2 3s) 2 S

3.82

3.80

3.75

3.74

3.35

3.29

3.15

1 .84

( I s 2 2p) 2 P

± 1.8

1.8

0

( Is 2 2s) 2 S

0. I

-0.62

Fig. 41. Approximate energy level diagram for lithium and

the compound states calculated theoretically. Values for the compound states are taken mainly from the work of Moores

and Norcross (1972) and Fung and Matese (1972). The energy

values, in eV, are only approximate. The electron affinity is taken

from Weiss (1968).

Ng

5.14

Na+(2R6

) 'S

Na

XENON

5p 5

( 2 P 3 / 2) 5p 5( 2 P |/2 ) o

1 *

\ 1 *

1 2

Fig. 40. Energy level diagram for xenon. Numerical values are

listed in Appendix VTH.

3.6 I 3.19

( 2p 6 3d) 2 P

( 2p6 4s) 2 S

3.04

2.10

(2p6 3p) 2 P

2

2

3 p

( 2p6 3s) 2 S 0.15

0.54

Fig. 42. Approximate energy level diagram for sodium and

the compound states calculated theoretically. Values for the com- pound states are taken mainly from the work of Moores and

Norcross (1972) and Fung and Matese (1972). The energy

values, in eV, are only approximate. The electron affinity is taken from Weiss (1968), whose calculated value of 0.539 eV is in excellent agreement with recent photodetachment experiments

of Hotop, Patterson, and Lineberger (0.542±0.01 eV).

31
Fig. 43. Total cross section for scatter- ing of electrons by sodium. Full curve

theory of Moores and Norcross (1972);

X —experiment of Brode (1929) divided by two; O—experiment of Perel, Englander, and Bederson (1962) nor- malized to theory at 5 eV. [Trom Moores

and Norcross (1972).]

penments ( Andrick and Ehrhardt, 1966) . The information in these rare gases is more limited than in the case

of He, since information on the excitation of elec- tronically excited states of these gases is only now

becoming available (Swanson et al., 1971, 1973).

Optical experiments with a good energy resolution in the

electron beam are also very sparse [Sharpton et al. (1970) observe a sharp structure in photon emission at

18.6 eV in neon.]

Figures 34-36 show the experimental evidence for resonances in neon, and Fig. 37 shows an energy level diagram of Ne with the resonances included. Appendix

V gives a comparison between the available experiments in tabulated form. A clearcut assignment of the

higher-lying compound states is not yet available. The

characteristics of Ar, Kr, and Xe are similar to those of neon. Energy level diagrams are shown in Figs. 38-40

and the energy values are listed in Appendixes VIVIII.

B. Resonances above the Ionization Potential

Above the ionization potential of Ne, Ar, Kr, and Xe,

a number of features have been detected, some of which

are undoubtedly resonances associated with singly

excited states of the neutral atom. The energy range

of these features spans the regions 42-50 eV in Ne,

24-32 eV in Ar, 22-27 eV in Kr, and 18-20 eV in Xe.

These features are discussed in connection with the

transmission experiment by Sanche and Schulz (1972),

in connection with the trapped-electron method by

Grissom, Garrett, and Compton (1969), and in con- nection with positive ion detection by Bolduc, Quemener, and Marmet (1972). The reader is referred to these papers for an up-to-date discussion and for a list of previous references. One of the difficulties inherent

in these studies lies in distinguishing between reso- nances and the onset of highly excited autoionizing

states of the neutral atom. Thus one has to rely heavily on measurements of the structure in the photoionization

continuum, which provides the location of optically

allowed transitions to highly excited states (see, e.g., Ederer, 1971) . Some of the energies at which resonances

are believed to occur in Ne and Ar are listed in Appendix IX.

V. LITHIUM AND SODIUM

Electron scattering in alkali atoms has been of considerable interest in the past years (Bederson

and Kieffer, 1971), but high-resolution experiments

with monochromatic electron beams have only recently

become available. Thus much of our knowledge re- garding resonances in these atoms comes from theory.

There is general agreement that at low energies (^0.15

eV) the spin exchange cross section in both Li and Na

has a sharp rise (Karule, 1965; Burke and Taylor,

1969; Norcross, 1971; Moores and Norcross, 1972).

This sharp rise is attributed to the existence of a

3P

compound state at about 0.15 eV. The width of this resonance is believed to be relatively large (>0.1 eV).

The 3P resonance also affects the phase shift of the

elastic cross section (Moores and Norcross, 1972).

The elastic cross section calculated from these phase

shifts agrees with the cross section measured by Rubin

et al. (unpublished)

In the vicinity of the ( \s22p) 2P state of lithium, two

resonances, lD and hP, are postulated (Burke and

Taylor, 1969) . For reasons which are not entirely clear,

Fung and Matese (1972) do not find these states using

their multiconfiguration Hartree-Fock method; possibly

the width of these states is too large. However Fung and

32
Energy CeV) Energy (eV)

Fig. 44. Differential experimental

cross section for elastic scattering of elec- trons on sodium. The angle of observation is indicated. Scales (b) and (c) are expanded with respect to scale (a) by

factors of 3.7 and 25, respectively.

EFrom Andrick, Eyb, and Hofmann

(1972).]

Matese find three compound states lying below the

(ls2Ss) 2S state and four states below the ( ls23p) 2P

state of Li. A schematic diagram, constructed from the

results discussed above is shown in Fig. 41. In sodium, an analogous situation prevails (Moores

and Norcross, 1972) and the appropriate energy level diagram is shown in Fig. 42. Fung and Matese find only

a single compound state in the 3-eV region of Na.

The existence of the lP and XD resonances just below

the threshold of the first electronic state should dominate the excitation function to that state, and it appears

that this is the case in Na (Enemark and Gallagher,

1972; Moores and Norcross, 1972).

The energy dependence of the total elastic and the

differential elastic cross section in sodium exhibit a dramatic cusp at the energy of the 2P state at 2.1 eV.

This cusp is shown in Fig. 43 for the total cross section, as derived from the close-coupling theory of Moores

and Norcross. The experimental results of Andrick,

Eyb, and Hofmann (1972) for the differential elastic cross section are shown in Fig. 44. The close-coupling

theory of Moores and Norcross is in very good agree- ment with the experiment. The structure shown in

Figs. 43 and 44 is strongly influenced by the presence of

the XP and lD states near 2 eV (Norcross and Moores,

1972).

It is noteworthy that the calculated cross sections for photodetachment of electrons from Li- and Nain

33
z

UJ

croc Fig. 45. Transmission experiment o

in Hg. The three low-lying resonances o

are clearly visible as dips in the ^ transmitted current. [From Fano and >_ Cooper (1965).] ^

V)z

<

crh

T

1 I 3 4 5 6

ELECTRON ENERGY , eV

their ground states show a sharp peak near 2 eV

(Norcross and Moores, 1972). This effect is attributed

to the presence of the XP resonance near the threshold of

the first excited state of the neutral atom.

VI. MERCURY

Kuyatt, Simpson, and Mielczarek (1965) observe

many resonances in their study of transmission of

electrons through mercury. All resonances appear as

dips in the transmitted current. An example of their

data is shown in Fig. 45 and the positions of these

resonances are shown on the energy level diagram of

Fig. 46 in conjunction with the known electronically

excited states of Hg. The lowest three resonances (marked 1, 2, 3) have been given the assignment

(6s6p2

)

iPy2 , 4A/2 , 4Ps/2 (Fano and Cooper, 1965). The

ground state of Hg is (Sd1^2

)

1 ^.

Kuyatt et al. point out that the resonances at higher

energies (near 8 eV) lie too high in energy to be at- tributed to higher levels (

2Z>, 2S, 2P) of the 6s6p2 configuration. Rather, Kuyatt et al. suggest that the

parents of some of the resonances in the 8-eV region are

ELASTIC RESONANCES

2 a 3

MERCURY

5d ,0 6s(

2 S]6p A

4 5 67 8 9

5d'°6s(2$) 6d

5d 9

6s

2

( 2

D5/2 )6p

3

P2

5d 10 6s ( 2

S ) 7s 3Si

*03

8$

3

S.

10 II 12 13 5d 9

6s

2

( 2

0V2 )6p

3

pJ

7d

« O

8d

'0 2

‘So 9s

30*

'02,

3

0|,2,3

5d'°6p 2

Po 3

Rn

LIMIT HgR (2

S I/Z )

10.437 eV 1

ENERGY. eV

Fig. 46. Energy level diagram for Hg and the associated resonances. The resonances are numbered and their energies are listed in Appendix IX. [From Kuyatt, Simpson, and Mielczarek (1965).]

34
Fig. 47. Excitation function of the 5461-A line of Hg. (a) Low-resolution results of Jongerius; (b) result obtained by Smit

and Fijnaut (1965) using the retarding-potential difference method with a resolution of 0.1 eV. [[From Smit and Fijnaut

(1965).]

states of the configuration 5d26s26p. The resonances would then have configurations such as 5d?6s26p2

. The structures observed in transmission experiments can be compared with structures observed in optical

excitation functions; care must be exercised in excluding

structures resulting from sharp thresholds of higher

energy levels which may contribute structure in low

levels due to cascading.

Figure 47 shows the structure obtained by Smit and

Fijnaut (1965) using a relatively narrow electron

energy distribution (~0.1 eV) and observing the

5461-1. line in Hg. These results are in very good agree- ment with the work of Zapesochnyi and Shpenik (1966)

who also used monoenergetic electrons for their observations and in addition to Hg (X=2537 k, 5461 k,

3650 k, 4916 A) examined a wide variety of optical

excitation functions in He, Zn, Cd, Na, and K. Zapesochnyi and Shpenik list the positions of the structure they observe. Appendix X compares their observed

structures with the structures listed by Kuyatt et al. (1965). On the whole, there seems to be good agree- ment. It should be noted that Zapesochnyi and Shpenik

interpret the observed structures in terms of cascading.

However, it appears that the interpretation in terms of resonances could be equally valid.

VH. OXYGEN (O)

The determination of the location of compound states

in atomic species which occur naturally as molecules is very difficult, as pointed out in connection with the

discussion of atomic hydrogen. Normally, one attempts

to form a beam of the atomic species and crosses this

beam with monochromatic electrons. A novel method

for measuring compound states has been recently

presented by Edwards, Risley, and Geballe (1971)

and applied to atomic oxygen. In this method, a beam of

stable O

-

ions with about 2 keV of kinetic energy is incident on a rare gas target (He) and the electrons

resulting from this interaction are energy-analyzed and

recorded. Structure in the energy spectrum of the elec- trons is observed and is associated with the existence of resonances. Figure 48 shows an example. The peaks in

Fig. 48 seem to arise from the reaction

0"+He—»0-*+He—>0+He+e,

where O

-* denotes the compound state.

Fig. 48. Electron energy spectrum obtained after colliding a 2-keV beam of 0~ with He. The electron energies given above

the peaks are corrected for the velocity of O

- and are the proper

energies for compound states. The peaks are interpreted as resulting

from the formation of compound states up atomic oxygen. [From

Edwards, Risley, and Geballe (1971).]

35
Since the electrons are ejected from a moving 0“

particle, the measured electron energy must be corrected, and the “unshifted” energy must be determined.

The energies indicated above the peaks of Fig. 48 refer to these corrected, “unshifted” values. Edwards et al. calibrate their energy scale by observing the reactions

0

_+H2 and 0

-+Ar. In the former reaction, electrons

resulting from compound states H

-

(

1Z)) at 10.13 eV

and from H~( 1 S) and H“(3P) were observed, although

the latter two states could not be clearly resolved. In

the reaction 0

-+Ar, the two low-lying resonances of

Ar could be observed, and in fact the observed splitting

(173 meV) is in agreement with other experiments (see

Table II). These calibration experiments establish the

reliability of the observations in oxygen. The energy

level diagram of Fig. 49 shows schematically the configuration suggested by Edwards et al. to interpret their

observations.

In order to test the results of the above experiment,

Ormonde, Smith/ Torres, and Davies (1973) performed

a multi-configuration close-coupling calculation. They

calculate elastic and inelastic cross sections and

search for resonances. The ZP and ZD terms, which are

possible parents for resonances are retained in the

theory. A single resonance is found at 10.38 eV (0.25 eV

above the experimental value quoted above), with a width of 20 meV. The discrepancy between theory and

experiment in the energy of the resonance is attributed

by Ormonde et al. (1973) to limitations of the theory.

The assignment of the resonance given by Edwards

et al. ( 1971) does not appear to be altered by the results of the theory.

A search for the higher-lying resonance (12.115 eV)

found experimentally by Edwards et al. was also undertaken by Ormonde et al. (1973) using the close-coupling

theory. No sharp resonances were found, but a shape

resonance in the 2P° partial wave was found near 11.5

eV, with a width about 1 eV. This shape resonance is probably in addition to the sharp structure at 12.115

eV found by Edwards et al. Very recently, Matese, Rountree, and Henry (1973)

undertook a configuration-interaction study of doublet

resonances in atomic oxygen. They calculate the following levels of O

-

:

2p3 (*S°)3s3p(2P) at 9.50 eV,

2pz (

2 Df) )3s2

(

2 D°) at 12.05 eV,

2pz

( 2P°) 3s2

(

2P°) at 13.65 eV,

2pz (

AS°)3p2

(

2P°) at 10.87 eV.

A reasonable estimate of possible errors in the abovequoted energies is ±0.1 eV. Matese et al. suggest that

the 12.115-eV peak observed experimentally by

Edwards, Risley, and Geballe corresponds to the

2p

z ( 2D°)3s2

(

2 D°) state, thus confirming the original

assignment for the upper state of Edwards et al., as plotted on Fig. 49.

ACKNOWLEDGMENTS

The author is very grateful to U. Fano, F. Linder, L.

J. Kieffer, C. E. Kuyatt, A. V. Phelps, and H. S. Taylor, all of whom read portions of the manuscript and

generously supplied many comments and corrections. A

portion of this review was written at JILA, University

of Colorado, Boulder and the author is grateful for the

hospitality of the JILA staff, and for the excellent

editorial services rendered by Mrs. Lorraine Volsky

and her staff. The author also wishes to acknowledge

the support he received, at various stages, from the

Westinghouse Research Laboratories, the National

Science Foundation, the Army Research Office, and the

Office of Naval Research. To his colleagues at Yale,

particularly to A. Herzenberg, P. D. Burrow, M. J. W.

Boness, and L. Sanche go thanks for many stimulating

discussions and for help in unravelling the many effects described in this paper. To his wife, Rose, go thanks for

her acquiescence that resonances should take precedence

over a lot of other things.

36
APPENDIX I

Resonances in H (below n= 2)

State Energy (eV) Width (eV) Method Author

lS 9.61 0.109 cc Burke and Schey (1962), Smith et al. (1962)

9.559 var O’Malley and Geltman (1965)

9.557 var Bhatia et al. (1967)

9.56 Gailitis (1965)

9.55 Hol^ien and Midtdal (1966)

9.56 0.048 Burke and Taylor (1966)

9.575 0.0543 cc Burke (1968)

9.560 0.0475 ccc Burke (1968)

9.587 0.0501 ps. St. Burke, Gallaher, and Geltman (1969)

9.56±0.01 0.043dz0.006 Exp McGowan (1967)

9.558±0.01 Exp Sanche and Burrow (1972)

1 5 10.178 var O’Malley and Geltman (1965)

10.177 var Bhatia et al. (1967)

10.178 0.00241 cc Burke (1968)

10.178 0.00219 ccc Burke (1968)

3S 10.149 var O’Malley and Geltman (1965)

10.146 var Bhatia et al. (1967)

10.151 1.89X10-5 cc Burke (1968)

10.150 2.06X10"4 ccc Burke (1968)

IP 10.178 var O’Malley and Geltman (1965)

10.179 2.26X10"5 cc Burke (1968)

10.177 4.50X10-5 ccc Burke (1968)

3P 9.727 var O’Malley and Geltman (1965)

9.731 var Bhatia et al. (1967)

9.768 0.00797 cc Burke (1968)

9.740 0.00594 ccc Burke (1968)

9.759 0.00571 ps. St. Burke, Gallaher, and Geltman (1969)

9.71±0.03 >0.009 Exp McGowan (1967)

9.73±0.12 Exp Kleinpoppen and Raible (1965)

9.70±0.15 Exp Schulz (1964)

9.738±0.01 0. 0056±0.0005 Exp Sanche and Burrow (1972)

w 10.160 0.0078 cc Burke (1968)

10.125 0.0088 ccc Burke (1968)

10.128±0.01 0.0073±0.002 Exp Sanche and Burrow (1972)

10.13±0.015 Exp Ormonde et al. (1969)

3p 10.194 0.0008 cc Ormonde e/ al. (1969)

10.190 0.0002 6-state Ormonde et al. (1969)

10.198 var O’Malley and Geltman (1965)

zs 10.202 var O’Malley and Geltman (1965)

XP 10.203 var O’Malley and Geltman (1965)

Abbreviations: cc: close-coupling calculations, ccc: close-coupling plus correlation, ps.st: pseudo-state calculations. var: variational calculations. Exp: experiment.

37
APPENDIX II Values for the ls^s) 2 ^ resonance in helium.

Energy Width Method Author

19.30±0.05

Experiment

72° elastic Schulz (1963)

19.31db0.03 . .

.

Transmission Kuyatt et al. (1965)

19.285db0.025 . .

.

Total (elastic) Golden and Bandel (1965)

19.3±0.1 . .

.

90° elastic McGowan (1965)

19.30d=0.01 0.008 Transmission Golden and Zecca (1970, 1971)

19.34±0.02 . .

.

Transmission Sanche and Schulz (1972)

19.35d=0.02 . .

.

90° elastic Mazeau et al. (1972)

0.008 Differential Gibson and Dolder ( 1969)

0.015-0.020 Differential Andrick and Ehrhardt (1966)

19.355±0.008 . .

.

Differential Cvejanovic et al. (1973)

19.5(+0.1, - 0.2) 0.008

Theory

Variational Kwok and Mandel (1965)

19.33

0.03

0.039 Close-coupling Burke et al. (1966)

19.67 . .

.

Variational Young (1968)

19.3 . .

.

Stabilization Eliezer (1970)

19.34 . .

.

Bound-state Weiss and Krauss (1970)

19.69 . .

.

Perkins (1971)

19.363 0.014 Quasi-projection

,

Temkin et al. (1972)

19.4 0.015 Variational Sinfailam and Nesbet (1972)

APPENDIX III Position of resonances below ionization in helium (eV).

Metastable

Transmission experiments production Differential

Feature Sanche and Pichanick and

number Schulz Kuyatt et al. Simpson Ehrhardt and

(Fig. 13) (1972) (1965) (1968) co-workers Designation

1-1' 19.30-19.37 19.31-19.37 2

2S

2-2' 19.80-19.90

19.43-19.47

19.818 Wigner cusp+235

3-3' 20.58-20.62

20.34

20.59

20.45 2

2P

Wigner cusp+2115

4

5-5'-5"

21.19

22.34-22.42-22.50

20.99

21.50-21.55

22.34r-22.39 22.44

21.00 2

2D

22.42 S

2S

6-6'-6" 22.60-22.65-22.73 22.54-22.60 22.55/22.67 22.55/22.60 3

2P

7-7-7" 22.88-22.92-22.97 22 . 81-22 .85 22.75/22.86 22.75/22.85

8 23.05 23.05

9-9' 23.35-23.43 23.30-23.44 23.39 n= 4

10-10' 23.48-23.55 23.49

ll-ll'-ll" 23.82-23.88-23.93 23.75-23.82 n= 5

12 24.03

38
APPENDIX Ilia

Larger structures in the optical excitation functions of He.

Preliminary data.

Energy

eV

Wavelength

of observation

(A) Ref.

Possible

designation

22.96 7065 (a) 4

2S

23.12 7065 (a)

23.25 7065 (a)

23.31 7065 (a)

23.47-23.62 3889 (b) y>(?)

23.41 5876 (a)

23.50 5876

23.86 5876 (a)

4472 (a)

4922 (a)

23.94 5876 (a)

4472 (a) 5

2S

5047 (c)

Energy

eV

Wavelength

of observation

(A)

Possible

Ref. designation

4713 (c)

24.0 4472 (a)

4922 (a)

3188 (b)

24.08 5047 (a)

4713 (a)

Transition 3

3 5'-23P 3

3D-23P 43D-23P 41D-21P

Wavelength

(i)

7065 5876 4472 4922

Transition 4

1 S-21P 4

3 5-23P 33P-23 S 43P-235

Wavelength 5047 4713 3889 3188

(A)

a Kurepa and Heddle (1972).

b Kisker (1972b).

0 Heddle, Keesing, and Kurepa (1973).

The data have been arbitrarily selected by the author

to indicate the main peaks observed in optical spectra.

Many more, smaller structures have been reported. This

table must therefore be considered preliminary, subject

to change. This does not apply to the structures for

which the wavelength is underlined. These are large and

well-defined. The structure for which the wavelength is doubly underlined is “enormous”.

APPENDIX IV

Position of resonances above the ionization potential in He.

Authors (2s2 2p) 2P (2s2p2

) 2D Authors (2s2 2p) 2P (2s2p2

)

2D

Experiments Quemener et al. (1971) 57.15±0.04 58. 23 zt 0.04

Kuyatt et al. (1965) 57.1±0.1 58.2±0.1 Grissom et al. (1969) 57.21 58.31

Golden and Zecca (1970) 56.7/56.9

57.87/58.08

Theories

Eliezer and Pan ( 1970) 57.3 58.3

Burrow and Schulz

(1969)

56.93=t0.1 58.04zt0.1 (stabilization)

Nicolaides (1972) 57.3 58.4

Sanche and Schulz 57.16zt0.05 58.25it0.05 (projection and cor- (1972) relation)

39
APPENDIX V

Position of resonances in neon (eV)

.

Feature

designations®

Transmission experiments

Sanche and Kuyatt

Schulz et al. (1972) (1965)

Metastable

production

Pichanick

and Simpson

(1968) Designation

1-1' 16.10-16. 12c 16.04 (2pY(3s)^P,l2 2-2'

3-3' (A)

16.19-16.22®

16.85-16.91

16.135

18.18

18.29

16.92

(2py(3Sy*pw

4(5, C) 18.55 18.46 18.35-18.43 Optical excitationb 5852 A

5-5' (D, E) 6(F, G)

78

9

18.65-18.70

18.95

19.47

19.57

19.65

18.56 18.58-18.66

18.86-18.97

Kisker (1972b)

19.50-19.54

19.60-

10(5) 19.71 19.69 -19.70

19.77-19.82

ll-ll'(J) 19.97-20.03 19.83 19.91-19.99

12-12' (7) 20.07-20.13 20.1 20.03-20.07

-20.19

20.60-20.64

20.70-20.74

a The “feature designations” refer to Fig. 25 (numbers) and Fig. 26 (letters) , respectively.

b The first energy refers to a maximum, the second to a minimum.

°The widths of the 2P3 /2 , 2Pi/2 resonances have been deduced from experiment by Haselton (1973). He finds

r=8.95±0.34meV.

APPENDIX VI

Position of resonances in argon (eV)

.

Metastable

Transmission experiments production

Sanche and

Schulz

(1972)

Kuyatt

et al. (1965)

Pichanick and

Simpson

(1968) Designation

11.10-11.13 11.064-11.094 3^4522 P3 /2 11.27-11.30 11.235-11.267 2Pi/2 11.71 11.72 3/>54j4^(?)

11.91 11.88-11.98 3pHs4p(?)

12.89-12.92 12.80-12.93

12.95-13.06-13.11 13.08

13.22-13.28 13.17-13.24

13.33 13.37

13.45-13.50 13.55

14.03-14.07-14.10

40
APPENDIX VII

Position of resonances in krypton (eV)

Transmission exp.

Sanche and

Schulz

(1972)

Differential

elastic and

inelastic

Swanson

et al. (1973)

Metastable

production

Pichanick

and Simpson

(1968) Designation

9.50-9.53 9.52 4^65522P3/2 10.16-10.19 10.14 10.05 2Pi/2 10.66-10.69 10.67 10.63

11.29 11.29 11.10-11.20

11.40 11.42

11.54 11.42

11.67 11.67 11.70

11.97-12.04-12.10 11.97 11.94-12.04

12.04 12.28

12.10 13.08

Optical excitation experiments in krypton® (Kisker, 1972b).

4502 A 4464 1 4274 k 4376 1

12.90-12.95

12.93-13.00 12.97-13.04

13.19-13.25 13.13-13.18 13.11-13.18

13.23- 13.24-13.30

13.36-

a Given are values for max-min.

Swanson, Cooper, and Kuyatt (1973) compare the resonances in krypton with optical absorption data of Rb i. Such a comparison leads them to interpret the resonances in the energy range 10.5 eV-12 eV (i.e., all but the two

lowest states) as 4^>55s4d states. The 4p

5 ion core can have J= \ or f

APPENDIX VIII

Position of resonances in xenon (eV).

Metastable

Transmission experiments production

Sanche and Kuyatt Pichanick

Schulz et al. and Simpson

(1972) (1965) (1968) Designation

7.80-7.90-7.92

8.48

7.74-7.77 5^6s22P3/2

9.11-9.26

9.52

9.02 9.0 2Pi/2

9.56 9.5

9.65

10.92

11.00

10.81-10.86 10.3

41
Appendix VIII—Continued

Optical excitation experiments® (Kisker, 1972c)

1

I

4624 1 4671 1 4079 k 4583 k 4734 1

11.02-11.05

11.12-11.15 11 . 11- 11.16-11.20

11.22-11.31

11.40-11.46

-11.27

11.39-11.45

11.53-11.58

12.13-12.23

11.51-11.55

11.61-11.65

11.83-11.90 11.75-11.87

12.03-12.09

12.19-12.28 12.20-12.27

11.81-11.95

12.03-12.10

-12.20

a In this table, the first energy corresponds to an observed maximum, the second energy value on the same line corresponds to an observed minimum.

APPENDIX IX

Suggested resonances in Ne and Ar.

Energy

eV Method Observer Designation

41.98 Transmission

Neon

Sanche and Schulz (1972)

42.1 Trapped electrons Grissom et al. (1969)

43.05 Transmission Sanche and Schulz (1972)

44.35 Transmission Sanche and Schulz (1972)

44.25 Trapped electrons Grissom et al. (1969)

47.6 Transmission Sanche and Schulz (1972)

47.57 Trapped electrons Grissom et al. ( 1969)

24.44 Ar1-

Argon

Bolduc et al. (1972) 3s3pHs2 2S

24.53 Transmission Sanche and Schulz (1972)

26.87 Transmission Sanche and Schulz (1972)

27.91 Transmission Sanche and Schulz (1972)

28.9 Transmission Sanche and Schulz (1972)

42
APPENDIX X

Position of resonances in mercury (eV)

Kuyatt et al. (1965)

Transmission

Zapesochnyi and Shpenik (1966)

Fano and Cooper

(1965)

Feature No.

(Fig. 38)

6IPi

X=2537 A

£*=4.89 eV

7

3 Si

5461 A

7.73 eV

6

ZD

3650 A

8.9 eV

&S0 4916 A

9.2 eV Designation

i 4.07 • • • • • • . .

. .

(6s6p2

) iP,/2

2 4.30 • • • • • • • • • • • • (6s6^) 4P3/2 3 4.89 • • • • • • • • • . .

(6s6p2ypm

• • • 5.0

• • • 5.3

• • • 5.6

4 7.81

5 7.94

6 8.14

7 8.22 8.5 8.2 • • • 8 8.83 • • • 8.8 • • • 9 8.99 9.0 9.0 9.1

10 9.75 9.7 9.6 9.8 9.5

11 10.29 10.0 10.2 10.2 10.2

12 10.58 10.4 • • • . .

. .

13 10.88 . .

• • • . .. .

• • • 11.2 11.1 11.1 11.4

• • • . .

11.9 11.7 11.9

• • • . .. .

'—'12 .

12.4

• • • 12.5 '—'12 .

12.6

•The writing of this review was supported in part by the National Bureau of Standards, Office of Standard Reference

Data, as part of the National Standard Reference Data

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45
-
Resonances in Electron Impact on Diatomic Molecules*

George J. Schulz

Department ofEngineering and Applied Science, Mason Laboratory, Yale University, New Haven, Connecticut 06520

In this review we present the energies, configuration, and other properties of resonances (also called “compound states” and “temporary negative ions”) in diatomic molecules. Much of the information is presented in the form of tables and energy level diagrams. Vibrational, rotational, and electronic excitation

are discussed whenever these processes have given information on resonances; often these excitation processes proceed via resonances. The paper is divided according to molecular species (H2 , N2, CO, NO,

O^, but the main conclusions are discussed by the nature of the processes involved. Key words: Compound states; cross-sections; diatomic molecules, H2 , Ns, CO, NO, 02 ; electron impact;

electronic excitation; energy levels; resonances; rotational excitation; temporary negative ions; vibrational excitation. CONTENTS

I. Introduction. 47 A. Classification of Compound States 50 B. Parentage of Core-Excited Feshbach Resonances. 52

II. Hydrogen 53 A. Resonance at Low Energy: 0-4 eV ( 22„+

) 53

1. Elastic Cross Section _ 53

2. Vibrational Excitation in H2 via 22«+ 53

3. Rotational Excitation via the 22u+ State and

Angular Distributions 55

4. Dissociative Attachment at 3.75 eV 57

5. Effect of Rotational Levels of the H2 Target

Molecule of H“ Formation near 3.75 eV 59

6. Associative detachment: H“+H—>H2_—>H2 +e. 60

B. Resonance in the 10-eV Region ( 22ff+

) 63 C. Core-excited Resonances in the 11—15 eV Region . . 64

1. Band “a” 68

2. Band “b” 69

3. Band “c” 70

4. Band “d” 70

5. Band “e” 71

6. Band ‘ f” 71

7. Band “g” 72 HI. Nitrogen 72 A. Resonance at Low Energy (1.7-4 eV) 2nfl 72

1. Elastic Cross Section via 2nff 72

2. Vibrational Excitation via 2 nfl ; 73

3. Threshold Behavior of the Cross Section to d = 1 81

4. Angular Distributions. 81

5. Pure Rotational Excitation via 2 nff 82 B. Core-Excited Resonances in the 11-15 eV Region 82

1. Band “b”-22ff+ 82

2. Shape Resonances and Inelastic Thresholds. .

. 83

3. Structures 5 and 6 83

4. Bands “c” and “d” 84

C. Bands “a” and “a'”: Core-Excited Shape Resonances 84 D. Resonances above the Ionization Potential in N2 . . 84

TV. Carbon Monoxide 85 A. Resonance at Low Energy (1-3 eV) 2 n 85

1. Elastic Cross Section via 2 n 85

2. Vibrational Excitation via 2 n 85

3. Angular Distributions 85 B. Dissociative Attachment (9.65-12 eV) 86

G'. Core-Excited Resonances in the 10-15 eV Region 86

1. 22+ Resonances (10.04 eV, 10.28 eV) 86

2. Shape Resonances and Inelastic Thresholds .. . 87

3. Band “a” 87 D. Resonances above the Ionization Potential in CO 87 V. Nitric Oxide, NO 88 A. Compound State at Low Energy (0-1.5 eV) X 32~ 88

1. Elastic Scattering 88

2. Vibrational Excitation (0-1.4 eV) 89

3. Equilibrium Internuclear Separation and Elec- tron Affinity: Photodetachment Spectroscopy 90 B. Dissociative Attachment (7-10 eV) 90 C. Core-Excited Resonances in NO 90

1. Bands “a” to “d” 90

2. The 12 eV-18 eV Region 91

VI. Oxygen 92 A. Compound State at Low Energy: X 2nfl (0-1 eV) 92

1. Elastic Scattering 92

2. Vibrational Excitation of O2 at Low Energy

, (0-1.0 eV) 93

3. Potential Energy Curve for O2 (X 2n„) 95

4. Equilibrium Internuclear Separation and

Electron Affinity: Photodetachment Spectroscopy 95

5. Three-Body Attachment in O2 96

B. ' Dissociative Attachment (4.4-10 eV) : 2IIU State. . 98 C. Core Excited Resonances 99

1. Band “a” 99

2. Band "b” 1 100

VII. Conclusions 100 A. Shape Resonances 100 B. Core-Excited Shape Resonances 100 C. Binding of Rydberg Resonances 101 D. Thresholds of Inelastic Cross Sections 101 Acknowledgments 101 Appendixes

I. Core-Excited H2~ States 102

II. Core-Excited D2~ States 103 m. Branching Ratios for Series “a” in H2 103

V. Shape Resonances Associated with B 3nfl and A 32u+

States in N2 (8-11 eV) 104

VI. Resonances in CO (10-15 eV) 105 VII. Vibrational Spacings and Franck-Condon Probabilities for Four Bands in NO106

ViJtl. Resonances in NO and Their Grandparents (12-18

eV) 106 IX. Spacing of Vibrational States of 02~ X(2nff) 106 X. Vibrational Cross Sections and Resonance Energies in O2-

at Low Energies 107 XI. Core-Excited Resonances in 02 108 References 108

This paper is a continuation of the one immediately

preceding, which deals with resonances occurring when

electrons are incident on atoms. In the present paper

we present a review of the energy levels, the designations, and the general properties of compound states in

diatomic molecules. An attempt is made to present much

of the information in the form of tables and energy level diagrams.

I. INTRODUCTION

Compound states are formed by the interaction of an

incident electron with a target molecule in which the

incident electron is temporarily captured in the neighborhood of the molecule. The complex thus formed can

also be called a temporary negative ion or a resonance.

47
Table I. Semantics of resonances.

: ?

First name Last name Parent Energy vis a vis parent Some characteristics

i Examples

i 0D:

Single-particle

Shape

( 1 particle, 0 holes)

• • • Ground electronic state above (0-4 eV) Vibrational excitation;

dissociative attach- ment at low energy

N2 (2.3 eV)

H2 (2-4 eV)

u

|)fi

Core-excited

Particle-hole

Feshbach;

Type I; closed-channel

Mostly Rydberg

excited state below (~0.5 eV) Bands correlated to grandparent; sharp

structure; many

decay channels

N2 (11.48 eV)

H2 (Bands “a”-

“g”) ' se

(f N2 (9-11 eV)

H2 (8-12 eV)

ic

(2 particles, 1 hole) Shape);

Type II; open-channel

Rydberg or valence excited

state

above (0-2 eV) Dissociative attachment

Doubly core-excited

(3 particles, 2 holes)

Feshbach

Shape

Doubly excited Rydberg and

valence states

below

above

Above ionization; 2-electron decay

He (57.16 eV)

N2 (22 eV)

The latter term indicates that the attachment of the

electron often occurs at a definite energy, leading to sharp structures in the cross section. However, sometimes the lifetime of the compound state is so short

that the width of the state, as given by the uncertainty

principle, is large. The terms compound state, temporary

negative ion, or resonance are used interchangeably and

authors have even used superfluous nomenclatures such

as “temporary negative ion resonance.”

Fig. 1. Total cross section in H2 (Golden et at., 1966) and

elastic portion alone (Linder and Schmidt, 1971a). The absolute magnitude of Linder’s curve is normalized to Golden’s value at the lowest energy. The difference between the two curves represents the sum of all inelastic cross sections. ["From Linder and

Schmidt (1971a). J

The first reference to the possibility that compound o states might exist can be traced to a paper by Franck i

;

and Grotrian (1921). Experimental evidence for struc-

’ ture in the total cross section (e.g., N2 ) became avail- !

’ able shortly thereafter, but a resonance model was not

v = 0 v = 1 v = 2

J , .

0 100 200 300 400

energy Loss C channel number^

Fig. 2. Energy loss spectrum of 4-eV electrons after collision with H2 molecules. The peak marked v=0 represents elastic scattering. The peaks marked v=l, 2, 3, and 4 represent the

excitation of vibrational quanta of the neutral molecule via the

short-lived negative ion state 22u+. [From Ehrhardt, Langhans,

Linder, and Taylor (1968) .J

4S
applied to these observations at that time. Although

there was a need to understand such structures in the

cross section and also the large vibrational cross sections

observed experimentally (e.g., H2 ), the resonance model

remained confined for a long time to nuclear physics

alone. The application of the resonance model to molecules in the early 1960’s led to a rapid progress in our

understanding of electron impact on molecules and

solved many long-standing puzzles in atomic physics.

Compound states in molecules which have been observed to date have a lifetime in the range 10-10-10~15 sec {T=fi/T, where r is the lifetime and T is the width of

the state). They decay by the emission of an electron

into various final states which are accessible energetically. The beauty of molecules is the variety of decay

Fig. 3. Total vibrational cross section to v=l in H2 . Experi- mental results using double electrostatic analyzers: Linder and

Schmidt (1971a) ; O Ehrhardt et al. (1968) ; V Trajmar et al. (1970); A Schulz (1964). Experimental results using swarms

O EngeLhardt and Phelps (1963) ; Crompton et d. (1970)

Experimental results using the trapped-dectron method: • • • Burrow

and Schulz (1969). Theory: — Henry and Chang (1972). [From

Henry and Chang (1972).]

channels that are possible for compound states: vibrational and rotational excitation, electronic excitation,

elastic scattering, dissociative attachment, three-body

attachment, and others. Often, a major portion of the

cross section for these processes proceeds via a com- pound state. This is especially true in the case of vibrational excitation and in several instances of electronic

excitation near threshold. Dissociative attachment can

be completely understood in terms of the formation of a compound state which subsequently autoionizes and

also separates into a neutral atom and a negative ion.

The lifetime of the compound state, together with the

separation time, determine the magnitude of the dis- sociative attachment cross section.

The preferential decay of some compound states into

inelastic channels offers certain advantages for the

Fig. 4. Vibrational cross section to v=2 in hydrogen. The slope

of the cross section near threshold is determined using the trapped

electron method and is indicated by the dashed lines, marked

TEM (Burrow and Schulz, 1969) . Also shown are the double

electrostatic analyzer data of Ehrhardt et d. (1968) and Schulz

(1964a). [From Burrow and Schulz (1969).]

study of compound states. When the bulk of the in- elastic cross section consists of the decay of the com- pound state, then the direct-scattering contribution is nearly absent and one can observe the resonant contribution alone, without interference with the nonresonant contribution, When one considers the BreitWigner formula, which governs the shape of single

Fig. 5. Vibrational cross section to v=3 in hydrogen. The

cross section near threshold is determined by Burrow and Schulz

(1969) using the trapped electron method, shown by the open

circles. The double electrostatic analyzer data of Ehrhardt et d.

(1968) are shown by the solid line. The dashed line is an inter- polation. [From Burrow and Schulz (1969).]

49
6

Fig. 6. The real and imaginary parts of the potential energy curves for the 22u+ and 22s+ states of H2“. On the left-hand side are shown the potential energy curves for H2 ( —), and the potential energy curves for H2-

derived by Bardsley et al. (1966a) and by Chen

and Peacher (1968a) . The dotted curve indicates the real part of the potential curve for the 22u+ state which is needed to obtain agree- ment with the vibrational cross section of Ehrhardt, et al. (1968). The repulsive curve for H2-

(

220+

) of Chen and Peacher (1968a) is in very good agreement with the curve derived by Eliezer, Taylor, and Williams (1967), which is shown in Fig. 25(a). The potential energy curves for the lowest states of H2 (

120+ and 32u+

) are taken from Kolos and Wolnicwicz ( 1965) . The right-hand side of the figure

shows the calculated widths of the 22u+ and 22ff+ states. [[From Chen 1969.

3

compound states, namely,

a(E)cc \ A+(Tin Tont yi*/(E-E0+hiT) | 2

, then the term A, representing the direct contribution

to scattering, is small compared to the resonance term

in inelastic processes. Above, Tin is the partial width

for decay into the ground state, rout is the partial width

for decay into the excited state, and T is the total width, related to the partial widths by r = rin+rout. Eo is the resonant energy.

Other review papers have recently appeared: Taylor

et al. (1966), Bardsley and Mandl (1968), Burke

(1968), Massey and Burhop (1969), Chen (1969),

Herzenberg (1970, 1971), Taylor (1970). The nomenclature and general approach used in this review have

been strongly influenced by these papers. Phelps ( 1968)

has recently reviewed vibrational and rotational cross

sections; Takayanagi and Itikawa (1970) have reviewed

rotational cross sections. Golden, Lane, Temkin, and

Gerjuoy (1971) have reviewed low-energy scattering ex- periments and rotational excitation and have given a review of experimental techniques. The aim of the

present review is the tabulation and discussion of ex- perimental values for compound states: their positions,

widths, and classifications. Theoretical considerations

are brought in only in those cases where they are needed

for the discussions, but no attempt is made to include

the bulk of theoretical considerations. Experimental I methods are briefly discussed in the paper immediately ; preceding, which deals with compound states in atoms. 1

A. Classification of Compound States

We can classify compound states in molecules, in an 1 analogous manner to that in atoms (see preceding

O

x>

E (ev)

Fig. 7. Curve A: Energy dependence of pure vibrational cross

section, a(v=0—>1, A,; = 0). Curve B: Energy dependence of rotational-vibrational cross section, <7-(fl=0—>1, .7 = 1—>3). Points

are experimental (Linder and Schmidt, 1971a), Unes are theoretical (Henry and Chang, 1972). [From Henry and Chang (1972).]

50
Fig. 8. Curve A: Angular distributions

for pure vibrational excitation <x(v—

0—>1 ; Aj = 0) . Curve B : Angular distribu- tion for rotational-vibrational excitation,

<r(v=0—>1; j = l—>3). Points are experimental (Linder and Scbmidt, 1971a) and

lines are theoretical. [From Henry and

Chang (1972).]

paper), into two major categories depending on the

state of the target molecule to which the incident elec- tron attaches. Table I may serve as a helpful guide to the semantics of compound states. When the incident electron is trapped in the potential

connected with the ground electronic state, we speak

of shape resonances or single particle resonances. The

two terms are synonymous. In this case, the centrifugal,

polarization, and exchange forces combine to create a

potential with a penetrable barrier. Thus, it is the shape

of the potential which is responsible for the trapping

of the particle and for the resonance. Shape resonances

associated with the ground electronic state have been

substantiated in all diatomic molecules studied to date

(H2 , D2 , HD, 02 , N2 , NO, CO). They occur at low energies (0-4 eV), exhibit a lifetime in the range 10-15 sec

to 10~10 sec or even longer, and decay into vibrational

and rotational levels of molecules and sometimes into

negative ions by dissociative attachment. In all cases described in this review, vibrational excitation proceeds

predominantly via shape resonances; resonances also play an important role in rotational excitation. Thus

shape resonances are very important in our understanding of low-energy impact on molecules.

Since typical vibrational times are ^lO-14 sec, shape

resonances may be short-lived, long-lived, or comparable to vibration times. When the lifetime is short (e.g.,

H2 ), the energy dependence of the vibrational cross section exhibits a broad peak; when the lifetime is long

(e.g., 02 ), the compound state itself can vibrate and

the energy dependence of the cross section to a given

final vibrational state exhibits a series of spikes at the

location of the vibrational levels of the compound state. When the lifetime of the compound state is comparable

to typical vibration times (e.g., N2 , CO) an intermediate situation prevails. In such a case, the compound

state may perform about one vibration before decaying

and the cross section to the final vibrational state will exhibit several broadened spikes.

The location on the energy scale and the particular

properties of shape resonances are described under a

separate heading for each molecule.

Core-excited resonances are associated with an elec- tronically excited state of the molecule, which is called

the “parent.” Core-excited resonances thus consist of a “hole” in one of the orbitals normally occupied by an

electron, and of two “particles”, i.e., electrons in nor- mally unoccupied orbitals. We can also visualize reso51
Fig. 9. Ratio a(v=0—*1, Aj=0)/a(v=0—>1, j — 1—>3) vs

scattering angle at an electron energy of 4.5 eV. Experiment: O

Ehrhardt and Linder (1968); Linder and Schmidt (1971);

Theory: A—Abram and Herzenberg (1969); B—Henry (1970);

C—Henry and Chang (1972). [From Henry and Chang (1972).

j

nances consisting of two “holes” and three “particles”;

such resonances have been recently postulated (Pavlovic et al., 1972) and are well known in atoms (e.g.,

the 2s~2p state in Henear 57 eV). Higher hole-particle

states appear to be plausible.

Core-excited resonances can lie either below or above

their parent. When they lie below their parent, one may

say that they exhibit a positive electron affinity. Such

states are called Feshbach-type (after Feshbach, 1958,

1962) or Type I, or closed-channel resonances (decay

into the parent state is forbidden). When core-excited resonances lie above their parent, they are called Type

II or core-excited shape resonances. These resonances

are similar to single-particle shape resonances, except

that they are associated with an electronically excited

state.

B. Parentage of Core-Excited Feshbach Resonances

The parents for core-excited resonances may be, in

principle, either valence or Rydberg excited states. Singly excited states of molecules may be classified into valence and Rydberg states. Both these types of excited states of the neutral molecule are formed by

the promotion of a single electron from the ground

state configuration into an orbital which is not filled in the ground state. When the promotion takes place into a low-lying vacant orbital, the principal quantum number of the electron does not change, and we designate

the excited state as a valence state. When the principal

quantum number does change by unity or more, we

designate such an excited state as a Rydberg state. Rydberg states lie at higher energies and the orbitals

being filled look like atomic orbitals. This gives rise to a Rydberg series of electronic states whose limit corre- sponds to an ionization limit of the molecules.

Calculations (Weiss and Krauss, 1970) on the binding of the additional electron show that preferentially

Rydberg excited states have a positive electron affinity

for a fixed internuclear separation in the FranckCondon region. We therefore expect to find Feshbachtype resonances, which lie below their parent, mostly

associated with Rydberg excited states. In this case, the temporary negative-ion complex consists of two

electrons in Rydberg orbitals trapped in the field of a

positive ion core, which is called the “grandparent”

state. The parent (or parents) consists of a single

Rydberg electron bound by the field of the same ionic

core. Core-excited Feshbach resonances have lifetimes

(10~12-10~13 sec) which are long compared to the vi- brational period of a molecule and therefore can give

rise to bands, each of which consists of a progression of

vibrational levels. Since the two Rydberg electrons

trapped by the ion core are located far outside the ion

core we expect the negative ion and its grandparent

positive ion core to have similar vibrational spacings

;

and Franck-Condon probabilities. One can therefore

compare the vibrational spacings and Franck-Condon

probabilities for a given band of negative ion vibronic

states with the corresponding values for the many possible positive ion states of a molecule in order to identify

the parentage and electron affinity of the band under

investigation. This type of correlation has been made

collision energy [eV]

Fig. 10. Pure rotational excitation in H2 . Shown is the cross section cr(j = 1—>3). The circles are the experimental results of Linder and Schmidt (1971a). The lines are the theories of Henry

and Lane (1969), of Hara (1969), and of Lane and Geltman

(1967). The swarm data shown in the inset are recalculated for

cr{j = 1—>3) by Linder and Schmidt (1971a) from the original

experiment of Crompton et al. (1969) which gives <r(j — 0—>2). [From Linder am1 Schmidt (1971a).]

52
Fig. 11. The energy dependence of the total cross section for dissociative attachment in H2 , HD, and D2 near

3.7 eV. The process shows a very large

isotope effect and proceeds via the

*2U+ states of H2“. Part (a) shows the experimental results of Schulz and

Asundi (1967) and part (b) shows

the unfolded cross sections as re- ported by Chen and Peacher (1968a) . It should be noted that the experimental curves of Schulz and Asundi,

shown on the left side of the diagram,

have peak cross sections differing by

orders of magnitude (1.6X10-21 cm2 for H2 , 1XKL22 cm2 for HD, and 8

10-24 cm2 for D2) . Whereas the H /H2 cross section was obtained with an

electron energy distribution of 0.1 eV

the curves for HD and D2 had to be

taken with an energy distribution of 0.45 eV in order to gain sensitivity.

This accounts for the difference in the threshold behavior. The rising

portion of the D“/D2 cross section, indicated by dashes, is real having

been reproduced by Ziesel and Schulz

(unpublished). It could result partially from the wings of the 22„+ re- sonance near 10 eV.

by Sanche and Schulz (1971, 1972), who find that many

experimentally observed negative ion bands can be

simply correlated with grandparent positive ion states. They find that the compound states usually lie about

4 eV below the grandparent from which they are derived, i.e., the binding energy of the two Rydberg

electrons is 4 eV. Resonances associated with valence excited states are

also known, but as pointed out above, they do not seem

to lead to sharp structures in cross sections. Their

effect has been studied in dissociative attachment and

in vibrational excitation; they may also play a role in

excitation of electronic states of molecules. It is pointed

out by Pavlovic et al. (1972) that at higher energies

the density of doubly excited valence states becomes

large and that resonances associated with each valence

states may make a dominant contribution to excitation

functions at energies in the 20-eV range.

n. HYDROGEN

The ground state of H2 consists of two electrons in

the lso-g ( = <r0 U) orbital (Herzberg, 1950). The lowest unfilled orbital, in the notation of the united molecule,

is 2pau, which is equivalent to <r„l s. It is this orbital

which the incident electron occupies when forming a resonance at low energy. In escaping from this orbital

the electron must tunnel through a p-wscve barrier.

Bardsley et al. (1966b) and Eliezer et al. (1967) have

shown that the ground state of H2“ is indeed a shape

resonance and that its designation is 22„+. The angular

distribution measurements of Ehrhardt et al. (1968) on

electrons having excited the v= 1 vibrational state of

H2 show a p-wave character (minimum at 90°) and

thus confirm the designation given above.

A. Resonance at Low Energy : 0-4 eV (

22w+)

1. Elastic Cross Section

The lifetime of the 2 2u+ state is very short and the

width very large; therefore there is little or no evidence

for the 2 2m+ state in the elastic cross section (Golden

and Nakano, 1966). Figure 1 shows the energy dependence of the total cross section as measured in a Ramsauer-type apparatus by Golden and Nakano and

the elastic cross section only, as measured by Linder

and Schmidt (1971a). No clear-cut evidence of the

action of a resonance can be seen in these curves. Rather, one has to study other decay channels to establish the existence of this state. Vibrational excitation, rotational excitation (including angular distribution), as well as dissociative attachment, are the possible decay channels that can be usefully studied by

electron impact in order to establish the existence of

such resonances. Also, angular distribution measure- ments are very useful in establishing the existence of resonances. These are discussed separately for each

molecule and a summary is given in Sec. VII. The ex- perimental and theoretical considerations regarding

elastic and rotational cross sections in H2 have been

recently reviewed by Golden et al. (1971) and the

reader is referred to this reference.

2. Vibrational Excitation in Hz via 2 2M+

It is only in the past 10 years that experiments on

vibrational excitation have led to the present-day under53
>~xlO cm

2

J*g

4 a.< 3.01— Co

"5 2.0k

0) tom

o 10

1- u

-Chen and Peacher

Spence & Schulz,*'’

300 500 700 900 1100 1300 1500 Temperature, °K

Fig. 12. Temperature dependence of the cross section for H“

formation from H2 at 3.75 eV. The experimental results (Spence

and Schulz, 1971) show that the negative ion formation is inde- pendent of rotational excitation of the target, whereas the theory

of Chen and Peacher (1967) shows a strong dependence. [From

Spence and Schulz (1971).]

standing of the process. The first observation of a large

vibrational cross section was due to Ramien (1931)

whose results at 3.5 and 7 eV were essentially correct but were widely disbelieved because no simple interpretation could be found (Massey and Burhop, 1952).

The use of a rather complex experimental method

(Hertz diffusion) and the limited nature of the observation (only two energies given) contributed to the

skepticism.

Subsequent experiments by Schulz (1964) and by

Engelhardt and Phelps (1963) confirmed the large cross section for vibrational excitation, as did the experiments of Ehrhardt et al. (1968). This large vibrational

cross section was successfully interpreted in terms of

Fig. 13. The cross section for total electron detachment for the reaction of 0” with CO. The lower dashed line is the 1 /d fit while the upper line is the polarization cross section. The closed

circles are data points. The magnitude is calibrated by assuming

that the detachment rate at thermal energies is 5.6X 10-10 cm3 sec

-1 (Ferguson, 1968), but this value is known to an accuracy of only

±30%. The polarization cross section was calculated using 19. 5X

10-25 cm3 as the polarizability of CO. [From Mauer and Schulz

(1972).]

the resonance model by Bardsley, Herzenberg, and

Mandl (1966b) and the energy dependence of the measured vibrational cross section could be well reproduced.

The energy-loss spectrum for 4-eV electrons in H2 is shown in Fig. 2, which clearly shows peaks due to the

excitation of four vibrational states. The energy dependence of the vibrational cross section for v=\. is shown in Fig. 3 in comparison with the newest theory

due to Henry and Chang (1972). The theory of Faisal

Electron Energy (eV)

Fig. 14. Formation of stable negative ions, H~, by dissociative attachment in hydrogen via a repulsive curve. Shown are the

results of Rapp et al. (1965) and Schulz (1959a) . The broad peak

around 10 eV is interpreted as the reaction e-\- H2—>H2-

(22ff+) —

>

H~-j-H. The peak near 14.2 eV is interpreted in terms of the formation of excited H, e+H2—>H_+H(22 5, 2

2 P). The small

structure near 12 eV shown on Schulz’s curve has been studied

in detail by Dowell and Sharp (1968) and is shown in Fig. 16.

and Temkin (1972) is also in agreement with the

experiments.

Although Fig. 3 presents fairly good agreement between experiments, it is pointed out by Crompton et al. (1970) and also discussed by Golden et al. (1971) that

the slope near threshold, as determined from electron

beam experiments by Burrow and Schulz (1969) or by

Ehrhardt et al. (1968) is too large to fit the measured

transport coefficients. In order to perform such an

54
Fig. 15. Isotope effect in dissociative attachment in the neighborhood of 10 eV in H2 , HD, and D2 . [Taken from Rapp, Sharp, and

Briglia (1965).]

analysis, Crompton et al. have to. assume a reasonable

energy dependence for the rotational cross section and

that their approximation to the solution of the Boltzmann transport equation is applicable. To that extent, a discrepancy exists in the threshold behavior, as deduced from beam and from swarm experiments.

Crompton’s results based on an analysis of transport

coefficients are also shown in Fig. 3. The cross sections for excitation of the second and

third vibrational states of H2 come from electron beam

experiments and are shown in Figs. 4 and 5, respectively.

The experimental results presented lead to the conclusion (Bardsley et al., 1966b; Eliezer et al. 1966) that

the 2 2w+ state of H2~ is involved in the excitation

process. The width of this state is several eV, as can be

seen in Fig. 6, which shows the dependence of the

width on internuclear separation. Also, shown in Fig. 6

is the dependence on internuclear separation of the

real part of the potential energy curves. Breig and Lin (1965) and Takayanagi (1965) calculate the vibrational cross section to v = 1 without invoking a compound state, but they include the dependence

of the polarization on the internuclear separation. Breig

and Lin obtain fairly good agreement with the experimental observations. (See, e.g., Chen, 1969.) The argument is sometimes made that the resonance model is not needed for an interpretation of vibrational excitation. However, it is often easier to understand the

physical processes involved and the processes become more explicit and readily understandable when one uses the resonance model. There seems to be no compelling

reason to “hide” the compound state. The resonance model becomes even more useful for an understanding

of the isotope effect in dissociative attachment, as will be discussed below.

3. Rotational Excitation via the 2 2u+ State and Angular Distributions

The general problem of rotational excitation of molecules has been very recently reviewed by Golden, Lane,

Temkin, and Gerjuoy (1971) and by Takayanagi and

Itikawa (1970). The reader is referred to these reviews

for reference. Of interest for the present purposes is pure rotational excitation and rotational excitation

which accompanies vibrational excitation, both processes proceeding via the 2 2u+ compound state in H2 . Figure 7 shows that the energy dependence of the cross section for simultaneous rotational and vibrational ex55
Table II. Summary of experimental data on H2“. This table gives the band designation which we use in the present review (Bands

“a”-“g”) . For each author, listed in the first column, we give the nomenclature he used for a given band (e.g., “Series I,” “strong”) \j and also the final state in which the band was observed (e.g., X b

32u+

) , and the energy of the first resonance, in eV.

Possible equivalence®

4 4 ~

4

Band designation “a” “b” “c” “d” “e” “g”

Kuyatt et al. (1966) “strong” Xe “weak”

(transmission) 11.28 11.46

Comer and Read (1971a) X %+(») X^0+

(i>>8) 11.30 10. 93* 11.19*

Weingartshofer et al. “Series I” “Series I” “Series II”

(1970) X*2a+

, b*Xu+ BVU+ BVu+ CHI*

11.30 11.30 11.50 13.63 Sanche and Schulz (trans- 11.32 X 11.43 13.66 15.09

mission) (1972)

Width, T (eV) <0.016 (H2 )« 0.03° <0.016* 0.08b 0.03 (D2) Symmetry %+ *2,+ 2n„ 2n„ (?) %+

Observed in H2 , HD, D2 h2 Ho, HD, D2 h2 h2 h2 , d2 h2 , d2 Re (A) c 0.97±0.01 1. 175±0.01 0.97

a (eV) c>d 0.345±0.015 0. 19±0.015 0.345

b (eV) Cid 0.0135±0.003 0.005 ±0.003 0.0135

E0 (eV) c,d 11.40 11.11 11.40

a The arrows indicate that band “a” could be identical to band “d” and that band “c” may be identical to band “e.” See text.

b From Weingartshofer et al. (1970).

0 From Comer and Read (1971a)

.

d Defined by the equation E = E0 -\-a(v-\-%) -b(v-{- f)

2

. e The symbol X indicates that band “b” is observable only in the high vibrational states ( v>8) of the ^/"state and thus cannot be observed in transmission experiments.

1 Extrapolated to a = 0; see Appendix I.

* From Joyez, Comer, and Read (1973).

citation (t> = 0—>1; j= 1—>3) is similar to the cross sec- tion for vibrational excitation alone (u = 0—>1; Aj=0)

and thus both processes seem to be dominated by the

2 S„+ resonance. Angular distribution measurements by

Ehrhardt and Linder (1968) and by Linder (1969)

(Fig. 8), shows that pure vibrational excitation exhibits a pa-wave dependence, i.e., the scattered electrons

exhibit a minimum at 90 degrees. These observations

are in agreement with the theory which predicts an

approximate angular distribution of the form (1+

2 cos

2 0). [See Bardsley and Read (1968), Ehrhardt,

Langhans, Linder, and Taylor (1968), and O’Malley

and Taylor (1968).J

When rotational levels are excited in addition to vi- brational levels, a flat (isotropic) angular distribution

is observed. Figure 8 shows the results for the transition Aj=2, Av=l. The ratio of the vibrational cross section without rotational excitation to that with rotational excitation, cr(A^ = 0; Av = 1 )/cr(3<—1; Az>=l) is shown in Fig. 9 in comparison with the theories of Abram and Herzenberg (1969), of Henry (1970), and

^ of Henry and Chang (1972). The theory of Abram , and Herzenberg is based on the quantum mechanical

impulse approximation and neglects the kinetic energy , of rotation of the molecule during the collision. The i work of Henry and Chang uses the theory of frame ! transformation as developed by Chang and Fano

(1972). The p-wave nature of the ratio is obvious

from the figure.

As far as pure rotational excitation, in which the

vibrational quantum number does not change, is concerned, there are available the experimental data of Ehrhardt and Linder (1968) and the improved data

of Linder and Schmidt (1971a). It is the latter data

that are shown in comparison with theory in Fig. 10. As pointed out most recently by Linder and Schmidt

56
(1971a), all the rotational effects can be interpreted

by considering both the direct-excitation component

and the resonance component to the phase shifts. The

theory of Abram and Herzenberg (1969) which is based on a pure resonance model accounts well for the angular

distributions observed by Linder and Schmidt (1971a)

for pure rotational excitation, a(j= 1—>3).

The suggestion has been advanced by Frommhold

(1968) that electrons of thermal energy (10-100 meV)

exhibit resonant behavior in exciting rotational states

of H2 and D2 . Evidence for this hypothesis comes from

the pressure dependence of the drift velocity, which is

( observed by Frommhold and by Crompton and Robertson (1971) in swarm experiments.

Recently, Raith and Land (1972) used a time-offlight electron spectrometer to perform a transmission

experiment in H2 and D2 in order to confirm the exist- ence of resonances at very low electron energies in H2 and D2 . In H2 , they observe structures in the trans- mitted current at about 24 meV and in the range 60-90

meV. In D2 the results are qualitatively different, with

structure appearing between 26 and 60 meV. The

width of the 24-meV structure in H2 is approximately

3 meV, of which about 1.5 meV can be attributed to Doppler broadening. Rotational excitation is expected

to be governed by the selection rule A/=0, ±2, where

l is the orbital quantum number of the scattered elec- tron. Thus we expect inelastic processes to have thresholds at 44 meV (for 7 = 0—>2) and at 75 meV (for

7=1—>3) in H2 and at half these values in D2 . The

observed structure thus lies below the first inelastic

process in H2 and above it in D2 . If the structures observed in the experiment of Raith and Land are reso- nances, which is by no means certain, one must await

Fig. 17. Derivative of transmitted current vs electron energyin H2 . Four progressions of negative ion states are labelled “a,”

“c,” “f,” and “g.” See Table II. Band “b” seems to be observable

only in high vibrational states, and thus does not seem to appear

in transmission experiments. Band “d,” if it exists as a separate

entity, is energetically coincident with band “a.” For the lower

portion of the figure, which shows bands “f” and “g,” the gain has been increased by a factor of seven. [From Sanche and

Schulz (1972).]

Fig. 16. Fine struc- ture in dissociative at- tachment in H2 . [Taken

from Dowell and Sharp

(1968).]

a theoretical interpretation for an understanding of this phenomenon.

The preliminary theoretical work by Kouri (1968)

has not confirmed the reality of this process, and further

developments must be awaited. At this writing, the

existence of resonances in the energy range 10-100 meV

is puzzling, since no molecular orbitals are available

at such low energies, and since close-coupling calculations (Henry and Lane, 1969) do not give an indication

for rotational resonances.

4. Dissociative Attachment at 3.75 eV

The 2 2m+ state of H2-also plays a role in dissociative

attachment. It is characteristic of many compound

states that they decay into all channels that are energetically accessible and allowed by selection rules. The

dissociative attachment channel opens up at an electron

energy (D—A), where D is the dissociation energy of H2 (4.48 eV) and A is the electron affinity of H (0.75

eV) . Thus one would expect a threshold for H~ formation from H2 at 3.73 eV. Figure 11 shows the experimental result of Schulz and Asundi (1967), who ob57
Fig. 18. Energy dependence of the absolute differential cross sections for excitation of vibrational states in H2 above 11 eV. The

scattering angle is 85°. For each curve the cross section scale should

be multiplied by the factor indicated. The zero lines are shown

broken. The structure observed in the vibrational states y=l to v=8 is associated with series “a.” For v=9 to z>=ll, series “a”

is visible in the energy range 12.48-13.33 eV, and series “b”

appears at the low-energy end, i.e., in the energy range 11.49- 11.74 eV. [From Comer and Read (1971a) .3

served the onset for H~ production at the predicted

value. Also shown in Fig. 11 are the unfolded cross sections for the three isotopes of H2 (Chen and Peacher,

1968). The isotope effect was first interpreted by

Demkov (1964) as a consequence of the smaller survival

probability factor for heavier atoms. Thus, D2 requires a longer time to separate and remains in the region of

autodetachment for a longer time than does H2 . The

formation of D~/D2 is therefore smaller than H~/H2 . Bardsley, Herzenberg, and Mandl (1966b) give a simple

expression for the cross section leading to dissociative

attachment:

Q-=Qo exp— 0

rR' T(R)dR\

RO MR) )

Here, Qo is the cross section for formation of the com- pound state and the exponential term represents the probability that the system in fact survives to a stabilization point R'. The term T is the width (and

Collision energy (eV)

Fig. 19. Energy dependence of the absolute differential cross section for excitation of high vibrational states in H2 above 11 eV. The scattering angle is 85°. The zero lines are shown broken. Only

series “b” is shown. [From Comer and Read (1971a).]

58
!

n/V is the lifetime) of the compound state with respect

to autodetachment. This width is a function of the

internuclear separation R. The integration extends from

the formation point Ro to the stabilization distance R'

and v(R) is the relative velocity of separation of the

1 nuclei. We can replace the exponent by the appropriate

average width T and by the time r, which is needed for

the products to reach the stabilization point. We then

1 write

Q-=Qo exp( — Yt/H).

It should be noted that the total width is the sum of

the partial widths for decaying into the various vibrational states of the (H2 -f-e) system. Separation into

three particles (H+H-fe) is energetically possible at energies above 4.46 eV. In this model the isotope effect

arises from the variation of the survival probability

(exp —Yt/H) with mass. It is pointed out by Chen and

Peacher (1968a) that the above expressions are only

approximate and that the capture cross section, result- ing from the nuclear overlap integral, becomes as sensitive to the mass as the survival probability itself. Nevertheless, the simplicity of separating the dissocicollision energy [eV]

Fig. 20. Energy dependence of the absolute differential cross sections for different scattering angles and into two different exit channels, v=2 and 4 of the electronic ground state. The zero lines are dashed. The length of the bars to the left represent the scaling factors in units of 1.0X10-19 cm2/sr. The resonances are members

of band “a.” [From Weingartshofer et al. (1970).]

Fig. 21. Energy dependence of the absolute differential cross sections to the v = 3 vibrational level of the electronic ground state

of H2 for four different scattering angles. The zero lines are dashed. The length of the bars to the left of each curve represents the

absolute scaling factors in units of 1.0X10-19 cm2/sr. The res- onances are members of band “a.” [From Weingartshofer,

Ehrhardt, Hermann, and Linder (1970).]

ative attachment cross section into two physically

meaningful simple terms has accounted for the extensive use of the above expressions. Also, Chen and

Peacher’s considerations have not as yet been tested

against experiment.

5. Effect of Rotational Levels of the H2 Target

Molecule on H~ Formation near 3.75 eV

Chen and Peacher (1967) predict theoretically a profound effect of rotationally excited levels of H2 for the

reaction e+H2—»H2~—>H-

-f H at 3.75 eV. In this reac- tion the products depart with zero kinetic energy, and

Chen and Peacher predict a large increase in the survival

factor leading to an increased cross section for this process as the population of higher rotational states is increased. Chen and Peacher's suggestion seems to stem

from the effect of the centrifugal repulsion on the time

the nuclei take to separate. To test this theory, and to determine the effect of rotational levels, Spence and

Schulz (1971a) have studied the temperature dependence of the dissociative attachment cross section in H2 at 3.75 eV.

59
Fig. 22. Energy dependence of the absolute differential cross section for excitation into a narrow band (~60 meV)

at 10.47 eV in H2 . The final state is the

dissociative continuum, b

3 2u+. The zero

line is dashed. The length of the bar to the left of the curve represents the absolute scaling factor in units of 1.0X

10-19 cm2/sr. The insert illustrates the

autoionization of the H2_

ion into the energy band. [From Weingartshofer,

Ehrhardt, Hermann, and Linder (1970). J

10 11 12 13 14 15

collision energy [eV]

The experimental cross section at the peak of the

3.75 eV process is plotted as a function of gas temperature in Fig. 12. Spence and Schulz (1971a) find that

the cross section is independent of temperature in the

range 300-1300°K and conclude that rotational excitation of H2 plays no role in the dissociative attachment

process at 3.75 eV in the above temperature range.

Also shown are the theoretical points calculated using

the theory of Chen and Peacher (1967) normalized to the experimental data at 300°K. In this calculation it

is assumed that the electron capture cross section is independent of the initial rotational state, which

should be a reasonable assumption in the present case. It is, actually, not surprising to find that the dis- sociative attachment cross section is independent of the

rotational states of the target. The vibrational time,

and thus the dissociation time, are shorter than rotational times and one would therefore suppose that the

molecule is essentially nonrotating during the capture

and the breakup process. In fact, Bardsley, Mandl,

and Herzenberg (1966b) calculate wdth good success the

dissociative attachment in H2 by regarding the axis of

the diatomic molecule as fixed, thus ignoring rotational

motion. The experimental results of Fig. 12 seem to confirm such a model.

6. Associative Detachment: H~-\-H—^H2~—^H2 -\-e

There is a close relationship between dissociative at- tachment reactions at low energy, which are discussed

in the preceding paragraphs, and low-energy associative detachment reactions of the type H~+H—»H2~—

H2 -j-e. Associative detachment is the inverse of dis- sociative attachment and at low energies of the colliding

partners, the two processes proceed via the same com- pound state, in this case H2~. For a review of associative

detachment cross sections at thermal energy, see Fergu- son (1970). In the case of H

-

-j- H, the reaction partners

approach each other along the potential energy curves

2 Sm+ and 2 S0+. The former exhibits a short lifetime for

autodetachment; thus all or almost all collisions which

proceed along this potential energy curve lead to asso- ciative detachment. The 2 2fl+ curve is repulsive and

reactions proceeding along this curve at low energy

lead only to reflection or elastic scattering. One can

therefore expect that the low-energy associative detachment cross section should be about one-half of that

given by the Langevin polarization cross section. This

prediction has been approximately checked for thermal

ions (Schmeltekopf et al., 1967).

Since associative detachment proceeds via the same

intermediate state as dissociative attachment, there is a strong connection between the two processes. However, in associative detachment there is the probability

that the resulting molecule is left in a highly excited

vibrational state, provided that the compound state

is short lived. Thus detailed balancing cannot be used

for predicting the bulk of the associative detachment

cross section from its inverse, since dissociative attachment is generally studied only for molecules in their

lowest vibrational states. For the case of H

_+H—»H2 +e, theoretical treat- ments are also available. Bates and Massey (1954)

and also Dalgarno (1961) have suggested that associative detachment cross sections could be large and that

they could play an important role in upper atmosphere

reactions. Recently, more complete theoretical treat- ments have become available. [Herzenberg (1967),

Chen and Peacher (1968) and Browne and Dalgarno

(1969), and also the review by Chen (1969)]. The

main conclusions from these considerations are: At low

60
H + H

H + H

Fig. 23. A schematic summary of the decay of five energetically distinct compound states into various decay channels. In the middle

of the figure we show the positions of bands “a” through “g,” and on the left and right we show states of H2 . The arrows point to those decays that have been experimentally determined, but not all decay channels could be given on the figure. Band “f” seems to decay into the Cmu state without change of vibrational quantum number, and this is properly recorded on the figure. Band “b” seems to decay

only into high vibrational states of the X lH,g+ ground state. Decay into H+H-

(dissociative attachment) is also indicated.

energy the cross section becomes very large due to Langevin spiralling arising from long-range polarization (Herzenberg, 1967); the compound state is essential for an understanding of the process ; the H2 produced

in the reaction is highly excited (Herzenberg, 1967;

Chen and Peacher, 1968b) and an inverted population

may result. Experimentally, the reaction H

-+H—*H2+e has not

yet been studied using ion beams because of the diffi- culties associated with this type of experiment. However, similar reactions

(e.g., 0

-+C0—>C02”—»C02 +e;

O

-+

2—>H20

——»H20~\~c)

have been studied both in swarm experiments (see,

e.g., Ferguson, 1968, Moruzzi et al., 1968) and in beam

experiments (Mauer and Schulz, 1973). In both these

reactions, a compound state is involved. In the case of

C02~ the state is 2nu (Claydon, Segal, and Taylor,

1970; Krauss and Neumann, 1972), and in the case of

H2-

, the state is 2 2„+ and has been previously discussed.

The C02~(2nu ) state has a lifetime which is somewhat

longer (Burrow and Sanche, 1972, give a width,

T = 0.13-0.26 eV) than the compound state in H2 (r~l eV).

The experiments of Mauer and Schulz (1972) show

that at very low energies, the cross section is given by

a 1/v functional form, where v is the relative velocity.

Thus polarization dominates, consistent with previous swarm experiments (Moruzzi et al., 1968; Ferguson,

1970). Because Mauer and Schulz used a beam experiment, they could extend the range of incident ion

energies; they find that at higher energies (e.g., 1.5 eV

in the center of mass for the reaction 0

-+CO) the

cross section rises and exhibits a maximum, as shown

61
Fig. 24. Position of com- pound states, as observed in various decay channels. On

the bottom, the position of various bands is shown, as observed in transmission 1 experiments. The shaded 1 region shows the extent off the discrepancy between i experiments. Higher on the

figure, we show the posi- tions of the compound

states as observed in various excited states and in the emission of radiation (marked RAD). The as- signment to various bands

is noted.

in Fig. 13. This rise is due mainly to the following

effect: At very low ion energies, ions can reach the

region of large associative detachment, which occurs at

relatively small internuclear separations, only via an

attractive curve. Ions entering the process along re- pulsive curves cannot get close enough for associative

detachment to take place. However, at higher kinetic

energies, even ions entering the reaction along repulsive curves can get close enough to the neutral species to

detach. Thus, the cross section exhibits a subsidiary

rise at 1.5 eV in the case of 0

-+C0 and at 0.25 eV in

the case of 0~-f-H2 . Mauer and Schulz (1972) also performed an energy

analysis of the detached electrons and found that the

reaction leads predominantly to very low-energy elec- trons, near zero eV. Thus very high vibrational states

of C02 are excited.

The experimental evidence from the reaction 0~-f62
(a) (b) Fig. 25. (a) Potential energy curves for H2~ state (broken curves) which give the best fits ‘to experimental data. Corresponding

curves for some H2 states (full curves) are also shown (Sharp, 1971) . It should be noted that the energy scale is taken with respect to

the bottom of the ground-state potential curve. [From Comer and Read (1971a). 3 (b) Potential energy curves for H2~ derived from

alculations. The full curves represent the calculated compound states and the dashed curves are some of the parent H2 states. (A)

Hr *2/ consisting of C 1nu*7r„2/>'; (B) H2_ 22/ consisting of C 8nu *iru2^'; (C) H2_22ff+ consisting of B 12u+*<ra ls'; (D) H2~ 22/ consisting of 32u+»<ruls/

; (E) H2“ 22u+ consisting of X 1 2ff+*cru ; (F) H2 X 12u+

; (G) One configuration result for H2

32u+ lag lau . This curve

lies about 0.32 eV above the “exact” 32u+ curve, but is used as a comparison with the H2“ calculation consisting of this configuration

dIus an extra electron; (H) Two configuration result for H2 TR ( lcrff l7ru -f- la-ul^) . The minimum of this curve lies about 0.14 eV above

he experimental minimum. The H2 a

32ff+ curve lies so close to this one that they are indistinguishable on this scale; (I) Same as H

’or CTL and E 1Xg+

; (T) H2 B 12u+

. CFrom Eliezer, Taylor, and Williams (1967).]

30—*C02 +e indicates that the theoretical predictions

or H

-+H, —»H2 +e, as outlined above, are probably

:orrect. B. Resonance in the 10-eV Region (

22ff+

) The first excited state of H2 is the (ls(rg )(2pau yxu+

itate. In the notation for separated atoms this becomes

V0 1$) (<rM ls) 3 2u+. The dominant configurations of the

impound state associated with this excited state is

[ls<Tg ) (2pau )

2 22ff+ or, in the notation of separated

itoms, (cgls) (<rw l.y) 2 2 2ff+. Agreement exists on this assignment (Bardsley, Herzenberg, and Mandl, 1966a;

Eliezer, Taylor, and Williams, 1967; Bardsley and

Mandl, 1968).

When the real part of the potential energy curve for

the 2 2ff+ is calculated as a function of intemuclear separation, it is found (Bardsley and Mandl, 1968; Eliezer

et al., 1967) that the potential energy curve crosses the potential energy curve of the parent, i.e., the 3 2w+

state. As long as the potential energy curve for H2-

lies below the parent we are dealing with a core-excited resonance of the Feshbach type. When the potential

energy curve lies above the parent we are dealing with

a core-excited shape resonance. In this case the assignment varies as a function of internuclear separation.

Information regarding the 2 20+ state of H2~ comes from experiments on dissociative attachment. In other

channels, this state has not yet been observed. A comparison of two recent experiments on negative ion for- mation with H2 in the range 7-17 eV is shown in Fig. 14. An interesting isotope effect, not as dramatic as the one for the 2 2*+ state, has been discovered by Rapp

63
Fig. 26. The absolute total cross section for scattering of electrons on N2 , as obtained using a modified Ramsauer technique.

The total cross section includes elastic and inelastic components.

The structure above 1.8 eV is indicative of the pseudovibrations

of the 2na compound state. The structure below 1.8 eV has not been substantiated by other experiments, although attempts at confirming it have been made. The structure below 1.8 eV must

be considered in doubt at the present time. [From Golden (1966).

et al. (1965). These results are shown in Fig. 15. Similar

considerations as those discussed in Sec. IIA4 also apply here. In fact, Bardsley, Herzenberg, and Mandl

(1966b) have obtained a good theoretical fit to the curves of Fig. 15, and they point out that decay of the

2 20+ state of H2~ to the 3 2u+ excited state is more probable than decay to the ground state. The overlap is more favorable when the compound state can decay

into its parent (

3 2u+) state. This may explain why

it has not been possible to detect the decay of the

H2_

(

2 20+

) state to the ground electronic state. The

total width of the 2 2ff+ state is estimated to be T = 0.8

eV and the entry width from the ground electronic state is 0.004 eV.

The potential energy curves for the 2 2u+ and the 2 20+

states, derived by Bardsley et al. (1966a) and by Chen

and Peacher (1968a), have already been discussed in connection with Fig. 6. Also shown are the imaginary

parts of the potential curves, i.e., the width T, as a

function of internuclear separation. The potential en- ergy curves of Eliezer et al. (1967) are shown in Fig. 25(b).

The H~ formation via the 2 2<,+ state extends well

into the 11-12 eV region, in which a multitude of reso- nances are observed in elastic and inelastic scattering

(see Sec. IIC). It is therefore not surprising that highresolution experiments on negative ion formation would

show structure in the 11-12 eV region. The decay of bound compound states into the dissociative attachment channel was observed by Dowell and Sharp

(1968) and is shown in Fig. 16. The mechanisms for this coupling have been discussed by Eliezer et al. (1967) in terms of a radiationless intramolecular transition. The structure shown in Fig. 16 is further discussed

in Sec. IIC.

C. Core-Excited Resonances in the 11-15 eV Region

Resonances of the core-excited (Feshbach) type in

II2 were discovered by Kuyatt, Mielczarek, and Simpson (1964) in the energy range 11.62 to 13.31 eV by

I’lG. 27. Energy dependence of the “elastic” cross section in N2 at various angles of observations. The experiment uses an

electrostatic monochromator and an electrostatic analyzer, which

accepts only “elastically” scattered electrons. Since the resolution

is not sufficiently good to resolve rotational states, all rotational transitions are included in the measurement. [From Ehrhardt

and Willmann (1967).]

64
observing elastically scattered electrons. These struc- tures were confirmed by Golden and Bandel (1965) in a Ramsauer-type experiment for both H2 and D2 . Menendez and Holt (1966) found the structure in the

excitation of the v= 1 and v=2 vibrational states of

the ground electronic state, H2 (X 1S0+

), thus indicating a decay of the resonances into vibrational states. Heideman, Kuyatt, and Chamberlain (1966) were the

first to observe the decay of these compound states into

electronically excited states of H2 by studying the en- ergy dependence of the a = 0 and v= 1 vibrational

States of the B 1 2u+ state of H2 . Also, it was understood

both theoretically (Eliezer et al., 1967) and experimentally (Kuyatt et al., 1966) that more than one compound state contributes to the observed structure,

and that the isotopes HD and D2 exhibit a set of similar structures but that they show differences in the

relative strength of the series. Experimentally, five series of resonances have been

definitely identified, and as many as seven can be in- voked to explain the experimental data. Comer and

Read (1971a) have suggested a classification scheme,

Fig. 28. Angular dependence of “elastically” scattered elec- rons at various fixed electron energies E. A common scale is used

ir all curves. [From Ehrhardt and Willmann (1967).

Fig. 29. Energy dependence of the vibrational excitation in N2 at a scattering angle of 20°. Excitation to eight vibrational states (z/=l —8) is observed in the region of the 2nff compound state. QFrom Ehrhardt and Willmann (1967).

which was later adopted by Sanche and Schulz (1972),

and which is followed in the present review. We designate the different bands with the letters “a” to “g.”

Table II provides a listing of the bands and indicates

the names given to the bands by different authors,

the decay channel in which the bands were observed,

and the energy of the first feature. The table is presented to provide a “dictionary” which is helpful in

reading the original literature. It should be noted that series “a” and “d” have the same starting energy and the same spacing. The need

for postulating two separate series with similar molecular parameters is brought about by angular distribution measurements (Comer and Read, 1970). Series

“a’* is of the 2-type and thus is expected to exhibit an

isotropic behavior. Weingartshofer et al. (1970) observe

structure in the B *2M state at the positions of the resonances in series “a.” However, the angular distri- bution in this channel of decay is not isotropic. Therefore, Comer and Read find it necessary to postulate a

state of II symmetry around 11.40 eV. They have

considered the possibility that the observed anisotropy

65
1 /V-T

I I I L 1 1 I 13 2J0 2J5 M) 35 40

Electron Energy, eV

Fig. 30. Energy dependence of the vibrational excitation in N2

. The angle of observation was 72 degrees. As in Fig. 29, eight vibrational states are visible in the region of the 2nfl compound

state. The similarity of the curves with those shown in Fig. 29

indicates that the structures in the vibrational cross sections are independent of angle of observation. [From Schulz (1964).]

of the resonances in the B states results from a d-wave component in the entrance channel, but have

discarded this interpretation because it leads to an unreasonably large d-wave amplitude in the entrance

channel.

The above considerations relay heavily on angular

distribution measurements which, in molecules, may

not be as well understood as one would wish. For exam- : pie, Black and Lane (1971) point out that in certain : decay channels transitions may show preference for a change in rotational quantum number, e.g.,y = 0—>j=\.

Such an effect would upset the simple interpretation ; of angular distribution measurements and may render ’ unnecessary the assignment of a separate series for bands “d” and “e.” More detailed analysis must be ! awaited.

These uncertainties are taken into account in Table ’ II. Arrows point to series “a” and “d” and to series “c” and “e,” indicating that future consideration may

show that “a” = “d” and “c”=“e.” In energy, these 1 two sets of series (“a” and “d”; “c” and “e”) are 1 almost coincident. 1 Samples of recent experimental results, as observed 1 in different decay channels, are shown in Figs. 17-22.

Figure 17 shows the results of a transmission experiment by Sanche and Schulz (1972) in which the derivative of the transmitted current is measured directly.

This experiment, following closely in concept the ex- periments of Kuyatt et al. (1964) and Schulz (1964),

exhibits higher sensitivity to sharp structures than

previous transmission experiments. In the experiment

of Sanche and Schulz (1972), optical focussing effects are largely eliminated by the use of an axial magnetic

field and the detection sensitivity is enhanced by modulating the electron energy in the collision chamber.

The advantage of the transmission experiment is the overview that it provides for a large region of energy. However, many details of resonances, such as the decay channel and the angular distribution of scattered

electrons, cannot be easily extricated from transmission

experiments.

Figures 18 and 19 show the results of Comer and

Read (1971a) for which a double electrostatic analyzer was used. By studying resonances in high vibrational

states of the electronic ground state, Comer and Read

are able to eliminate all interference effects between

resonant and nonresonant scattering; in fact they dis- covered series “b” by observing resonant structure in vibrational levels above z> = 8, as is shown in Fig. 19. It

Table III. Position of maxima in the elastic and inelastic cross sections of N2 (Ehrhardt and Willmann, 1967).

Energy, eV

v' z> = 0 v— 1

0 1.89 1.93

1 2.15 2.24

2 2.40 2.55

3 2.65 2.82

4 2.89 3.07

5 3.13 3.31

6 3.36 3.53

7 3.58 3.76

66
should be noted that most of the structure visible in

che lower vibrational states of Fig. 18 consists of series

‘a”. The values of the resonant energies obtained by

Comer and Read are tabulated for H2~ in Appendix I, ^.nd for D2" in Appendix II. The results for D2~ are very similar to those for H2-

. Studies similar to those of Comer and Read, using a

similar technique had been previously undertaken by

iVeingartshofer et al. (1970). Their results (in absolute

units) at different angles of observation are shown in

Figs. 20 and 21. In addition to the X vLg+ decay channel,

vVeingartshofer et al. examined other decay channels:

the dissociation continuum, b

3 2M+ (see Fig. 22); c

3ETW ;

jz 3 2„+

; and several vibrational levels of the states

lILu, B' and D TC. The branching ratios for the

decay into some of these channels are listed, in absolute

xnits, in Appendix III. Molecular radiation emanating

:rom the B

1

SM+ state of H2 and D2 also shows the

appropriate resonances, as has been shown by McGowan and Williams (1969) and by Pichanick et al. (1971).

Figure 23 shows a schematic diagram of the five mergetically distinct compound states of H2“ and some

of the decay channels. Figure 24 shows the energies

at which various resonances have been observed in

different channels of decay. On the bottom of the

Fig. 31. Position of the peaks in the cross section vs quantum

number of the final state. If the 2Hg compound state were longdved compared to vibrational times, the solid lines would be

horizontal, i.e., the peaks would occur at the same energy regardess of the final vibrational state. The effect shown on this figure indicates that the lifetime of the 2n„ compound state is comparable

to a vibrational period. [From Schulz (1964) .]

16-

QJ3

0

1 . 6

-

Z

z>

CQu

<

z

o

h-u

U4

t/J LDtnO

cat V

0.8

-

0.

'.2

0.4-

V0<4-

7' i /y. a

*

/

/ ! \\ . I i 4 + N V */ V. ,'SJ ** & 4 r, „ 4 * 4^ •

* -4*>

,A1% °o3 'f r \ \ / / / \K

wL/. u -**? •*,

>"VP' t 4- y\ + +

/+^++

.-v'> .

0< Ob7 t+4

T4’---*—*• * 4-.

o <t o^-

ol

1—1—I—I—I—III''

1.4 2J.

aoe

i i i i i i i i i i i i i 2J6 3.0 3.4 3£ ELEaRON ENERGY (eV)

Fig. 32. Comparison of experimental and theoretical vibrational cross sections for resonant e-N2 scattering. Crosses are the experimental results of Schulz (1964). The curves show various

theoretical attempts to fit the experimental cross sections without

allowing for the variation of T with intemuclear separation. None

of these theoretical curves reproduce the regularity of the experimental structure. The broken curve: Herzenberg and Mandl

(1962); chain curve: Chen (1964); dotted curve: Hasted and

Awan (1969). [From Birtwistle and Herzenberg (1971) .] 67
Fig. 33. Comparison of the theoretical cross section for vibrational excitation using a variable T. The dashed curve (Birtwistle

and Herzenberg, 1971) is theoretical, using a variable T, and the full curve is experimental

(Ehrhardt and Willmann, 1967) . The theoretical cross section is calculated using the parameters of Table IV. [From Birtwistle and Herzenberg (1971) . ]

figure, the position of resonances is indicated as they

appear in transmission experiments. The energy positions of the transmission experiments of Kuyatt et al. (1966) and of Sanche and Schulz (1972) are shown.

The shaded region indicates the spread of values, which

rarely exceeds 50 meV. Thus the agreement is considered excellent. Higher on Fig. 24, we show decay into high vibrational states of the ground electronic state, into the

b

3 2u+ continuum, and the B 1 2„+ state as well as the

C

^ states in the low vibrational levels. Decay into the B 1 2u+ state followed by the emission

of a photon is also indicated. Whereas McGowan and

Williams (1969) observe a “strong” and a weak series,

Pichanick et al. (1971) observe only the “strong” series. The shaded area indicates the degree of uncertainty

between the two above-mentioned experiments. The

short lines indicate the positions of the “weak series”

in the radiation. The “strong” lines agree best with

series “c” (or “e”) and the weak ones with series “a”

(or “d”). Why this is so, i.e., why one band seems to dominate in radiative decay when it is not observed in

inelastic channels, is not understood.

Below we discuss some of the more prominent fea- tures of the different bands. Appendixes I and II list the energies in tabular form for H2 and D2 . A set of potential energy curves has been derived

from purely experimental information by Comer and

Read (1971a) and is shown in Fig. 25(a). A quasivariational calculation of Eliezer et al. (1967) gives

very good agreement with some of the experimental

observations and points to the proper designation of the states. Eliezer et al. find that the lowest two com- pound states have 2 2ff+ symmetry and that they consist

of the C 3IIM and C TG states, respectively, with an

electron attached which has (rru2p') symmetry. See

Fig. 25(b).

1. Band “a”

Band “a” seems to decay into all possible decay

channels. The agreement between various groups as to

Table IV. Characteristics of N2~ ( 2nff ) resonance at 2.3 eV.

Birtwistle and

Herzenberg (1971) Krauss and Mies

(1970)

Ro —Ro (cm) a. 0. 095 (±0. 003) X 10-8 0.12X10-8

hu (eV) b 0.244rb0.003 0.24 xec 0.0051±0.0017 0.0046

r(i?0 ) (eV) d 0.57±0.02 0.8

a R0~, Ro are the equilibrium internuclear separations for N2" and N2 , respectively.

b hu is the vibrational spacing of N2“.

c xe is the anharmonic constant.

d r(i?0 ) is the width at R0

.

68
rc R)it>

potential

->R

Fig. 34. The “boomerang” model of the

nuclear wave function

applied to the N2-

ion. This schematic model is discussed by Herzenberg

(1968). It is based on

the assumption that the magnitude and R de- pendence of T(R) are such that only a single

outgoing and a single

reflected wave matter. [From Birtwistle and

Herzenberg (1971).]

Nj potential

Afi M /

Emitted

electron

Incident - electron

(XitQoinq nuclear wave

in

Reflected nuclear wave

in (almost annihilated by

autoionization near RJ

Intermediate NT state

Final N2 state

Initial Estate

Nuclear separation R

the location on the energy scale is very satisfactory.

Small discrepancies in energy probably result from the

method of evaluating the position of the resonances.

Also, interference effects can shift the position of the

peaks, which are not necessarily the true positions of

the resonances. The results of Weingartshofer et al. (1970) and of Comer and Read (1970a), who observe

resonances in those channels in which very little interference takes place (e.g., high vibrational states), are

free from such errors. Eliezer et al. (1967) assign to this band the configuration (<Tgls) (Tru2p)(Tru2p') 2 2g+

, consisting predominantly of (C 3IIw +e). When one arbitrarily adds 0.25

eV to Eliezer’s calculated values, excellent agreement

exists between theory and experiment, (see Appendix

I). In any case, the spacing calculated by Eliezer et al. for band “a” agrees with experiment and thus the

assignment appears convincing. Comer and Read obtain values of 0.975 A and 11.40 eV for the equilibrium

internuclear separation and the energy minimum, re- spectively, whereas the values deduced by Eliezer et al. are 1.03 A and 11.18 eV. Band “a” seems to be firmly

established.

2. Band “b”

Band “b” has been observed only by Comer and

Read (1971a) in high vibrational levels of the ground

state of H2 . They obtained a natural width of 30 meV

69
Fig. 35. Excitation function for v=l in N2 near threshold. Shown are the results of Engelhardt, Phelps, and Risk (1964)

obtained from an analysis of swarm experiments, the double

electrostatic analyzer measurements of Schulz (1964), and the

slope near threshold obtained using the trapped-electron method

(TEM) by Burrow and Schulz (1969). The low-energy portion

of the theoretical cross section (Chen, 1964a) is identical to that

of Engelhardt, Phelps, and Risk below 1.2 eV. [From Burrow and

Schulz (1969).]

for band “b” and suggested that the new resonance

has the configuration (ag ls)(a-u ls)2iXg+

, representing an electron bound to the B l ?iu+ excited state of H2 . This band has not been observed in any transmission

experiment. The assignment is still in doubt, especially

since the potential energy curve for the (o^ls) (au ls)2 compound state should have a larger equilibrium internuclear separation than the parent B l 'Lu+ state (H. S. Taylor, private communication). In order to interpret

their experiment, Comer and Read (1971a) must as- sign a smaller equilibrium internuclear separation to the (o-gls) (o-uls) 2 state compared to the parent B 1 2M+

state, as shown in Fig. 25(a).

3. Band “c”

Band “c” has been observed in the transmission ex- periments of Kuyatt et al. (1966) and of Sanche and

Schulz (1972) in both H2 and D2 . In their early work,

Comer and Read (1971a) observed band “c” only in

D2 and not in H2 . They assign to band “c” the configuration (u0 U) (Tru2p) (ct0 2s) 2IIm. Recently, however,

Joyez, Comer, and Read (1973) were able to observe

band “c” in a high resolution experiment in H2 . Their

value for the width is T<16 meV and the starting

energy is about 11.19 eV, with subsequent values

at 11.50, 11.80, and 12.07 eV. If the starting value of

11.19 for band “c” is substantiated, then the quantum

numbers for band “c” as assigned by the other investigators listed in Appendix I will have to be incremented

by unity.

As pointed out previously, band “c” appears strongly

in vacuum uv emission.

The calculated progression of Eliezer et al. (1967)

for the configuration 2 Sa+ (o-fl l5) (iru2p) (iru2p') agrees well with most of the experimental energy positions, as shown in Appendix I. However, there is a problem in understanding the angular dependences found by Comer

et al. The detailed understanding of bands “c” and “e” is still missing and the above considerations must be con- sidered as preliminary.

4. Band “d”

This band was postulated by Comer and Read ( 197 la)

from an analysis of the results of Weingartshofer et al. (1970). On the basis of the angular distribution of elec- trons observed by Weingartshofer et al. in the B 1SM exit channel, Comer and Read suggest that the com- pound state involved must have 2ne symmetry. Although the results of Weingartshofer are coincident in

u

—

J

<

z 100

UJ

OC5

75 ^

50h

25

0 .

V=1 E=2,8eV

J 1 I L

SCATTERING ANGLE (deg)

Fig. 36. Angular dependence of the cross section for vibrational excitation to t> = l, 3, and 5 in N2 . The electron energy is indicated. The subsidiary peaks near 90° result from tf-wave

scattering. [From Ehrhardt and Willmann (1967).]

70
energy with series “a,” Comer and Read suggest that

the compound state is not the same since series “a”

involves a

2 2g+ state. However, Black and Lane (1971)

have recently pointed out that angular distributions are not a simple guide to the assignment of symmetries

because different rotational transitions may be dominant in various decay channels. Thus Black and Lane

show that the rotational transition j = 0—>j = 1 dominates in the process e+H2 (X 1 20+)—»H2~(e+C 1ntt )—i

H2 (B 1 2u+)+e. If such mechanisms are present, angular

distributions will have to be analyzed in more detail.

5. Band “e”

Under the heading of band “e” we list the measure- ment of Weingartshofer et al. (1970) who observed

inelastically scattered electrons having excited the

B 12tt+ state.

Fig. 37. Pure rotational excitation (7 = 1—>3) in the region

of the 2Ua compound state in N2 . Shown are the theoretical results of Oksyuk (1966) , Burke and Sinfailam (1970) , and Chen (1966b)

and the momentum transfer cross section of Engelhardt, Phelps,

and Risk (1964).

Comer and Read advocate such a separation because

of a discrepancy in the energy scale, but there is a good

possibility that band “e” may be the same progression

as band “c”.

6. Band “f”

Band “f” extends from approximately 13.5 to 16 eV

in H2 and from 13.5 to 14.5 eV in D2 . This band corre- sponds to the 13.63-eV progression found by Ehrhardt

and Weingartshofer (1969) in the CTL decay channel

of H2 . It has also been observed by Golden (1971) in a

transmission experiment using a derivative technique

similar to that of Sanche and Schulz (1972). In trans- mission experiments, band “f ” exhibits a width of about

90 meV in both H2 and D2 , in good agreement with the

natural width of 80 meV estimated by Ehrdhardt et al. (1969). The 2 20+ symmetry for band “f” was assigned

by these authors.

Band “f” shows peculiar characteristics: it decays

1 1.0 .5 12.0 .5 13.0 incident electron energy eV

Fig. 38. Transmission of electrons by N2 , showing a sharp

“window”-type resonance at 11.48±0.05 eV. The zero of current has been displaced. Additional structure occurs at 11.75 and

11.87 eV. The latter is partly due to an inelastic threshold (E 32ff +) . The nitrogen pressure was ~0.04 Torr. [From Heide- man, Kuyatt, and Chamberlain (1966a).]

preferentially to identical vibrational levels of the

CTL state, i.e., in the decay process the vibrational

quantum number does not change (Weingartshofer et

al., 1970). This is clearly evident from Figs. 23 and

24. It is therefore likely that the potential energy curve

responsible for band “f” has the same shape and the same equilibrium internuclear separation as the C 1nM or D TL states.

Fig. 39. Energy dependence of the differential elastic cross section for N2 at 40° and 85°. The largest structure shown occurs

at 11.48 eV and is coincident in energy with the transmission peak shown in Fig. 38. The designation is 2Zg+. The energies of the other structures are listed in Appendix V. [From Comer and

Read (1971b).]

71
Fig. 40. Energy dependence of the differential vibrational

cross sections for scattering of electrons from N2 . The exit channels

are vibrational levels of the electronic ground state and the

scattering angle is 70°. The curves do not have the same cross section scale but the peak intensities can be obtained from Table

II. The zero lines are shown broken. [From Comer and Read

(1971).]

7. Band “g”

Figure 17 shows that band “f” appears perturbed

by the presence of other structures. This new band is labelled “g” and tabulated in Appendix I. It appears

much more clearly in D2 where bands “f” and “g” do

not overlap. Three features around 16 eV in the data

of Golden (1971) in H2 which he attributed to autoionization could be members of band “g.”

III. NITROGEN

A. Resonance at Low Energy (1.7-4 eV) 2IIff The earliest experiments on the total cross section in

N2 showed a broad peak in the region around 2.3 eV

in N2 (Ramsauer and Kollath, 1931), but it was not

until the early 1960’s that an understanding of this effect became available, largely as a result of improved

experimental techniques and the pioneering theoretical

contribution of Herzenberg and Mandl (1962). From

an experimental viewpoint one obtains the most detailed information on the nature of the compound state involved by studying structure in the elastic and vibrational cross sections vs energy and by studying angular • distributions of the scattered electrons. It should be

recalled that, in the case of H2 , the dissociative attach- 3 ment decay channel provided valuable understanding.

However, since no stable N~ ion exists, such a study k is not feasible in N2 . : The history of this discovery has been well reviewed

p by Massey and Burhop (1969), by Chen (1969), by ij Birtwistle and Herzenberg (1971), and by Bardsley ! and Mandl (1968). Following the total cross section fl measurements by Ramsauer and Kollath (1931), Haas i (1957) established that the vibrational cross section ti exhibits a peak in the 2.3-eV energy range and that a 1 , temporary negative ion is involved. Schulz (1959) con- ti firmed these observations using the trapped-electron ]c method, but not until he used double electrostatic j analyzers (Schulz 1962a, 1964a, 1966) could he estab- tl lish the details of the resonance process. j The nitrogen molecule has the configuration (<r0 H)

2

tl (<Tu ls) 2 (o-g2s)2 (cru2s)2 (iru 2py((Tg2p)2

. The first unfilled

| S

j orbital is irg2p ( = 3dirg in the united-molecule notation)

and the incident low-energy electron temporarily occu- t( pies this orbital. As the electron escapes, it encounters ; jy a d-wave barrier through which it must tunnel. This

shape resonance has a symmetry 2ILg and it is centered e

' around 2.3 eV. It dominates the low-energy electron e: impact cross sections in N2 , as shall be discussed in the

p following sections. A summary of shape resonances in C( other molecules is given in Sec. VII. p,

1. Elastic Cross Section via 2II0 The energy dependence of the total scattering cross

section, obtained by Golden (1966) using a modified

Ramsauer apparatus, is shown in Fig. 26. The struc- ture in the cross section above 1.8 eV is clearly visible, ij This structure can be observed in a Ramsauer-type

apparatus when the energy distribution of the electrons

Fig. 41. Angular distribution for the two resonant peaks “j observed in the v = 1 exit channel (see Fig. 40) . [From Comer and

Read (1971b).]

J 72
is narrow. The structure above 1.8 eV had been previously observed in the vibrational cross section by

Schulz (1964) and interpreted as evidence for the 2nfl compound state, which in N2 is sufficiently long-lived

to show vibrational structure. Below 1.8 eV, Schulz did

not observe any structure or other evidence for a com- pound state, whereas the total cross section of Golden,

shown in Fig. 26, exhibits such structure below 1.8 eV. In order to resolve this discrepancy, Ehrhardt and

Willmann (1967) re-examined the elastic and inelastic

differential cross sections as well as the total cross section, but were unable to reproduce the structures below

1.8 eV. In order to insure the proper working order of their apparatus, Ehrhardt and Willmann studied the

dow-energy structure in NO, which had previously been

measured by Boness and Hasted (1966), and confirmed

this structure both in the total cross section as well as in the elastic cross section. Thus it is highly probable

that the structure below 1.8 eV, shown in Fig. 26, is spurious.

The differential elastic cross section at different scat- tering angles is shown in Fig. 27 and the angular distri- bution is shown in Fig. 28. The structure in the elastic cross section above 1.8 eV, as well as in the vibrational excitation indicates the

; existence of a compound state whose lifetime is comparable to or longer than a vibrational period. The

compound state is formed by the addition of an elec- tron in a TTg orbital to the ground electronic state of N2 (Gilmore, 1965; Krauss and Mies, 1970), and this

Fig. 42. Derivative of the transmitted current vs electron energy in N2 (11-15 eV) . The giant resonance marked 1-1' is the

zZg+ state and forms the starting member of band “b,” whose

parents are the E 32e+ and a

1Z0+ Rydberg states of N2 . The grandparent is the ground state of N2+ . Structures 3 and 4 are shape res- onances. The other resonances, including bands “c” and “d”

which appear on the higher sensitivity run on the bottom of the

figure, have the A 2nu state of N2+ as a grandparent. [From

Sanche and Schulz (1972).]

Fig. 43. Derivative of the transmitted current vs electron energy in N2 (7-12 eV). Structure in the region 7-9 eV is due to

inelastic processes involving the B 3ne state of N2 . The locations

of the B ma state, the B1 32Mstate, and the a

12„~ state of N2 are indicated. Band “a” is a progression of core-excited shape

resonances associated with the B 3nc state, and the large structure

(1-1') is the first Feshbach resonance, 22fl +. The bottom trace

is taken with a higher sensitivity. [From Sanche and Schulz

(1972).]

assignment is proven by angular distribution studies

(Ehrhardt et ah, 1967, 1968) of inelastically scattered

electrons.

2. Vibrational Excitation via 2ILg The vibrational excitation cross sections for the excitation of the first eight levels of the ground electronic state of N2 clearly show structure which is characteristic

of the compound state. Figures 29 and 30 show the

vibrational cross sections at 20° and 72°, respectively,

as obtained by two different groups. The shape and

general behavior of the cross sections are in good agree- ment. Table III lists the positions of the maxima of the features, as observed in the v = 0 and v=l decay

channels. Actually, the positions of the peaks occur at

different positions, depending on the channel of observation, i.e., the peaks shift to higher energies for

higher vibrational states. This effect, first discussed by

Schulz (1964), is shown in Fig. 31. This feature, as well as the regularity of the structure in the vibrational

cross section, stimulated theoretical interest in the

73
0° ENERGY LOSS

E

3 Z

+g ,AE = 11.87 eV

20° ENERGY LOSS

a" I g

, AE = I2.23 eV

20° ENERGY LOSS

E

3 Ig, AE = 11.87 eV

IMPACT ENERGY

METASTABLES

(eV)

c3

Ak.

(0

(c) Threshold V=0 E

3 2

+

X

X x exp

• 1 +2cos2 0

x

J I I L 50

scattering angle

100 0-

(B)

/ !

v's 0 E

3!*

I: e.4ofi

i -

Vf.wr

\ , j

* < •

s i \ !

• ty l vko ei;

I f » ; : ft ©=55a

r Ml's* : \ | V / V

<V f

•/ X

.

n.f * .. V"'

V=0 E

3 r*g

M A

0= 70®

O'-"/..

v=o e

3!;

© =90®

><». /-.«

|

. .V7~ 12 125 1^5

incident energy (eV)

‘"vw^U/ ^’V .wr\- Avu ^

Fig. 44. (A) Threshold region for excitation of the £ 32s+ and a" states of N2 . Shown are the differential cross sections of Heidemann et al. (1966a) at 0°, and Ehrhardt and Willmann (1967) at 20°. Also shown is the excitation function for metastables (Lawton and Pichanick, 1973). [From Lawton and Pichanick (1973).] (B) Energy dependence of the differential excitation cross section for the E 32g+ (v=0) state of N2 , at different angles of observation. The sharp peak near 11.90 eV has a half-width of 35±5 meV

at 90° and exhibits the angular behavior shown in Fig. 44(C). [From Mazeau, Hall, Joyez, Landau, and Reinhardt (1972b).] (C)

Angular distribution of electrons having excited the E 32ff + (u=0) state in N2 at 11.90 eV. Also shown is an angular distribution of the form (1+2 cos20), normalized to the experimental data at 90°. The good agreement between the angular distributions points to a

p<r partial wave, indicating that the threshold behavior is dominated by a shape resonance. [From Mazeau, Hall, Joyez, Landau,

and Reinhardt (1972b).]

'

74
75
Fig. 45. Energy dependence of the differential cross section

for vibrational excitation to v—2 in N2 for three angles of observation. The energy range is 15 to 30 eV. The peak in the vibrational

cross section possibly indicates the existence of a high density of overlapping compound states around 20 eV. The curves for v=l

and v=3 are similar to that shown. [From Pavlovic, Boness,

Herzenberg, and Schulz (1972).]

problem. However, the early theoretical approaches,

although correct in principle, could not reproduce un- ambiguously these properties (Herzenberg and Mandl,

1962; Chen, 1964; Hasted and Awan, 1969).

It was pointed out by Herzenberg (1968) that it is essential to consider the variation of the width T with

Table V. Derived properties of the 11.48-eV core-excited Feshbach resonance in N2“. a

Symmetry

Parent

Re (A) 1.115±0.01

a (eV) 0.270±0.02

b (eV) 0 . 002 ±0.002 r (eV) 6 XIO-4

£0 (eV) 11.345

a The quantities a and b are the Morse parameters of the potential curve defined so that the energy E of the vibrational level v, with respect to the v—0 level of the ground state, is given by E = —b(v-\-%) 2

. Re is the equilibrium internuclear

separation. [From Comer and Read (1971).]

internuclear separation. Such a variation is expected

from the dependence of the penetrability of the centrifugal barrier with the energy of the emitted electron,

which varies with R. Without allowing for such a variation, theory cannot reproduce the simplicity and regularity of the experimental results (see Fig. 32), and it certainly cannot reproduce the simple shift in peaks

shown in Fig. 31. Birtwistle and Herzenberg (1971) used a variable T

in their theory and obtained excellent agreement with

experiment, as shown in Fig. 33.

Fig. 46. Combined angular and energy dependence of the differential cross sec- tion for vibrational excitation to v = 2 in 20 N2 . The energy dependence of the process observed depends on the angle of observation. The complexity of the curves makes it probable that a superposition of many compound states is involved. [From Pavlovic, Boness, Herzenberg,

and Schulz (1972).]

76
Table VI. Geneology of Feshbach resonances in N2 .

Resonance N2~ Grandparent N2+

Binding

Designation Energy, eV Spacing Designation Energy, eV Spacing eV

“b” ( 22/) 11.48 0.27 15.6 0.27 4.1 11.75

12.02 “5” 12.64 0.23 A 2nu 16.7 0.23 4.1 “6

12.87 “c” 13.00 0.23

“d” 13.88 0.22

The best fit to the experiment was obtained when

Birtwistle and Herzenberg (1971) used the parameters

for N2 shown in Table IV. For comparison, Table IV

also shows the parameters for the N2“ state from ab

initio calculation of Krauss and Mies (1970). The

excellent agreement obtained from these completely

independent approaches is most gratifying.

The model of Birtwistle and Herzenberg (1971) leads to the conclusion that the N2~ compound state has only

collision energy CeVD

Fig. 47. Energy dependence of the elastic differential cross section for CO at different scattering angles. The first peak is only weakly indicated as a shoulder at 1.5 eV. T/2 is an approxi- mate measure of the half-width of the compound state. The

structures are better developed in the vibrational cross section

(see Fig. 48). The intensity scales for all curves are the same. [From Ehrhardt, Langhans, Linder, and Taylor (1968).]

Electron Energy, eV

Fig. 48. Energy dependence of differential vibrational excita- tion in CO at an angle of observation of 72°. The structure result- ing from the 2n compound state is more pronounced than in

elastic scattering but broader than the equivalent structure in N2 [From Schulz (1964).]

77
e-CO elastic channel

Fig. 49. Absolute cross sections for vibrational excitation of the CO molecule. The arrows point to the threshold energies of the individual vibrational states. [From Ehrhardt, Langhans,

Linder, and Taylor (1968).]

time enough to vibrate once before autoionization takes

place. Thus the N2-

(

2IIff ) state lies intermediate in

lifetime between long-lived compound states [e.g.,

02- (X 2nfl )J and short-lived compound states [e.g.,

H2“(22u+

)J. This “boomerang” model is shown schematically in Fig. 34.

Fig. 50. Threshold behavior of the cross section for exciting the v = l state in CO. Shown are the results of Hake and Phelps

(1967) . The portion of the data by Hake and Phelps indicated by the dashed line are only approximate. Also shown are the

results of Ehrhard et al. (1968), Schulz (1964), and the trappedelectron data (marked TEM) giving the slope near threshold (Burrow and Schulz, 1969). [From Burrow and Schulz (1969).]

1.0 -

: i.o ev :•

• !.U5eV ! . 2.0 eV

•

: . 3.5 ev 9

•

•

—i

—r

—f

r

•

•

i

•

•

•

•

• • ## #

* 1 *

•

•

•

•

•i

•

•

i •

ii

i

•

•

•

•

•

1 1 L_* n

«/>

oU

e-CO inelastic channel v = l

1.0

*> 0

: 1.55eV • 1.83eV

: \ .

• 2.35eV •

•

•

•

• . 3 OeV

- • X •

•

0 30 60 90 *3 30 60 90 *

0 30 60 90 *

0 30 60 90 e-CO inelastic channel v = 2, 3,4,6

v = 2

k v = 3

k v = 4 <

II o>

• 2.25eV . • 2.25eV . . 1.80eV . . 2.05 eV

• • •

• • • •

• •

• • • • • •••

• #

•

1 1 L_fcl— i i i ^ —* i i ^ —i—i—*-•

0 30 60 90 0 30 60 90 0 30 60 90 0 30 60 30

scattering angLe C degrees D

Fig. 51. Angular dependences of elastic and inelastic scattering

of electrons by CO molecules at different collision energies. In

the elastic channel (upper row) the angular dependence changes

rapidly with energy since the scattering contains several partial waves with varying phase shifts (energy close to threshold).

The constancy of the curve shapes for all inelastic channels at energies within the resonance region demonstrates that a com- pound state with a well-defined set of quantum numbers exists. [From Ehrhardt, Langhans, Linder, and Taylor (1968).]

INTERNUCLEAR SEPARATION (&)

Fig. 52. Hypothetical potential energy curves for COsys- tems showing the possible decay of the 22

+ resonance at 10 eV

into the 0“(2 P) +C(3P) and 0(3 P) +C

_

(4 5') dissociative attach- ment channels. The onsets for the negative ions are taken from

the work of Stamatovic and Schulz (1970). [From Sanche and

Schulz (1972).]

78
Fig. 53. Formation of 0~ from CO by

dissociative attachment. Shown are the

curves of Stamatovic and Schulz 1970

(points) and their calibration against the

onset of Xe+. Also shown are the results

of Chantry (1968) by the dashed line and of Rapp and Briglia (1965) by the

crosses. The structure near 10 eV on the curve by Stamatovic and Schulz is caused

by the 22+ resonance existing at 10.04 eV. [From Stamatovic and Schulz (1970).]

9.00 10.00 11.00 12.00 13.00

Electron Energy, eV

Fig. 54. (a) Energy de- pendence of the differential cross section in CO. The

exit channels are the v=0

and v= 1 vibrational states

of the ground electronic

state. The positions of the resonances are listed in Appendix VI. [From Comer

and Read (1971c).] (b) Energy dependence of the

elastic cross section in the

vicinity of the 22

+ res- onance at 10.04 eV at dif- ferent angles of observation. The shape is characteristic

of an ^-wave resonance. [From Pavlovic (to be published).]

i

i

i—i—i—i—

|—i—i—i—-i—

i—i—i—i—i—

Vv.-'.VvS.* * '

^ = 0 80°

60

1 « • i i I i—i—i—i—I—i—i—i—i—

10.0 10.5 1 1.0 Collision energy (eV)

(a)

1.5 9.6 10.0 10.4

Electron Energy, eV

(b)

79
DERIVATIVE

OF

TRANSMITTED

CURRENT

(ARB.

UNITS) I t I T ijnn

10.39 eV * ) —(- scattering angle

1*2 o'1 -eCO. Resonances 1-4 are associated with the b 32+ and B 12+ parent

states of CO. The locations of these

states and the j and c states are indicated. Band “a” whose grandparent is the A 2n state of C0+, appears near the end of the spectrum.

The gain on the lower curve has been

increased by a factor of 8. The smaller

structures on that curve represent

variations in the transmitted current

of about 0.01% which is the detection

limit of the present experiment.

[From Sanche and Schulz (1972).]

(B) Schematic energy level diagram

of CO and the compound states. The

lines with the arrows show the pre- ferred decay channels for the com- pound states. On the left side of the diagram are shown the low states of CO, i.e., am (6.01 eV) ; a' 32+ (6.86 eV); Am (8.03 eV); b 32+ (10.39

eV) ; and B *2+ (10.78 eV). The preferential decay is based on the work of Comer and Read and of Mazeau et al. The decay into C+0~ (dissociative

attachment) is shown on the right

side. (C) Differential excitation functions for the b 32+ t)' = 0 level in CO.

The curves on the left show the energy dependence at 40°, 70°, and 90°. The

downward pointing arrows point to shape resonances at 10.7 and 11.2 eV. The upward pointing arrows indicate Feshbach resonances (11.3 and 12.2 eV). The diagrams on the right side show angular distributions at specified electron energies. The points on the diagram in the center (10.7 eV) rep- resent the function (1+7 cos20), normalized at 90°. [From Mazeau,

Gresteau, Joyez, Reinhardt, and Hall (1972a).]

80
Fig. 55. (D) Differential excitation function of the B 12

+ v'=0 level at 40°. Arrows indicate Feshbach res- onances at 11.3 and 12.2 eV. [From Mazeau et al. (1972a).] (E) Differential cross sections at 40° and 80°

scattering angles for elastic scattering and for vibrational

excitation to the v—1 state in CO. The top two curves are experimental elastic cross sections at 40° and 80°. The

appropriate cross section scale for these two curves is read on the right; all other curves are read on the left. The two

curves marked “40° exp” and “80° exp” are experimental

vibrational cross sections at 40° and 80°, respectively, for z>=0—>1. (Note peak near 20 eV.) Also shown are

theoretical results for 40° and 80° using the polarized Born

approximation based on the potentials of Takayanagi and

Geltman, 1965 (TG) ; Sampson and Mjolsness, 1965 (SM)

Crawford and Dalgarno, 1971 (CD) . [From Chutjian et al. (1972).]

3: Threshold Behavior of the Cross Section to v=l

The “direct” component of the vibrational cross sec- tion in N2 is small and therefore the onset of an appreciable cross section for vibrational excitation is delayed.

This can be seen in Fig. 35, which compares three

measurements in the threshold region. The small cross

section near threshold may be due to direct excitation or to the residual effect of the compound state.

4. Angular Distributions

It has already been pointed out that angular distribution measurements are a powerful tool for the deter81
mination of the symmetry of compound states. Under

favorable circumstances the angular distribution of in- elastically scattered electrons is determined uniquely

by comparing the symmetries of the resonant state,

the initial state, and the final state. The conditions

under which a unique angular distribution can be obtained from symmetry considerations are listed by

Bardsley and Read (1968) and by O’Malley and

Taylor (1968):

(a) The scattering must be dominated by a single

resonant state, so that nonresonant scattering and the

contributions from other resonances are both negligible.

This situation is often found in the study of inelastic

collisions, but for elastic scattering there are always

considerable nonresonant contributions.

(b) The molecule does not rotate appreciably during

the lifetime of the resonant state. (c) It must be assumed that when the resonant state

is expanded in spherical harmonics the contribution

from the lowest allowed value of / are dominant. For

resonances at low energies this is nearly always true. (d) It must also be assumed that the Born-Oppenheimer separation of electronic and vibrational motion

is valid.

In the case of the N2~(2IIff ) resonance near 2.3 eV,

the extra electron must go into the Tr

g orbital. It must

have even orbital angular momentum ( l>2 ) and the

projection of the angular momentum on the molecular

axis must be unity. We may speak of a dx-wave. The

expected d-wave behavior of the cross section to vari- ous vibrational states of N2 should show a subsidiary

peak near 90°. The experimental results of Ehrhardt

et al. (1968), shown in Fig. 36, exhibit such behavior,

and thus the angular distribution measurements confirm the designation of 2IIff for the first shape resonance

in N2 .

5. Pure Rotational Excitation via 2IIe Pure rotational transitions can also be excited by

compound states. It has already been pointed out that

experiments on the “elastic cross section” exhibit struc- ture in the energy dependence which can be attributed

to the 2IIg resonance. However, beam experiments

do not have the resolution necessary for a study of

rotational excitation, or for distinguishing rotational

levels in vibrational transitions. Thus, in the case of N2 and in fact all molecules except H2 , one has to rely on

theory. The results of the theory, for rotational excitation J= 1—>3, are shown in Fig. 37. Wide discrepancies

exist in the region of the 2Ug compound state. The

results of Chen (1966b) using projection operators seem to be much below the close-coupling results of Burke and Sinfailam (1970) and those of Oksyuk

(1966). It should be noted that in the resonance region

quantum jumps /= 0—>4 or J=l—>5, i.e., A/ = 4, are

possible in addition to the usual quantum jumps,

AJ=2. Chen (1966b) has calculated the cross sections for these transitions, with and without vibrational excitation.

B. Core-Excited Resonances in the 11-15

eV Region

As pointed out previously, Feshbach-type resonances

are more likely to occur below Rydberg excited states

of molecules. In N2 , the lowest Rydberg state is the

E 32g+ state (Mulliken, 1957) at 11.87 eV and one would expect that a sharp resonance would occur about

0.5 eV below this state. Such is actually the case. Heidermann, Kuyatt, and Chamberlain (1966a) dis- covered a very sharp resonance at 11.48 eV, using a transmission experiment (Fig. 38). Comer and Read

(1971b) performed a different scattering experiment

in which the decay of the resonance could be observed

for a = 0, 1, 2, and 3 of the ground electronic state. Their results are shown in Figs. 39 and 40 and the

angular distributions for electrons having excited the v= 1 state are shown in Fig. 41. From these observations, Comer and Read deduce that the symmetry of the 11.48-eV resonance is 2 2ff+ and that the most likely

parent is the E 3 20+ state. Actually, Fig. 40 shows that a progression is involved here, of which the 11.48-eV

state is the first member. The other members of this band, which we choose to call band “b” are listed in

Appendix IV in comparison with other experiments.

Table V lists the parameters of the 2 20+ state. It should

be noted that the 11.48-eV 2 S0+ resonance has also been observed as a sharp peak in the optical excitation

function (A = 3371 A) of the C 3Uu state (Kisker, 1972).

The results of the recent transmission experiment of Sanche and Schulz (1972) are shown in Figs. 42 and 43. The features are numbered and the more obvious progressions are given letter names. The energy values are tabulated in Appendix IV, in comparison with other

experiments.

The total production of metastable states has been

measured by Lawton and Pichanick (1972) and their

results are shown in Fig. 44(A). The differential in- elastic cross sections to the E 3 2ff+ (v=0 and z>=l),

a" ^g+ (v = 0), and other electronically excited states,

have been studied by Mazeau et al. (1972b). Samples

of their results on the energy dependence and the angular distribution of scattered electrons are shown in Figs. 44(B)-(E). Figure 44(F) is a schematic energy

level diagram of the N2 and N2~ systems and the decay

scheme for various resonances. We have indicated in

separate columns shape resonances and Feshbach reso- nances. Below we discuss the properties of individual bands,

as deduced from the various experiments. In Appendixes IV and V we list the energies of the resonances.

1. Band “&”-%+

Three members of band “b” are listed in Appendix

IV. The 2 2„+ resonance at 11.48 eV consists of two

82
electrons of the Rydberg orbital symmetry 3s<rg temporarily bound in the field of the grandparent X 2 2ff+

core of N2+. This is evidenced by the fact that both

the spacing between the vibrational levels of band “b”

and the amplitudes of the structures are close in magnitude to the corresponding values for excitation of the

ground state X 22ff+ of N2+. The spacing between the

structures of band “b” is 270 meV and the ratio of

magnitudes of the two peaks is 10db0.5. These experimental results agree well with the values for the X 2 2ff+

state of N2+

, which has a spacing of 271 meV between

the z>=0 and v= 1 states and which has a ratio of 9.96

for the Franck-Condon probabilities for exciting these

vibronic states. Table VI shows these comparisons: The binding between the lowest member of band “b” and the grandparent X 220+ state of N2+ is 4. 1 eV. This value repre- sents the binding of the two 3sag electrons to the positive ion core. It is noteworthy that the value of about

4.1 eV does not change as different grandparents are considered, and in fact the value remains constant even for other molecules (see Table X). But the value

is applicable only to the lowest band. The same grandparent can give rise to other bands, lying higher in

energy.

Only the zeroth level of the X 2 hg+ grandparent state

is strongly excited in molecular transitions from the

ground state of N2 and we would expect that a similar

situation prevails for the resonances associated with

the X 22ff+ grandparent state. Thus we would not expect

to observe a long progression of vibronic states of the

2hg+ resonance.

2. Shape Resonances and Inelastic Thresholds

Structures 3 and (4-4') of Fig. 42 (at 11.92 and

12.2 eV) have been identified as ^-wave shape reso- nances associated with the E 3 2fl+ Rydberg state of N2 (Sanche and Schulz, 1972). The first of these lies near

the threshold for the E 3 Xg+ state (11.87 eV), so that one would expect a dramatic influence of the 11.92-eV

^>-wave shape resonance on the threshold behavior of

the E 32e+ state. That the E 3 2e+ state and also the

a" state at 12.26 eV show a very sharp rise near

threshold has been observed by many investigators

(Heideman et al., 1966a; Ehrhardt and Willmann,

1967 ; Swanson et al., 1971; Mazeau et al., 1972b;

Lawton and Pichanick, 1973).

Figures 44(A) and 44(B) clearly show that the

cross section as well as the differential cross section to the E 320+ state rise very steeply near threshold. A

priori, a sharp rise near threshold can arise from three causes

(i) The existence of a shape resonance just above

the threshold. The angular distribution in this case would exhibit a p-type (e.g., pa) behavior.

(ii) The existence of a Feshbach-type resonance

below the threshold can influence the inelastic cross section above threshold (Ehrhardt and Weingartshofer,

1969; Taylor, 1970). In the case of N2 , we would be

dealing with the “wings” of the 2 2ff+ resonance which

lies 390 meV below the E state. Herzenberg and D. TonThat point out that the opening of a new channel of decay (as is the case when the electron energy passes

through the energy of an excited state) leads to an

abrupt increase in the total width T. This effect

is especially pronounced when the electronic state is the “parent” of the resonance, since the decay width

into the parent is generally large. Herzenberg and D.

Ton-That have worked out these considerations for the case of the 2 S resonance in helium decaying into

the 2

3 S state, showing that a sharp peak in the excitation cross section of the 2

3 S state near threshold results. It is expected that the model will be valid in other

cases as well. It leads to an j-wave behavior in the

angular distribution of inelastically scattered electrons.

(iii) The existence of a “virtual” state, similar to one existing near the 2

1 6’ threshold in helium (see

preceding paper).

In order to distinguish between the three possibilities

outlined above, Mazeau et al. (1972b) studied the

angular distribution of the electrons having excited

the E 3Xg+ (v=0) state. Figure 44C shows that the

angular distribution near the threshold of the E state approximates the shape expected for a ^cr-wave. This

experiment demonstrates that the threshold behavior

of the E 3 2ff+ state is dominated by the ^-wave reso- nance near 11.9 eV, and also confirms the assignment

given to this resonance by Sanche and Schulz (1972).

The resonance (4-4') of Fig. 42, which lies between

12.1-12.2 eV, is also believed to be a shape resonance (Mazeau et al., 1972b; Sanche and Schulz, 1972),

probably of 2II symmetry. The angular distribution of the scattered electrons having excited the E 3 2ff+ (v = 0)

state near 12.1 eV exhibits, approximately, the shape

characteristic of a pr-wave (Mazeau et al., 1972b).

The sharp onset of the excitation function is characteristic of the E 3Xg+ and the a" 1 2e+ states at 11.87

and 12.26 eV, respectively. Other inelastic cross sections, examined by Swanson et al. (1971), (A 3 2w+

, B 3n„ B' 32w~ a' 12u—, a Wtt , C 3Uu , E 3Ug, a" %+) do

not exhibit a sharp rise near threshold.

3. Structures 5 and 6

The energy of the lowest Feshbach resonance composed of two Rydberg electrons trapped in the field of the A 2nu core of N2+ can be estimated by adding to the energy of the 2 2g+ resonance (11.48 eV) the differ- ence between the ionization potential for the X 2 2ff+ and the A 2IIU states of N2+. Such an estimate gives

12.62 eV for the energy of that 2IIM resonant state which would consist of two 3s<jg electrons bound to the

A 2II„ core. Resonances 5 and 6 of Fig. 42 (at 12.64

and 12.87 eV) probably belong to that state. In fact,

83
resonance 5 lies at 12.64 eV, only 20 meV above the

estimated position (Sanche and Schulz, 1972). The

parent of these structures can be the F 3IIU state lying

at 12.75 eV. This state has a

2 IIM core with an extra 3sag electron attached. Mazeau et al. (1972b) suggest

that the G(3IIM ) state at 12.8 eV could be admixed.

Structures 5 and 6 are also replicated in the differential cross section of the E 3 20+ (v = 0) state and these

structures appear at 12.54 and 12.78 eV, respectively, as shown in Fig. 44(B) and in Appendix IV. Structures

5 and 6 are not visible in the £ 3 2ff+ (z;=l) decay

channel.

4. Bands “c” and “d”

Two short bands (“c” and “d”) in the 13-15 eV

energy range are shown in Fig. 42. They start at 13.00

and 13.88±0.05, respectively. Here the overlap between the different resonances makes an accurate reading of the spacing between the vibrational members of

each band difficult. Nevertheless, the average spacing

of 230±5 meV for band “c” and 225±5 meV for band

“d” lies close to the value of 228 meV for the corre- sponding average spacings of the vibrational levels of

the A mu state of N2+ which is the suggested grandparent for the two bands. Mazeau et al. (1972b) suggest

that the parent of band “c” is the state H which they

have recently discovered. The state H is a triplet, and

its z> = 0 level lies at 13.15±0.01 eV. The spacing of the

two lowest vibrational levels is 240 meV.

The band “c” has been observed in the decay channels E 3 Hg+ (» = 0, ®=1), a" 1 SB+ (» = 0), and also C 3nw by Mazeau et al. (1972b). The energies of bands “c”

and “d” are listed in Appendix IV.

C. Bands “a” and “a' ” : Core-Excited

Shape Resonances

At lower energies (7-11 eV) other structures are

visible in the total scattering cross section of N2 . These

structures are clearly seen in derivative transmission

spectra for N2 shown in Fig. 43. The progression of

dips between 7 and 9 eV in the transmission spectrum

is interpreted predominantly as the excitation of vibrational levels of the B 3ng valence state of N2 and indi- cates that the cross section for excitation of the B

state rises sharply at threshold. This finding confirms

similar conclusions derived from studies using the

trapped-electron method (Brongersma and Oosterhoff,

1969, 1967; Hall et al., 1970).

The next structures (band “a” in Fig. 43) form a very well-developed progression of 18 vibrational levels which extends from 9 to 11 eV. The energy of each

structure and the corresponding spacings are given in

Appendix V. When one attempts to correlate the energies of this progression with vibrational energy levels of the known states in this energy region, namely the

B' 3 2u“, a' 1 SB“, a

l Hg , and W lAu valence excited

states, it is found that none of these states nor any

combination of them could reproduce the spacing oi band “a” (Sanche and Schulz, 1972).

Structures at the same energies as band “a” have

also been observed, superimposed on a continuum, in i the excitation function to various vibrational states (»=1 — 5) of the B 3ng valence state of nitrogen. This

is shown in Fig. 44D.

We are dealing here with a vibrational progression

of core-excited shape resonances, similar to those exist- ing near 2.3 eV in N2 , i.e., the 2ng state of N2_

. Many

of the features of band “a”, when 'observed in the decay into the B 3Ug parent state are reminiscent of the features already discussed in connection with the 2.3-eV shape resonance in N2 . The position on the en- ergy scale of the peaks observed in different vibrational

decay channels of the B 3II0 state shift. This can be

clearly seen in Fig 44D and in Appendix V, where

the energy values are tabulated. The shifting of the

peaks is reminiscent of a similar effect already dis- cussed in connection with the 2.3-eV shape resonance

in nitrogen (see Figs. 31 and 33), and the Boomerang

model (Fig. 34) developed by Herzenberg (1968) and

by Birtwistle and Herzenberg (1971). A band similar: to band “a” is also associated with the A 3 2u+ state, as evidenced by the structure in the cross section to various vibrational states of the A 3 2u+ final state, in the energy range 8.22-9.57 eV (Fig. 44E). As in the case of band “a”, the locations of the peaks shift on

the energy scale. The parent of this band is the A 3 2u+

state. Appendix V gives the energies of the structures, as observed in the v = 2-6 states of the A 3 2u+ elec- tronic state. The energy level diagram, Fig. 44F, indicates schematically some of the decay channels. The core-excited

shape resonance associated with the A 3 2„+ state is marked “a'”. D. Resonances above the Ionization Potential in N2 Pavlovic et al. (1972) have observed vibrational ex- citation for the levels v= 1, 2, 3 in N2 in the energy

range 20-24 eV. They also observed the angular dis- tribution of electrons having excited these states and

found that the angular distribution depends strongly on

the incident energy, and in fact the shape of the energy

dependence depends on the angle of observation. These

anomalies in the angular distribution, coupled with the

large size of the observed cross section, led Pavlovic

et al. to prefer an interpretation in terms of resonances

associated with doubly excited states of the nitrogen

molecule rather than singly excited Rydberg states. Further experimental work will, however, be needed i before this model is reliably proved.

Resonances associated with doubly excited states of atoms (e.g., 2s2 2p in the case of He) are well known.

In the case of small systems such as helium, one expects

these resonances to be spaced well apart compared to their width, whereas in systems with more electrons

(e.g., N2 ) there is the possibility of many doubly ex84
cited states which are closely spaced (~0.25 eV), each

of which may have an associated compound state. Thus

it may not be possible to resolve individual states,

especially since the states themselves may be relatively

broad.

The resonances discussed above would have two holes

in the normally filled shells of N2 , ( KK)(ag2s)2 (av 2s )

2

(<Tg2p)2 (TTu2py and would have three electrons in the

vacant orbitals, (

irg2p ) and (

<ju2p ). Pavlovic et al. (1972) calculate that, in the 22-eV region, the spacing

of such resonances is less than 0.25 eV. We note that the resonances discussed in the previ- ous section (core-excited shape resonances, a and a', connected with the A 3SU+ and B 3II0 states, respectively) have one hole in the normally filled shell and

two electrons in the vacant orbitals, whereas the reso- nances near 2.3 eV (connected with the ground X 1 Sfl+

state of N2 ) have zero holes and one electron in the

vacant orbitals. Thus the shape resonances invoked by

Pavlovic et al. follow logically from the two types

already discussed.

Figures 45 and 46 show the energy dependence and

the angular dependences observed by Pavlovic et al. (1972) for the excitation of v = 2. The energy dependence of the cross section for exciting a= 1 and v=3 is very similar to that shown.

A measurement and an analysis of the angular dis- tribution of electrons having excited the v= 1 vibrational state of N2 (and also CO) has been performed

by Truhlar et al. (1972) with the aim of testing whether

a simple nonresonant mechanism can explain the vibrational excitation near 20 eV. Such a model appears to be applicable in the 20-eV energy range in the case of

H2 (Trajmar et al., 1970). Truhlar et al. find that a resonance model must be involved in the case of N2 and CO in order to interpret the experimental results on vibrational excitation near 20 eV. It should be

noted that the experimental results of Truhlar et al. (1972) are in good agreement with those of Pavlovic

etal.( 1972).

IV. CARBON MONOXIDE

The electron configurations and the resulting levels

of compound states of diatomic molecules are determined essentially by the number of electrons. Therefore

N2 and CO, being isoelectronic molecules, should exhibit

very similar properties. In fact this is the case. However, the positions of the compound states and their

widths differ somewhat.

The CO molecule is not symmetric with respect to inversion so that the g—u symmetry is not preserved.

Also, the permanent dipole of CO often cannot be

ignored. The following review of the carbon monoxide

molecule follows closely the discussion of N2 . A. Resonance at Low Energy (1-3 eV) 2II The configuration of CO is identical to that already

listed for N2 , except that the subscripts g and u now

lose their meanings (see Table IX). As a consequence,

the 3d% orbital contains a p-wave component (Bardsley

and Mandl, 1968; O’Malley and Taylor 1968; Read,

1968). Thus the trapped electron tunnels through

a />-wave barrier which is not as high as a d-wave barrier and, as a result, the width of the state is expected

to be larger (the lifetime is shorter) than in N2 . These

expectations agree with the experimental results.

1.

Elastic Cross Section via 2II The energy dependence of the differential elastic cross section for CO is shown in Fig. 47. Compared to N2 , the structure in the cross section is less pronounced,

although the peak in the neighborhood of 2 eV is especially clear at 20 and 40 degrees. The individual resonances become more obvious when the vibrational

cross sections are studied. Ehrhardt et al. (1968) esti- mate' the width at 0.4 eV.

2.

Vibrational Excitation via 2II The energy dependence of the vibrational cross section, as observed at an angle of 72 degrees, is shown in

Fig. 48. This curve, obtained by Schulz (1964) is in all respects similar to the curve obtained at 20 degrees

(Ehrhardt et al., 1968), indicating that the shape of

the cross section does not depend on angle. The sum

of all vibrational cross sections has a relatively smooth

behavior, with a single peak at 1.7 eV and a magnitude

8X) 0-,, = 3.5 X 10-16 cm2

. V=1 In obtaining this value, Ehrhardt et al. (1968) took into

account the variation of the cross sections with angle.

The vibrational cross sections in absolute units is shown

in Fig. 49. A notable difference exists between N2 and CO if one

observes that the cross section for v= 1 has a long tail which extrapolates to the onset for v=\ (see Phelps,

1968) whereas N2 shows a tail which is smaller by an

order of magnitude. A direct dipole-type process is probably responsible for the difference. Figure 50 shows

the details of the threshold region for excitation of v = 1 in CO, as determined by different methods of measure- ment.

The other notable difference between N2 and CO is the larger width of the observed structure. As already

noted, this larger width is a result of the barrier being

predominantly of a p-wave character in CO, with d wave mixed in. In N2 , the barrier is predominantly

d wave.

3.

Angular Distributions

Figure 51 shows the angular distributions obtained by

Ehrhardt et al. (1968) for electrons which are scattered

elastically and inelastically. Qualitatively, the curves

for the inelastically scattered electrons show a ^-type

behavior of the curves, with a minimum at 90 degrees.

85
A fairly good, but not perfect, fit to the experimental

curves was obtained by O’Malley and Taylor (1968)

whose theory gives the angular distribution in the form

(1+7 cos

2 0). The deviation between this expression

and the experiment is of the order of 10%. Read (1968) was able to improve the fit to the angular distribution of

inelastically scattered electrons in CO, using a mixture

of pr and dir waves. The mixing of the pir and dir waves is left as a parameter and the mixing parameters

are adjusted until a good fit to the experimental angular

distribution is obtained.

B. Dissociative Attachment (9.65-12 eV)

Dissociative attachment in CO leads to the formation

of 0~ via the reactions (Chantry, 1968)

e-j- CO—+)"+ C (

3P) [9.62 eV]

and

H-CO-M3-+C0D) [10.88 eV].

A much smaller cross section (~6X10~23 cm2 ) exists

for the reaction (Stamatovic and Schulz, 1970)

e+CO^O+C~(4S) [10.20 eV].

Whereas the experimentally observed appearance

potentials for the reaction leading to 0

_+C, given in

brackets above, occur at the expected position for these

reactions, the formation of O+Cis “delayed” by

about 360 meV from the energetically lowest value that can give the reaction (9.84 eV). A hypothetical potential energy diagram showing some of the observed

features is shown in Fig. 52. Figure 53 shows the dissociative attachment cross section for 0~ formation as measured by Stamatovic

and Schulz (1970), by Chantry (1968), and by Rapp

and Briglia (1965). Stamatovic and Schulz detect

structure in the dissociative attachment curve near

10 eV, which can be interpreted by the presence of the

2 2+ core-excited resonance (to be discussed in the

following section) interacting with the potential energy

curve responsible for O

-

formation.

C. Core-Excited Resonances in the 10-15 eV Region

Core-excited resonances in CO strongly resemble

those of N2 . Just as in N2 , the lowest Rydberg state of

CO, b

3 2+

, can support a strong core-excited resonance

of the Feshbach type. This resonance, discovered in a transmission experiment by Sanche and Schulz (1971a), was further studied by Comer and Read (1971c), by

Swanson et al. (1971, 1972) and by Mazeau et al. (1972a). Uniform agreement exists on the location of

this resonance as measured by Sanche and Schulz,

i.e., 10.04dz0.03 eV, with a width about 45 meV.

Angular distribution measurements (Mazeau et al., 1972a; Pavlovic et al., 1973) show that the resonance

exhibits itself in the j wave and thus the symmetry

is 2 2+.

Figure 54(a) shows the energy dependence of the

differential cross section for the v = 0 and v=l exit channels of the ground electronic state at angles of 80

and 60 degrees, respectively, and Fig. 54(b) shows the

elastic differential cross section at other angles of observation. The transmission experiment of Sanche and

Schulz is shown in Fig. 55(A). The features are numbered and the positions of the features are listed in Appendix VI in comparison with the features observed

by Comer and Read (1971c) and Mazeau et al. (1972a).

The principal decay channels are indicated on the

energy level diagram [Fig. 55(B)], mostly based on the

work of Mazeau et al. (1972a), Swanson et al. (1972),

and Comer and Read (1971c). The excitation function

of electronically excited states at different angles of observation is shown in Figs. 55(C) and 55(D).

The features observed in CO are discussed in greater

detail below.

1. 2 2+ Resonances ( 10.04 eV, 10.28 eV) Structures (1-1') to (4-4') in the derivative trans- mission spectrum of CO, shown in Fig. 55(A), exhibit a remarkable resemblance to the structures (1-1') to (4-4') in N2 and can be interpreted similarly. Structures

1-1' (10.04 eV) and 2-2' (10.28 eV) can be identified as two members of a vibrational sequence of Feshbach

resonances whose parents are the b

3 2+ and B 1 2+

states of CO at 10.39 and 10.77 eV, respectively. The

grandparent is the X 2 2+ ground state of CO+ and the resonance itself has a symmetry 2 2+. The binding of the

two 3sag electrons with respect to the grandparent

state is 4.1 eV, similar to other cases studied (see

summary, Table X).

The 2 2+ resonance at 10.04 eV also influences dis- sociative attachment as has been discussed by Sanche

and Schulz (1972), who reinterpreted the dissociative

attachment experiments of Stamatovic and Schulz

(1970) and pointed out that the structure near 10 eV

in the O

-

production from CO may be due to the 2 2+

resonance. Also, the formation of C

- from CO can be

interpreted in terms of this resonance. Although compound state formation is expected to be

similar in the isoelectronic molecules N2 and CO, the

2 2+ resonance in CO has a natural width (T~40 meV)

which is almost two orders of magnitude greater than

that found for the 2 2g+ resonance at 11.48 eV in N2 (T~0.6 meV). The larger width in CO probably

results from the partial decay of the 2 2+ resonance into

the 0~(2P) +C(3P) channel. In N2 dissociative processes are not observed and the potential energy curve corresponding to the one leading to 0“+C in CO

could occur at a different energy where it would not

interact with the 2 2ff+ state of N2~. Thus the natural

width of the 2 2ff+ state in N2 would be small since this state decays predominantly to the ground state of the

molecule.

The decay of the 2 2+ resonance has been studied by

86
Mazeau et al. (1972a) and by Swanson et al. (1972).

They find that the 2 2+, z)=0 resonance at 10.04 shows a

preference for decay into high vibrational levels of valence-excited electronic states: the v = 3 state of a

3II, the z> = 4 state of A TI, and the v — 25 or 26 state

of a' 3 2+. Schematically, these observations are shown

on the energy level diagram, Fig. 55(B). One can understand the experimentally determined decay scheme by

considering the equilibrium internuclear separation of the various states (Mazeau et al., 1972; Swanson et al., 1972). The 2 2+ compound state, being a Rydberg

j state, should have an equilibrium internuclear separation close to that of the positive ion X 2 2+ (re = 1.11 A)

or the two parents b

3 2+ (re =l.ll A) or B 1 2+

( re =

1.12 A); this places re for the compound state near

1.11 A. The decay takes place to electronic states with a larger equilibrium internuclear separation

(X l H+: r= 1.13 A; a

3II: 1.20 A; A TI: 1.23 A; a' 3 2+:

1.35 A). Thus, high vibrational quantum numbers will be preferred in the decay, especially when the final state has an re very large, as is the case for the a

3 2+

state.

2. Shape Resonances and Inelastic Thresholds

Structures 3 and (4-4') of Fig. 55(A) at 10.42 and

10.7 eV, respectively, are probably shape resonances, by analogy with similar structures observed in nitrogen.

Angular distribution measurements in the b

3 2+ decay

channel indicate that the 10.7-eV resonance has a

2n

symmetry. Figure 55(C) shows this measurement of the

angular distribution, and also the differential excitation

cross section to the b

3 2+ state at 10.39 eV. The excitation cross section to the b

3 2+ state shown

in Fig. 55(C) exhibits a sharp rise near threshold and a number of structures above threshold. At first sight,

this excitation function appears similar to the excitation

cross section to the E z 'Lg+ state in N2 [Fig. 44(B)]].

However, there is a notable difference: Whereas the

angular distribution near the threshold of the E zHg+

state in N2 exhibited a p-wave dependence [see Fig.

44(C)]] characteristic of the decay of a ^>-type shape

resonance, in the case of the b

3 2+ state in CO, we see from Fig. 55(C) that the angular distribution is iso- tropic. Thus, an s wave is indicated.

We have already pointed out in Sec. IIIB2 that the

decay of the wings of the 2 2+ resonance, lying 350 meV

below the threshold of the b

3 2+ state, can cause a sharp

structure in the threshold behavior. This appears to be the case. The large width of 2 2+ resonance in CO,

about 45 meV (vs only 0.6 meV for the 2 2ff+ resonance

in N2 at 11.48 eV) would provide a favorable circum-

, stance for the observation of the decay of the 2 2+

resonance into an inelastic channel.

3. Band “a”

At higher energies in CO, the transmission experiment (Fig. 55) shows many overlapping resonances and

Fig. 56. Comparison of experiments on the structure in the low-energy cross section of NO. The top curve represents a

recorder tracing of electrons scattered over a wide acceptance

angle (mostly elastic) (Spence and Schulz, 1971b). The middle

curve is the differential elastic cross section (Ehrhardt and

Willmann, 1967). The bottom curve, which has been shifted by

about 0.4 eV to overlap the present results, represents the trans- mission experiment of Boness, Hasted, and Larkin (1968). The

structure is interpreted as the resonant contribution to the elastic cross section and the spacing of the structure is interpreted as the spacing of the NO- 32“ system. [From Spence and Schulz

(1971b).]

identification of particular bands is not possible.

However, one can identify six vibrational levels belonging to a common progression (band “a”) near

the end of the spectrum shown in Fig. 55. This progression starts at 13.95±0.05 eV with a spacing of 205,

190, 185, 175, and 165±5 meV, respectively. The probable grandparent is the A 2 II state of CO+.

D. Resonances above the Ionization Potential in CO

It was pointed out in Sec. HID that there exist resonances above the ionization potential of nitrogen,

in the range 20-24 eV. A similar process exists in carbon

monoxide. Chutjian et al. (1972) and Truhlar et al. (1972) have measured the cross section for excitation

of the v=l vibrational state in CO [see Fig. 55(E)]]

and find a broad peak around 20-eV energy. They find

that theories relying on potential scattering alone are

87
Fig. 57. Width of resonances in the elastic cross section of NO.

Open symbols represent the experimental observations and the dashed line is drawn through these points. Filled-in symbols

with the solid line drawn through them represent the “real” width

of the resonances, obtained by deconvolution. In the deconvolution both the electron-energy distribution and the resonances are assumed to be Gaussian. The data shown are those of Spence and

Schulz (1971) and of Ehrhardt and Willmann (1967). The width

is defined as the full width at half-maximum. [From Spence and

Schulz (1971b).]

not adequate to explain this peak and conclude that a resonance or a series of resonances must be involved

to explain the cross sections near 20 eV.

V. NITRIC OXIDE, NO

A. Compound State at Low Energy (0-1.5 eV) X 32

-

Nitric oxide, like O2 , forms a stable parent negative

ion and thus NO has a positive electron affinity. The

lowest negative ion state is the X 3 2~ state whose

zeroth vibrational level is stable with respect to autodetachment; however, the higher vibrational states autodetach since they lie energetically above the v = 0

state of NO (X 2IIr ). For an understanding of electron

Table VII. Parameters of NO (X 3£ ).

Electron scattering:

(Spence and

Schulz)

Photodetachment

(Siegel et at.)

Equilibrium separa- 1 . 286 Aa 1.258±0.010 Ab tion, re Electron affinity, 50 meV 24(-f 10, -5) meVb EA (NO)

170±20 meV 182±25 meV

(OgXe 1.0±0.25 meV ...

a Values obtained using Badger’s rule.

b Preferred values.

scattering, one wishes to know the electron affinity, the

vibrational spacings of NO-

, the anharmonicity, and the

equilibrium internuclear separation. Information re- garding these parameters comes from various types of experiments, discussed below, which shed light on the

nature of the shape resonance in NO.

1. Elastic Scattering

The values of the vibrational spacings of the lowlying shape resonance are deduced (for both 02 and

NO) primarily from electron scattering experiments:

The energy dependence of the elastic cross section

exhibits structure at the positions of the vibrational

levels. The vibrational cross section to various states of

NO also exhibits relatively sharp peaks at the positions

of the vibrational states of NO-

.

Fig. 58. Approximate cross sections for vibrational excitation

of NO by electron impact. The vibrational spacing of the neutral molecule is indicated below the curves, and the vibrational spacing

of NO- above the curve. [From Spence and Schulz (1971b).]

Figure 56 shows the structure in the elastic cross section as observed by Spence and Schulz (1971b),

by Ehrhardt and Willman (1967), and by Boness,

Hasted, and Larkin (1968). The spacing of the peaks is about 160 meV and the agreement between various

experiments appears good. Interestingly, the width

of the observed peaks increases as the quantum number

increases, from 70 meV for the first peak to 100 meV

for the fifth. This effect can be clearly seen from Fig. 57. A similar broadening may also occur in O2 , but has not

been observed experimentally because the width of the

peaks in O2 is much narrower than in NO, and thus the

experimentally observed width of the peaks in O2 are almost entirely caused by the instrumental resolution.

Any changes in the natural width are hidden, in the

case of O2 , by the instrumental resolution.

88
2. Vibrational Excitation ( 0-1.4 eV) The vibrational cross section, as measured by Spence

and Schulz (1971) using the trapped-electron method,

exhibits (similar to the case of O2 ) a series of spikes

superimposed on a slowly rising background (“direct”)

cross section. The results are shown in Fig. 58. Here, the

vibrational levels of the compound state (as determined

by the elastic scattering experiments of Fig. 56) are shown by the vertical lines. The agreement between the

location of the “spikes” in the vibrational cross section

and the location of the compound states from elastic scattering is very good and justifies the model used.

One important result obtained by Spence and Schulz

involves the observation that the z> = 4 state of NO is accidentally coincident in energy (within ±10 meV)

with the v' = 6 state of NO-

. The trapped-electron

method has a high sensitivity for detection of such

coincidences. This comes about by plotting the positions

of the peaks in the trapped-electron current as a function of well depth. If an excitation function contains a dominant spike (resulting from a resonance), then the

peak of the trapped-electron current occurs at the

energy of the spike and a plot of the position vs well

depth is a horizontal straight line. Otherwise, such a

plot is a straight line with slope of unity.

Spence and Schulz (1971b) observe that the

branching ratio, i.e., the ratio of cross sections for various final states of NO via a given state of NO-

, is

Fig. 59. Potential-energy curves for NO(X 2Hr) and

NO~(X 32

-

). The width of the levels of NO- have been omitted. In order to bring the NOcurve into agreement with the results

of photodetachment experiments, one should shift the minimum

of the NOcurve to 1.258 A and the spacings of the vibrational

levels should be decreased. [From Spence and Schulz (1971b) .]

0 NO

Paquct et al. (1971) Rapp & Briglia (1965) o o o o Chantry (1968)

•V •* *“0 ”0 o

•

ooc \* “O

•A.\h

o<*b0 o o \

o

•o .\\ JO °v

1

D

O

• o

«. o o M °o O

’°o

7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 ELECTRON ENERGY (eV)

Fig. 60. Negative ion formation by dissociative attachment in NO. Shown are the results of Paquet, Marchant, and Marmet

(1971), of Chantry (1968), and of Rapp and Briglia (1968). Dissociative attachment in NO leads exclusively to electronically excited N. [From Paquet, Marchand, and Marmet (1971).]

close to unity, in sharp contrast to the case of O2 . They deduce that the barrier height involved in the

case of NO is lower than that in O2 and that probably a p wave dominates the electron escape. The resulting

lower barrier leads to a short lifetime of NO- (~10-14 sec) compared to the lifetime of O2- (~10~10 sec).

The assumption of a p-wave barrier is consistent with

the theoretical considerations of Bardsley and Read

(1968) who point out that the partial waves which are being mixed are the pr and dr waves (see Sec. VII).

Bardsley and Read also point out that in resonance formation and decay at low energies, a ^>-wave component is much more efficient than a d-wave component.

The centrifugal barrier through which the incoming or outgoing electron must tunnel is much higher for d waves than for p waves. Although d waves may be more important than p waves in the interior of the

molecule, this is not necessarily true near the surface.

Spence and Schulz (1971b) deduce the values of co e from the spacing of the peaks in the elastic and the

vibrational cross sections, and they calculate the

equilibrium internuclear separation for NOusing

Badger’s rule (Badger, 1935). Table VII shows a comparison of the values thus calculated with the values

from photodetachment experiments. The schematic

potential energy curve deduced by Spence and Schulz

is shown in Fig. 59. In order to bring the NOcurve into

agreement with the results of photodetachment experiments, one should decrease re to 1.258 A and should

decrease the spacing of the NOlevels somewhat so that

the coincidence of the level v' = 6 of NOwith i> = 4

of NO can be maintained and so that the v

f = 0 level comes to —0.024 eV.

89
DERIVATIVE

OF

TRANSMITTED

CURRENT

(ARBITRARY

UNITS)

Fig. 61. Derivative of transmitted current vs electron energy

in the 5-7.5 eV region in NO. Four bands belonging to a Rydberg

series of NOstates are shown; each band consists of a vibrational

progression. The spacing of each vibrational progression agrees with the vibrational spacing of the X 12+ ground state of NO+

, which is the grandparent. [From Sanche and Schulz (1972). 3

3. Equilibrium Internuclear Separation and Electron

Affinity : Photodetachment Spectroscopy

Values of the electron affinity of NO (and also of O2 ) have been in a state of violent fluctuation until very

recently. But as a result of the recent photodetachment experiments of Siegel et al. (1972), a reliable

value is now available:

IL4 (NO) = 24(4-10, -5) meV.

In the experiments of Siegel et al., an argon-ion laser

photodetaches electrons which are energy-analyzed. A

Franck-Condon factor analysis of the observed cross sections determines the molecular constants for NO-

:

coe = 1470zb200 cm-1

; re — 1.258=1=0.010 A; and Be =

1.427d=0.02 cm-1

, and also the electron affinity quoted

above (24 meV). The very recent value of McFarland

et al. (1972) is 28=1=14 meV, in good agreement with

Siegel. Older values of the electron affinity of NO are

listed by Siegel et al. (1972) but they all seem less reliable: The other values are 900=1= 100 meV (Farragher

et al., 1964), 650 meV (Stockdale et al., 1969), 90=1=100

meV (Berkowitz et al., 1971), 0 (Lacman and Herschbach, 1970), and 50 meV (Spence and Schulz, 1971b).

B. Dissociative Attachment (7-10 eV)

Dissociative attachment in NO, leading to the formation of 0~, indicates the existence of a repulsive potential energy curve in the region 7-10 eV, as shown by the

negative ion production of Fig. 60. The structure observed by Paquet et al. (1971) may well be due to the

traversal of the repulsive curve responsible for 0~

production through the potential energy curves

responsible for the core-excited resonances. Noteworthy

is the conclusion of Chantry (1968), who determined

front kinetic energy measurements of the O

-

ion, that

the dissociative attachment process leads exclusively

to the formation of electronically excited N, i.e., e+NO—

0

-+N(2Z>).

C. Core-Excited Resonances in NO

Fewer experiments on core-excited resonances are available in NO than in the molecules previously dis- cussed. Differential measurements have not yet become

available. Nevertheless it was the NO molecule which

revealed the interpretation of core-excited resonances in terms' of Rydberg compound states (Sanche and

Schulz, 1971). Figures 61 and 62 show a plot of the

derivative of the transmitted current vs electron energy

in the energy range 5-18 eV. The features on Fig. 61

!

are given letter designations and are discussed below.

1. Bands “a” to “d”

The location of four bands of resonances, “a”, “b”,

“c”, and “d”, is indicated in Fig. 61 by vertical lines

ELECTRON

ENERGY, (eV)

Fig. 62. Electron transmission

spectra for NO in the 12-13 eV, 14r-l5 eV, and 17-18 eV regions. Each seg- ment shows resonances associated with the b

3n, A 1U, and B *11 excited

states of NO+ which are the respective

grandparents. The binding of the first compound state in each segment rela- tive to the corresponding grandparent state is nearly constant. [From

Sanche and Schulz (1972).]

90
pointing to each vibrational member of a given band.

The first 3 bands have four vibrational members and the

bands start at 5.04, 5.41, and 5.46 eV, respectively.

Band “d” starts at 6.45 eV and six vibronic states belonging to that band have been observed; four of

these are shown in Fig. 61. The vibrational spacings of each band and the Franck-Condon probabilities for

bands “a”, “b”, and “d” are compared with the cor- responding values for the X x 2+ ground state of NO+

in Appendix VII. Bands “a”, “b”, and “c” have about

the same spacing, which agrees well with the spacing of

the grandparent NO+ core. Band “d” deviates slightly

from the grandparent spacing. Franck-Condon probabilities for bands “a”, “b”, and “d” agree qualitatively

with those of the NO+ ion core, even though bands

“a”, “b”, and “c” overlap. All Franck-Condon probabilities listed are normalized to v=l for comparison

purposes.

The comparisons suggest that all four bands in NO

are composed of two Rydberg electrons temporarily

bound to the same X 1 2+ core of NO+. The parent of

band “a” is probably the A 2 2+ Rydberg state of NO

which lies at 5.48 eV. The A state, whose electron

affinity from the above argument is 0.45 eV, cor- responds to an electron in a Rydberg orbital of the symmetry 3sa bound to the X 1 2+ core of NO+. The addition

of another 3so electron to the core gives the 1 2+ symmetry for band “a”. Bands “b” and “c” which lie 0.07 and 0.02 eV

below the A 2 2+ state of NO, respectively, could result

from the addition of a 3pa or 3pir electron to the A state. Alternatively, the parents of bands “b” and “c”

could be the C 2II and D 2 2+ states of NO, which lie at 6.49 and 6.60 eV, respectively. As far as band “d” is concerned the only likely parents are the C and D

states of NO.

Paquet, Marchand, and Marmet (1971) have

Fig. 63. The energy

level diagram of rele- vant NO+ grandparent

states (left side of dia- gram) compared with

the energy level diagram

of the NOstates ob- served in the present

experiment (right side

of diagram). The two

energy scales have been

displaced by the binding energy of the lowest member of band “a”

with respect to its grandparent X 12+ state

of NO+. Each state of NO+

, shown on the left of the diagram, gives

rise to a Rydberg series of NOstates. [From

Sanche and Schulz

(1972).]

22 r- >A 21

*/> UJK

19 +o

2 17

O 15

0£

- A 1

<

I—zLUI—oa.

NO+

NO'

B'n

A'n

b

3 n

•d’\

lv + X 2

/"

19

17 ^

15

13

— 5

11 O

ae

LUZLU 9 <

»—Z

7 £

O

Fig. 64. Comparison of four experiments on the structure in the electron impact cross section in 02 . The top curve shows the wide-angle total cross section (Spence and Schulz, 1970), the next curve shows the differential elastic cross section (Boness

and Schulz, 1970). The bottom two curves represent transmission experiments. The curve by Boness and Hasted (1966) is shifted by 0.4 eV and the curve by Hasted and Awan (1969) is shifted by 0.25 eV, both to lower energies. The agreement in the spacing

of the structures is considered good. The indicated quantum numbers refer to the C>2~(X 2Uff ) state. [From Boness and Schulz

(1970).]

recently postulated the presence of two long-lived

bound negative ion states at 7.8 and 8.2 eV, in order to explain two peaks they observe in the cross section

for 0~ formation from NO at these energies. The postulated states should appear in the total scattering cross

section. The 5th vibrational member of band “d,” which

lies at 7.83 eV, could possibly account for the 7.8-eV

peak in the O

-

data at Paquet et al.

2. Region 12 eV-18 eV

The resonances shown in Fig. 62 for the energy range

12-18 eV seem to have as their grandparents excited states of NO+. At least ten bound excited states of NO+

are known at the present time and four of these, namely

the b

3n, A TI, c TI, and B TI ion states, can be con91
Table VIII. Molecular orbital configuration of the ground states and of shape resonances in diatomic molecules. The

extra electron, which is responsible for the shape resonance, occupies the lowest vacant orbital shown in the fourth column. a

Molecule Molecular orbitals of ground state Ground

state

Lowest

vacant

orbital Compound

state

Dominant

partial wave h2 (Iso-ff)

2 2pau

22u+ pa

n2 ( 1 s<re)

2

( 2p<ru) 2

( 2s<Tq)

2

( 3p<ru) 2

( 3sag)

2

( 2pxu) 4 V,+ 3d>TTg

2nff dx o2 (ZdXgY 3dirg

2n„ dx

CO (\.sa) 2 {2sa)'i {2pa) i {2px) i (3sa) i (3pa)'1 *2+ 3px 2n dx-\-px

NO (3px) 2nr 3px 32~ dx~\-px

a The notation used is the “united atom” notation of Herzberg (1950) . See also Bardsley and Mandl (1968) . The notation used in the column entitled “dominant partial wave” is dx, px, and p<r. The first, Latin letter, refers to the angular momentum of the electron

partial wave at infinity, i.e., 1 = 2, and 1, respectively. The Greek letter refers to the component of this angular momentum along the internuclear axis of the molecule as the electron comes close to the molecule.

sidered as possible candidates for compound state formation from the ground state since their internuclear distances lie close to the internuclear distance

of the NO ground state. These states are listed in

Appendix VIII where their energies are given. Also

shown in Appendix VIII are the position of the reso- nances in the energy range 12-18 eV. In the last column

of Appendix VIII we calculate the “binding” energy by

taking the difference between the energies of the

assumed grandparent and the lowest value of the

resonance. The constancy of the binding energy indi- cates that the proper grandparents have been assigned

and that the potential well which binds the two 350- electrons does not change. The binding energy of band

“a” (previously discussed) with respect to the X 1 2+

ground state is 4.23 eV, in very good agreement with

the other values for the binding energy shown in

Appendix VIII.

The various structures listed in Appendix VIII have

been interpreted by Sanche and Schulz (1972) as core- excited Feshbach resonances or as core-excited shape

resonances, and their parents have been suggested. For

example, the 12.57-eV feature listed in Appendix VIII

is interpreted as the v= 1 state belonging to the progression starting at 12.36 eV, since the spacing and the

Franck-Condon factors agree with those of the b

3II grandparent state. An energy level diagram of the zeroth vibronic level of each NOstate is shown on the right side of Fig. 63. On the left side of this figure the energy levels of the

NO+ grandparent states are shown. The two scales

have been displaced by the difference in energies between the lowest member of band “a” with respect to

its grandparent, the X 1 2+ core of NO+ (4.23 eV), in

order to show the relationship between the NO+

state and its grandchildren NOstates. This comparison

demonstrates that the binding energy of two 3sa

Rydberg electrons does not depend on the configuration

of the positive ion core. It also illustrates that in NO

only Rydberg excited states give rise to core-excited resonances in the total scattering cross section.

VI. OXYGEN

A. Compound State at Low Energy: X 2Ug (0-1 eV)

The lowest compound state of O2 is the X 2Ug state. The vibrational states v' = 0 to v' = 3 of 02- (X 2II(7 ) lie below the z>=0 state of (^(V 3 ^

-

) and cannot autodetach. These vibrational states of O2-

are therefore

stable. For higher quantum numbers, autodetachment

can take place and these higher vibrational states form

the lowest compound state of O2 . As in the case of NO,

a variety of experiments must be brought to bear on the

problem in order to gain a full picture which has

recently emerged. The important experiments are

elastic scattering, inelastic scattering (i.e., vibrational

excitation), photodetachment, various measurements

of the electron affinity, and three-body attachment.

The molecular orbital notation for the lowest states

of O2 and O2 is given in Table VIII, Sec. VII.

1. Elastic Scattering

The structure, consisting of peaks, in the elastic differential and total cross sections of electrons on O2 gives us the information on the position of the vibrational levels of the O2-

system. Figure 64 shows a compilation of several experiments, suitably presented.

The spacings are also listed in Appendix IX. The assignment of the proper vibrational quantum number does

not come from the elastic experiment alone. Rather,

the electron affinity of O2 must be known in order to achieve such an assignment and a backward extrapolation, using the measured spacings and the anharmonicity, must be performed. Until recently the value

for the electron affinity was being questioned (see Sec. VI A3) but we can now be confident that the values of Pack and Phelps (1966) (0.43=b0.02 eV) and of Celotta et al. (1972) (0.440dr0.008 eV) are correct.

92
intensity

[aro.umtsj

When the backward extrapolation is performed and

terminated at the electron affinity of 0.44 eV, one obtains a value of 132 meV (Spence and Schulz, 1972) or 135 meV (Linder and Schmidt, 1971b) or 140 meV

(Gray et al., 1971) for the spacing of the lowest vibrational states, i.e., v'=0—>v'=l of 02-

. These values

compare to a value of 135 meV deduced by Holzer

et al. (1968) from Raman spectroscopy of alkali

halide crystals in which 02~ is trapped. The agreement J

between all these values appears to be good. ja, A high-resolution (10 meV) transmission experiment §

by Land and Raith (1973) shows that the z>' = 4 peak is Z

split by spin-orbit coupling into 2n3/2 and 2IIi/2 com-

* ponents, separated by 20±2 meV. The center of the §

?/=4 state is determined to be at 91 ±5 meV. «o

2. Vibrational Excitation of 02 at Low Energy S (0-1.0 eV) *

The vibrational cross section in 02 should consist of a

“direct” component and a “compound-state” component at the position of the compound state, 02“.

collision energy [eV] Fig. 65. Measured vibrational cross sections to v=l, 2, 3, 4

of 02 . The horizontal line at each curve indicates the zero line of the stored signal. Two runs of the energy dependence of elastic scattering are also shown in the upper part of the figure. The

scattering angle is 60° for all curves. The vertical lines indicate the energy position of the resonance peaks. The threshold onsets

of the excitation functions are marked by small arrows. Energyintegrated cross sections in absolute units are listed in Appendix X. [From Linder and Schmidt (1971b) .]

scattering angle

Fig. 66. Angular distribution of electrons having excited the

v = 1 and v — 2 vibrational states in 02 . The points are experimental

(error ~10%) . The lines represent theoretical models with and

without rotational states of the compound state. The curves have

been normalized at or near 90°. [From Linder and Schmidt

(1971b).]

This model was invoked by Hake and Phelps (1967)

and by Schulz and Dowell (1962) to explain swarm and

trapped-electron experiments, respectively.

Recent trapped-electron experiments by Spence and

Schulz (1970) led to the conclusion that the vibrational

cross sections in 02 consist of series of spikes at the

position of the compound state which had been pre- viously established from elastic scatterings. This finding

is corroborated by the differential cross section meas- urements of Linder and Schmidt (1971), whose data

are shown in Fig. 65. The trapped-electron method possesses a high sensitivity for detecting when a level of 02 and a level of 02~

occur accidentally at the same energy. Spence and

Schulz find that the v'=S level of 02-is coincident in

energy with the z>=3 level of 02 , thus fixing the relative

positions of the vibrational levels of the two systems.

This coincidence has been confirmed by Linder and

Schmidt, who find that the coincidence between these

two levels is within 1 meV, as well as by Land and

Raith (1973).

In order to obtain an absolute magnitude from their

differential cross section, Linder and Schmidt have to know the angular distribution of the scattered elec- trons. Figure 66 shows that the experimentally ob93
QUANTUM NUMBER OF COMPOUND STATE, v' Fig 67. Plot of energy-integrated cross section for vibrational

excitation to v=l, 2, 3, 4 vs quantum number of compound state, as measured by Linder and Schmidt (1971b). The cross sections

consist of a series of narrow spikes at the positions of the vibrational levels, v', of the compound state.

served angular distribution is isotropic. The lifetime of

the X 2IIg compound state, 02-

, is long (i.e., ^lO-10 sec

for the lowest vibrational member, t/ = 4), as will be

discussed below. For such a long-lived object, one has

to include rotation in the theory and the result of such

a theory yields a near-isotropic angular distribution, as shown in Fig. 66. It is pointed out in Sec. VII that the

partial wave in which the resonance occurs is dir. The absolute magnitude of the energy-integrated

vibrational cross sections for the v= 1, 2, 3, 4 state of 02 are shown in Fig. 67 and are listed in Appendix X.

Spence and Schulz also measured the energy-integrated

cross sections, but their set of measurements is less complete than that of Linder and Schmidt.

Disturbingly, Spence and Schulz’ values are by a

factor of 10 lower than the values of Linder and

Schmidt for those states which are measured in both

experiments. No clear-cut criticism can be found in

either experiment. However, the values of Linder and

Schmidt must be preferred at this time since they

agree better in order of magnitude with the analysis of swarm experiments (Hake and Phelps, 1967) although

a detailed comparison is not yet possible because the

analysis of swarm experiments has not been performed

with the proper set of relative cross sections.

An interesting feature of the data can be brought out by plotting the branching ratio of the cross sections

for v = 2 to v = 3 and v=\ to v = 2 vs quantum number of the compound state as is done in Fig. 68. Both curves show an enormous rise as the quantum number v' is lowered, indicating that a given compound state (especially for low quantum numbers, v') prefers to decay to the lowest possible state of the neutral molecule. The lowest possible state of the neutral molecule

is reached by the emission of an electron with the

highest possible energy, in the reaction 02_—>02 (a)+e.

A high-energy electron penetrates the potential barrier

with a higher probability than a low-energy electron.

Thus the emission of a high-energy electron is favored.

For d-wave scattering which is involved in the present

reaction, the barrier penetration is proportional to E5/2 (Blatt and Weisskopf, 1952), where E is the energy of the electrons.

When the ratio of electron energies of the ejected

electrons leading to various decay channels is large

(as is the case at low quantum numbers v') a large

branching ratio results. It should be noted that the

branching ratio for low-lying vibrational states in N2 and CO is close to unity. This results from the fact that

Fig. 68. Ratio of vibrational cross sections vs quantum

number, v', of compound state. From data of Linder and Schmidt

(1971b).

94
Fig. 69. (a) Approximate potential energy curves for O2 and O2-

. The O2-curve should have its minimum at 1.341 A (Celotta et al., 1972). The center of the v' = i state is located at 0.091±0.005 eV and it has a fine structure splitting ( 113/2 —111/2) of 20±2 meV (Land

and Raith, 1973) . The v = 3 level of C>2 (X 32g~) is coincident in energy with the v' = 8 level of 02~(X 2ng) (Spence and Schulz, 1970)

[From Boness and Schulz (1970) .3 (b) Ab initio calculations of adiabatic potential energy curves for O2-

. [From Michels and Harris (1971).]

the ratio of energies of the ejected electrons is also close to unity since the compound state in N2 is located near 2.3 eV and the spacing of vibrational levels is about 0.3 eV. Thus the barrier penetration in N2 does

not differ much for the decay channels leading to the

low vibrational states. The widths of the »' = 4— 10 vibrational states of 02~(X 2ns ) have been calculated by Koike and Watanabe (1973) who find a value of 0.004 meV for the

i>'=4 state. This value has a confidence limit of a factor

of about two (Watanabe, private communication) and

thus it is in good agreement with the estimate of 0.002 meV made by Herzenberg (1969) from the

absolute magnitude of the vibrational cross section in

02

.

The calculated values of Koike and Watanabe are

listed in Appendix X.

3.

Potential Energy Curve for 0<r(X 2U0 ) Using a Morse-function representation together with

parameters derived from electron spectroscopy, Boness

and Schulz (1970) derived the potential energy curve

for the 02-(X 2nff ) state. This curve, together with the curve for the ground state of 02 (X 3 2ff-

), is shown in

Fig. 69(a). The curve is drawn so that the v=3 level of 02 (X 3 2ff~) coincides in energy with the v' = S level of 02-(X 2nff ). This coincidence has been established by

Spence and Schulz (1970) and by Linder and Schmidt

(1971). In order to bring the 02-curve into agreement

with the results of Celotta et al. (1972), it should be

shifted to smaller intemuclear separations by 0.036 A,

so that the minimum of the potential energy curve would be at 1.341 A. Ab initio calculations for the low-lying potential

energy curves have been performed by Michels and

Harris (1971) and by Krauss, Neumann, Wahl, Das,

and Zemke (1973). The agreement between the two

sets of theoretical calculations appears to be good. The

set by Michels and Harris is shown in Fig. 69(b).

4.

Equilibrium Intemuclear Separation and Electron

Affinity. Photodetachment Spectroscopy

As in the case of NO, the electron affinity of 02 was a matter of dispute for a long period of time. The various

values have been summarized, as of 1970 by Boness

and Schulz (1970). At that time it appeared that only

the value of Pack and Phelps (1966), obtained from

drift-tube studies of' attachment and detachment

coefficients in thermal equilibrium, was free of serious

objections. The value of Pack and Phelps (0.43 eV)

has recently been confirmed in a conclusive experiment

involving photodetachment. The value of Celotta et al. (1972) is 0.440±0.008 eV. Other recent values for the electron affinity con- verge on the above value. Among these are the experiments of Nalley and Compton (1971), and those of Berkowitz et al. (1971) as interpreted by Chantry

(1971).

The photodetachment experiment of Celotta et al. (1972) also gives a value of the equilibrium internuclear separation, re = 1.341±0.010 A, making obsolete

95
Table IX. Parameters of 02~(X 2nff )

. a

Celotta et at. (1972)

Boness and

Schulz

(1970)

Linder and

Schmidt

(1971b)

Gray et al. (1971)

0 Equilibrium separation, re A 1.341±0.010 ... ... ...

Electron affinity, eV 0.440±0.008 ... ... ... Be (cm"1) 1 . 17±0.02 ... ... ...

hue (meV) ... 135 135 140

hweXe (meV) ... 1.5 1.0 3.0

a Additional features: The fine-structure splitting is 22 ±2 meV (Land and Raith, 1972) .

(1

the previous determination of Boness and Schulz

(1970), obtained by use of Badger’s rule from the

vibrational spacings of O2-

. Table IX lists the parameters for Oi~{X 2IIff ) deduced

from photodetachment spectroscopy and from electron

impact spectroscopy. It is seen that the values deduced

from these two types of experiments complement each

other. The value deduced by Boness and Schulz (1970)

from the vibrational spacing of 02“ using Badger’s

rule (i.e., re — 1.377 A) is not listed since the value

deduced from photodetachment spectroscopy is considered more reliable. From the foregoing discussion it should be fairly

obvious that photodetachment spectroscopy is a powerful tool for determining electron affinities and the

structure of negative ions. In both of the cases in which

a stable negative ion exists, namely O2 and NO, no

evidence exists for excited negative ions lying below the

neutral species, i.e., only one electronic state exhibits a

positive electron affinity. Photodetachment experiments

do not, however, rule out the possibility of the existence

of excited states of C>2~ which have a large equilibrium

internuclear separation. The calculations of Michels and

Harris (1971) show that only the X 2Hg state of 02“

lies below the ground state of O2 . Thus one must con- clude that the only stable state of O2-

which lies energetically below the ground state of O2 is the X 2Ug state. Figure 69(b) shows the potential energy curves for

02“ as calculated by Michels and Harris (1971). In

addition to the X 2IIff state, Michels and Harris find 12

other attractive states arising from the limit 0+0~. All

these states are qualitatively similar, exhibiting shallow

potential wells at large internuclear separations (1.8-

2.0 A). The existence of a large number of autodetaching

states, O2-

, is consistent with the experiments, on

associative detachment (Ferguson, 1968). The thermal

rate constant for the associative detachment reaction,

0~+O—»02~—O2 +c, is large [Ferguson (1968) gives a value of 3X 10-10 cm3 sec

-1 at 300°KJ, and it is reasonable to suppose that some of the O2-

states shown in

Fig. 69(b) serve as intermediates.

Recently, Lineberger and Patterson (1972), using

two-photon photodetachment spectroscopy, discovered an excited state of a negative ion which lies below the

ground state of the neutral molecule. The molecule is C2 . The ground state of the negative ion, C2~(2 Sff+

) lies ~3.5 eV below the neutral ground state, C2

1 Sff+. About 2 eV above C2~(2 Se+

) there is an excited state of the negative ion, C2-

(

2 2M+). It may be of interest to study such systems using electron spectroscopy to obtain complementary data.

5. Three-Body Attachment in O2 Three-body attachment, i.e., the reaction e+202—> ( 02-+C>2 , is now known to proceed via the X 2Ug

' compound state of O2 . The reaction can therefore be 1 written as a two-step process: e+02—

02~*, followed by

'

Fig. 70. The three-body attachment coefficient of production

of O2-

in O2 in comparison with the theory. The theory is normalized to the experimental data at the second peak. The vibrational

levels of the 02”(X 2ne) state are indicated by the lines on top. The structure in the three-body attachment coincides with the

positions of the vibrational states of O2-

. This figure shows that three-body attachment on O2 proceeds via the low-lying com- pound state of O2 . QFrom Spence and Schulz 1972) .3

96
Fig. 71. The cross section for 0~

formation by dissociative attachment

in O2 . The value of Craggs et al. (1957)

(— •-) is undoubtedly too high. The

values of Buchelnikova (1959) ( ), of Schulz (1962b) ( ), of Rapp et al. (1965) ( ) , and of Christophorou et al. (1965) ( —) all agree very well. [From

Chen (1969).]

O2 *

2 KD2 “l- O2 . Here, Ch-* denotes a particular

vibrational level of the O2- (X 2II0 ) state. The general

features of this model have been deduced by Chanin,

Phelps, and Biondi (1962) who clearly established the

three-body nature of the process from their swarm data.

The modern approach to the theoretical considerations

is due to Herzenberg (1969). The swarm experiments of Chanin et al. show a smooth variation with energy of the three-body attachment coefficient as would be

expected for swarm experiments.

If one performs -an experiment with essentially monoenergetic electrons, the three-body attachment coeffiFig. 72. The dependence on temperature of the peak dissociative attachment

cross section in O2 . Shown are the results of Spence and Schulz (1969) , of O’Malley

(1967), and of Henderson, Fite, and

Brackmann (1969). [From Spence and

Schulz (1969).]

300 500 1000 1500 2000 2500

Temperature, °K

97
Fig. 73. Temperature dependence of energies of onset and

energies at which peak of dissociative attachment occurs in O2 . Shown are the results of the same authors as Fig. 72. [[From Spence

and Schulz (1969) .]

cient shows pronounced structure at the positions of the

vibrational levels of the O2-

system. The experimental

results of Spence and Schulz (1972) are shown in

Fig. 70, in comparison with the theory. The good agreement between the energy levels of the Of system obtained from elastic scattering (shown on top of Fig. 70)

and the positions of the peaks is convincing evidence

that the process proceeds via the 02~(X 2IIff ) state.

B. Dissociative Attachment (4.4-10 eV): 2IIM State

Dissociative attachment in 02 has been studied in

great detail and Fig. 71 shows that good agreement

Fig. 74. Cross section for excitation of the 02(0 yAg) metastable

state. Shown by the points are the data of Linder and Schmidt

(1971) and of Trajmar, Cartwright, and Williams (1971). The

solid curve, due to Burrow, shows that portion of the cross section

to the a

1A0 state which proceeds via the 02“(2nu) state. The cal- culated curve represented by the solid line is normalized to the experimental value of Trajmar et al. at 7 eV. TFrom Burrow

(1973).]

exists between the results of various experiments. The

cross section for 0~ production starts rising near 4.4 eV,

reaches a maximum of about 1.3 X10-18 cm2 at 6.7 eV,

and then drops. No structure of any kind has been

detected in this cross section, nor is there a signal

below 4.4 eV at room temperature (the theoretical

onset for the reaction is about 3.6 eV), to a sensitivity

0.1% of the peak cross section. Spence and Schulz

(1969) and Chen (1969) have reviewed the subject

matter recently.

ELECTRON ENERGY, (eV)

Fig. 75. Derivative of transmitted current vs electron energy

in O2 . Structures 1-17 are interpreted as resonances whose grandparent is the ground state of O2L A well-developed progression

of ten resonances, marked band “a”, appears near the end of the spectrum. The grandparent of band “a” is the a

4nu state of 02+. [From Sanche and Schulz (1972).]

Noteworthy are the studies of the dependence on gas

temperature of the onset and the absolute magnitude

of the dissociative attachment cross section. These

studies, performed by Henderson, Fite, and Brackmann

(1969) and by Spence and Schulz (1969) show that the

magnitude of the cross section increases as the gas

temperature is raised and that the onset is lowered at higher temperatures. Figures 72 and 73 show the

results of these studies.

98
The single peak at 6.7 eV suggests that a single com- pound state, 2Uu , is responsible for dissociative attachment around 6.7 eV, although many more compound

states exist in this energy range. This view is reinforced

by the parametrization study of O’Malley (1967),

who used the shape and the magnitude of the experimental cross section at room temperature and the temperature dependence to arrive at the shape of a single

potential energy curve and the value for the width of the

state. It is pointed out by O’Malley, and confirmed

experimentally by Henderson et al. (1969) that the

temperature effects in 0“/02 production can be ex- plained solely on the basis of the vibrational excitation

of the target molecule, and that rotational excitation

does not play a significant role. Vibrationally excited molecules have a large FranckCondon region and if the electron is captured while the

O2 molecule is at a large internuclear separation, the

survival probability for negative ion formation is enhanced. As a result, the dissociative attachment cross section increases for higher vibrational states. The angular distribution of the O

-

ions resulting

from electron impact on O2 in the energy range 5.75-

8.40 eV has been studied by Van Brunt and Kieffer

(1970). They find that the experimentally observed

angular distributions can be explained most simply in

terms of a transition to a single 2IIM repulsive state of

O2-

. They arrive at this conclusion by comparing the

experimentally observed angular distributions with the

theory of O’Malley and Taylor (1968) and the symmetry arguments of Dunn (1962). The interpretation in

terms of a single compound state is consistent with the

evidence coming from the temperature dependence of dissociative attachment and also with the measure- ments of the 0“ kinetic energy (Schulz, 1962b; Chantry

and Schulz, 1967). Van Brunt and Kieffer (1970) do

not exclude the possibility that another closely spaced

resonance also contributes, but they find this alternative

less attractive.

Burrow (1973) has recently measured the dis- sociative attachment cross section from the a

1Ag state of 02 , i.e., the reaction eH- 02 (a 1Aff )—>02-

(

2nt4 )-^

0

_

(

2P)H-0(3P) and finds that this cross section is larger by a factor of about 3.5=1= 1 compared to the

ground-state dissociative attachment cross section.

This measurement, coupled with an analysis based on

O’Malley’s theory, enables Burrow to calculate that

portion of the excitation cross section to the a

lAg state which proceeds via the 2IIU state, i.e., the reaction

e+02 (X %“)—*02-

(

2nu )—>02 (a lAg )+e. The contribution from the decay of the compound state is found

to be a large portion of the total excitation cross section at its maximum. The energy range over which

this mechanism is important, together with experimental measurements of the a

xAg excitation function, are shown in Fig. 74. The most likely means of excitation to the 1 Ag state from threshold to 5 eV and above 15 eV is provided by nonresonant exchange scattering. The cross section for this process has been calculated by Julienne

and Krauss (1972) using the Ochkur-Rudge approximation to the exchange amplitude. The calculated cross section is somewhat smaller than the experimentally

measured values.

Wong, Boness, and Schulz (1973) have recently

observed vibrational excitation to the v= 1, 2, 3, and 4

levels of the electronic ground state of 02 , in the energy

range 4-15 eV, with a peak near 9 eV. For an interpretation of this process, Wong et al. invoke some of the

O2- compound states which exist in this energy range,

e.g.,

2 2u

~, 42w_

, and 2IIU states and possibly others.

C. Core-Excited Resonances

The only information regarding core-excited reso- nances in O2 comes from the transmission experiments

of Sanche and Schulz (1972). Figure 75 shows the

derivative of the transmitted current vs electron

energy in the range 8-13 eV. The structures are labelled

and are listed in Appendix XI. Because of the extreme

complexity of the spectrum, especially in the energy

range 8.5-12 eV, Sanche and Schulz were not able to identify the structures in detail. The structures (1-1') and (3-3'), spaced 220 meV

apart probably have as a grandparent the 02+ (X 2II{7 ) state, which has a spacing of 232 meV. These two

resonances thus consist of two electrons in ( 3sag ) Rydberg otbitals, attached to the X(2Tlg ) core. The

“binding” of the two electrons, i.e., the energy difference

between the lowest resonance (8.04 eV) and the

02+(X 2Ug ) state, is 4.02 eV, a number similar to that

found in other molecules (see Table X).

Structures 2 and 4 lie 40±5 meV above structures

(1-1') and (3-3'), respectively. They could reflect spin-orbit splitting of the 2IIe state of O2-

into a

2n3 /2 configuration for resonances (1-1') and (3-3') and a

2nl/2 configuration for resonances 2 and 4. The observed

doublet spacing is larger than the value of 24 meV

for the splitting of the ground state of C>2+.

1. Band “a”

At higher energies a well-developed progression of ten resonances appears in the spectrum starting at 11.81±0.05 eV. Sanche and Schulz (1972) compare the

vibrational spacings and Franck-Condon probabilities

of band “a” with those of the <z 4IIu grandparent

state of C>2+. They find that there is remarkable agree- ment, whereas no such correspondence can be found

when the experimental data are compared with other

states of 02+

, i.e., the X 2IIff , A 2Uu , b

4 2y, and B 2 2y

of 02+. This suggests that band “a” results from vibrational structure of a

4IIW Rydberg negative ion, formed by the

addition of two Rydberg electrons of the 3sag orbital

symmetry to a 02+ core in the a

4IIU valence excited

state. The likely parents of the O2-

state could be

99
formed by the addition of a single 3sag electron to the

02+ (a 4nM ) core, thus forming 3II and 6II Rydberg

states. These states lie at 12.50 eV (

3n) and 12.24 eV

(

6n), respectively, and the observed progression lies about 0.6 eV below the 6n state. Since a value of 0.6 eV

is a reasonable value for the electron affinity, Sanche

and Schulz (1972) consider this a further confirmation

that the 3,5n states of 02 are the parents of band “a”. Again, the “binding” of the two 3sag electrons to the

grandparent is about 4.4 eV.

The quantum number of each vibrational level

listed in Appendix XI is determined by fitting the

Franck-Condon probabilities of the 02 ion to those of the 02+ ion. The zeroth level of the 02~ progression

cannot be observed because its Franck-Condon

probability is small.

2. Band “b”

Another band of 02“ states (band “b”) consisting

of a progression of four vibrational members has been

observed above ionization (Sanche and Schulz, 1972)

and is listed in Appendix XI. In this case the vibrational

spacings are close to those of the b

2 2

_

state of 02+. The 3 2ustate which lies 0.210 eV above the zeroth

level of band “b” and constitutes the lowest Rydberg

excited state belonging to the b

42pstate of the positive

ion system is the suggested parent for this progression.

VII. CONCLUSIONS

In this section we summarize some of the features

discussed in the text, not by molecular species, but by

the process involved.

A. Shape Resonances

All molecules discussed in this review exhibit shape

resonances associated with the ground electronic state. These can be understood by referring to Table VIII.

Listed are the molecular orbital configurations of the

ground state of the respective molecule; the designation

of the ground state; the lowest vacant orbital into

which the electron attaches to form the shape reso- nance; the designation of the compound state; and the

dominant electron partial wave responsible for forming

the compound state. The angular distribution measurements and the

widths of compound states can be understood in terms

of the partial wave which is dominant. In homonuclear

diatomic molecules, having a center of symmetry, the

allowed values of the angular momentum in the partial wave are either all even or all odd. Therefore it is unlikely that higher allowed partial waves, beyond those

indicated, provide a significant contribution. In

heteronuclear diatomic molecules, where there is no

center of symmetry, one has to consider mixtures of

partial waves. The dominant mixtures are indicated in

Table VIII. For those molecules for which the lifetime

of the compound state is short compared to the rotation

time (all listed molecules except 02 ), the angular dis- tribution measurements show the behavior characteristic of the partial waves indicated. In heteronuclear

molecules, the admixture of the two components must

be adjusted properly in order to obtain agreement with

the > experiments, as has been done by Read (1968)

for CO. Read (1968) has shown that “pure” partial

waves, i.e., pa, pir, da, dir, and d8 exhibit the characteristic shapes for p waves and d waves, in the sense that a minimum exists at 90° for the pa and pir waves and a maximum exists at 90° for the da, dir, and db waves. However, the detailed shape is somewhat

different from that of p and d waves: the pa and pir waves do not lead to zero cross sections at 90°, and

neither do the da, dir, and db waves show a zero near 60°. When the lifetime of the compound state is comparable to or long compared to the rotational time,

then the angular distribution becomes nearly isotropic, as is the case in 02 , and little information can be gained

from angular distribution measurements, beyond the

lifetime considerations.

The mixture of partial waves which one has to consider in the case of CO and NO contains p-wave components in the partial wave. Because the p-wave component leads to a much lower barrier than a d wave, the

decay via the ^-wave barrier is favored over escape via

the d-wave barrier. Although d waves may be more

important in the interior of the molecule, the p wave may dominate the decay and thus be responsible for the angular distribution and lifetime. These considerations explain the shorter lifetimes of the compound

states in CO and NO, compared to N2 and 02 .

B. Core-Excited Shape Resonances

Singly or doubly excited states of molecules also can bind an extra electron by the centrifugal barrier, thus

forming shape resonances. The most extensive study

has been made for the case of N2 , in which the singly

excited valence states, A 3 2u+ and B 3IIff , have as- sociated shape resonances. The progression of vibrational levels of these shape resonances are often long,

exhibiting up to 18 vibrational states. These core- excited shape resonances have properties which are very

similar to shape resonances associated with the ground

state. Core-excited resonances consisting of a doubly

excited core plus an electron also have been postulated,

for example in N2 near 22-eV energy.

Although other molecules have not been studied in sufficient detail, it can be expected that core-excited

shape resonances are the rule rather than the exception

and that future energy level diagrams of negative

molecular ions will show a fantastic number of com- pound states. It should be noted that repulsive states of molecules

also can have associated shape resonances, as is the case in H2 .

100
C. Binding of Rydberg Resonances

A recurrent theme throughout this review is the

observation that most core-excited Feshbach resonances

are associated with Rydberg excited states of the

molecule. These states can be considered as being

formed by the attachment of two electrons in Rydberg

orbitals to the positive ion core, which we call the

“grandparent.” The lowest configuration that is possible

contains the positive ion core plus two 3s<rg electrons.

Table X lists the “binding energy” of these two elec- trons to the various positive ion cores of H2, NO, CO,

N2 , and 02 . The “binding energy” is determined by

taking the difference between the energy of a particular

state of the positive ion and the experimentally observed energy of a particular resonance which we

associate with this positive ion core. The association

between the positive ion core and the resonance comes

from a comparison of the vibrational spacings and

Franck-Condon factors. The data used for constructing

Table X are taken from Sanche and Schulz (1972) and

are fully discussed in the body of this review.

It is obvious from Table X that all the molecules

listed have binding energies for the two 3scrg electrons

of about 4 eV.

Table X. “Binding” energy of two 3s<rg electrons to grandparents.

Molecule

Positive ion Associated resonance Energy

eV

“Binding”

energy

State eV

Energy

eV

h2 X 22« + 15.42 11.32 4.1 n2 XV + 15.51 11.48 4.03 a 2nu 16.62 12.64 3.98

CO X 22+ 14.1 10.04 4.1 a m 16.6 13.95 • • • NO 9.27 5.04 4.23

&

3n 16.56 12.36 4.20 a m 18.32 14.19 4.23 b *n 21.72 17.51 4.21 o2 xma 12.06 8.04 4.02

a

4nu 16.10 ~11.69a 4.4

18.16 14. 27b 3.9

a The level v = 0 is not observed. The value given is an extrapolation.

b The assignment as 2=0 is uncertain.

D. Thresholds of Inelastic Cross Sections

It is pointed out in Sec. IIIB2 that the threshold

behavior of inelastic cross sections is often dominated

by nearby resonances. Both core-excited shape reso- nances (which lie above the electronic state) and

Feshbach resonances (which lie below their parent)

are important. Sometimes, the influence of these two

types of resonances can be distinguished and energy

ranges can be specified which are dominated by the

influence of one or the other resonance. This is the case

for the 2

Z S excitation function of helium. In other

cases, the threshold is dominated only by a nearby

shape resonance (E 3 2ff+ state in N2 ). In still other

cases the threshold behavior is dominated by a Feshbach resonance lying below the respective excited state

(6 3 2+ state in CO). The. width of the Feshbach reso- nance appears to be a dominant factor. ACKNOWLEDGMENTS

The author is indebted to many people and to many

agencies who made possible his participation, over the

past eighteen years, in the exciting developments

partially described in this report. Support for this work came at various stages from the Westinghouse Research

Laboratories (1954-1966), from the National Science

Foundation, the Defense Atomic Support Agency, the

Advanced Research Projects Agency, and the Army

Research Office, Durham. To these agencies go the

thanks of the author for providing the funds which

enabled him and his colleagues to participate in the

progress of this field. Needless to say, many other

advances, not reported in this survey, resulted from the

above-mentioned support.

The scientists from whom the author learned about

atomic collision processes along the way include U.

Fano, E. Gerjuoy, A. Herzenberg, A. V. Phelps, H. S. Taylor, and many others.

The author received comments, suggestions, and

corrections from J. Comer, U. Fano, E. Ferguson,

F. Linder, C. Kuyatt, C. Lineberger, P. D. Burrow, A.

Herzenberg, A. V. Phelps, H. S. Taylor, and M. J. W.

Boness and wishes to express his thanks to them for reading portions of the manuscript.

A portion of this review was written while the author

enjoyed the hospitality of JILA and special thanks go to L. J. Kieffer for his interest in this review, for carefully

reading the whole manuscript, and for suggesting many

changes and corrections. Mrs. L. H. Volsky of JILA

and Mrs. M. R. Harrison of Yale provided editorial as- sistance. Lastly, the author is greatly indebted to his

wive, Rose, whoselflessly tended to the problems of life, the family, and the home, and gave up a great many

things for the cause of science.

101
APPENDIX I Comparison of the values obtained by different authors for the H2~ states (eV).

Vibrational

quantum number

(H2~)

Transmission Inelastic Theory

Eliezer

et al.

( 1967 ) a

Sanche

and Schulz

(1972)

Kuyatt

et al. (1966)

Comer

and Read

(1971a)

Weingartshofer et al. (1970)

Bands “a” and “d! 0 11.32 11.28 11.30 11.30 11.32

1 11.62 11.56 11.62 11.62 11.62

2 11.91 11.84 11.91 11.92 11.91

3 12.19 12.11 12.19 12.20 12.18

4 12.44 12.37 12.45 12.46 12.44

5 12.68 12.62 12.68 12.70 12.68

6 12.86 12.89 12.93

7 13.10

8 13.28

Band “b”

2 11.27

3 11.47

4 11.63

5 11.75

6 11.85

7 11.96

Bands “c” and “e”

0 11.43 11.46 11. 19b 11.50 11.46

1 11.74 11.72 11.50b 11.79 11.75

2 12.03 11.99 1 1 . 80b 12.08 12.03

3 12.32 12.27 12.07b 12.38 12.31

4 12.58 12.53 12.58

5 12.83 12.77 12.84

6 13.06 12.97

Band “f”

Golden (1971)

0 13.66 13.62 13.63

1 13.94 13.91 13.93

2 14.20 14.19 14.20

3 14.45 14.46 14.47

4 14.69 14.72 14.70

5 14.93 14.97 14.92

6 15.18 15.21

7 15.43 15.44

8 15.65 15.66

9 15.85 15.87

10 16.07

11 16.26

Band “g”

15.09

15.32

15.57

15.77

a The theoretical values of Eliezer, Taylor, and Williams (1967) for band “a” were incremented by 0.25 eV

for purposes of direct comparison with the experimental values of Sanche and Schulz (1972).

b From Joyez, Comer, and Read (1973).

102
APPENDIX n

Vibrational

quantum

number (D2“)

0

123

4

5

6

78

9

10

Comparison of the values obtained by different authors for D2“ states (eV).

Transmission

Sanche Kuyatt

and Schulz et al. (1972) (1966)

Inelastic

Comer and

Read

(1971a)

Transmission

Inelastic

Vibrational Sanche Kuyatt Comer and

quantum and Schulz et al. Read

number (D2“) (1972) (1966) (1971a)

Band “a” Band “c”

11.34

11.56

11.76

11.97

12.17

12.36

12.55

12.71

12.88

13.05

13.22

11.28

11.48

11.69

11.89

12.09

12.28

12.47

12.64

12.85

11.32

11.54

11.75

11.96

12.15

12.32

12.48

12.61

12.75

1 11.67 11.65

2 11.89 11.87

3 12.09 12.07

4 12.26 12.23

Sanche and Schulz (1972)

Band “f” Band “g”

0 13.66 15.05

1 13.86 15.22

2 14.06 15.39

3 14.25 15.55

4 14.43 15.71

5 14.57

APPENDIX m

Relative branching ratios for the decay of resonance series “a” in H2 in terms of absolute cross sections (10-17 cm2 ). The estimated error for the cross sections is in the order of 20%.

Exit channel v'=0 v'=l v' = 2 v'=3 v'=4 v' = 5 W2 +v=2 . .

0.27 0.39 0.09 0.14 0.14

v= 1

. .

0.41 0.29 0.39 0.18 0.10

i>=0 0.67 1.4 0.76 0.21 . .

. .

b

3 2u+ a 11.02 eV • • • 0.11 0.10 0.042 0.020 0.008

10.76 eV 0.031 0.087 0.063 0.039 0.015 ... 10.47 eV 0.042 0.063 0.048 0.024 0.007 . .

10.17 eV 0.033 0.045 0.022 0.011 0.004 . .

b

32u+—Integrated values 2 .

2.5 2.5 1.4 1.0

v=5 • • • 0.09 . .

. .

. .

. .

v=4 0.04 0.2 0.06 0.02 ... . .

v=3 0.14 0.23 0.02 . .

. .

v=2

v= 1 v=0 Pronounced interference structure

a Within an energy band of A£^60 meV. From Weingartshofer et al. (1970).

103
APPENDIX IV

Energies of resonances in N2 (11-15 eV).

Feature Differential elastic Trapped Total

number Transmission and inelastic electron metastable E %+, a" 1 V

Sanche and Heideman Lawton and

Fig. Schulz et al. Comer and Read Hall et al. Pichanick Mazeau et al. 42 (1972) (1966a) (1971b) (1970) (1973) (1972b)

“b” 11.47-11.51 11.48 11.48

11.74-11.78 11.75 11.75 band “b”

12.02

3 11.92 11.87 11.87 11.87 11.90

4-4' 12.18-12.27 12.205 12.25 12.12/12.25 12.14

5 12.64 12.59 12.54

6 12.87 Ehrhardt and Will- 12.78

mann (

1 2e+

) 12.80

“c” 13.00 13.0 13.03 12.98

13.23 13.24 13.21

13.50 13.52 13.44

13.70 13.66

“d” 13.88

14.12 14.2 13.73

14.36 13.86

14.57

All structures are Feshbach-type resonances except structures 3 and 4-4', which are identified as shape reso- nances. Additional shape resonances have been observed by Mazeau et al. (1972b) at 12.40 eV in the E 3 Sff+ (v= 1)

channel and at 12.70 eV in the E 3 2ff+ (v = 0) channel.

APPENDIX V

Energies and spacings of shape resonances connected with the B 3IIff state in N2 . Transmission B 3II9 decay channel (Mazeau et al., 1972c)

(Sanche and Schulz, 1972) Energy,0 eV

Energy,a eV Spacing,15 meV v= 1 v=2 v = S v=4 v—5

9.070

9.23 9.220 9.155

9.35 130 9.360 9.300

9.49 125 9.500 9.445 9.400 9.365

9.61 120 9.635 9.590 9.540 9.505

9.73 120 9.760 9.730 9.675 9.645 9.600

9.85 115 9.885 9.860 9.810 9.780 9.730

9.96 115 10.005 9.980 9.940 9.910 9.860

10.07 110 10.120 10.095 9.065 10.035 9.990

10.18 105 10.200 9.175 10.155 10.115

10.29 105 10.305 9.285 10.265 10.230

10.39 100 10.405 9.395 10.375 10.345

10.49 100 10.505 9.495 10.480 10.450

10.58 90 9.595 10.575 10.555

10.67 90 9.695 10.670 10.655

10.76 90 10.765 10.745

10.85 85 10.850 10.835

10.93 85 10.930 10.920

11.02 85 11.000

11.075

11.150

104
APPENDIX V—Continued

Energies of shape resonances connected with the A 3 2„+ state. A 3 2w+ decay channel (Mazeau et al., 1972c) d

v—2 3 4 5 6

8.225 (15)

8.315 (15) 8.307 (10)

8.415 (10) 8.415 (10) 8.395 (10)

8.515 (10) 8.522 (10) 8.503 (5)

8.610 (10) 8.620 (10) 8.595 (5) 8.603 (5) 8.553 ( 5 ) 8.705 (10) 8.715 (5) 8.690 (15) 8.698 (5) 8.653 (10)

8.800 (10) 8.800 (10) 8.778 (15) 8.785 (5) 8.745 (10)

8.880 (5) 8.878 (15) 8.870 (5) 8.837 (10)

8.960 (10) 8.950 (15) 8.958 (5) 8.925 (5)

9.040 (5) 9.030 (15) 9.040 (5) 9.008 ( 5 ) 9.120 (10) 9.110 (15) 9.115 (5) 9.088 ( 5 ) 9.195 (10) 9.178 (15) 9.183 (10) 9.168 ( 5 ) 9.263 (10) 9.245 (15) 9.250 (5) 9.238 ( 5 ) 9.312 (15) 9.315 (5) 9.300 ( 5 ) 9.375 (15) 9.373 (5) 9.358 ( 5 ) 9.428 (15) 9.430 (10) 9.418 ( 5 ) 9.480 (10) 9.482 (10) 9.468 ( 5 ) 9.538 (10) 9.515 ( 5 ) 9.575 (10) 9.562 (10)

a Absolute error of the energy is ±0.05 eV. Relative error =1=0.003 eV.

b The spacings are given to the nearest 5 meV.

c Error approximately dblO meV (see Mazeau et al., 1972c).

d In parentheses are given the probable errors, in meV.

APPENDIX VI

Energies of features in CO (10-15 eV).

Feature

number

Transmission

Sanche and Schulz

(1972)

Differential

Comer and Read

(1971c) Mazeau et al. v= 1 v=2 Designation

^ 17 / Zd ) b

3 2+

, *> = 0

a

1-1' 9.98-10.04 10.02 10.02 10.04b 2 Z+ d = 0

2-2' 10.24-10.29 10.28 v= 1 3 10.42 10.38 10.46

4-4' 10.65-10.72 10.80 10.7 2n

5 11.27 11.3

6 12.17 12.2

Band “a” 13.95

14.155

14.345

14.530

14.705

14.870

a The threshold for the b

3 2+ state is 10.39 eV.

b Determined from elastic scattering at 90°. The calibration is performed against the (ls2,y2 )

2 S resonance in helium which the authors locate at 19.35=b0.02 eV. QSanche and Schulz find 19.34=1=0.02 eV.]

105
APPENDIX VII

Comparison of vibrational spacings and Franck-Condon probabilities observed for four bands of NOwith

appropriate values for NO+ (X x 2+

) Sanche and Schulz (1972).

Av

Vibrational spacings (meV)

NO- banda NO+(Z 1 S+)

“a” “b” “c” “d” Experimental Theoretical

0-1 286 290 292 282 290

1-2 286 290 288 284 287

2-3 282 284 286 275 283

3-4 275 278

4-5 275 273

Franck-Condon probabilities

NO~ banda NO+(X x 2+)

V “a” “b” “c” “d” Experimental Theoretical

0 0.84 0.57 ... 0.66 0.7 0.48

1 1 1

. .

.

1 1 1 2 0.62 0.64 . .

.

0.7 0.7 0.92

3 0.16 0.24 . .

.

0.19 0.5 0.49

a “a”, “b”, “c”, “d” represent designations of bands, which start at 5.04, 5.41, 5.46, and 6.44±0.05 eV, respectively.

APPENDIX VIII

Resonances in NO and their grandparents (12-18 eV)

(Sanche and Schulz, 1972).

Resonance®

NOenergy eV

Grandparent

NO+

Designation

Energy

eV

Binding

eV

12.36(® = 0)

12.57 (v= 1)

12.73(5)

12.94(5)

5

3n 16.56 4.20

14.19(® = 0)

14.52(5)

a m 18.32 4.13

... cm 20.46

17.51(w = 0)

17.94(5)

B 1n 21.72 4.21

5.04(v = 0) X l2+ 9.27 4.23

a The features marked (z> = 0) are interpreted as the

lowest states of core-excited Feshbach resonances. The

features marked (5) are interpreted as core-excited

shape resonances.

APPENDIX IX

Spacing of vibrational states of O2- X(2nff ) in meV.a

Vibrational

transition

Spence and Linder and

Schulz Schmidt

(1970) (1971b)

Gray

et al. (1971)

4—>5 117 125 128

5—>6 113 123 125

6—>7 110 120 121

7—*8 108 119 118

8-9 106 117 115

9-10 115 113

10-11 113 109

11-12 111 105

12-13 110

13-14 107

14-15 104

15-16 103

16-17 101

17-18 99

Extrapolated

0-1 135 135 140

a The state v' = 8 is located near 569 meV (Linder and

Schmidt, 1971b) and it is nearly coincident with the

v = 3 state of 02 (Spence and Schulz, 1970).
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107
APPENDIX XI

Core-excited resonances in O2 as observed in a transmission experiment (Sanche and Schulz, 1972).

1-1' 2 3-3' 4 5-5'

8.03-8.06 8.12 8.24-8.28 8.34 8.47-8.54

6-6' 7-7' 8-8' 9-9' 10-10'

8.71-8.78 8.90-8.98 9.08-9.11 9.16-9.23 9.36-9.44

11-11' 12 13—13'— 13 14-14' 15-15'

9.53-9.61 9.73 9.86-9.92-9.98 10.43-10.48 10.55-10.61

16-16' 17-17'

10.74-10.82 10.91-11.00

Band “a”

11.81 11.93 12.05 12.17 12.29 v= 1 v=2 v=3 ^ = 4 ^=5

12.40 12.51 12.62 12.73 12.84

v=6 v=7 v—S v — 9 v-10

Band “b”

14.27 14.43 14.58 14.72

•The writing of this review was supported by the National Bureau of Standards, Office of Standard Reference Data, as part of the National Standard Reference Data Program.

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(unpublished).

U. S. GOVERNMENT PRINTING OFFICE : 1973-542-650/55

110
u.s. DEPT, of comm. 1. PUBLICATION OR REPORT NO. 2. Gov’t Accession

BIBLIOGRAPHIC DATA No. SHEET NSRDS-NBS-50

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Resonances in Electron Impact on Atoms and Diatomic

Molecules

5. Publication Date October 1973

6. Performing Organization Code

7. AUTHOR! S) George J. Schulz

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Joint Institute for Laboratory Astrophysics,

National Bureau of Standards, Boulder, Colorado 80302

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Reprinted from Reviews of Modern Physics, Vol. 45, 378-486, July 1973.

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

Two reviews are presented on the energies, configuration and other properties of

resonances in electron impact on atoms and diatomic molecules. Included are discussions of the experimental methods which are useful for studying resonances

and of the results obtained by various investigations. Much of the information

is presented in the form of tables and energy level diagrams.

17. KEY WORDS (Alphabetical order, separated by semicolons) Atoms; compound states; cross-sections;

diatomic molecules; electron impact; energy levels; resonances; temporary negative

ions.

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TO NTIS.

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21. NO. OF PAGES

118

22. Price

$1.35

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