vNational Bureau of Standards

Library, E-01 Admin. Bldg.

OCT 6 1981

19113**

.-'

in NBS TECHNICAL NOTE 968

°»eAu ov

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

Cross Section Measurements,

heoretical Analysis and Evaluations

for Energies Above 10 MeV
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The

Bureau's overall goal is to strengthen and advance the Nation's science and technology and

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and the Institute for Computer Sciences and Technology.

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The National Bureau of Standards was reorganized, effective April 9, 1978.
Total Photon Absorption Cross Section

Measurements, Theoretical Analysis and

Evaluations for Energies Above 10 MeV

OF STANDARD?

Jim 2 1 197P

~Tec.w\\Qjx\ ricsVe.

H. A. Gimm

Nuclear Physics Division

Max-Planck-Institute for Chemistry

D6500 Mainz, West Germany

and

J. H. Hubbell

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

Sponsored by the NBS Office of Standard Reference Data

Washington, D.C. 20234

CO /

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology ^ ^- NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued June 1978
National Bureau of Standards Technical Note 968

Nat. Bur. Stand. (U.S.), Tech. Note 968, 77 pages (June 1978) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1978

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-01941-1 Price $2.40

(Add 25 percent additional for other than U.S. mailing).
FOREWORD

The National Standard Reference Data System was established in 1963 for the purpose of promoting the critical evaluation and dissemination of numerical data of the physical sciences. The program is coordinated by the Office of Standard Reference Data of the National Bureau of Standards, but involves

the efforts of many groups in universities, government laboratories, and private industry. The primary aim of the program is to provide compilations of critically evaluated numerical data. These

tables are published in the Journal of Physical and Chemical Reference Data , the NSRDS-NBS Publication

Series of the National Bureau of Standards, and through other appropriate channels.

The present report consists of tables of calculated atomic photoabsorption cross sections for energies above 10 MeV and a comparison with selected experimental results. This work was carried out

as part of the program of the NSRDS X-Ray and Ionizing Radiation Data Center.

David R. Lide, Jr., Chief

Office of Standard Reference Data

TOTAL PHOTON ABSORPTION CROSS SECTION MEASUREMENTS, THEORETICAL ANALYSIS AND EVALUATIONS

FOR ENERGIES ABOVE 10 MeV

H. A. GIMM

Max-Planck-Institute for Chemistry

Nuclear Physics Div., D6500 Mainz

J. H. HUBBELL

National Bureau of Standards

Washington, D. C. , 20234

Atomic photoabsorption cross sections have been calculated in the energy

range from 10 MeV to 350 MeV. For Pb, Ta, Sn and Cu total y-ray absorption

cross sections were measured between 10 MeV and 160 MeV and compared with the theoretical results. An estimate of the uncertainties in the calculated atomic

cross sections is given.

Key words: Coulomb corrections; pair production cross section; screening

corrections; total photon absorption cross section; total photonuclear

absorption cross section; triplet production cross section.

1. INTRODUCTION

In recent years total photon absorption cross sections, (k) , have been measured with an accuracy of a few tenths of a percent for light elements (Li, Be, C, 0, A£, Ca) at photon energies k ranging from 10 MeV to between 150 and 220 MeV [1] . The aim of these measurements was to obtain nuclear

absorption cross sections, ,(k), for Y-radiation which are the difference between the total nucl

absorption cross sections, (k) , and the nonnuclear or atomic cross sections, (k) , resulting

from the electromagnetic reactions of the photons with the atom:

On ,(k) = cj (k) - a (k) . (1) nucl tot a

Unfortunately, the nuclear absorption cross sections constitute only a small fraction — at most

5-7% — of the total absorption cross section. This means that in order to extract the nuclear absorption

cross section from the measured total absorption cross section, it is essential to know the atomic cross sections as accurately as possible. Figure 1 depicts this situation very clearly.

Besides this nuclear physics aspect it would be desirable to have precise photon absorption cross

sections in fields like radiation shielding analysis and medical dosimetry.

Report written at the National Bureau of Standards under a contract from the NBS Office of Standard

Reference Data.

Figures in brackets indicate the literature references at the end of this paper.
In section 3 of this paper, an attempt is made to compute the atomic cross sections for Y

-radiation

on the basis of most recent theoretical evaluations. These results are compared with earlier computations reported in literature. Section 4 describes total absorption measurements performed on high Z elements (Cu, Sn, Ta, Pb) , where the nuclear part of the total cross section is known from (Y»n)-

experiments. Therefore, in this case the experimental total absorption cross sections can be used to check the computed atomic cross sections. Section 5, finally, compares all experimental values with the theoretical atomic cross sections and gives an estimated accuracy of these calculations.

2. NOTATION, CONSTANTS

k photon energy in units of the electron rest-mass energy m c

E photon energy in MeV

Z atomic number

a total absorption cross section for Y-radiation

tot r

a . nuclear absorption cross section for Y-radiation nucl r

a atomic (or electronic) photoabsorption cross section

a

' cross section for the atomic photoeffect

ph

cross section for Compton effect

cross section for pair production in the electron field (triplet production)

a cross section for pair production in the nuclear Coulomb field

P

AS screening correction for pair production in the nuclear field

AS screening correction for triplet production

ACoul Coulomb correction for pair production in the nuclear field

f , radiative correction rad

f retardation correction

ret

tp atomic ground state wave function

q momentum transfer to an atom or electron in m c units

o

F(q,Z) atomic form factor, F(0,Z) = Z

S(q,Z) inelastic (or incoherent) scattering function, S(°°,Z) = Z

a fine structure constant = 7.2972 x 10

m c electron rest-mass energy = 0.511006 MeV

o

bJ

c

f conversion factor for momentum transfer: q [A ] = 20.60821 q' [m c]

All cross sections are given in mbarns (mb)

.

2
3. ATOMIC PHOTOABSORPTION CROSS SECTIONS

The atomic cross sections for Y~ray absorption at energies above 10 MeV can be written as the sum of the partial cross sections for the photoelectric effect, O , for Compton effect, , for pair production in the Coulomb field of the nucleus, a , and for pair production in the electron field

of the atom (triplet production), a :

a = a , + a + a + a (2) a ph c p t

Figures 2-4 show the energy dependence of these partial cross sections for lithium, calcium and

lead. Table I gives the numerical values for the atomic photoabsorption cross sections and for the partial cross sections evaluated in this paper.

Report NSRDS-NBS 29 [2] reviews all theoretical and experimental results concerning the atomic

cross sections up to 1969.

In the following paragraphs the methods used to compute the partial atomic cross sections are outlined and compared with previous calculations.

3.1. Photoelectric Cross Section

The photoelectric cross sections of this paper (table I) were computed by using an empirical

formula given in Ref . [2]:

4 a. + b. Z -p. Oph

= Z»f £ -\^-z

E

- (3) 1=1 l

with

f = 1 + 0.01481 ln 2 Z - 0.000788 ln 3 Z (4)

and

i a

.

b

.

c

.

p

.

i l 11 1 1.6268 x

10~ 6 -2.683 x

10~9 4.173 x 10

_2

1

2 1.5274 x

10~ 6 -5.110 x

10~ 10 1.027 x 10

_2

2

3 1.1330 x 10~ 6 -2.177 x 10~ 9 2.013 x 10"2 3.5

4 -9.12 x 10"8

4

This formula is estimated to be accurate within approximately 5%. But since the photoelectric

effect is only important for high Z elements and low energies (table I) , this results in an uncertainty

of less than 0.05% of the total cross section for lead at 10 MeV.
3.2. Compton Cross Section

Hubbell et al [3] have calculated bound-electron Compton cross sections by applying incoherent

scattering functions to the Klein-Nishina formula. However, it turns out that the binding effect can be neglected at energies above 10 MeV since for these energies it is smaller than 0.04% of the Compton cross

section. Therefore the Compton cross sections have been computed by using the Klein-Nishina formula [4]:

„ _ 9lr T 2 Tl+k / 2(l+k) &n(l+2k)\ £n(l+2k) l+3k 1 ,~

°c " 27T r

o Li? \l+2k k / +

2k (l+2k) 2 J

(3)

Radiative and double Compton effect corrections of 0.3 to 1.3% of the Compton cross section

evaluated by Mork [5] and tabulated in [2] have been added to the results of formula (5). Table I gives

the final Compton cross sections in column 4.

The Compton cross section is an essential fraction of the total absorption cross section at small

energies (see figs. 2-4). But fortunately it decreases rapidly with energy. Therefore, the corrections

of the Compton cross section are less than 0.3% of the total cross section in the energy region and for the elements considered in this paper. The uncertainty of the total absorption cross section arising

from the uncertainty of the Compton cross section is estimated to be less than 0.1%, and even smaller

for high energies and heavy elements.

3.3. Pair Production in the Coulomb Field of the Nucleus

The pair production cross section is the most important part of the atomic absorption cross section,

especially for high Z elements (figs. 2-4). For lead e.g., it constitutes about 74% of the total cross section at 10 MeV and about 97% at 150 MeV, but even for a light element such as lithium it is 43% at

50 MeV and 64% at 200 MeV. Therefore most of the efforts were concentrated on the evaluation of precise

pair production cross sections.

Bethe and Heitler have calculated the pair production cross section in the nuclear Coulomb field in

a plane wave approximation [6]. For high Z elements however, this approximation is not appropriate,

and therefore a "Coulomb correction" has to be applied which takes into account that the outgoing leptons

can no longer be represented by plane waves. A second important effect is the screening of the nuclear

Coulomb field by the surrounding atomic electron cloud. The Z and energy dependence of both effects is shown in figure 5 which illustrates the importance of the Coulomb and the screening corrections. For lead at 150 MeV e.g., they constitute 11% and 27% resp. of the total cross section. A third correction

has to be applied to account for radiative effects.

In this analysis the pair production cross section, o , is written as:

a = (a - AS - ACoul) f , ,,.. p BH rad (6)

where a is the unscreened plane wave approximation of Bethe and Heitler, AS the screening correction

BH ACoul the Coulomb correction and f , the radiative correction.

rad
The formulation of the pair production cross section in terms of formula (6) is not obvious because

screening, Coulomb and radiative corrections are not independent of each other. Reference [7] justifies

separating the screening and the Coulomb correction by the argument that screening is mainly related to small momentum transfers in the pair production process whilst the Coulomb correction is due to large momentum transfers or small impact parameters. It is, however, not quite clear what error is introduced

by splitting the two corrections into separate terms. A rough estimate based on the mentioned momentum

transfer considerations results in an uncertaincy of less than 0.1% of the total absorption cross section

[8]. This 0.1% uncertainty contribution has been independently estimated by 0verb<^ [9], assuming the worst case of a heavy element where F(q,Z) » 0.01 for q » 1 mc, resulting in a few tenths of a percent screening correction to the Coulomb correction, applied to a Coulomb correction of as much as 10%.

The main part of formula (6), the unscreened pair production cross section, o , was computed

BH using Maximon's expansion [10]:

BH

= Z

2 a r

Q

2 p| In 2k - -^|| +

(£) (6 £n 2k - 3.5 + | «,n

3 2k - £n 2 2k - j it 2 in 2k + 2 £(3) + \)

- (D'fei - * * I)

00 with ?(3) = S ~T = 1-2020569 (Riemann's Zeta function). n=l n

The radiative correction, f ,, was taken from reference [11] and is given by: rad

f rad - 1 + °-°093 t 2k I 2.11 (8)

According to reference [11] the uncertainty of the radiative correction caused by applying or not applying

the screening effect is negligible (less than 0.05% of the total absorption cross section).

Very recently, 0verb^ evaluated the Coulomb correction cross section [12] combining his former low energy (up to 5 MeV) results [13] with the high energy approximation of Davies, Bethe and Maximon (DBM)

[7] (fig. 6):

with

ACoul = Z

2 a r o2 [4 f (Z)(| - \ + £? - -£j) - g(k,Z)]

f(Z) = a

2 (vr-T + 0.20206 - 0.0369a 2 + 0.0083a" - 0.002a 6 + ... ) ,

(9)

(10)

a = a Z , (11)

g(k,Z) = i [c

x in 2 I

+ c

2 £n I

+ C3 (l - £)] + ^ [c

4 £n 3 | + c5 *n 2 | + c& (l - |)J , (12)
c

± = a

2 (-6.366 + 4.14a2

) , (13)

c 2 = a

2 (54.039 - 43.126a 2 + 11.264a"*) , (14)

c 3 = a

2 (-52.423 + 49.615a2 - 14.082a") , (15)

(16)

c 5 = - 12.705a 2 (1 - 3.086a2

) , (17)

(18)

The energy and Z dependence of the Coulomb correction term computed from formula (9) is shown in figure 5 as percentage of the total absorption cross section. Errors in the above Coulomb correction fit

(equations (9)-(18)) are estimated by 0verb$ [12] to be of the order of 0.1% of a . BH

The screening correction AS can be calculated by applying the atomic form factor

Z iqr

F(q,Z) = E <* I e n

I ^ > < 19 > n=l

(q = recoil momentum, ty = ground state wave function, r electron coordinate) to the unscreened

recoil distribution — (k,q) of the nucleus:

dq

ss . J'

1 m (k , q) [,.(,. m^f] dq (20)

The recoil distribution used in this report was derived by Jost, Luttinger and Slotnick [14]. It is reported throughout the literature with various misprints; the correct formula (without the screening

factor [x.Ii^)]2 ) is:

8az r da o dq W" ^>k) (21)

I(q,k) = (l - \ q

2) Ji + (l -

q

2 - 2qk + ^M) £n (^ + ^=1) +

( 3 + f| + ^f=4) ^F(Fl)

+ —'- - \~ ± (4 + q

2

) + 4- (4 - l)l in ttf^-ttt

/1+4/q 2 L l i Vq /J /l+4/q2 + /E=l7y

(22)

with

y = j (2qk - q

2

) , (23)

J

x = L 2 (-Xj) + L 2 (-x 2

) + j in 2 \ + (in v) (| In v - «.n 2qk) + ^ , (24)
: = _1 = A

i vA

' * 2 v

A = \ (q + v^4) ,

(25)

(26)

2 v = (/Fl + /y) • (27)

L2 is the Spence function or dilogarithm [15] defined by:

-x L

2 (-x)=-J ^L^dt (28)

L2 (-x) can be expanded

(-x)

1 L2 (-x) = -£ ±-^j- for | x | < 1 (29)

Another useful relation is:

2 \ „2 L 2 (-x) = L 2 (^) - \ Hn (1 + x) in (^) - — for x > (30)

In the present calculation formula (29) was used for |x| < 0.6 and formula (30) for the other values.

The limits of the integral in formula (20) are given by the minimum and maximum recoil momenta:

q = k - /k 2 -4 < q< k+ /kz -4 = q t (31)

Figure 7 shows the recoil distribution of formula (21) for various photon energies.

In previous papers [16,17] the atomic form factors, F(q), used were either derived from the Thomas-Fermi model or based on nonrelativistic Hartree-Fock calculations. Recently, atomic form factors

have become available which are calculated from relativistic charge densities obtained by the HartreeFock self consistent field method [18,19]. Since the recently measured total-absorption cross sections

reported in [1] and [32] are of sufficient precision to distinguish between pair-production cross sections

calculated using these different atomic models, it is possible here to show quantitatively the importance

of using the latter relativistic F(q) values, in preference to Thomas-Fermi or non-relativistic HartreeFock values, in computing theoretical estimates of the pair-production cross section.

In this paper three different sets of form factors are used:

a) form factors based on the Thomas-Fermi statistical model and described by the Moliere

approximation [20]

3 a. F(q,Z) = 1 - q

2 £ ^-CT (32) i=l i
with c. = b. Z

1 ' 3 /121 and

1 1

aj = 0.1, a 2 = 0.55, a 3 = 0.35,

bj = 6.0, b 2 = 1.2, b 3 = 0.3,

b) nonrelativistic form factors extracted from reference [3] which were based on nonrelativistic

Hartree-Fock calculations for small momentum transfers (q < 10 A ~ 0.5 m c) and extrapolated

for higher q values by the Bethe-Levinger relativistic K-shell formula [21],

c) relativistic form factors computed from atomic charge densities [18] by numerical Fourier

transformation using Filon's integration method [22]. The charge densities were obtained from

a self-consistent field program by Liberman et al [23]. These form factors were calculated

independently by 0verb^ [9] who used the same method, and they are found to be consistent

within approximately 0.7% with those derived from Fricke's [18] charge densities.

The numerical integration of equation (20) was performed by using a Simpson integration routine

with automatic step selection, integrating over two q regions (q < q < 1 m c and 1 m c < q < q2 ) and adding the two results. The integral over the small q-region contained the main part of the sum, since the integrand falls off very rapidly. As a check, the unscreened pair production cross section

has been computed from the JLS recoil distribution:

f

q2 , a (k)- M2 (q,k) dq (33) unscr. J dq

Comparing these results with the unscreened cross sections calculated from formula (7), no significant

deviations were found within the accuracy of the numerical integration (10 ). This agrees with Knasel's

calculation of the unscreened pair production cross section [24] who also used the JLS formula. The

consistency with formula (7) still holds in the energy region below 3 MeV where Knasel found deviations

due to his approximation in evaluating the Spence function in the JLS recoil distribution (formulas

(22), (24), (28-30)).

When integrating formula (20), the form factors of set b) and c) , which were given in form of tables, were interpolated by a cubic spline function. A check was made by applying quadratic Lagrangian

interpolation as well, resulting in no significant change of the screening correction values.

Table II gives the results of the screening correction computation for the three sets of form factors. Figure 5 shows the ratio of the screening correction (calculated with the relativistic form factors,

set d) and the total absorption cross section.

The screening correction cross sections obtained with relativistic form factors agree within a few tenths of a percent with the values calculated by 0verbtf [9]. For Li and Be the agreement is in the range of 1-2%. Compared with the total absorption cross section, this is, however, less than 0.1 percent.

In figure 8 the differences between the screening cross sections obtained with the relativistic

(set c) rsp. the nonrelativistic (set b) form factors and those obtained with Thomas-Fermi form factors

(set a) are plotted in units of the total atomic absorption cross section. The different behaviour of
the curves for different elements reflects the shell structure of the atom which is not included in the Thomas-Fermi model but is included in the two other sets of form factors. Figure 8 also shows that the influence of relativistic effects is important for heavy elements.

3.4. Pair Production in the Field of the Atomic Electrons (Triplet Production)

The cross section for pair production in the field of the atomic electrons can be written in analogy to formula (6) for the pair production in the field of the nucleus as:

°t " ( °o " AS

t>

f rad ' (34)

where a is the unscreened triplet production cross section, AS the screening correction term for this process and f , the radiative correction factor. The Coulomb correction which is important for pair production in the nuclear field can be neglected for triplet production.

Borsellino and Ghizetti calculated the unscreened triplet cross section including retardation [25] which arises from the fact that the velocity of the recoiling electron is not negligible in comparison

with the velocity of light. The formula they derived is given by the following expression:

°BG

(k) "Z « V B *n 2k " Tf

+ I (_ | £n » 2k + 3 W 2k - 10 + Wa to 2k +

123 ± 12, ± 16b

j

+ -1

(§ £n 3 2k . 4 £n 2 2k + =l±J2a £n 2k _ 123 ± 32a ± 64b

)

, 1 /. 2 -, 53 , ., 2915 - 288a \ + p- (£n 2k - -g £n 2k

glS )

1 / 49 . ,. 115 \ + ^

\- 18 in 2k " 432 )

1 / 77 . „. . 10831 \ + IF (" 36 £n 2k +

8640")

. 1 / 641 . ,. , 64573 \ + ttt - ^TT^r x.n 2k +

k?(bI 300 36000/

1 / 4423 394979 \ , 1 ,„. k^ (" 1800 £n 2k +

216000 ) +

•••

(35)

with a = - 2.4674 and b = - 1.8031.

Recently Haug calculated the unscreened triplet cross section [26] including exchange terms arising

from the indistinguishability of the two electrons involved in the triplet process and including the interaction between the incident photon and the initial electron. These two terms cancel partially and decrease with energy. They have been neglected in formula (35). However, a correction term, A, extracted from Haug ' s paper (Table III) has been applied to formula (35) in order to compute the unscreened cross section, a : o

a = a„_ + A (36)

O u\j

The radiative correction factor of formula (34) has been derived by Mork and Olsen [11] and is almost

independent of energy. In this paper a value of 1.01 was used.

9
The triplet screening correction, AS , was calculated in a similar manner as the screening for pair production in the nuclear field (formula (20)) thereby first neglecting retardation:

AS

o

'q o - /

' £ «.» (l - i*

a) *

C37, — is the unscreened recoil distribution (formula (21) divided by Z) of Jost, Luttinger and Slotnick,

S(q,Z) is the incoherent scattering function as defined by [3]:

z iq(r -r ) 2 S(q,Z) = X! <* I e I *o>~ l F^' Z>l < 38 > m,n=l

(p is the ground state wave function of the atom and F(q,Z) the atomic form factor. r and r are

th th m n

the space coordinates of the m and n electron.

The values for the incoherent scattering functions S(q,Z) were taken from reference [3]. They are derived from nonrelativistic Hartree-Fock calculations; relativistic incoherent scattering functions are not available.

Since the JLS recoil distribution in formula (37) neglects the retardation effect in the triplet

production process, the screening AS has to be corrected by a factor f : o

' ret

AS = f „ AS (39)

t ret o

The cross section for pair production in the nuclear Coulomb field does not include retardation

(formula (7)) whereas the cross section for triplet production does include this effect (formula (35)), the factor f can be computed as the ratio of these unscreened cross sections for Z = 1: ret

f ret = °o /0BH

(40)

Table IV and figure 9 show the energy dependence of the retardation factor, f is considerably

different from 1 for low energies. Fortunately the screening cross section itself is small in this

region, therefore errors which might be introduced by the approximation in formula (39) are less severe.

The results of the triplet screening calculations are given in Table V. Figure 10 and 11 show the screening correction cross sections in units of the unscreened triplet cross section and of the total

absorption cross section, resp. Although the triplet screening is a big effect as compared with the triplet cross section itself, it is only a fraction of less than 1.3% of the total cross section.

Hubbell has calculated screened triplet cross sections [2] in a high energy approximation using a method developed by Wheeler and Lamb [27] which neglects retardation. For high energies and without

retardation, the screening corrections of this paper agree within 1% with those obtained by Hubbell. Knasel [24] applied a method similar to the one used in this work. He first calculated screened triplet cross sections for hydrogen and helium without retardation and thereafter added a term to correct the total triplet cross section for retardation instead of only correcting the screening values as described

in this paper. But nevertheless there is good agreement between both results.

10
4. TOTAL ABSORPTION CROSS SECTION MEASUREMENTS

Total absorption cross sections for Li, Be, C, 0, A£, Si and Ca have been measured in the energy

range of 10 MeV to energies beyond meson threshold in an earlier experiment [1] in order to obtain

nuclear absorption cross sections. Measurements on heavy elements (Cu, Sn, Ta) were performed at certain energies between 10 and 160 MeV [32]. Lead was measured in the entire energy range from 10 to 160 MeV [32]. Figure 12 shows the experimental total absorption cross sections, the numerical values

are given in table VI.

The total absorpto-^r. cross sections were obtained in a narrow beam attenuation experiment using a bremsstrahlung beam with fixed end energy from the Mainz linear accelerator. The experimental set-up

consisted mainly of two 11-channel magnetic Compton spectrometers with an energy resolution of 1% [28], one used as the main yspectrometer , the other used for normalization purposes. The cross sections,

O (k) , were deduced from the number of registered photons in a certain energy bin with (N) and without (N ) the absorption target in the photon beam by applying the absorption law:

N px

- -f— a (k) N(k) = N (k) e A t0t

(41)

with N = Avogadro's number, A = atomic weight of the absorbing material and px = density times

length of the absorber.

The errors due to counting statistics are always indicated by error bars at the experimental values. All other types of errors or systematic uncertainties are discussed in detail in reference [1]. The uncertainties arising from the measurement of the absorber properties px are less than 0.1% for Cu, Sn, Ta and Pb. The overall systematic error is estimated to be less than 0.2% for all high Z elements.

5. DISCUSSION OF EXPERIMENTAL RESULTS AND THEORETICAL CALCULATIONS

The aim of the total absorption cross section measurements for high Z elements was to check the nonnuclear cross sections calculated in this paper rather than to perform a precise measurement of the nuclear cross section. Since the screening and the Coulomb correction terms for pair production in the electromagnetic field of the nucleus increase with the atomic number (see section 3.3) and the nuclear

cross sections can be approximated very well by the (Y. n ) cross section , absorption cross section measurements for high Z elements constitute a good test for the atomic cross sections, especially for

the mentioned corrections.

In figure 13 the difference between the pair production screening corrections as they were calculated

by applying relativistic and nonrelativistic form factors, is plotted in units of the total absorption

cross section. For heavy elements, especially for lead, this difference is more than 1% of the total

cross section. Therefore, it should be possible to test the calculated screening values with the experimental data. Assuming that the nuclear cross section is negligible above approximately 50 MeV and assuming that the partial atomic cross sections — excluding the screening correction for pair production — are known precisely from the calculations in section 3. an "experimental screening correction,"

AS , can be evaluated according to formula (1), (2) and (6):

11
o = c? - (a , + a + a + (a - AS - ACoul) f , ) (42) nucl tot \ ph c t BH exp rad/ '

or with a = for high energies: nucl ° °

AS = (a , + a +o + (c_„ - ACoul) f ., - a )/f (43) exp \ ph c t BH rad tot'/ rad v y

In figures 14-21 this experimental screening correction is plotted as well as the screening

corrections calculated with relativistic and nonrelativistic form factors. For all measured high Z elements the relativistic form factors are favored compared with the nonrelativistic ones. Moreover,

the deviations from the calculated values are within the uncertainties of the experimental cross sections

Therefore, the screening corrections obtained by using relativistic form factors are considered to be appropriate and are used in the following considerations as well as in table I of section 3.

The nuclear absorption cross sections for lead and tin are shown in figure 22 and 23. These cress sections were obtained by subtracting the calculated atomic cross sections from the measured total absorption cross sections without any adjustment or fitting procedures. The lines in figure 22 and 23 indicate the experimental (Y> n) cross sections computed from Lorentz line parameters given in reference [29]. In lead the deviations from zero for high energies are less than 0.4% of the total cross section and are not within the experimental uncertainty of 0.2%. Figure 24-27 display the giant resonance region of the nuclear absorption cross section for Pb, Ta, Sn and Cu. The curves in these

plots again represent the (Y>n) cross sections. There is excellent agreement with the (Y»n) results

2 for Pb, Ta and Sn. For copper the total absorption cross section and the (Y> n ) cross section differ

by roughly 30%, but this discrepancy can easily be explained by the (Y>p) cross section which is of that order of magnitude [30,31] and has to be added to the (Y>n) cross sections to give the total cross

section.

Figures 28-33 show the nuclear absorption cross section for Y~radiation in the elements Li, Be, C,

0, AJZ. and Ca derived from the experimental data of a previous experiment [1] and the atomic cross sections

calculated in this paper. Since for these elements the nuclear cross section is not known from other

experiments, the only way of checking the atomic cross sections is to see if the resulting nuclear cross sections remain positive at all energies. This condition — giving an upper limit for the atomic cross sections — holds within the experimental uncertainties [1] for all elements investigated and for all energies.

6. CONCLUSION

Atomic cross sections for Y~ray absorption have been calculated in the energy range from 10 to 350 MeV using the most recent theoretical evaluations available. Comparing these results with the measured total absorption cross sections for high Z elements it was found that it is appropriate to use relativistic form factors to compute the screening correction term in the pair production cross

section. On the basis of this approach, the calculated atomic cross sections are consistent with the experimental results for all energies covered by the experiment for low Z as well as for high Z elements

.

2The slight difference in the peak position might be due to an error in the energy calibration and needs

further investigation.

12
The deviations of the calculated atomic cross section for lead at high energies from the experimental values is smaller than 0.4%. Since the main uncertainties for high Z elements arise from

either the Coulomb or the screening correction which both decrease with decreasing atomic number, the uncertainty caused by these corrections in light elements should be considerably smaller. For low Z elements the difference of the screening values for relativistic and nonrelativistic form factors

(fig. 13) might give an upper limit of about 0.1% for the uncertainty of the total absorption cross section as far as the pair production is concerned. The uncertainty of the Compton cross section should

be at most of the same magnitude for energies around 10 MeV (see sec. 2.2) and less for higher energies.

The triplet cross section constitutes not more than 20% of the total cross section (for Li at high

energies, fig. 2). Assuming an accuracy of the triplet cross section of 1%, this would result in an uncertainty of 0.2% of the total cross section. The foregoing estimates are rather conservative since

the fraction of the total absorption cross section which is due to triplet production decreases with

increasing atomic number as well as the fraction due to Compton effect. The atomic cross sections for light elements are therefore estimated to be accurate to approximately 0.2% of the total absorption cross

section.

The authors thank H. M. Gerstenberg for his assistence in adapting the Mainz programs and data tapes

to the NBS computer facility. The authors also thank E. G. Fuller, L. C. Maximon, H. A. Olsen and

I. 0verb$ for their suggestions and comments on this paper.

7 . REFERENCES

[1] Ahrens, J., Borchert, H. , Czock, K. H. , Eppler, H. B., Gimm, H., Gundrum, H., Krb'ning, M. , Riehn, P., Sita Ram, G., Zieger, A., and Ziegler, B. Nucl. Phys. A 251, 479-492 (1975).

[2] Hubbell, J. H. , Photon cross sections, attenuation coefficients and energy absorption coefficients

from 10 keV to 100 GeV, NSRDS-NBS 29, U.S. Government Printing Office, Washington, D.C. (1969).

[3] Hubbell, J. H. , Veigele, Wm. J., Briggs, E. A., Brown, R. T., Cromer, D. T., Howerton, R. J., J. of Physical and Chemical Reference Data, 4_ No. 3, 471-538 (1975).

[4] Klein, 0., Nishina, Y. , Z. Physik 52, 853-868 (1929).

[5] Mork, K. J., Phys. Rev A4, 917-927 (1971).

[6] Bethe, H. A., Heitler, W. , Proc. Roy. Soc. (London) A 146, 83-112 (1934).

[7] Davies, H. , Bethe, H. A., Maximon, L. C. , Phys. Rev. 93, 788-795 (1954).

[8] Maximon, L. C. , private communication.

[9] 0verbtf, I., Private communication; Arkiv for Det Fysiske Seminar i Trondheim, No. 10 (1977),

received after completion of this paper.

[10] Maximon, L. C. , J. Res. Nat. Bur. Stds. 72B, 79-88 (1968).

[11] Mork, K. J., Olsen, H., Phys. Rev. 140B, 1661-1674 (1965).

[12] 0verb«S, I., Phys. Lett. 71B, 412-414 (1977).

[13] 0verb«S, I., Mork, K. J., Olsen, H. A., Phys. Rev. 175, 1978-1981 (1968); and Phys. Rev. A8, 668-685

(1973).

[14] Jost, R., Luttinger, J. M. , Slotnick, M. , Phys. Rev. 80, 189-195 (1950).

[15] Motz, J. W., Olsen, H. , Koch, H. W. , Rev. Mod. Phys. 36, 881-928 (1964).

[16] SdSrenssen, Nuovo Cim. (10) 38, 745-770 (1965); and 41, 543-558 (1966).

[17] Borie, E., Arenhovel, H. , Z. Physik 255, 459-463 (1972).

[18] Fricke, B. , private communication.

[19] 0verb«S, I., Nuovo Cimento, 40B, No. 2, 330-338 (1977).

[20] Thomas, L. H. , Proc. Camb. Philos. Soc. 23, 542-548 (1927).

Fermi, E. , Z. Phys. 48, 73-79 (1928)

Moliere, Z. Naturforsch. 2a, 133-145 (1947).

13
[21] Levinger, J. S., Phys. Rev. 87_, 656-662 (1952).

[22] Handbook of Math. Functions, Nat. Bur. Stds., Applied Math Series (1964).

[23] Liberman, D. A., Cromer, D. T. , Waber, J. T., Computer Phys. Commun. _2, 107 (1971).

[24] Knasel, T. M. , DESY Rep. 70/2 and 70/3 (1970).

[25] Borsellino, A., Helv. Phys. Acta 20, 136-138 (1947); Nuovo Cimento 4_, 112-130 (1947);

Rev. Univ. Nac. Tucuman, A6, 7-35 (1947).

Ghizetti, A. G. , Rev. Univ. Nac. Tucuman A6, 37-50 (1947).

[26] Haug, E. , Z. Naturforsch. 30a , 1099-1113 (1975).

[27] Wheeler, J. A., Lamb, W. E. , Phys. Rev. 55, 858-862 (1939).

[28] Ahrens, J., Borchert, H. , Zieger, A., Ziegler, B., Nucl. Instr. and Meth. 108, 517-523 (1973).

[29] Berman, B. L. , Atlas of Photoneutron Cross Sections Obtained with Monoenergetic Photons, Lawrence Livermore Lab., Livermore, UCRL-78482 (1976).

[30] Photonuclear Reaction Data, Center for Radiation Research, Nat. Bur. Stds., Washington, D.C. (1973).

[31] Chrien, R. E. , Benade, A. H. , Phys. Rev. 119, 748-754 (1960).

[32] Ahrens, J., Gimm, H. , Sita Ram, G. . Zieger, A., Ziegler, B., unpublished.

14
Table I: Calculated atomic cross sections, Ga

(k), in the energy range of 10 to

350 MeV for Z = 3, 4, 6, 8, 13, 20, 29, 50, 73, 82. Columns 3-6 give

the partial cross sections a

h

(k) , Gc (k), Ot (k) and <J p

(k).

Z- 3

E TOTAL PHOTO COMPTON TRIPLET PAIR

(MEV) (MB) (MB) (MB) (MB) (MB)

10.0 1.7621+02 3.9286-05 1.5346+02 3.51 16+00 1.,9245+01

12.0 1.6C48+02 3.2206-05 1.3422+02 4.3744+00 2.,1889+01

14.0 1 .4896+02 2.7282-05 1.1963+02 5. 1506+00 2«,4174+01

16. 1 .4019+02 2.3662-05 1.0815+02 5.8532+00 2,,6183+01

18.0 1.3332+02 2.0888-05 9.8856+01 6.4937+00 2<,7973+01

20.0 1.2783+02 1.8695-05 9.1159+01 7.0806+00 2.,9587+01

22*0 1.2335+02 1.6919-05 8.4671+01 7.6210+00 3,,1054+01

24.0 1 .1964+02 1.5450-05 7.9119+01 8.1212+00 3,,2397+01

26.0 1.1653+02 1.4216-05 7.4309+01 8.5865+00 3,,3635+01

28.0 1 . 1390+02 1.3164-05 7.0098+01 9.0212+0 3,.4781+01

30.0 1 .1165+02 1.2257-05 6.6376+01 9.4288+00 3.,5848+01

32.0 1 .0972+02 1.1467-05 6.3061+01 9.8123+00 3.,6844+01

34.0 1 .0804+02 1.0773-05 6.0088+01 1.0174+01 3.,7778+01

36.0 1 .0658+02 1.0157-05 5.7404+01 1.0517+01 3.,8657+01

38.0 1.0530+02 9.6087-06 5.4968+01 1.0843+01 3.,9485+01

40.0 1.0417+02 9. 1161-06 5.2747+01 1.1152+01 4<,0268+01

45.0 1.0188+02 8.0805-06 4.7960+01 1.1864+01 4,,2054+01

50.0 1.0016+02 7.2561-06 4.4025+01 1.2503+01 4.,3633+01

55. 9.8850+01 6.5843-06 4.0728+01 1.3080+01 4.,5042+01

60.0 9.7838+01 6. 0263-06 3.7923+01 1.3606+01 4, 6310+01

65.0 9.7053+01 5.5555-06 3.5507+01 1.4068+0 1 4,,7459+01

70.0 9.6442+01 5.1529-06 3.3403+01 1.4532+01 4,,8506+01

75.0 9.5964+01 4.8048-06 3.1553+01 1.4944+01 4<.9466+01

80.0 9.5590+01 4.5006-06 2.9912+01 1.5328+01 5.,0351+01

85.0 9.5299+01 4.2327-06 2.6444+01 1.5686+01 5..1169+01

90.0 9.5073+01 3.9949-06 2.7122+01 1.6022+01 5<,1929+01

95.0 9.4901+01 3.7824-06 2.5926+01 1.6338+01 5.,2636+01

100.0 9.4773+01 3.5913-06 2.4839+01 1.6636+01 5,,3298+01

125.0 9.4569+01 2.8672-06 2.0605+01 1.7908+01 5..6055+01

150.0 9.4751+01 2.3861-06 1.7680+01 1.8913+01 5,,8158+01

175.0 9.5086+01 2.0432-06 1.5523+01 1.9735+01 5,.9828+01

200.0 9.5480+01 l»7865-06 1.3862+01 2. 0425+01 6.,1194+01

225.0 9.5895+01 1.5871-06 1.2543+01 2. 1015+01 6,,2337+01

250.0 9.6308+01 1.4278-06 1.1471+01 2.1527+01 6..3310+01

275.0 9.6710+91 1.2975-06 1.0580+01 2.1979+01 6,,4151+01

300. 9.7094+01 1.1890-06 9.8268+00 2.2361+01 6 .4886+01

325.0 9.7458+01 1.0972-06 9.1810+00 2.2742+01 6,,5535+01

350.0 9.7802+01 1.0186-06 8.6205+00 2.3068+01 6<,6113+01

15
Table I: Continued

Z= 4.

5 TOTAL PHOTO COMPTON TRIPLET PAIR

(MEV) (MB) (MB) (MB) (MB) (MB)

10.0 2.4350+02 1.6129-04 2.0461+02 4.6822+00 3,,4203+01

12.0 2.2369+02 1.3217-04 1.7896+02 5.8326+00 3. 8896+01

14. 2.0 933+02 1.1193-04 1.5951+02 6 . 86 73+0 4,,2948+01

16.0 1 .9851 + 02 9.7051-05 1.4420+02 7.8041+00 4, 6506+01

18.0 1 .9014+02 8.5658-05 1.3181+02 8.6579+00 4<,9674+01

20.0 1.8351+02 7.6656-05 1.2155+02 9.44 02+0 5,.2523+01

22. 1.7816+02 6.9363-05 1.1289+0 2 1.0160+01 5,,5110+01

24.0 1 .7379+02 6.3336-05 1.0549+02 1.0827+01 5,,7474+01

26. 1 .7017+02 5.8272-05 9.9079+01 1. 1446+01 5<.9648+01

28.0 1.6715+02 5.3956-05 9.3464+01 1.2025+01 6,,1658+01

30. 1 .6459+02 5.0236-05 8.8502+01 1.2567+01 6,,3525+01

32.0 1 .6243+02 4.6995-05 8.4082+01 1.3077+01 6.,5266+01

34.0 1.6057+62 4. 4 146- ©5 8.0117+01 1.3559+01 6,,6896+01

36. 1.5898+02 4.1623-05 7.6538+01 1.40144-01 6,.8425+01

38.0 1 .5760+02 3.9373-05 7.3291+01 1.4446+01 6,,9865+01

40.0 1.5641+02 3.7353-05 7.0329+01 1.4857+01 7,, 1224+01

45.0 1 .5406 + 02 3.3107-05 6.3946+01 1.5801+01 7,,4315+01

50.0 1.5238+02 2.9728-05 5.8700+01 1.6646+01 7,,7039+01

55.0 1.5118+02 2.6974-05 5.4304+01 1.7408+01 7,,9466+01

60.0 1.5031+02 2.4687-05 5.0564+01 1.8102+01 8.. 1647+01

65.0 1.4970+02 2.2758-05 4.7343+01 1.8736+01 8<3622+01

70.0 1.4928+02 2.1108-05 4,4538+01 1.9321+01 8,,5421+01

75.0 1.4900+02 1.9681-05 4.2071+01 1.9863+01 8,,7069+01

80.0 1 .4884+02 1.8435-05 3.9882+01 2.0367+01 8.,8589+01

85.0 1 .4876+02 1.7237-05 3.7925+01 2.0837+01 8.,9995+01

90. 1.4874+02 1.6363-05 3.6163+01 2.1278+01 9,.1302+01

95.0 1.4878+02 1.5492-05 3.4568+01 2.1693+01 9«,2521+01

100. 1.4886+02 1.4709-05 3.3118+01 2.20 84+01 9,.3661+01

125.0 1 .4966+02 1.1743-05 2.7474+01 2.3752+01 9,,8435+01

150.0 1 .5075+02 9.7720-06 2.3573+01 2.5071+01 1..0211+02

175.0 1 .5189+02 8.3676-06 2.0697+01 2.6152+01 1,,0504+02

200.0 1.5301+02 7.3161-06 1.8482+01 2.7061+01 1.,0746+02

225.0 1.5406+02 6.4994-06 1.6724+01 2.7841+01 1,,0950+02

250.0 1.5505+02 S.e467-06 1.5294+01 2.8519+01 1«,1124+02

275. 1.5598+02 5.3132-06 1 .4106+01 2.9116+01 1.1275+02

300.0 1 .5683+02 4.8689-06 1.3102+01 2.9648+01 1.,1408+02

325.0 1.5762+02 4.4931-06 1.2241+01 3.0125+01 1..1525+02

350.0 1 .5835+02 4. 1712-06 1.1494+01 3.0556+01 1,,1630+02

16
Table I: Continued

Z= 6

e TOTAL PHOTO COMPTON TRIPLET PAIR

(MEV) (MB) (MB) (MB) (MB) (MB)

10*0 3.9082+02 1. 1637-03 3.0692+02 7.0232+00 7.6883+01

12.0 3.6458+02 9.5283-04 2.6844+02 8.7486+00 8.7390+01

14*0 3.4601+02 e. 06 45-04 2.3927+02 1.0300+01 9.6442+01

16.0 3.3238+02 6.9895-04 2.1630+02 1. 1705+01 1.0437+02

18.0 3.2211+02 6. 1669-04 1.9771+02 1.2984+01 1.1 141+02

20. 3*1421+02 5.5172-04 1.8232+02 1.4156+01 1.1773+02

22.0 3.0803+02 4.9911-04 1.6934+02 1.5234+01 1.2345+02

24.0 3.0314+02 4.5565-04 1.5824+02 1.6231+01 1.2867+02

26.0 2.9923+02 4.1915-04 1.4862+02 1.7158+01 1.3345+02

28.0 2.9609+02 3.8805-04 1.4620+02 1.8022+01 1.3787+02

30.0 2.9356+02 3.6125-04 1.3275+02 1.8832+01 1.4197+02

32.0 2.9150+02 3.3791-04 1.2612+02 1.9592+01 1.4579+02

34.0 2.8984+02 3.1739-04 1.2018+02 2.0309+01 1.4935+02

36.0 2.8849+02 2.9923-04 1.1481+02 2.0988+01 1.5270+02

38.0 2.8741+02 2.8303-04 1.0994+02 2.1630+0 1 1.5584+02

40.0 2.8654+02 2.6849-04 1.0549+02 2.2241+01 1.5881+02

45.0 2.8511+02 2.3793-04 9.5920+01 2.3643+01 1.6555+02

50.0 2.8443+02 2. 1362-04 8.8051+01 2.4896+01 1.7149+02

55.0 2.8427+02 1.9381-04 8.1456+01 2.60 26+01 1.7679+02

60.0 2.8446+02 1.7737-04 7.5846+01 2.7052+01 1.8156+02

65.0 2.8489+02 1.6349-04 7.1014+01 2.7991+01 1.8589+02

70.0 2.8550+02 1.5163-04 6.6807+01 2.8855+01 1.8984+02

75. 2.8624+02 1.4137-04 6.3107+01 2.96 56+0 1 1.9347+02

80.0 2.8705+02 1.3242-04 5.9823+01 3.0400+01 1.9683+0 2

85.0 2.8792+02 1.2453-04 5.6887+01 3.1095+01 1.9993+02

90.0 2.8882+02 1. 1752-04 5.4244+01 3.1746+01 2.0283+02

95.0 2.8974+02 1.1127-04 5.1853+01 3.2358+01 2.0553+02

100.0 2.9067+02 1.0564-04 4.9678+01 3.2935+01 2.0806+02

125.0 2.9529+92 8.4327-05 4.1211+01 3.5395+01 2.1868+02

150.0 2.9956+02 7.0169-05 3.5359+01 3.7335+0 1 2.2687+02

175.0 3.0338+02 6. 0081-05 3.1 045+01 3.8919+01 2.3341+02

200.0 3.0676+02 5.2530-05 2.7723+01 4.0244+01 2.3879+02

225.0 3.0976+02 4.6664-05 2.5087+01 4.1374+01 2.4330+02

250.0 3.1243+02 4.1977-05 2.2941+01 4.2351+01 2.4714+02

275.0 3.1483+02 3.8146-05 2.1159+01 4.3208+01 2.5046+02

300.0 3.1698+02 3.4955-05 1 .9654+01 4.3966+0 1 2.5337+02

325.0 3.1893+02 3.2257-05 1.8362+01 4.4642+01 2.5592+02

350.0 3.2070+02 2.9946-05 1.7241+01 4.5250+01 2.5820+02

17
Table I: Continued

Z- 8.

c TOTAL PHOTO COMPTON TRIPLET PAIR

(MEV) (MB) (MB) (MB) (MB) (ME)

10.0 5.5508+02 4.6661-03 4.0922+02 9 .3638+00 1.3649+02

12.0 5.2465+02 3.8176-03 3.5792+02 1,, 1664+01 1.5505+02

14. 5.0378+02 3.2293-03 3.1902+02 1<,3731+01 1.7102+02

16.0 4.8899+02 2.7 977-03 2.6841+02 1 - 56 02+01 1.8498+02

18.0 4.7828+02 2.4676-03 2.6362+02 1.,7305+01 1.9736+02

20.0 4.7041+02 2.2C70-03 2.4309+02 1.,8863+01 2.0845+02

22.0 4.6457+92 1.5561-03 2.2579+92 2<0296+01 2.1848+02

24.0 4.6023+02 1.8220-03 2.1098+02 2 .1620+01 2.2762+02

26.0 4.5702+02 1.6757-03 1.5816+02 2.,2850+01 2.3601+02

28.0 4.5468+02 1.5512-03 1 .8693+02 2.3997+01 2.4375+02

30.0 4.5301+02 1.4439-03 1. 7700+02 2<,5071+01 2.5093+02

32.0 4.5187+02 1.3504-03 1.6816+02 2..6079+01 2.5762+02

34.0 4.5114+02 1.2683-03 1.6 023+02 2.,7029+01 2.6387+02

36.0 4.5074+02 1.1956-03 1 .5308+02 2..7926+0 1 2.6974+02

38.0 4.5061+02 1.1308-03 1.4658+02 2.,8777+01 2.7525+02

40.0 4.5070+02 1.0726-03 1.4066+02 2.9584+01 2.8046+02

45.0 4.5162+02 9.5044-04 1.2789+02 3«,1437+01 2.9229+02

50.0 4.5322+02 8.5322-04 1.1740+02 3..3091+0 1 3.0273+02

55.0 4.5524+02 7.7403-04 1.0861+02 3<4582+01 3.1205+02

60.0 4.5752+02 7.0829-04 1 .0113+02 3<5936+01 3.2045+02

65.0 4.5994+02 6.5284-04 9.4665+01 3,,7174+01 3.2808+02

70.0 4.6243+02 6.0545-04 8.9076+01 3,.8313+01 3.3504+02

75.0 4.6494+02 5.6446-04 8.4142+01 3.,9367+01 3.4143+02

80.0 4.6 743+02 5.2867-04 7.9765+01 4 .0347+01 3.4732+02

85.0 4.6589+02 4.9715-04 7.5650+01 4,,1260+01 3.5278+02

90.0 4.7229+02 4.6518-64 7.2326+01 4.,21 15+01 3.5785+02

95.0 4.7463+02 4.4418-04 6.9137+01 4 .2918+01 3.6258+02

100.0 4.7691+02 4.2172-04 6.6237+01 4.,3675+01 3.6700+02

125.0 4.8732+02 3.3659-04 5.4947+01 4,.6890+01 3.8548+02

150.0 4.9614+02 2.6C06-04 4.7145+01 4.9412+01 3.9959+0 2

175.0 5.0362+02 2.3979-04 4.1394+01 5<, 1461 + 01 4.1076+0 2

200.0 5.1000+02 2.C564-04 3.6565+01 5,,3167+01 4.1986+02

225. 5. 1551+02 1.8622-04 3.3449+01 5,,4614+01 4.2745+02

250.0 5.2031+02 1.6752-04 3. 0568+01 5,,5861+01 4.3386+02

275.0 5.2455+02 1.5222-04 2.8213+01 5<,6950+01 4.3938+02

300.0 5.2830+02 1.3549-04 2.6205+01 5«,7910+01 4.4418+02

325. 5.3164+02 1.2872-04 2.4483+01 5<8763+01 4.4839+02

350.0 5.3465+02 1.1549-04 2.2588+01 5«.9528+01 4.5213+02

18
Z=13

Table I: Continued

E

(MEV)

TOTAL

(MB)

PHOTO

(MB)

COMPTON

(MB)

RI PLET

(MB)

PAIR

(MB)

10.0

12.0

14.0

16.0

18.0

20.0

22.0

24.0

26.0

28.0

30.0

32.0

34,0

36.0

38.0

40.0

45.0

50*0

55,0

60.0

65.0

70.0

75. a

80.0

85.0

90.0

95.0

100.0

125.0

150.0

175.0

200.0

225.0

250.0

275.0

300.0

325.0

350.0

1 .0389+03

1.0C76+03

9.8916+02

9.7862+02

9.7316+02

9.7106+02

9.7125+02

9.7302+02

9.7590+02

9.7957+02

9.8378+02

9.8836+02

9.9319+02

9.9817+02

1. 0033+03

1.0084+03

1.0211+03

1.0336+03

1.0455+03

1.0568+03

1.0676+03

1 .0777+03

1.0873+03

1 .0964+03

1.1050+03

1.1131+03

1.1207+03

1.1280+03

1 .1593+03

1.1841+03

1.2042+03

1.2210+03

1.2351+03

1.24 73+03

1.2579+03

1.2672+03

1 .2754+03

1.2828+03

4.7052-02

3.8427-02

3.2462-02

2.8095-02

2.4760-02

2*2131-02

2.0006-02

1.8252-02

1.6781-02

1.5529-02

1.4450-02

1.3512-02

1.2687-02

1.1958-02

1.1307-02

1.0724-02

9.4991-03

8.S251-03

7.7321-03

7.0741-03

6.5192-03

6. 0451-03

£•€352-03

5.2774-03

4.9622-03

4.6826-03

4.43 29-03

4.2084-03

3.3580-03

2.7936-03

2.3915-03

2.0907-03

1.8570-03

1.6704-03

1.5178-03

1.3908-03

1.2834-03

1.1914-03

6.6498+02

5.8163+02

5.1842+02

4.6866+02

4.2838+02

3.9502+02

3.6691+02

3.4285+02

3.2201+02

3.0376+02

2.8763+02

2.7327+02

2.6038+02

2.4875+02

2.3819+02

2.2857+02

2.0783+02

1.9C78+02

1.7649+02

1.6433+02

1.5386+02

1.4475+02

1.3673+02

1.2962+02

1.2326+02

1.1753+02

1.1235+02

1.0763+02

8.9290+01

7.6611+01

6.7265+01

6.0 067+01

5.4354+01

4.9706+01

4.5845+01

4.2583+01

3.9784+01

3.7356+01

.5210+01

•8940+0 1 .22 89+01

.5316+01

.8068+01

.05 83+01

•2893+01

.5025+01

.7003+01

.8846+01

•0569+01

• 21 86+01

•3708+01

•5144+01

•6504+01

.7793+01

.0746+01

•33 74+01

•5734+01

.7870+01

.9816+01

.1602+01

.3248+01

.4772+01

.6189+01

.7512+01

.8750+01

.9912+01

•4820+01

•8634+01

•1711+01

.4263+0 1 .6424+01

•8283+01

•9907+01

•1339+01

.2614+01

.3759+01

.5870+02

.0699+02

•4842+02

•8462+02

• 1669+02

•4543+02

.7143+02

.9513+02

• 1688+02

.3695+02

.5556+02

•7289+02

•8909+02

•0427+02

.1854+02

•3200+02

.6255+02

.8940+02

•1324+02

•3460+02

•5388+02

.7138+02

.8736+02

•0202+02

•1553+02

•2804+02

.3964+02

.5046+02

•9518+02

.0288+03

.0553+03

.0766+03

•0944+03

.1093+03

.1221+03

•1333+03

•1430+03

•1516+03

19
Table I: Continued

Z=20.

E TOTAL PHOTO CCMPTOM TRIPLET PAIR

(MEV) (MB) (MB) <MB) (MB) (MB)

10.0 1.8894+03 2.5C67-01 1.0231+03 2.3372+01 8.,4264+02

12.0 1 .8792+03 2.8575-01 8.9481+02 2.90 89+01 9 .5498+02

14.0 1 .8834+03 2.4100-01 7.9756+02 3.4215+01 1..0514+03

16.0 1 .8957+03 2.0831-01 7.2102+02 3.8840+01 1 . 1356+03

18.0 1.9124+03 1.8340-01 6.5904+02 4.3041+01 1..2102+03

20. 1.9317+03 1.6380-01 6.0773+02 4.6876+01 1 .2769+03

22.0 1.9523+03 1.4797-01 5.6447+02 5.0393+01 1 ..3372+03

24. 1.9733+03 1.3492-01 5.2746+02 5.3635+01 1 .3921+03

26.0 1.9945+03 1.2398-01 4.9539+02 5.6639+01 1«.4424+03

28. 2. 0155+03 1.1468-01 4.6732+02 5.9434+0 1 1 .4886+03

30.0 2.0361+03 1.C668-01 4.4251+02 6.2044+01 1.,5315+03

32.0 2.0562+03 9.9716-02 4.2041+02 6.44 89+01 1 .5712+03

34.0 2.0758+03 5.3606-02 4. 0058+02 6.6788+01 1 ..6083+03

36. 2.0547+03 8.8201-02 3.8269+02 6.8955+01 1..6430+03

38.0 2.1 131+03 E. 3386-02 3.6645+02 7.1003+01 1.,6756+03

40.0 2.1309+03 7.9068-02 3.5164+02 7.2943+01 1 .7062+03

45.0 2.1727+03 7. C005-02 3.1573+02 7.7378+01 1.,7755+03

50. 2.2111+03 6.2805-02 2.9350+02 8.1316+01 1 .8362+03

55.0 2.2465+03 5.6546-02 2.7152+02 8.4847+01 1 . ,8900+03

60.0 2.2791+03 S.2C67-02 2.5282+02 8.8038+01 1.,9382+03

65.0 2.3094 + 03 4.7992-02 2.3671+02 9.0942+01 1 .9817+03

70.0 2.3374+02 4.4494-02 2.2269+02 9.3603+01 2,,0211+03

75.0 2.3635+03 4.1470-02 2.1036+02 9.6055+01 2..0571+03

80.0 2.3879+03 3.8832-02 1.5541+02 9.8324+01 2.,0901+03

85.0 2.4107+03 3.6509-02 1.8962+02 1.0043+02 2.. 1206+03

90.0 2.4320+03 3.4448-02 1.8Cei+02 1.0240+02 2.,1488+03

95.0 2.4521+03 3.2607-02 1 .7284+02 1.0424+02 2..1750+03

100.0 2.4709+03 3.0953-02 1.6559+02 1.0597+02 2.,1994+03

125.0 2.5510+03 2.4691-02 1.3737+02 1. 1325+02 2..3004+03

150.0 2.6134+03 2.C536-02 1.1786+02 1.1891+02 2.,3766+03

175.0 2.6634+03 1.7578-02 1.0348+02 1.2347+0 2 2 .4364+03

200.0 2.7046+03 1.5365-02 9.2411+01 1.2725+02 2.,4849+03

225.0 2.7392+03 1.36 46-02 8.3622+01 1.3044+02 2..5251+03

250.0 2.7687+03 1.2274-02 7.6471+01 1.3318+02 2.,5591+03

275.0 2.7943+03 1.1152-02 7.0531+01 1.3558+02 2..5882+03

300.0 2.8166+03 1.0218-02 6.5512+01 1 .3768+02 2.,6134+03

325.0 2.8363+03 9.4286-03 6.1207+01 1.3956+02 2.,6356+03

350.0 2.8539+03 8.7523-03 5.7470+01 1.4124+02 2.,6552+03

20
Table I: Continued

Z=29.

E TOTAL PHOTO CCMPTON TRIPLET PAIR

(MEV) (MB) (MB) (MB) (MB) (ME)

10.0 3.2734+03 1.9124+00 1.4834+03 3.3824+01 1.7542+03

12.0 3.3263+03 1.5545+00 1.2975+03 4.2074+01 1.9852+03

14. 3.3904+03 1.3086+00 1 .1565+03 4.9462+01 2.1832+03

16.0 3.4587+03 1.1295+00 1.0455+03 5.6120+01 2.3559+03

16.0 3.5275+03 9.9327-01 9.5561+02 6.2159+0 1 2.5087+03

20.0 3.5950+03 8.8626-01 8.8121+02 6.7665+01 2.6453+03

22.0 3.6605+03 7.9999-01 8.1848+02 7.2708+01 2.7685+03

24.0 3.7234+03 7.2858-01 7.6482+02 7.7351+01 2.8805+03

26.0 3.7838+03 6.6951-01 7.1832+02 8. 1647+0 1 2.9831+03

28.0 3.8414+03 6.1859-01 6.7761+02 8.5640+01 3. 0776+03

30.0 3.8565+03 5.7555-01 6.4164+02 8.9365+0 1 3.1650+03

32.0 3.9491+03 5.3779-01 6.0555+02 9.2850+01 3.2461+03

34.0 3.9993+03 5.0468-01 5.8085+02 9.6123+01 3.3219+03

36.0 4.0473+03 4.7539-01 5.5450+02 9.9205+01 3.3927+03

38.0 4.0931+03 4.4932-01 5.3136+02 1.021 1+02 3.4591+03

40.0 4.1368+03 4.2595-01 5.0588+02 1.0487+02 3.5217+03

45.0 4.2383+03 3.7694-01 4.6361+02 1.1115+02 3.6632+03

50.0 4.3297+03 3.38D3-01 4.2558+02 1.1671+02 3.7871+03

55.0 4.4126+03 3.0640-01 3.9370+02 1.2168+02 3.8969+03

60.0 4.4881+03 2.8018-01 3.6659+02 1.2615+0 2 3.9951+03

65.0 4.5573+03 2.5809-01 3.4323+02 1.3022+02 4.0836+03

70.0 4.6208+03 2.3922-01 3.2290+02 1.3393+02 4.1637+03

75.0 4.6794+03 2.2293-01 3.0501+02 1.3734+02 4.2368+03

80.0 4.7336+03 2.0871-01 2.8915+02 1.40 48+02 4.3038+03

85.0 4.7839+03 1.9620-01 2.7496+02 1.4340+02 4.3653+03

90.0 4.8307+03 1.8510-01 2.6218+02 1.461 1+02 4.4222+03

95.0 4.8743+03 1.7519-01 2.5062+02 1.4864+02 4.4749+03

100.0 4.9152+03 1.6629-0 1 2.4011+02 1.5101+02 4.5239+03

125.0 5.0860+03 1.3259-01 1.5518+02 1.6094+02 4.7258+03

150.0 5.2161+03 1.1025-01 1.7090+02 1.6855+02 4.8766+03

175.0 5.3189+03 9.4355-02 1.5005+02 1.7463+0 2 4.9941+03

200.0 5.4023+03 8.2463-0 2 1.3400+02 1.7962+02 5.0886+03

225.0 5.4716+03 7.3234-02 1.2125+02 1.8381+02 5.1665+03

250.0 5.5301+03 6.5862-02 1.1088+02 1.8738+02 5.2318+03

275.0 5.5804+03 5.9838-02 1.0227+02 1.9047+02 5.2876+03

300.0 5.6241+03 5.4824-02 9.4593+01 1.9318+02 5.3359+03

325.0 5.6623+03 5.0586-02 8.8750+01 1.9557+02 5.3779+03

350.0 5.6962+03 4.6955-02 8.3332+01 1.9771+02 5.4151+03

21
Table I: Continued

Z=50.

E TOTAL PHOTO COMPTON TRIPLET PAIR

(MEV) (MB) (MB) (ME) (MB) (MB)

10.0 7 .7054*03 2.1539+01 2.5576+03 5.8026+01 5.0682+03

12.0 8 . 0353+03 1.7424+01 2.2370+03 7.2092+01 5.7088+03

14.0 8 .3515+03 1.4616+01 1.9939+03 8.4649+01 6.2583+03

16.0 8 . 6491*03 1.2580+01 1.8025+03 9.5932+01 6.7381+03

18.0 8 .9275+03 1.1039+01 1.6476+03 1.0614+02 7.1627+03

20.0 9 .1871+03 9.8319+00 1.5193+03 1. 1541+02 7.5425+03

22.0 9 .4290+03 8.8616+00 1.4112+03 1.2389+02 7.8851+03

24. 9 .6548+03 8.0648+00 1.3186+03 1.3167+02 8.1964+03

26.0 9 .8659+03 7.3989+00 1.2385+03 1.3885+02 8.4812+03

28.0 1 .0064+04 6.8342+00 1.1683+03 1.4551+02 8.7431+03

30.0 1 .0249+04 6. 3493+00 1. 1063+03 1.5171+02 8.9852+03

32.0 1 . 0424+04 5.9285+00 1.0510+03 1.5750+02 9.2097+03

34.0 1 .0589+04 5.5598+00 1.0015+03 1.6293+02 9.4188+03

36.0 1 .0744+04 5.2343+00 9.5673+02 1.6802+02 9.6141+03

38.0 1 .0891+04 4.9446+00 9.1613+02 1.7283+02 9.7971+03

40.0 1 .1030+04 4.6853+00 8.7911+02 1.7736+02 9.9689+03

45.0 1 .1348+04 4.1420+00 7.9933+02 1.8768+02 1.0357+04

50.0 1 .1630+04 3.7115+00 7.3376+02 1.9678+02 1.0695+04

55.0 1 .1882+04 3.3620+00 6.7880+02 2.0489+02 1.0995+04

60.0 1 .2109+04 3.0725+00 6.3205+02 2.1217+02 1 .1261+04

65.0 1 .2315+04 2.8290+00 5.9178+02 2. 1876+02 1.1501+04

70.0 1 .2502+04 2.6211+00 5.5672+02 2.2477+02 1.1718+04

75.0 1 .2674+04 2.4417+00 5.2589+02 2.3027+02 1.1915+04

80.0 1 .2832+04 2.2853+00 4.9853+02 2.3534+02 1.2096+04

85.0 1 .2978+04 2.1477+00 4.7406+02 2.4003+02 1.2262+04

90.0 1 .3113+04 2.0257+00 4.5204+02 2.4439+02 1.2414+04

95.0 1 .3238+04 1.9169+00 4.3210+02 2.4844+02 1.2556+04

100.0 1 .3356+04 1.8191+00 4. 1398+02 2.5224+02 1.2668+04

125.0 1 .3841+04 1.4494+00 3.4342+02 2.6808+02 1.3228+04

150.0 1 .4207+04 1.2C46+00 2.9466+02 2.8018+02 1.3631+04

175.0 1 .4494+04 1.0305+00 2.5871+02 2.8981+02 1.3944+04

200.0 1 .4726+04 9.0040-01 2.3103*02 2.9770+02 1.4196+04

225.0 1 .4918+04 7.9945-01 2. 0905+02 3.0431+02 1.4404+04

250.0 1 .5080+04 7.1885-01 1.9118+02 3.0995+02 1.4578+04

275.0 1 .5218+04 6.5302-01 1.7633+02 3. 1483+02 1.4726+04

30 0.0 1 .5338+04 5.9823-01 1 .6378+02 3.1910+02 1.4855+04

325.0 1 •5443+04 5.5193-01 1.5302+02 3.2287+02 1.4967+04

350.0 1 .5536+04 5.1227-01 1.4368+02 3.2623+02 1.5066+04

22
Table I: Continued

Z=73.

£ TOTAL PHCTO CC3MFTON TRIPLET PAIR

(MEV) (MB) (MB) (MB) (MB) (ME)

10.0 1.. 4258+04 1.1040+02 3.7341+03 8,.4249+01 1.0329+04

12.0 1 .5029+04 8.8941+01 3.2661+03 1.> 0455+02 1.1569+04

14. 1..5744+04 7.4376+01 2.9111+03 1..2264+02 1.2636+04

16.0 1 .6405+04 6.3865+01 2.6317+03 1..3885+02 1.3570+04

16.0 1..7013+04 5.5931+01 2.4055+03 1,,5348+02 1.4398+04

20.0 1 .7575+04 4.9737+01 2.2182+03 1..6675+02 1.5141+04

22.0 1..8095+04 4.4769+01 2.0603+03 1..7885+02 1.5811+04

24.0 1 .8578+04 4.0697+01 1.9252+03 1,.8993+02 1.6422+04

26.0 1..9027+04 3.7301+01 1.8082+03 2..0014+02 1.6981+04

28.0 1 .9446+04 3.4426+01 1.7C57+03 2,,0959+02 1.7496+04

30.0 1 .9838+04 3.19€0+01 1.6152+03 2.,1837+02 1.7972+04

32.0 2 .0206+04 2.9822+01 1.5345+03 2.,2655+02 1.8415+04

34.0 2 .0551+04 2.7952+01 1.4621+03 2.,3420+02 1.8827+04

36. 2 .0877+04 2.6301+01 1.3968+03 2.,4138+02 1.9212+04

38.0 2 .1184+04 2.4834+01 1.3376+03 2,4813+02 1.9574+04

40.0 2 .1474+04 2.3522+01 1.2835+03 2 ,5*49+0 2 1.9913+04

45.0 2 .2136+04 2.0776+01 1.1670+03 2.6892+02 2.0679+04

50.0 2 ,2720+04 1.8603+01 1.0713+03 2..8160+02 2.1348+04

55.0 2 .3239+04 1.6841+01 9.91C5+02 2.,9287+02 2.1939+04

60. 2 .3706+04 1.5384+01 9.2279+02 3,.0295+02 2.2465+04

65.0 2 .4127+04 1.4158+01 8.6400+02 3.1206+02 2.2937+04

70.0 2..4509+04 1.31 13+01 8.1281+02 3..2034+02 2.3363+04

75.0 2 .4858+04 1.2212+01 7.6780+02 3«.2791+02 2.3751+04

80.0 2 .5179+04 1.1426+01 7.2785+02 3,.3487+02 2.4104+04

85.0 2 .5473+04 1.0736+01 6.9213+02 3,,4129+02 2.4429+04

90.0 2 .5745+04 1.0124+01 6.5997+02 3.,47 24+02 2.4728+04

95.0 2 .5998+04 9.5776+00 6. 3087+02 3.,5278+02 2.5005+04

100.0 2 .6233+04 9.0875+00 6.0441+02 3..5795+02 2.5262+04

125.0 2 .7201+04 7.2357+00 5.0140+02 3 ,7944+02 2.6313+04

150.0 2 .7925+04 6.0108+00 4.3020+02 3.,9576+02 2.7093+04

175.0 2 .8490+04 5.1405+00 3.7772+02 4 .0868+02 2.7698+04

200.0 2 .8944+04 4.49 03+0 3.3730+02 4.,1922+02 2.8183+04

225.0 2 .9318+04 3.9861+00 3.0522+02 4 .2802+02 2.8581+04

250.0 2 .9633+04 3.5837+00 2.7912+02 4,,3550+02 2.8914+04

275.0 2 .9901+04 3.2551+00 2.5744+02 4..4196+02 2.9198+04

30 0.0 3 .0133+04 2.9816+00 2.3912+02 4,,4760+02 2.94 44+04

325.0 3 .0335+04 2.7506+00 2.2341+02 4.,5257+02 2.9656+04

350.0 3 .0514+04 2.5528+00 2.0977+02 4,5700+02 2.9845+04

23
Table I: Continued

Z=82.

E T0-!"AL PHOT CCMPTCN TRI PLE' PAIR

(MEV) (MB) (MB) (MB) (MB) (MB)

10, 1

.

.7201+04 1.8087+02 4. 1945+03 9.4423+01 1.,2731+04

12. 1.. 8163 + 04 1.4552+02 3.6687+03 1.1713+02 1 .4232+04

14. 1.•9055+04 1.2156+02 3.2700+03 1.3733+02 1.,5526+04

16. 1,,9878+04 1.0429+02 2.956 2+03 1.5543+02 1 .6662+04

18. 2..0637+04 9. 1275+01 2.7021+03 1.7174+02 1..7672+04

20. 2.,1337+04 8.1121+01 2.4917+03 1.8653+02 1 ,8577+04

22. 2..1984+04 7.2985+01 2.3143+03 1.9999+02 1.,9397+04

24, 2,.2584+04 C. 6321+01 2. 1626+03 2.1232+02 2.,0143+04

26. 2.,3142+04 6.0766+01 2.0311+03 2.2367+02 2 .0827+04

28. 2.,3663+04 5.6065+01 1.9160+03 2.3417+02 2.,1457+04

30. 2.,4149+04 5.2036+01 1.8143+03 2.4392+02 2..2039+04

32. 2..4606+04 4.8545+01 1.7237+03 2.5300+02 2.,2580+04

34. 2.,5034+04 4.5491+01 1.6424+03 2.6148+02 2 .3085+04

36. 2..5437+04 4.2797+01 1.5690+03 2.6944+02 2.,3556+04

38. 2.,5817+04 4.0404+01 1 .5025+03 2.7693+02 2 .3997+04

40. 2..6176+04 3.8263+01 1.4417+03 2.8398+02 2.,4412+04

45. 2.,6994+04 3.3786+01 1.3109+03 2.9996+02 2 .5349+04

50. 2..7714+04 3.0244+01 1.2034+03 3. 1400+02 2.,6166+04

55. 2,,8354+04 2.7374+01 1.1 132+03 3.2645+0 2 2 .6887+04

60. 2..8928+04 2.5C00+01 1.0366+03 3.3760+02 2..7529+04

65. 2.,9446+04 2.3005+01 9.7053+02 3.4767+02 2..8105+04

70. 2..9917+04 2.1305+01 9.1302+02 3.5681+02 2.,8625+04

75. 3<,0346+04 1.9838+01 8.6246+02 3.6516+02 2 ,9098+04

80, 3,.0739+04 1.8560+01 8. 1759+02 3.7284+02 2.,9530+04

85, 3,,1100+04 1.7437+01 7 .7746+02 3.7992+02 2.,9926+04

90. 3,.1435+04 1.6441+01 7.4134+02 3.8647+0 2 3..0290+04

95, 3 ,1744+04 1.5554+01 7.0865+02 3.9257+02 3,,0628+04

100. 3.,2033+04 1.4757+01 6.7893+02 3.9826+02 3,.0941+04

125, 3..3219+04 1.1747+01 5.6321+02 4.2189+02 3,,2223+04

150. 3.,4106 + 04 9.7567+00 4.8324+02 4.3981+02 3 ( .3174+04

175, 3 ,4797+04 8.3430+00 4.2428+02 4.5398+02 3,,3911+04

20 0. 3,,5353+04 7.2871+00 3.7889+02 4.6552+32 3,,4502+04

225. 3,,5811+04 6.4684+00 3.4285+02 4.7515+02 3, 4987+04

250. 3.,6195+04 5.8151+00 3.1353+02 4.8333+02 3.,5393+04

275. 3..6524+04 5.2816+00 2.8918+02 4.9038+02 3, 5739+04

300. 3.,6808+04 4.8378+00 2.6860+02 4.9654+02 3,,6038+04

325. 3,.7055+04 4.4628+00 2.5095+02 5.0196+02 3, 6298+04

350. 3,,7274+04 4.1417+00 2.3563+02 5.0679+0 2 3,,6527+04

24
Table II: Screening cross sections AS for pair production in the nuclear

Coulomb field. Column 2-4 give the screening values obtained with

the different sets of form factors as described in section 3.3:

THF: Thomas-Fermi form factors, NONREL. : nonrelativistic form

factors, REL. : relativistic form factors.

SCREENING CORRECTIONS FOR Z~ 3

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 5.3671-02 1.8306-03 1 .8566-03

10.0 6.6796-02 2.7822-03 2. 7998-03

15.0 1.4868-01 1.3005-02 1.2824-02

20.0 2.5218-01 3.5964-02 3.5200-02

25.0 3.7130-01 7.5146-02 7.3246-02

50.0 1 .0877+00 5.2386-01 5. 0736-01

75.0 1.8810+00 1.2617+00 1.2226+00

100.0 2.6883+00 2. 1197+00 2. 0575+00

125.0 3.4850+00 3.0089+00 2.9258+00

150.0 4.2614+00 3.8892+00 3.7875+00

175.0 5. 0126+00 4,7434+00 4.6254+00

200.0 5.7368+00 5.5650+00 5.4326+00

225.0 6.4336+00 6.3519+00 6. 2066+00

250.0 7. 1042+00 7.1052+00 6.9484+00

275.0 7.7491+00 7.8258+00 7.6586+00

300. 8.3702+00 8.5161+00 8.3395+00

325.0 8.9691+00 9. 1786+00 8.9934+00

350.0 9.5461+00 9.8141+00 9.6211+00

SCPEENING CORRECTIONS FOR Z= 4

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 1. 1450-01 7.8031-03 7.9905-03

10.0 1.4226-01 1.1719-02 1.1898-02

15.0 3.1388-01 5.1265-02 5. 0895-02

20.0 5.2795-01 1.3230-01 1.3049-01

25.0 7.7165-01 2.6C70-01 2.5502-01

50.0 2.2086+00 1.4611+00 1.4166+00

75.0 3.7736+00 3. 1084+00 3. 0238+00

100.0 5.3488+00 4.8421+00 4.7253+00

125.0 6.8916+00 6.5391+00 6. 3956+00

150. 8.3840+00 8.1637+00 7.9953+00

175.0 9.8193+00 9.7091+00 9.5160+00

200.0 1.1196+01 1.1178+01 1.0960+01

225.0 1.2515+01 1.2575+01 1.2332+01

250.0 1.3780+01 1.3907+01 1.3638+01

275.0 1.4992+01 1.5178+01 1.4883+01

300.0 1.6156+01 1.6394+01 1.6075+01

325.0 1.7276+01 1.7560+01 1.7217+01

350.0 1.8352+01 1.8678+01 1.8312+01

25
Table II: Continued

SCREENING CORRECTIONS FOR Z= 6

E THF NCNREL. REL.

CMEV) (MB) (MB) (MB)

9.0 3.3221-01 5.5661-02 5.6170-02

10.0 4.1160-01 8.0945-02 8. 1354-02

15.0 8.9556-01 3.0522-01 3.0376-01

20.0 1 .4876+00 6.9596-01 6.9016-01

25.0 2.1513+00 1.2299+0 1.2178+00

50.0 5.9627+00 5.0030+00 4.9529+00

75.0 1.0020+01 9.2193+00 9.1395+00

100.0 1.4042+01 1.3317+01 1.3210+01

125.0 1.7933+01 1.7219+01 1.7080+01

150.0 2.1660+01 2.0929+01 2. 0750+01

175.0 2.5215+01 2.4459+01 2.4235+01

200.0 2.8601+01 2.7822+01 2.7550+01

225.0 3. 1826+01 3.1029+01 3.0708+01

250.0 3.4902+01 3.4093+01 3.3724+01

275.0 3.7838+01 3.7022+01 3.6606+01

300.0 4.0646+01 3.9829+01 3.9367+01

325.0 4.3339+01 4.2525+01 4.2018+01

350.0 4.5918+01 4.51 10+01 4. 4561+01

SCREENING CORRECTIONS FOR Z= 8

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 7. 0572-01 2*1647-01 2.0447-01

10.0 8.7241-01 3.0570-01 2.8811-01

15.0 1.8776+00 1.0020+00 9.5091-01

20.0 3.0898+00 2.0453+00 1.9604+00

25.0 4.4347+00 3.3242+00 3. 2388+00

50.0 1.2021+81 1.0969+01 1.0755+01

75.0 1.9967+01 1.8832+01 1. 8569+01

100.0 2.7758+01 2.6459+01 2.6148+01

125.0 3.5231+01 3.3801+01 3.3430+01

150.0 4.2336+01 4.0834+01 4.0396+01

175.0 4.9074+01 4.7554+01 4. 7044+01

200.0 5.5461+01 5.3966+01 5.3384+01

225.0 6.1519+01 6. C080+01 5.9427+01

250.0 6.7278+01 6.5915+01 6.5195+01

275.0 7.2758+01 7.1484+01 7.0700+01

300.0 7.7986+01 7.6811+01 7.5967+01

325.0 8.2987+01 8. 1915+01 e. 1016+01

350.0 8.7768+01 8.6801+01 8.5849+01

26
Table II: Continued

SCREENING CORRECTIONS FOR Z-13

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 2.5042+00 1.5212+00 1.4842+00

10.0 3.0824+00 2.0213+00 1.9722+00

15.0 6.5027+00 5.2543+00 5. 1449+00

20.0 1.0528+01 9.2075+00 9.0499+0

25.0 1.4918+01 1.3499+01 1.3307+01

50.0 3.8991+01 3.6947+01 3.6691+01

75.0 6.3533+01 6.1667+01 6. 1370+01

100.0 8. 7137+01 8.6028+01 8.5689+01

125.0 1.0944+02 1.0929+02 1. 0891+02

150.0 1.3039+02 1.3124+02 1.3082+02

175.0 1.5007+02 1.5186+02 1.5141+02

200.0 1.6858+62 1.7126+82 1.7077+02

22 5.0 1.8602+02 1.8951+02 1.8900+0 2

250.0 2.0251+02 2.0675+02 2. 0620+02

275.0 2. 1812+02 2.2304+02 2.2246+02

300.0 2.3295+02 2.3850+02 2.3789+02

325.0 2.4709+02 2.5321+02 2.5257+02

350.0 2.6056+02 2.6721+02 2.6655+02

SCREENING CORRECTIONS FCR Z=2©

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 7.6575+00 6.6170+00 6.7534+00

10.0 9.3846+00 8.3523+00 8.4949+00

15.0 1.9423+01 1.8279+01 1.8449+01

20.0 3.0990+01 2.9542+01 2.9758+01

25.0 4.3426+01 4.1783+01 4.2056+01

50.0 1.1003+02 1.0994+02 1. 1047+02

75. 1.7627+02 1.7831+02 1.7902+02

100.0 2.3888+02 2.4237+02 2.4322+02

125.0 2.9724+02 3.0177+02 3.0272+02

150.0 3.5152+02 3.5684+02 3.5788+02

175.0 4.0207+02 4.0804+02 4.0915+02

200.0 4.4931+02 4.5581+02 4. 5698+02

225.0 4.9358+02 5.0054+02 5.0177+02

250.0 5.3524+02 5.4261+02 S. 4387+02

275.0 5.7453+02 5.8225+02 5.8355+02

30 0.0 6.1173+02 6.1977+02 6.2109+02

325.0 6.4707+02 6.5540+02 6.5675+02

350.0 6.8067+02 6.8925+02

27

6.9062+02
Table II: Continued

SCREENING CORRECTIONS FOR Z = 29

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 1.9977+01 1.9171+01 2. 0911+01

10.0 2.4383+01 2.3587+01 2.5446+01

15.0 4.9603+01 4.8683+01 5. 0957+01

20.0 7.8159+01 7.7417+01 7.9999+01

25.0 1.0851+02 1.0824+02 1. 1109+02

50.0 2.6786+02 2.6881+02 2.7293+02

75.0 4.2297+02 4.2363+02 4. 2879+02

100.0 5.6729+02 5.6835+02 5.7421+02

125.0 7.0031+02 7.0258+02 7. 0888+02

150.0 8. 2297+02 8.2695+02 8.3353+02

175.0 9.3645+02 9*4240+02 9.4914+02

20 0.0 1. 0419+03 1.0499+03 1.0567+03*

225.0 1. 1403 + 03 1.1504+03 1. 1572+03

250. 1.2326+03 1.2446+03 1.2515+03

275.0 1.3193+03 1.2332+03 1.3401+03

300.0 1.4011+03 1.4169+03 1.4237+03

325.0 1.4787+03 1.4962+03 1.5030+03

350.0 1.5523+03 1.5714+03 1.5782+03

SCREENING CORRECTIONS FOR Z=50

e THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 8.0708+01 7.5823+01 9.7034+01

10.0 9.7e81+01 9.2686+01 1.1587+02

15.0 1.9405+02 1.8704+02 2. 1828 + 02

20.0 3.0035+02 2. 9176+92 3.2926+02

25.0 4.1158+92 4.0264+02 4.4513+02

50.0 9.7904+02 9.7778+02 1. 0366+03

75.0 1.5134+03 1.5196+03 1.5878+03

100.0 1.9995+03 2. 01 14+03 2. C860+03

125.0 2.4404+03 2.4573+03 2.5363+03

150.0 2.8421+03 2.8634+03 2.9458+03

175.0 3.2103+03 3.2356+03 3.3207+03

200.0 3.5499+03 3.5788+03 3.6661+03

225.0 3.8649+03 3.8971+03 3.9862+03

250.0 4.1586+03 4. 1937+03 4. 2844+03

275.0 4.4335+03 4.4714+03 4.5633+03

30 0.0 4.6920+03 4.7324+03 4.8255+03

325.0 4.9363+03 4.9790+03 5.0730+03

350.0 5. 1672+03 5.2120+03 5.3069+03

28
Table II: Continued

SCREENING CORRECTIONS FOR Z=73

E THF NONREL. REL.

(MEV) (MB) (MB) (MB)

9.0 2. 11394-02 2.07254-02 2.80274-02

10.0 2.55194-Q2 2.50784-02 3.30724-02

15.0 4.96974-02 4.92854-02 6.01454-02

20.0 7.6009+02 7.58194-02 8.89124-02

25.0 1.03264-03 1.03284-03 1.16224-03

50.0 2.39504-03 2.39994-03 2.60934-03

75.0 3.64814-03 3.66044-03 3.90274-03

100.0 4.77054-03 4.79394-03 5. 05734-03

125.0 5.77764-03 5.81354-03 6.09174-03

150.0 6.68804-03 6.73644-03 7.02564-03

175. 7.51744-03 7.57784-03 7.87554-03

200.0 8.27884-03 8.35014-03 8.65474-03

225.0 8.98214-03 9.06344-03 9.37364-03

250.0 9.63584-03 9.72624-03 1.00414-04

275.0 1.02464-04 1.03 454-04 1. 0664+04

300.0 1.08184-04 1.09254-04 1.12474-04

325.0 1.13584-04 1. 14714-04 1. 17974-04

350.0 1.18674-04 1.19864-04 1.23154-04

SCREENING CORRECTIONS FOR Z=82

£ THF NCNREL. REL.

(MEV) (MB) (MB) (MB)

9.0 2.83814-02 2.92394-02 3.91664-02

10.0 3.42124-02 3.51384-02 4.60764-02

15.0 6.62664-02 6.75554-02 8. 27924-02

20.0 1.00994-03 1.02564-03 1.21224-03

25.0 1.36844-03 1.38604-03 1.60104-03

50. 3.14954-03 3.17894-03 3.48504-03

75.0 4.77584-03 4.82214-03 5. 17874-03

100.0 6.22564-03 6.29034-03 6.67984-03

125.0 7.52234-03 7.60504-03 8. 01784-03

150.0 8.69184-03 8.79114-03 9.22144-03

175.0 9.75534-03 9.86964-03 1.03144-04

200.0 1.07304-04 1.08584-04 1.13134-04

22 5.0 1.16304-04 1.17704-04 1.22344-04

250. 1.24654-04 1.26164-04 1.30884-04

275.0 1.32444-04 1.34054-04 1.38834-04

300.0 1.39744-04 1.41444-04 1.46284-04

325.0 1.46624-04 1.46404-04 1.53294-04

350.0 1.53114-04 1.54964-04 1. 59904-04

29
Table III: Correction term for triplet production (formula 36) as extracted

from reference [26] . TRIPLET CORRECTION TERM DELTA/Z

E OELTA/Z

(MEV) (MB)

9.0 -1.5000-03

10.0 3.C00O-03

15.0 1.8000-02

20.0 2.6600-02

25.0 3.1200-02

50.0 2.5600-02

75.0 3.2636-0 2

100.0 2.9800-02

125.0 2.7587-02

150.0 2.5700-02

175.0 2.4178-02

200.0 2.2900-02

225.0 2.1738-02

250.0 2.0700-02

275.0 1.9809-02

300.0 1.9000-02

325.0 1.8213-02

350.0 1.7500-02

Table IV: Retardation factor for triplet pair production (formula 40)

RETARDATION FACTOR

E/MEV FACTOR

9.0 • 5156

10.0 • 5485

15.0 .6564

20.0 .7179

25.0 .7583

50.0 .8513

75.0 .8865

100.0 • 9093

125. • 9229

150.0 .9325

175.0 .9398

200.0 .9455

225.0 .9501

250.0 .9538

275.0 .9570

300.0 • 9598

325.0 • 9621

350.0 • 9642

30
Table V: Screening cross sections for triplet production.

TRIPLET SCREENING

CE IN MEV. CROSS SECTIONS IN MBARN)

E Z= 3 Z= 4 Z= 6 Z= 8 Z = 13

9.0 8.7396-07 7. 1117-06 9.6706-05 5.7588-04 7.8181-03

10*0 2.3531-06 1.6442-05 1.8419-04 1.0489-03 1.2530-02

15.0 4.6844-05 2.4868-04 1.8548-03 8.0172-03 5.8330-02

20.0 2.6394-04 1.2434-03 7.4737-03 2.60 17-02 1.3875-01

25.0 8.8867-04 3.7461-03 1.8973-02 5.6431-02 2.4613-01

50.0 1.9180-02 5.4451-02 1.6623-0 1 3*4143-01 1.0201+00

75.0 7.2284-02 1.6616-01 4.0383-01 7.3219-01 1.9967+00

100.0 1.5514-01 3.1399-01 6.7787-01 1. 1643+0 3.0448+00

125.0 2.5760-01 4.7912-01 9.6783-01 1.6162+00 4.1019+00

150.0 3.7167-01 6.5146-01 1.2650+00 2.0771+00 5.1388+00

175.0 4.9205-01 8.2589-01 1.5648+00 2.5401+00 6.1429+00

20 0.0 6.1528-01 9.9982-01 1.8642+00 3.0007+00 7. 1098+00

225.0 7.3919-01 1. 1719+00 2.1615+00 3.4560+00 8.0381+00

250.0 8.6247-01 1.3415+00 2.4554+00 3.9040+00 8.9296+00

275.0 9.8428-01 1.5082+00 2.7451+00 4.3435+00 9.7856+00

300.0 1 .1042 + 00 1.6718+60 3. 0298+00 4.7736+00 1.0608+01

325.0 1.2219+00 1 .8325+00 3.3096+00 5.1947+00 1 .1401+01

350.0 1 .2372+00 1.9900+00 3.5839+00 5.6056+00 1.2163+01

TRIPLET SCREENING

(E IN MEV, CROSS SECTIONS IN MBARN)

E Z=20 Z=29 Z=50 Z=73 Z=82

9.0 4.8475-02 1.6345-01 7.0793-01 1.7318+00 2.2653+00

10.0 6.9641-02 2.1953-01 9.0420-01 2.1679+00 2.8191+00

15.0 2.2772-01 5.9168-01 2.1154+00 4.7199+00 6.0272+00

20.0 4.5391-01 1.0793+00 3.5840+00 7.6529+00 9.6762+00

25.0 7.2970-01 1.6455+00 5.1957+00 1.0779+01 1.3527+01

50.0 2.4967+00 5.0182+00 1.3816+01 2.6793+01 3.2800+01

75.0 4.4641+00 8.6356+00 2.2153+01 4.1575+01 5.0241+01

100.0 6.4167+00 1.2178+01 2.9846+01 5.4809+01 6.5724+01

125.0 8.2993+00 1.5555+01 3.6903+01 6.6702+01 7.9568+01

150.0 1 .0097+01 1.8748+01 4.3395+01 7.7483+01 9.2072+01

175.0 1.1810+01 2.1761+01 4.9357+01 8.7337+01 1.0347+02

200.0 1.3440+01 2.4606+01 5.4976+01 9.6415+01 1.1394+02

225.0 1.4994+01 2.7296+01 6. 0165+01 1.0483 + 02 1.2363+02

250.0 1.6476+01 2.9847+01 6.5074+01 1.1268+02 1.3266+02

275.0 1.7892+01 3.2269+01 6.9676+01 1.2002+02 1.4109+02

300.0 1.9248+01 3.4577+01 7.4028+01 1.2694+02 1.4903+02

32 5.0 2. 0549+01 3.6781+01 7.8161+01 1.3348+02 1.5652+02

350.0 2.1797+01 3.8886+01 8.2086+01 1.3967+02 1.6361+02

31
Table VI: Experimental total absorption cross sections, atot (k) for Pb, Ta,

Sn, and Cu. The third column (DS) gives the statistical errors.

Z=82

s SIGMA DS

MEV MB MB

9.62 17035.24 28.16

9.88 17167. 06 21.49

10.13 17348.50 18.26

10.37 17462.61 16.73

10.61 17620.76 16.48

10.87 178C7.38 16.79

11 .12 17940.21 19.74

11 .35 18150.23 23.79

11 .59 18316.33 25.10

11 .86 18376.78 30.18

12.10 ieS57.69 27. 15

12.35 18731 .43 25.10

12.60 18867.24 20.99

12.86 19031.40 22.42

13.11 19184.27 21.96

13.37 19402.00 24.08

13.62 19555.66 25. 08

13.86 19646.39 25.52

14.13 19757.25 25. 17

14.40 19826.21 26.22

14.64 19873.02 25.30

14.68 19934.12 26.88

15.12 19974.38 28.95

15.37 20027.40 30.11

15.61 20089.94 31.40

15.85 2C12G.5S 31.21

16.11 20217.35 29.77

16.36 20237.52 30.76

16.62 20367.1

1

28.89

16.88 20445.24 28. 23

17.12 20583.90 3 0.72

17.36 20579.58 27.60

17.61 20677.25 28.16

17.88 20783.69 26.57

18.14 20849.55 28.34

18.39 20918.24 26. C8

18.63 21094.97 30.45

18.87 21111.68 29. 13

19.12 21213.37 29.88

19.37 21229.78 30.16

e SIGMA DS

MEV MB MB

19. 62 21368..45 31.,07

19. 88 21447, 14 31 , .55

20. 13 21480.,79 32., 17

20. 38 21554,.13 34.,67

20. 62 21638,.46 39,.43

20. 87 21676,.86 37,,75

21. 13 21761, 93 41 .04

21. 36 21946 .40 37,.65

21. 60 21922..56 34,.00

21. 82 22028,,53 32,.06

22. 06 221 11..65 28,.13

22. 29 22178,.52 26 .90

22. 56 22262,,80 26,.13

22. 83 22331,.21 26,.25

23. 10 22430.,14 26,.48

23. 37 22466,.54 27,.10

23. 64 22566.,52 26, 66

23. 90 22694,,60 33,.72

24. 13 22743.,21 37,,16

24, 38 22819,.17 39,.57

24. 63 22945..30 49,,32

24. 85 22941,,18 64,.24

25. 13 23006. 52 51 , ,07

25. 38 23098,.69 64 .84

25. 62 23162,.52 56,,27

25. 80 23223,.67 76,,04

26. 08 23346,.19 52,,75

26. 31 23468.,74 70,.31

26, 57 23399, 96 59,.55

26. 82 23424,.38 64,.67

27. 08 23599,.21 59,.43

27. 35 23655..65 60,,31

27, 59 23744,,03 61,,64

27. 86 23691, 15 57,,84

28. 10 23799,,96 60,,87

28. 37 23896, 50 57,,82

28. 61 24021,,16 63,,67

28. 68 24060. 18 57,,35

29. 10 24025.,09 61.,73

29. 37 24185. 25 54,,56

32
Table VI: Continued

z-ez

E SIGMA DS E SIGMA DS

MEV MB MB MEV MB MB

29,,61 24238..80 54,,62 49. 81 27637,,99 76. 48

29,.89 24249* 07 52* 29 50. 33 27755. 96 83..25

30,.80 24480

,36 42.,58 50. 81 27991,,06 78,.15

31 .26 24576* 75 40. 53 51. 36 28091, 07 90.,68

31..77 24716.,60 43.,30 51. 83 28097,,17 80..89

32 .27 24830. 00 45,,60 52. 35 28069.,77 87.,88

32,.77 24913.,95 46,,98 52. 82 28254.,88 79,.18

33 .24 25039* 82 45* 67 53. 38 28274, 95 94, 68

33,.74 25193.,36 46,,92 53. 86 28432.,33 85,.02

34,.26 25177, 63 48. 30 54. 40 28452. 14 91,,04

34,.78 25349.,00 50.,95 54. 85 28469.55 91,.67

35 .28 25379* 92 50. 04 55. 26 28652, 65 100, 79

35,.77 25463.66 49,.37 55, 74 28570.13 90,.09

36 .27 25703* 01 SC« 54 56. 16 28542. 16 113,.46

36 .72 25729.62 58,,67 56. 65 28699.42 99,.79

37 .21 25774*,24 52.,71 57. 06 28685. 87 117,.13

37..72 25878.35 53,,76 57. 57 28728.,54 98,.96

38,.23 25923.63 56,.71 58. 13 28688.40 100,.46

38 73 26 061.46 59.,66 58. 65 28997.04 98,.11

39,.23 26171.70 60,.61 59, 23 28964.95 99 .06

39 .75 26225.88 59.,69 59. 70 29028*,59 120,.81

40,.21 26299, 95 60,.44 60* 26 29014.84 95, 79

40,.70 26394*,26 65*,67 60. 67 29225* 05 161, 75

41 , .19 26572,.70 58,.36 61, 21 29221.93 115,.88

41 .76 26592.,19 62.,65 61. 71 29189,,68 120,.79

42,.23 26607.18 58,.46 62. 27 29315.32 91,.93

42,.76 26807,,97 61*,84 62. 79 29354. 77 115,.46

43 .26 26823,.80 59,.71 63. 28 29398.09 68,.51

43 .78 26986.02 70.,45 63. 81 29551

,

,55 1 15,.98

44 .24 26905.21 56,.21 64. 27 29488,.13 104 .52

44 .82 27039.40 61,,66 64. 67 29692.,39 124,.70

45 .33 27161 .42 69 .30 65. 23 29460, 57 99 .02

45 .84 27241.60 63. 75 65. 73 29669,,35 132,.80

46 .36 27213,.83 71,.20 66. 20 29641 .46 116,.46

46 .83 27401 .96 74,.99 66. 74 29790. 11 119 .66

47 .30 27421.93 72, 47 67. 26 29742.11 112 .28

47 .61 27469 .57 69 .44 67, 79 29990.75 119,.01

48 .29 27563,.86 71.,40 68. 18 29814,,85 120,.20

48 .77 27607,.62 68,.74 68. 76 30107,.27 110 .83

49 .33 27739.68 81. 26 69. 30 30111 .96 116,.89

33
Z = 82

Table VI: Continued

E

MEV

69.80

70.20

70.79

71 .27

71 .74

72.15

72.79

73.35

73.74

74.22

74.79

75.51

76.63

77.65

78.54

79.49

80.50

81 .54

82.57

83.53

84.51

e5.56

86.56

87.49

88.48

89.47

90.51

91 .50

92.45

93.48

94.54

95.51

96.49

97.51

98.42

99.40

100.44

101 .39

102.40

103.45

SIGMA

29932.23

30028.44

29989.44

30150.97

30133.39

30363.21

30403.61

30310.95

30488.40

30493.40

30495.83

30421.48

30512.45

30807.48

30635.72

30835.23

30976.13

30817.12

31077.08

31110.96

31 166.96

31368.52

31346.65

31240.86

31448.81

31476.94

315C9.08

31625.05

31766.04

31878.88

31779.30

31814.27

31866.57

31981.91

32026.14

32059.83

32147.12

32265.05

32325.19

32288.19

DS

MB

145.24

128.38

128.63

145.75

129.42

131.58

113.93

134.37

138.98

111.84

133.56

63.68

76.48

74.60

76.53

73. 91

74.94

67.51

74.67

77.20

70.62

80. 05

87.00

78.39

76.02

78.06

78. 17

79.05

77.18

75.10

75.68

73.45

62.96

65.11

69.88

62.85

65.10

68.43

65.26

70.37

E SIGMA DS

MEV MB MB

104. 44 32448,.50 67,.21

105. 48 32539,.56 74,.14

106. 47 32693, 27 78,.72

107. 52 32477,.33 80,.25

108. 62 32601 i .86 96,.06

109. 68 32546 .73 95,.73

110. 68 32873,.98 96,.13

111. 67 32798,.59 91,.00

112. 76 32925,.77 103,,57

113. 62 32993,.55 102,.30

1 14. 53 32936,. 16 112 • 52

115. 45 33023,.98 102,.97

1 16. 31 32868,.06 109,.90

117. 35 33 048,.40 96,,31

118. 27 33004,.34 121,.12

119. 24 33103,.05 109, 77

120. 42 33155,.73 109, 70

121. 52 33178,.06 109,.71

122. 49 33506,.95 123,.29

123. 43 33242..95 133,,62

124. 55 33382,.55 108,.83

126. 04 33330,.15 106,,13

128. 01 33466,.31 91,.73

130. 16 33596,.20 96,,28

131. 93 33615,.18 106,,32

133. 95 33836,.13 85..91

136. 07 33723,.34 82,,12

137. 89 33853,.77 91,,50

139. 91 33968. 16 74,.22

142. 06 34037,.52 70,, 13

144. 10 34153,.09 78..33

145. 80 34220,.63 75,.46

147. 88 34155, 45 60,.87

150. 04 34294,.88 74,,80

151. 89 34310. 18 68..04

154. 02 34297,.59 62,.63

156. 16 34367, 75 87.,47

157. 62 3450e,,77 87,,04

159. 62 34392. 88 75..60

161. 92 34631,,98 97,.44

34
Table VI: Continued

2=73

S SIGMA DS E SIGMA OS

MSV MB ME1 MEV MB MB

9..61 14182* 12 23. 11 32. 70 20422. 18 75,,68

9. 86 14239,,85 20. 75 33, 07 20294,,15 93,,61

10..11 14389. 38 22. 84 37. 24 21135. 43 129,,35

10.,36 14490.,66 22. 08 37. 69 21276,,10 92, 59

10..57 14572. 65 36. 11 38. 21 21307,,62 66,,70

11. 20 15005.,63 51. 97 38. 72 21298,,21 54,,88

11 . .40 14977. 59 32. 95 39. 20 21338. 86 52,,12

11 .,60 15031.,24 25. 57 39. 72 21324,,55 41,.62

11 . ,85 15191. 29 26. 38 40, 24 21467, 26 44,,91

12.,10 15341.,68 26. 89 40. 75 21562.,67 42,.71

12.,36 1S449. 29 25. C7 41. 23 21594,,09 51 , ,77

12.,63 15538.,74 41. 93 41. 70 21534,,94 49, 51

13.,98 16095. 20 165. 46 42. 20 21696, 00 57,,33

14.,15 16214.61 46. 39 42. 72 21666,,63 56,,82

14.,37 16235. 02 30. 75 43. 28 21689,,79 88,,41

14.,63 16379,05 27, 36 43. 70 21736,,47 106, 66

14.,89 16420.,43 28. 50 46. 91 22630,,98 143, 25

15.,14 16584.16 30. 65 47. 40 22542.,43 96,,16

15.,38 16646.88 29. 41 47. 90 22518,,45 81,,15

15.,62 16743.,98 33. 54 48. 39 22641

,

,07 69, 44

15.,86 16843,,68 41. 84 48, 89 226 86. 82 63,.92

18. 87 17446.,02 38. 30 49. 38 22896.,27 57,,57

19.• 13 17506,94 30. 88 49,,89 22884,.08 58, 68

19, 37 17628.,50 27. 05 50. 39 22858,,97 59, 27

19,.62 17665.66 32. 43 50. 88 22e77 77 60,.13

19, 88 17710. 12 27. 31 51, 37 22952,,20 60. 98

20. 13 17774.59 33. 83 51,,85 23083, 70 62. 40

20, 37 17790.,54 27. 77 52. 35 23087.,31 67,,82

20,,63 17897,47 32. 82 52,,85 23218 .02 77,.07

20, 86 17947.,34 32. 74 53. 36 23291, 78 87,.90

21 . ,09 18051.78 50. 31 53, 87 23297, 86 109, 94

28, 26 19541,,25 SO. 98 54. 36 23263.,68 141,,91

28, 76 19731, 41 47, 11 70,,67 25029,.01 192,.97

29, 25 19758.89 40, 64 71. 24 24701,,16 1 12,.08

29, 76 19909.19 36. 77 71. 82 24616,.90 110,.85

30, 26 19920,,77 31. 69 72, 22 24800,.76 103,.01

30 .78 20016.76 36. 91 72, 77 24779,,39 83,.70

31 , .23 20079, 52 42. 10 73,,32 24616,.21 91,.42

31 , 73 20127.,94 43. 81 73, 74 24843,,11 87,,55

32,.26 20300,.81 51, 70 74,,28 24816,.42 84,.15

35
Z=73

Table VI: Continued

5

MEV

74.83

75.25

75.55

76.52

77.47

78.50

79.49

80.28

81.09

93.56

94.56

95.55

96.54

97.53

98.51

99.52

100.51

101.45

102.45

103.41

104.46

105.47

106.48

107.49

108.48

113.12

SIGMA

MB

24821.60

25011.77

24964.67

25041.64

25192.47

25134.42

25193.93

25279.99

25201.72

25971.21

26165.84

26031.24

26126.65

26186.41

26314.99

26151 .93

26219.95

26235.58

26184. 86

26351 .14

26274.47

26357.66

26295.18

26754.36

26426.59

26772.87

CS

MB

93.90

90.97

60.90

67.36

62.27

67.18

101.18

137.67

231.60

167.93

141.33

120.28

127.67

10 0.59

89.78

90.74

91.75

106.29

93.44

95.08

110.59

121.81

139.99

168.11

209.30

258.09

E SIGMA DS

MEV MB MB

1 14, 19 26650, 24 161, 12

115. 26 27194,.10 120, 18

1 16. 35 27045.71 100,.49

1 17. 42 27153. 67 85,.43

118, 50 27055.06 92,.90

119. 61 27118. 48 97, 45

120. 59 27236,.57 102, 56

121. 32 27245, 28 115, 59

122. 22 27260.79 88,.08

123. 35 27294,.14 84,.74

124. 51 27265..12 85,.59

125. 63 27403, 58 90,.42

126. 14 27418, 40 67,.03

128. 28 27539,.47 91,.36

130. 05 27077, 83 298,.58

142. 60 27652, 44 218,.73

143. 96 27787. 88 113,.08

146. 01 27784.96 74,.00

148. 00 27967. 68 66,.11

149. 91 28062,.68 66,,56

152. 01 28079. 59 58,.51

154. 05 27984,.40 64,.53

156. 01 28151. 12 59,.94

157, 91 28177,.97 64,.30

159. 84 28156. 05 73,.97

161. 78 28299, 57 93, 14

36
Table VI: Continued

Z-5

E SIGMA DS E SIGMA DS

MEV MB MB MEV MB MB

9.62 7641 .16 13.29 19.62 9248,,39 24,,28

9,87 7686..26 10.58 19.88 9275.,08 21 , ,66

10.13 7739..68 9.24 20. 15 9290,,24 24.,67

10.37 7776. X 8.33 20.37 9361 , 30 29,,10

10.61 7822,,03 9.30 20.57 9397, 59 35,,84

10.87 7869. 91 9.82 20.86 9392.,06 23,,15

11 .12 7902,,01 11.94 21.14 9421,,00 38,,62

11.36 7973.,39 14.36 21.36 9418,,11 39,,23

11 .58 8027,,71 17.50 21.57 9483,,61 40,,04

11 .86 8060.,46 15.07 21.80 9506.,14 32,,06

12.10 8390,,52 20.51 22.07 9507,,63 28,,23

12.34 eic7«,52 16.89 22.36 9537,,37 39,,98

12.61 8210,,26 17.08 22.64 9599,,50 60,,09

12.86 6278,,51 19.01 22.79 9595.,49 33,,00

13.11 8325,,14 17.49 23.08 9653,,78 29,.10

13.36 8401 ,78 19.59 23.37 9624,.87 41,,00

13.61 €438., 15 17.82 23.65 9667,,72 33,,59

13.87 8485,,51 19.87 23.83 9699,,99 42,,28

14.11 8555,,38 18.24 24. 05 9703, 94 34,,34

14.39 8617,,06 18.56 24.33 9735,,81 35,,06

14.64 8662.,33 2C.48 24.64 9787,,22 34,,31

14.87 8757,,31 20.66 24.90 9841,,52 35,,14

15.12 e784,,58 19.34 25.15 9876, 41 35,,71

15.37 8799 .68 20.99 25.28 9825,, 10 63,,08

15.60 8859.,93 22. CO 25.56 9879,,52 34,,95

15.85 8913,.11 20.39 25.83 9882,,28 35,.61

16.11 8896.,44 22.66 26.12 9964, 81 31,,92

16.35 8928,.07 21.52 26.30 9978,,26 63,.06

16.64 8974.,03 20.72 26.56 9982,,32 35,,41

16.68 9012,.77 24.4 1 26.83 10032 .38 36,.15

17.10 9043,,06 31.47 27.10 10002,,94 36,,51

17.35 9078,.16 24.53 27.37 10043,.99 37,,17

17.61 9078,.09 24.14 27.57 10060, 35 44,,96

17.90 9098,,46 22.29 27.83 10129,,75 37,,59

18.14 9090 .70 27.59 28. 11 10128, 50 38,,06

18.39 9143,,67 21. 06 28.39 10144,,55 38,,76

18.64 9156 .02 26.66 28.56 10124,,57 44,.87

18.88 9178,,55 20.61 28.84 10174, 63 38,,16

19.12 9229 .36 21.16 29.13 10178,,75 38,,59

19.36 9219,.48 21.29 29.42 10235,,26 39, 45

37
Table VI: Continued

Z=50

E SIGMA DS E SIGMA DS

MEV MB ME MEV MB MB

29.58 10325.43 47.67 35.73 10676.72 90.97

29.85 10309.42 38.67 35.82 10720.30 89.94

30.15 10325.09 39. S2 36.15 10811.99 91 .36

3 0.45 10282.95 34.40 36.47 10924.47 95.59

30.68 10368.32 7C.40 36.79 10842.60 96.50

30.85 10360.55 40.03 47.90 11498.38 67.05

31 .12 10318.07 46.58 48.40 11648.85 69.40

31 .39 10388.82 36.01 48.89 11599.95 55.61

31 .61 10353.40 51.10 49.39 11603.97 56.92

31 .86 10456.79 42.91 49. 87 11652.46 49.33

32.11 10417.47 53.14 50.37 11631.12 50.85

32.38 10516.07 38.22 50.87 11667.46 51 .14

32.62 10463.55 53.82 51.36 11608.54 52.32

32.78 10608.14 56.77 51.85 11726.63 53.75

33.08 10496.45 46.04 52.38 11678.44 61.83

33.39 10559.73 40.48 52.86 11725.86 62.51

33.60 10598.73 80.34 53.40 11746.72 77.56

33.77 10563.26 47.64 53.88 11748.81 78.59

34.10 10642.79 48.98 100.36 13351.11 53.03

34.43 10591.44 49.42 101.34 13428.12 53.78

34.66 10670.28 89.84 102.47 13472.50 48.55

34.79 10644.45 61.79 1 03. 54 135 07.29 55.60

35.12 10595.53 61.09 104.56 13346.47 50.55

3E.45 1C672.01 62.65 105.59 13498.12 56.33

38
Table VI: Continued

Z = 29

E SIGMA DS E SIGMA DS

MEV MB MB. MEV MB MB

9.6? 3268.59 5.35 17.88 3622.49 6.9?^

9.87 328?. 29 4.28 18.14 3617.74 9.36

10.13 3289.47 3.69 18.39 3643.18 7.21

10.37 3291.01 3.29 18.64 365R.73 9.73

10.61 3297.38 3.6 8 18.86 3641.75 8.83

10.86 3304.98 4.17 19.11 3662.35 10.09

11.12 3315.72 5.19 19.36 3682.49 10.16

11.34 3321.82 8.64 19.64 3681.92 12.07

11.50 3325.58 14.97 46.92 4289.62 24.69

14. 17 3446.45 18.13 47.4? 4272.67 25.05

14.40 3457.99 13.37 47.90 4341.23 20.66

14.64 3453.70 19.55 48.39 4274.83 20.93

14.86 3452.69 14.00 48.87 4346.82 18.15

1 5.14 3495.30 10.19 49.36 4302.36 18.46

15.37 3498.20 9.42 49.84 4324.70 16.57

15.60 3529.89 8.74 SO. 34 4325.04 16.78

15.87 3536.93 7.78 50.83 4383. 17 17.26

16. 10 3553.03 9.19 51.36 4367. 16 19.32

16.35 3570.98 6.71 51.85 4365.92 19.72

16.64 3586.80 6.8K 52.38 4374. 17 22.79

16.87 3604.54 7.72 52.86 4381.60 22.93

17.11 3611.18 7.73 5 3.40 4399.66 28.48

17.36 36in.81 7.29 53.88 4385.71 28.51

17.61 3633.76 8.14 —

39
Figure 1 Total photoabsorption cross sections, a

tot ( k ) [1] Tne statistical errors of the experimental

points are smaller than the plotted circles. The lines indicate the calculated atomic cross

sections, a (k)

.

3000

2000

1500

10-O.

1000

700

500

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'NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-9682. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Total Photon Absorption Cross Section Measurements,

Theoretical Analysis and Evaluations for Energies

Above 10 MeV

5. Publication Date June 1978

6. Performing Organization Code

AUTHOR(S)

H. A. Gimm and J. H. Hubbell

8. Performing Organ. Report No.

PERFORMING ORGANIZATION NAME AND ADDRESS

Nuclear Physics Division

Max-Planck-Institute for

Chemistry

D6500 Mainz, West Germany

National Bureau of Standards

Department of Commerce

Washington, D. C. 20234

10. Project/Task/Work Unit No. 2401105

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

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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.)

Atomic photoabsorption cross sections have been calculated in the energy

range from 10 MeV to 350 MeV. For Pb, Ta, Sn and Cu total Y

_ray absorption

cross sections were measured between 10 MeV and 160 MeV and compared with the

theoretical results. An estimate of the uncertainties in the calculated atomic

cross sections is given.

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)

Key words: Coulomb corrections; pair production cross section; screening

corrections; total photon absorption cross section; total photonuclear

absorption cross section; triplet production cross section.

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UNCLASSIFIED

20. SECURITY CLASS

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21. NO. OF PAGES

77

22. Price $2.40

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