gfi"

°r %.\

*fe NBS TECHNICAL NOTE

"»«u of 901

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Comparison of Theoretical

nd Experimental Photoeffect Data

0.1keVtol.5MeV

C. 2*
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* ST

Comparison of Theoretical and Experimental «; •

Photoeffect Data 0.1 keV to 1.5 MeV ^^?

0[,

J. H. Hubbell

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

and

¥m. J. Veigele

Resource Science, Inc. Colorado Springs, Colorado 80903

C-t 3*

This work was supported by the

NBS Office of Standard Reference Data Washington, D.C. 20234

and

The Defense Nuclear Agency

Washington, D.C. 20305

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

0( 5 NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued April 1976
I •> * - J f

National Bureau of Standards Technical Note 901

Nat. Bur. Stand. (U.S.), Tech. Note 901, 43 pages (Apr. 1976) CODEN: NBTNAE
Comparison of Theoretical and Experimental

Photoeffect Data 0.1 keV to 1.5 MeV

J. H. Hubbell*

National Bureau of Standards

Washington, D. C. 20234

Wm. J. Veigele+ #

Resource Science, Inc.

Colorado Springs, Colorado 80903

Graphs of calculated and experimental atomic photoeffect cross sections as a function of photon energy 0.1

keV to 1.5 MeV are presented for all elements Z - 1 to

94. The calculated results presented are (a) the nonrelativistic Hartree-Fock self-consistent-field (SCF)

results of Veigele, Henry, et al., over the range 0.1

keV to between 1.0 and 8.0 keV for all elements Z - 1 to

94 and (b) the relativistic Hartree-Slater SCF results

of Scofield over the range 1.0 keV to 1.5 MeV for all

elements Z = 1 to 101. The "experimental" data-points

are derived by subtracting theoretical scattering cross sections from total attenuation coefficient measurements

in the literature. Differences between theoretical and

experimental photoeffect data are typically a factor of

two from 0.1 to 1.0 keV, 5-10% from 1.0 to 5.0 keV and 1-5%

from 5.0 keV up to energies, ranging from 20 keV for

carbon up to 500 keV for lead, above which the photoeffect cross section becomes fractionally too small to

be accurately determined from the total attenuation

coefficient.

Key words: Attenuation coefficients, cross sections,

gamma rays, photoelectric effect, photons, x-rays.

1. Introduction

The atomic photoeffect, in which an atom absorbs a photon and ejects an

electron, is the predominate process by which photon radiation is attenuated

by matter in the vacuum ultraviolet (VUV) (10 eV to 100 eV) and soft x-ray

(100 eV to 10 keV) portions of the electromagnetic spectrum. At higher

energies the attenuation is dominated by two other processes, first

incoherent scattering commencing in importance at around 10 keV for the

lowest-Z elements and at a few hundred keV for the highest-Z elements,

Work supported by the NBS Office of Standard Reference Data. Some support

was also received from the Defense Nuclear Agency.

Work done at Kaman Sciences Corp., Colorado Springs, Colorado 80907.

Work supported by the Defense Nuclear Agency.

1
then pair production which proceeds from a threshold of 1.022 MeV

(2 m c

2

) to dominate over all other processes in the high energy limit.

As an example, figure 1 shows the total measured attenuation cross section (small circles) for photons from 10 eV to 100 GeV in copper,

decomposed into the theoretical contributions from the above three

processes: photoeffect (x) , incoherent (bound-electron Compton) scattering

(d ) and pair production (k) , indicating the region where each

predominates . For lower-Z elements the incoherent scattering cross section

dominates over a broader range (for hydrogen, incoherent scattering dominates

the total cross section from a few keV to 100 MeV) and for higher-Z elements

the range of a-r NC0H dominance narrows to the point where for plutonium

(Z - 94) its contribution to the total reaches a maximum of 70% at 1.5 - 2.0

MeV and its relative importance rapidly decreases toward lower and higher

energies. Also shown in figure 1 are two additional processes: coherent

scattering ( G

pnH ) an<* tne photonuclear giant resonance (cpH J) of some significance But which contribute less than 10% to the total cross section

at any given energy.

Pratt, Ron and Tseng [1] have recently extensively reviewed the

existing calculations and measurements of the atomic photoeffect over the

range 10 keV to 100 MeV (including material extending down to 1 keV)

,

complementing an earlier review by Fano and Cooper [2] of theoretical and

measured photoeffect data over the range 10 eV to 10 keV.

In the latter (soft x-ray) region, where the atomic photoeffect can be taken directly from measured total attenuation coefficients with only

small or negligible corrections for the scattering contribution, additional

recent reviews and surveys of experimental photoeffect cross section data

include those by Henke and Tester [3], Hudson and Kieffer [4], [5] and

Zimkina and Fomichev [6]. Higher-energy photoeffect measurements, both

by direct methods (e.g., photoelectron and fluorescence x-ray coincidences)

and by indirect methods (subtraction of scattering and pair-production

contributions from total attenuation measurements) have also been recently

reviewed by Parthasaradhi [7].

In the above and other recent photoeffect reviews, the graphical and/

or numerical comparisons of theoretical and photoeffect data have in each

case been for a limited number of specific elements of interest, over limited ranges of photon energy. Thus we consider it a useful adjunct to

the above reviews, for an over-all perspective, to systematically compare

available experimental total and photoeffect cross sections in the extensive data-collections of Veigele [8] and Hubbell [9] with present state-ofthe-art theoretical photoeffect cross sections for all elements Z = 1 to 94 over the photon energy range 0.1 keV to 1.5 MeV.

For this purpose we have selected the low-energy photoeffect calculations by Veigele, Henry and Bates [8], [10] for Z = 1 to 94 and photon

energies 0.1 keV to from 1.0 to 8.0 keV, and the higher-energy calculations

Figures in brackets indicate the literature references at the end of this

paper

.

2
by Scofield [11] for Z 1 to 101, 1.0 keV to 1.5 MeV. These and some additional photoeffect calculations are listed and described in the

following section.

2. Photoeffect Calculations

Prior to 1960, as discussed in more detail in the review article by

Pratt et al. [1], theoretical numerical tabulations of the atomic photoeffect cross section, including those in the attenuation coefficient

tables of Davisson and Evans [12] and of Grodstein [13], were based

primarily on work (reviewed by Hall [14]) dating from the period 1930 to

1935:

(1) The Stobbe [15] exact nonrelativistic K- and L-shell results

in the point-Coulomb potential,

(2) The Sauter [16], [17] relativistic K-shell Born result in the

point-Coulomb potential,

(3) The Hall [18] and Hall and Rarita [19] high-energy limit

results for the K- and L-shells in the point-Coulomb potential,

(4) Exact relativistic point-Coulomb K-shell numerical results

for six cases (Z - 26, 50 and 84 at 0.35 and 1.13 MeV) by Hulme,

McDougall, Buckingham and Fowler [20], and

(5) A semi-empirical prescription by Slater [21] to take into

account inner-electron screening effects.

Renewed interest in theoretical understanding of the photoeffect

process began in the late 1950' s and continues to the present, resulting

from (a) increasingly exacting photon-interaction needs by the medical,

scientific and engineering communities, (b) availability of high-speed

computers and (c) new higher-accuracy photoeffect and total attenuation

coefficient measurements. New analytical work in this period includes

corrections by Erber [22], Pratt [23,24] and by Gorshkov and Mikhailov

[25] to the theoretical high-energy limit, extension of the relativistic

Born approximation by Gavrila [26,27] and Nagel [28], dipole-approximation calculations in the ultra-soft x-ray region by Cooper [29],

estimates of the quadrupole contribution by Guttmann and Wagenfeld [30],

and additional work more exhaustively reviewed by Pratt et al. [1] and

Fano and Cooper [2].

Based on the above work and further refinements, recent pilot and

systematic numerical calculations of the photoeffect cross section

include the following, listed approximately in chronological order:

(1) Hultberg et al. [31], [32]: relativistic, point-Coulomb,

K shell, 21 elements Z = 1 to 100, 1 keV to 10 MeV,

(2) Pratt et al. [33]: relativistic, point-Coulomb, K shell,

6 elements Z = 13 to 92, 200 keV to 2 MeV,
(3) Ailing and Johnson [34]: relativistic, point-Coulomb, KL-shells, Pb and U, 81 keV to 1.33 MeV,

(4) Matese and Johnson [35]: relativistic, exponential

screening, K-, L-shells, Ag, Hg, Pb and U, 81 keV to 1.33 MeV,

(5) Hall and Sullivan [36]: relativistic, Thomas-Fermi screening, Kshell, Fe, Sn, Po and U, 300 keV to 1.23 MeV,

(6) Rakavy and Ron [37], [38]: relativistic, Fermi-Amaldi screening

for Al, Fe, Sn and W, Thomas-Fermi screening for U, 1 keV to 2 MeV,

(7) Schmickley and Pratt [39]: relativistic, Hartree-Fock-Slater

screening, 14 elements Z « 13 to 92, 10 keV to 5 MeV,

(8) Bell and Kingston [40], [41]: non-relativistic, dipole-length and

-velocity formulations, Hartree-Fock screening, He, 25 to 310 keV,

(9) Combet-Farnoux and Heno [42], [43]: non-relativistic, HartreeFock-Slater screening, Ta, Pt, Au and Bi, 50 to 500 eV,

(10) Manson and Cooper [44] : non-relativistic, Hartree-Fock-Slater

screening, 9 elements Z - 18 to 100, 10 eV to 2 keV,

(11) Brysk and Zerby [45]: relativistic, Dirac-Slater screening, Al

and U, 1 to 150 keV,

(12) McGuire [46]: non-relativistic, dipole-length formulation, HartreeFock-Slater screening, Z 2 to 54, 6 eV to 62 keV,

(13) Amusia et al. [47], [48]: non-relativistic, Hartree-Fock screening,

Ar, Kr and Xe, 15 eV to 1 keV,

(14) Storm and Israel [49]: Brysk-Zerby program [45], Z = 1 to 100, 1 to

200 keV; extended table to 100 MeV by interpolation and extrapolation of

Schmickley and Pratt [39] and Rakavy and Ron [38] theoretical results,

above

,

(15) Cromer and Liberman [50]: relativistic, Dirac-Slater, Kohn-Sham

screening, Z 3 to 98, 5.4 to 22.2 keV,

(16) Veigele et al. [8], [10]: non-relativistic, Hartree-Fock-Slater

screening, Z - 1 to 94, 100 eV to 8 keV,

(17) Kennedy and Manson [51] : non-relativistic, Hartree-Fock and HartreeSlater, dipole-length and -velocity formulations, Ne, Ar, Kr and Xe,

10 eV to 1.5 keV,

(18) Scofield [11]: relativistic, Hartree-Slater screening, Z - 1 to

101, 1 keV to 1.5 MeV, and

(19) Hildebrandt et al. [52], [53]: non-relativistic, revised Slater

screening constants, dipole and quadrupole components given, Z 6 to 54,

5 to 25 keV.

4
In the most recent NBS x-ray cross section tabulation (NSRDS-NBS 29,

covering the energy range 10 keV to 100 GeV) [54], photoeffect cross sections

in the range 10 to 100 keV were obtained from total attenuation coefficient

measurements [9] by subtracting theoretical scattering contributions [49]

except for uranium which was taken directly from the above Rakavy-Ron [37],

[38] theoretical results. Above 100 keV, for all 23 elements in the NSRDSNBS 29 tabulation [54], the Rakavy-Ron results were combined with the highenergy numerical calculations and analytical formulas of Gavrila [26], Pratt

et al. [23], [33] and Hultberg [32] to extend the tabulations up to 100 MeV.

In the McMaster et al. [55], [56] LLL (Lawrence Livermore Lab.) - NBS

x-ray cross section tabulation, source of the 1 keV-1 MeV photoeffect values

in the present ENDF (Evaluated Nuclear Data File, ERDA) tape library [57], the

theoretical values of Schmickley and Pratt [39] were weighted into the iterative cubic log-log least-squares fit of photoeffect cross sections which were

otherwise obtained by subtraction of theoretical scattering contributions from

total attenuation coefficient measurements.

3. Explicit Photoeffect Measurements

In the photon energy range ^ 100 keV to 2.6 MeV, where the above "subtraction method" (total attenuation coefficient measurement minus theoretical scattering contribution) ceases to be useful, there exist a few explicit

measurements of total and subshell photoeffect cross sections, as summarized

by Pratt et al. [1] and by Parthasaradhi [7], with uncertainties of the order

of 4% to 15% or greater. Additional new measurements beyond those listed in

these summaries include:

(1) Sahota [58]: L-shell, fluorescence x-ray detection, U, 145, 192,

662 and 1250 keV,

(2) Allawadhi and Sood [59], [60]: K-shell, fluorescence x-ray

detection, 15 elements Z = 33 to 74, 37 and 74 keV,

(3) Gowda and Sanjeevaiah [61] - [65]: total and K-shell, photoelectron

detection, 8 elements Z = Al to Pb, 145, 279, 412 and 662 keV, and

(4) Goswami and Chaudhuri [66]: total photoeffect, cylindrical-shell

adaptation of the spherical-shell transmission method of Ghose [67], Pb,

662 and 1250 keV.

Because of the substantial inherent difficulties and uncertainties in

the above and earlier explicit measurements, this source of photoeffect data

has as yet been given little weight, as compared with theory, in constructing

photon cross section tabulations, and is not included in the graphical comparisons in figures 2 to 95.

4. Graphical Comparison of Experimental Points with Veigele et al.

and Scofield Theoretical Results

As can be seen^in figure 1, the photoeffect cross section, T, decreases

approximately as E~" from the K absorption edge up to 1 MeV, with a similar

MS dependence at lower energies in the segments between absorption edges
down to 1 keV. Above 1 MeV the photoeffect behavior is seen changing to the

high-energy-limit E~ dependence [17], [22] * [23]. Below 1 keV the slope of

the cross section again decreases, and the cross section, particularly for

medium- and high-Z elements, becomes characterized by outer-subshell maxima

and minima with little interpolable regularity as a function of E and Z.

In the region 1 keV to 1 MeV where t decreases rapidly as a function of

E, relative differences between photoeffect data are difficult to see on an ordinary log-log plot of t vs. E as in figure 1. Thus, in figures 2 to 95 we

have plotted T • ~E , instead of x, which reduces the number of logarithmic

cycles required to display the data and has the effect -of magnifying the

relative differences. The quantity T • E

3 is less suitable for graphing

purposes because of the absorption edges which, for all but the lightest

elements, superimpose an effective positive power of E on the energy-range

1 keV to 1 MeV as a whole for a net over-all dependence x a M! including

absorption edges.

In figures 35-95 (Z >^ 34) the number of logarithmic cycles used was determined for each figure by the x • E

2 maximum and minimum values from the

Scofield data in the range 1.0 keV to 1.5 MeV. As a result, some experimental

points and portions of the Veigele et al. calculated results near 0.1 keV are off-scale and not shown in these figures.

For elements H(Z = 1) to K(Z = 19), in figures 2 to 20, the Veigele

et al. calculated results extend only over the range 0.1 to 1.0 keV and hence

have only the 1.0-keV point in common with the 1.0 keV to 1.5 MeV range of

the Scofield results. For the remaining elements Ca(Z = 20) to Pu(Z = 94) the

Veigele et al results overlap the Scofield results by amounts ranging from

1.0 - 1.6 keV for Kr(Z = 36), Rb(Z - 37) and Sr(Z - 38) up to 1.0 - 8.0 keV

for Pu (Z = 94).

Since the Veigele et al. and Scofield values in this overlap region are

not identifiable as to which is which, numerical values in kilobarns/atom

(without the factor [E(keV) 2

]) at 1.0 and 2.0 keV are listed in table I.

Also in table I are percent differences obtained at 100% x (V-S)/S, where

V and S are the Veigele et al. and Scofield values, respectively, for a given element and energy.

Comparing the Veigele et al. results with those of Scofield at 1 keV,

the agreement is seen to be better than 10% for all elements except for -16%

for Cs(Z = 55) and +31% for Nd(Z - 60), the latter two differences attributable

to displacements in absorption-edge energies. For elements Z = 1 to 59

(excluding Z = 55) at 1 keV, where the photoeffect cross section is primarily

due to the K-, L- and M-shell atomic electrons, the results of Veigele et al. are systematically lower than those of Scofield by an average of 2%. For the

higher-Z elements Z = 61 to 94, where the photoeffect cross section in the

overlap region is primarily due to N-shell electrons, the trend reverses, with

the Veigele et al. results systematically higher than Scofield by an average

of 6% at 1 keV for Z = 61 to 89, and higher by an average of 9% at 2 keV for

Z = 90 to 94.
The experimental points (x's) in figures 2 to 95 are taken from the

automated 8000-data-point file of Veigele et al. obtained from 153 sources for

the period 1920 - 1970 cited and cross-referenced as to element in reference

[8], updated to Jan. 1974. Excluded from this file are data deduced for

elements from measurements made on compounds, and a number of discrepant datapoints. An additional relevant measurement-set reported by Del Grande and

Oliver [68] for uranium at 1 to 10 keV is shown as the circles in figure 93.

A characteristic feature of figures 2 to 95 is the diverging scatter of

experimental points toward higher energies. This divergence, commencing at a few hundred keV for the heaviest elements, occurs when the photoeffect,

obtained by subtracting theoretical scattering cross sections from total

attenuation coefficients, becomes small and similar in magnitude to the

uncertainties in the latter two quantities. Thus figures 2 to 95 indicate,

as a function of Z, approximate upper energy limits for obtaining meaningful

values of the photoeffect cross section from total attenuation coefficient

measurements

.

5. Conclusions

In the graphs in figures 2 to 95, the theoretical results of Veigele

et al. in the region 0.1 to 1.0 keV are seen to represent the experimental

data to within typically 10% to a factor of two, the best agreement being

found for elements available as gases. Differences of this order are attributable at least in part to chemical binding effects on the outer shell

electrons which determine the photoionization cross section in this energy

region

.

In the region 1.0 to 5.0 keV the Veigele et al. and Scofield values

represent the experimental data to within typically 5% to 10%. For the

high-Z elements where the theoretical sets systematically differ from each

other by 5% to 10% in this energy region, the available measurements for Au,

Fb, Bi and U suggest that the theoretical sets would be best joined by taking

the Veigele et al. set below and the Scofield set above the M_ absorption

edge.

Above 5 keV, up to energies ranging from 20 keV for carbon up to 500

keV for lead, the Scofield data, with a few exceptions, can be seen to

represent the available experimental data to within the 1% to 5% "envelope of

uncertainty" obtainable from measurements of the total attenuation coefficient.

Among the exceptions is tellurium (figure 53) for which the Scofield values

are systematically 10% to 30% lower than the extensive measurements of Biermann

(1936) [69], Schulz (1936) [70] and Wrede (1939) [71] over the range 1.3 to

97 keV, but for which the Scofield values agree within 1% with the L-edge

cross section measurements by Nordfors and Noreland (1961) [72] in the region

4.3 to 5.0 keV.

The above (Te) and other examples in figures 2 to 95 point out elements

and energy-regions where further attenuation coefficient measurements, taken

with modern detectors and sample-purities, would afford a more critical test

of present theory and would reduce the uncertainties in present photon cross section tabulations.
The authors thank Dean Kaul for his encouragement of this work, Martin

Berger for suggesting this presentation, Edith Briggs for data preparation

and Larry Bates for programming and computing assistance.

6. References

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[38] Rakavy, G. , and Ron, A., Atomic Photoeffect in the Range Ey = 1-2000

keV, Phys. Rev. 159, 50-56 (1967).

[39] Schmickley, R. D., and Pratt, R. H. , K-, L-, and M-Shell Atomic Photoeffect for Screened-Potential Models, Phys. Rev. 164 , 104-116 (1967).

[40] Bell, K. L., and Kingston, A, E., Photoionization of the Helium Atom,

Proc. Phys. Soc, London, 90, 31-37 (1967).

[41] Bell, K. L., Kingston, A. E. , and Taylor, I. R. , Photoionization of the

IS State of Helium, J. Phys. B 6>, 1228-1236 (1973).

[42] Combet-Farnoux, F., and Heno, Y., Calculation of Photoionization Cross

Sections of Gold and Bismuth Atoms in the Ultrasoft X-Ray Region, C. R.

Acad. Sci., Ser. B, 264, 138-141 (1967).

[43] Combet-Farnoux, F., Photoionization of Heavy Atoms: Theoretical Study

with a Non-Relativistic Central Potential Model, J. Phys. (Paris) 30,

521-530 (1969).

[44] Manson, S. T., and Cooper, J. W. , Photo-Ionization in the Soft X-Ray

Range: Z Dependence in a Central Potential Model, Phys. Rev. 165 , 126-138 (1968).

[45] Brysk, H. , and Zerby, C. D., Photoelectric Cross Sections in the keV

Range, Phys. Rev. 171 , 292-298 (1968).

[46] McGuire, E. J., Photo-Ionization Cross Sections of the Elements Helium

to Xenon, Phys. Rev. 175 , 20-30 (1968).

[47] Amusia, M. Ya., Cherepkov, N. A., Chernysheva, L. V., and Sheftel, S. I.,

Calculation of the Photo-Ionization Cross Section for Argon in the

Hartree-Fock Approximation, Zh. Eksp. Teor. Fiz. 56, 1897-1903 (1969);

Sov. Phys. JETP 29, 1018-1021 (1969).

10
[48] Amusia, M. Ya. , Cherepkov, N. A., and Chernysheva, L. V., Cross Section

for the Photoionization of Noble-Gas Atoms with Allowance for Multielectron Correlations, Zh. Eksp. Teor. Fiz. 60, 160-174 (1971); Sov.

Phys. JETP 33, 90-96 (1971).

[49] Storm, E. , and Israel, H. I., Photon Cross Sections from 1 keV to 100

MeV for Elements Z - 1 to Z = 100, Nucl. Data Tables A 7_, 565-681 (1970).

[50] Cromer, D. T., and Liberman, D., Relativistic Calculation of Anomalous

Scattering Factors for X-Rays, J. Chem. Phys. 53, 1891-1898 (1970).

[51] Kennedy, D. J., and Manson, S. T., Photoionization of the Noble Gases:

Cross Sections and Angular Distributions, Phys. Rev. A 5_, 227-247 (1972).

[52] Hildebrandt, G. , Stephenson, J. D., and Wagenfeld, H. , Photoelectric

Atomic Absorption Cross Sections for Elements Z = 6 to 54 in the Medium

Energy X-Ray Range (5 to 25 keV) . Part I., Z. Naturforsch. , Teil A,

30, 697-707 (1975).

[53] Wagenfeld, H. , Normal and Anomalous Photoelectric Absorption of X-Rays

in Crystals, Phys. Rev. 144 , 216-224 (1966).

[54] Hubbell, J. H. , Photon Cross Sections, Attenuation Coefficients, and

Energy Absorption Coefficients from 10 keV to 100 GeV, Nat. Stand. Ref.

Data Ser., Nat. Bur. Stand. 29 (1969), 80 p.

[55] McMaster, W. H., Del Grande, N. K., Mallett, J. H., and Hubbell, J. H.,

Compilation of X-Ray Cross Sections, UCRL-50174, Sec. 1 (1970), 18 p.,

Sec. 2, Rev. 1 (1969), 353 p., Sec. 3 (1969), 194 p., Sec. 4 (1969) 40 p.

[56] Hubbell, J. H. , McMaster, W. H. , Del Grande, N. K. , and Mallett, J. H.

,

Sec. 2.1 of Ibers, J. A., and Hamilton, W. C, eds., International

Tables for X-Ray Crystallography , Vol. IV (Kynoch Press, Birmingham,

1974) p. 47-70.

[57] Dudziak, D. J., ENDF Formats and Procedures for Photon Production and

Interaction Data, ENDF-102, Rev. Vol. 2, LA-4549 (1971).

[58] Sahota, H. S., Measurement of K-Shell Photoelectric Cross Sections in

Uranium, Phys. Lett. A 33 , 430-431 (1970).

[59] Allawadhi, K. L., and Sood, B. S., K-Shell Photoelectric Cross-Section

Measurements at 36.818 keV in Elements 33 <_ Z <_ 53, Curr. Sci. 42, 852

(1973).

[60] Allawadhi, K. L., and Sood, B. S., K-Shell Photoelectric Cross Sections

for Intermediate Z Elements at 37 and 74 keV, Phys. Rev. A 11_, 1928-

1932 (1975).

[61] Gowda, R. , and Sanjeevaiah, B,, Photoelectric Cross Sections of Al, Cu,

Zr, Ag, Sn, Ta and Pb for 145 keV y Rays, J. Phys. A £, 1041-1045 (1973).

11
[62] Gowda, R. , and Sanj eevaiah , B., K-Shell Photoelectric Cross Sections for

145-keV Gamma Rays, Phys. Rev. A 8. 2425-2428 (1973).

[63] Gowda, R. , and Sanjeevaiah, B., K-Shell Photoelectric Cross Sections of

Cu, Zr, Ag, Sn, Ta, Au, and Pb for 279.1- and 411.8-keV y Rays, Phys.

Rev. A 10 , 1188-1191 (1974).

[64] Gowda, R. , and Sanjeevaiah, B., Photoelectric Cross Sections for 279.1

keV and 411.8 keV y Rays, J. Phys. B _7, 1772-1775 (1974).

[65] Gowda, R. , and Sanjeevaiah, B., The Total and K Shell Photoelectric

Cross Sections for 661.6 keV Gamma Rays, Can. J. Phys. 53_, 846-849 (1975).

[66] Goswami, B., and Chaudhuri, N. , Photoelectric Cross-Sections of GammaRays for Low-, Medium-, and High-Z Atoms in the Energy Range 88 keV to

1.33 MeV, Nuovo Cimento A 24, 49-60 (1974).

[67] Ghose, A. M. , Photoelectric Cross Sections of Gamma Rays for Heavy

Elements, Nucl. Phys. 75, 539-548 (1966).

[68] Del Grande, N. K. , and Oliver, A. J., Soft X-Ray Cross Section Measurements for Uranium, Bull. Am. Phys. Soc. (Ser. 2) 18, 635 (1973).

[69] Biermann, H.-H., The Mass Attenuation Coefficients for Monochromatic

X-Rays in Cellophane, Al, Se, Ag, Cd, Sn, Sb, and Te to 10 £, Ann.

Phys. (Leipzig) 26, 740-760 (1936).

[70] Shulz, K. , The Mass Attenuation Coefficients of Monochromatic X-Rays

for Se, Ag, Cd, Te, Au, Pb, and Bi to about 2 R, Ann. Phys. (Leipzig)

27_, 1-14 (1936).

[71] Wrede, W. , The Mass Attenuation Coefficients for Monochromatic X-Rays

in 24 Elements between C (6) and Ce (58) for Wavelengths from 0.1279

to 1.433 £\ Ann. Phys. (Leipzig) 36, 681-695 (1939).

[72] Nordfors, B., and Noreland, E., The X-Ray L-Absorption Spectra of

48 Cd - 52 Te, Ark. Fys. 20, 1-23 (1961).

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12
Table I. Comparison of veigele et al. [8], [10] and Scofield [11] theoretical

photoeffect cross section values (in kilobarns/atom) at 1.0 and 2.0 keV.

The Veigele et al. values in parenthesis for 2 keV photons in Z = 70, 71 and 72 are interpolated from adjacent energies.

2.0 keV

Veigele et al. Scofield % diff.

T (kb) t (kb)

(Veigele et al. max. energy 1.0 keV)

1.0 keV

z Veigele et al. Scofield % diff.

t (kb) t (kb)

1 0.0109 0.011414 -4.5%

2 .404 .40177 + .8

3 2.63 2.6909 -2.3

4 8.86 9.0314 -1.9

5 21.4 22.046 -2.9

6 42.9 44.073 -2.7

7 76.0 76.990 -1.3

8 119. 121.92 -2.4

9 177. 178.17 - .7

10 257. 248.20 +3.5

11 24.5 24.900 -1.6

12 36.5 37.146 -1.7

13 51.7 52.999 -2.5

14 71.0 73.101 -2.9

15 96.5 98.248 -1.8

16 127. 129.19 -1.7

17 163. 166.55 -2.1

18 210. 211.01 - .5

19 259. 263.22 -1.6

20 315. 323.67 -2.7

21 382. 390.72 -2.2

22 452. 466.34 -3.1

23 530. 549.09 -3.5

24 629. 638.99 -1.6

25 715. 737.89 -3.1

26 821. 842.08 -2.5

27 931. 958.20 -2.8

28 924. 959.94 -3.7

29 1110. 1114.8 - .4

30 166. 168.07 -1.2

31 190. 195.91 -3.0

32 222. 227.55 -2.4

33 258. 263.23 -2.0

34 299. 303.12 -1.4

35 342. 347.37 -1.6

36 398. 396.30 + .4

37 444. 449.60 -1.3

38 499. 507.44 -1.7

39 562. 569.52 -1.3

40 627. 636.72 -1.5

52.1 53.034 -1.8%

63.8

76.7

91.3

108.

126.

147.

170.

195.

226.

256.

289.

325.

365.

409.

455.

(Veigele et al. max. energy 1.6 keV)

107. 108.75 -1.6

120. 122.06 -1.7

64.767 -1.5

78.151 -1.9

93.275 -2.1

109.77 -1.6

129.30 -2.6

150.45 -2.3

173.71 -2.1

199.25 -2.1

226.79 - .4

257.33 - .5

290.62 - .6

326.35 - .4

364.8 + .3

405.59 + .8

451.41 + .8

13
1.0 keV

z Veigele et al. Sco field % diff.

t (kb) T (kb)

41 707. 708.56 - .2%

42 778. 786.27 -1.1

43 847. 869.65 -2.6

44 948. 958.39 -1.1

45 1040. 1052.9 -1.2

46 1160. 115.4 + .5

47 1250. 1259.4 - .8

48 1370. 1370.6

49 1480. 1487.4 - .5

50 1600. 1606.4 - .4

51 1720. 1733.5 - .8

52 1740. 1861.6 -6.5

53 1880. 1915.0 -1.8

54 2040. 2050.4 - .5

55 1740. 2065.0 -15.7

56 1860. 1946.1 -4.4

57 1960. 2094.1 -6.4

58 2200. 2257.3 -2.5

59 2370. 2474.0 -4.2

60 2080. 1585.1 +31.2

61 501. 492.46 +1.7

62 537. 523.56 +2.6

63 570. 556.64 +2.4

64 600. 595.74 + .7

65 655. 629.70 +4.0

66 702. 670.17 +4.8

67 750. 713.61 +5.1

68 808. 760.23 +6.3

69 871. 810.25 +7.5

70 931. 863.88 +7.7

71 977. 922.72 +5.9

72 1050. 985.30 +6.6

73 1120. 1051.3 +6.5

74 1190. 1120.9 +6.2

75 1260. 1193.6 +5.6

76 1330. 1269.6 +4.8

77 1430. 1350.5 +5.9

78 1530. 1432.3 +6.8

79 1630. 1517.6 +7.4

80 1750. 1604.9 +9.0

2.0 keV

Veigele et al. Scofield

x (kb) t (kb)

135.

150.

165.

185.

205.

227.

249.

273.

299.

326.

355.

387.

420.

459.

496.

533.

567.

620.

663.

704.

750.

801.

850.

892.

963.

952.

1010.

1070.

1130.

(932.)

% diff.,

136.28 - .9%

151.86 -1.2

168.71 -2.2

186.81 -1.0

206.31 - .6

227.10

249.61 - .2

273.72 - .3

299.50 - .2

326.83 - .3

355.83 - .2

386.71

419.20 + .2

453.49 +1.2

489.50 +1.3

527.02 +1.1

566.65

604.84 +2.5

645.73 +2.7

687.44 +2.4

731.37 +2.6

776.95 +3.1

825.04 +3.0

875.04 +1.9

923.16 +4.3

932.95 +2.0

980.77 +3.0

1037.0 +3.2

1031.3 +9.6

1088.1 -14.4

(978.) 999.98 -2.2

(1040.) 1063.4 -2.2

(Veigele et al. max. energy 1.7 keV]

(Veigele et al. max. energy 1.9 keV]

390.

415.

368.12

390.53

+5.9

+6.3

14
1.0 keV 2.0 keV

Veigele et al. Scofield % diff. Veigele et al. Scofield % diff.

T (kb) x (kb) t (kb) t (kb)

1820. 1695.5 +7.3% 439. 413.96 +6.0%

1920. 1788.4 +7.4 466. 438.35 +6.3

2010. 1883.7 +6.7 492. 463.61 +6.1

2120. 1981.9 +7.0 524. 489.76 +7.0

2130. 2041.9 +4.3 555. 516.93 +7.4

2250. 2143.0 +5.0 588. 545.01 +7.9

2360. 2248.1 +5.0 621. 573.97 +8.2

2470. 2322.7 +6.3 654. 603.79 +8.3

2520. 2433.8 +3.5 681. 634.72 +7.3

2300. 2543.5 -9.6 717. 666.43 +7.6

2440. 2660.6 -8.3 761. 698.71 +8.9

2530. 2613.8 -3.2 798. 732.29 +9.0

2650. 2730.7 -3.0 839. 767.22 +9.4

2830. 2850.5 - .7 889. 803.28 +10.7

15
Figure Captions

Figure 1.

Total measured cross sections (cf T0T , circles), and theoretical photoeffect (t) , coherent scattering toC0H) , incoherent scattering (aINC0H)

»

and pair production (k) cross sections for copper for photon energies

10 eV to 100 GeV. The total photonuclear cross section (a ) measured by Wyckoff et al. [73] is also shown.

Figures 2-95.

Comparisons of theoretical photoeffect data (curves) of Veigele et al.,

[8], [10] extending below 1 keV and Scofield [11] 1 keV to 1.5 MeV

with experimental data (points) for elements H (Z = 1) to Pu (Z = 94)

.

The data«(in units of barns/atom) in each case have been multiplied by

[E(keV)] . The number of vertical-scale graph cycles was in each case determined by the Scofield data. For elements Z ^ 34 this results in

an apparent low-energy cut-off in the Veigele et al. data which in

reference [8] and [19] extends down to 0.1 keV for all elements Z=l to 94,

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NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-9012. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Comparison of Theoretical and Experimental Photoeffect

Data 0. 1 keV to 1. 5 MeV

5. Publication Date April 1976

6. Performing Organization Code

7. AUTHOR(S)

J. H. Hubbell and Wm. J. Veigele

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2400105

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

NBS Office of Standard Reference Data

Washington, D. C. 20234

The Defense Nuclear Agency, Washington, D. C. 20305

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Graphs of calculated and experimental atomic photoeffect cross sections as a function of photon energy 0.1

keV to 1.5 MeV are presented for all elements Z = 1 to

94. The calculated results presented are (a) the non- relativistic Hartree-Fock self -consistent-field (SCF)

results of Veigele, Henry, et al. , over the range 0.1

keV to between 1.0 and 8.0 keV for all elements Z = 1 to

94 and (b) the relativistic Hartree-Slater SCF results

of Scofield over the range 1.0 keV to 1.5 MeV for all

elements Z = 1 to 101. The "experimental" data-points

are derived by subtracting theoretical scattering cross sections from total attenuation coefficient measurements

in the literature. Differences between theoretical and

experimental photoeffect data are typically a factor of

two from 0.1 to 1.0 keV, 5-10% from 1.0 to 5.0 keV and 1-5%

from 5.0 keV up to energies, ranging from 20 keV for

carbon up to 500 keV for lead, above which the photoeffect cross section becomes fractionally too small to

be accurately determined from the total attenuation

coefficient

.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Attenuation coefficients,* cross sections; gamma rays; photoelectric effect; photons;

x-rays

.

18. AVAILABILITY [X] Unlimited

I | For Official Distribution. Do Not Release to NTIS

_J Order From Sup. of Doc, U.S. Government Priptijie Office Washington, D.C. 20402,

I I Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIE

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

43

22. Price

USCOMM'DC 29042-P74

ft U.S. GOVERNMENT PRINTING OFFICE: 1976— 210-801/206

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