NBS Handbook 85 [1964], and the “mass absorption
coefficient” palp (sec. e.g., eq (8f-48) of Evans
{1963]), are approximate and neglect some of these
modes. The coefficients, Men/p, x/p, and Malp, are
differently weighted sums of the probabilities per
unit pathlength (in g/em2) for photoelectric absorp-
tion (u:/p), Compton collision (uc/p), and pair
production (tx/p):

ripo| Gli) en() mam

The weights f,, fc, and f, are conversion factors
which indicate, for the respective interactions, the
average fraction of the photon energy which is
eventually converted into kinetic energy of elec-
trons in the volume of interest. These weights,
therefore, must discount the amount of energy that
escapes from the volume of interest in the form of
secondary photons (which may include scattered
photons, annihilation radiation, bremsstrahlung,
and fluorescence radiation).

For fen/p the weights account for the escape of
Compton-scattered, fluorescence, annihilation, and
bremsstrahlung photons. For px/p the weights
account for the escape of all of these except brems-
strahlung photons. For a/p they account for the
escape of Compton-scattered photons only.

A certain part of the escaping photon radiation
may also interact with the medium in the volume
of interest and set electrons into motion there. This
possibility is automatically taken into account if
one includes in the flux 6(£, r) which multiplies
the coefficient not only unscattered (primary) pho-
tons, but also scattered photons, and all other
secondary photons, such as annihilation radiation.’2
On the other hand, the treatment must be con-
sistent. That is, if in eq (1.-9) one uses values
of Halp or px/p, from which the escape of certain
secondary radiations is not discounted, then one
should use values of @(E, r) computed without con-
sidering the contributions from these radiations.

R. Berger [1961] has evaluated the coefficients
Ss fc, and f;, including all energy transfer routes
shown in figure 1-4, and from them the mass
energy-absorption coefficient fen/p for air, water,
and 15 elements and yx/p for Al, Fe, and Pb over
the energy range 10 keV S E = 10 MeV. Tabulations
of Hen/p and fa/p have been made by Allison [1961]

% Calculations of $(E, r) ofte

ide only Compton scattered photon:
secondary fiux (see, for example, and Wilkins (1954). However,
10-MeV primary photons in lead, the annihilation photon flux has been theoretically
estimated to contribute from 4 10 7 percent to $(E, r) by Goldstein [1954] and by
Berger, Hubbell, and Reingold [1959], and contributions of this order of magnitude
have been observed experimentally by Hubbell, Hayward, and Titus [1957]. Also,
theoretical estimates of the fluorescence radiation component have been made by
Goldstein [1954], Veigele and Roper [1966], and Veigele and Balogh (1968).

16

for air, water, and seven elements over the range
10 keVSE=100 MeV. His procedures are es-
sentially the same as those of Berger, with the ex-
ception that in discounting the escape of annihilation
radiation he did not consider the possibility of
annihilation of the positron while in flight. Thus, for
heavy elements (Z > 26) the Allison data are slightly
different from those of Berger at energies above the
pair production threshold, i.e., for E > 1.022 MeV.
This effect of annihilation in flight amounts to
~ 2 to 3 percent at 10 MeV, and presumably more
in the region E > 10 MeV, which was not included by
Berger.

Various other authors have presented values of
Halp which, as has been discussed, discount only
the energy-escape by the deflected photon in
Compton scattering. Data in this approximation
include the tabulations by White [1952] and Storm,
Gilbert, and Israel [1958], and the graphical data
of Evans [1955, 1963].

1.6. Tabulation of Energy Absorption
Coefficients

In tables 1.-7 and 1.-8 we present values of
Hen/p, Halp, and j4x/p, for air, water, and 18 elements
over the range 10 keV SE =10 MeV. These data
are based on the interaction cross sections in
section 2 and hence are consistent with the attenua-
tion coefficients in table 1.-4 and in section 3.

For fa/p, values of Compton scatter losses
(1—fc)uclp were subtracted from entries in table
1-4, For jx/p, the compilation of fluorescence
yields and average fluorescence photon energies
of R. Berger [1961] was used plus values for Sn
and U from Wapstra et al. [1959].!° For jen/p the
weights f;, fc, and f, were taken directly or inter-
polated from Berger [1961], except values of f, for
Sn and U, for which bremsstrahlung yield data
from Berger and Seltzer [1964] were used.

Tn addition, in table 1-9, we have excerpted the
values of len/p over the range 10 MeV SE = 100 MeV
from the tabulation by Allison [1961]. We also
include, for comparison, values of a/p computed
from present cross sections for the same substances.
As discussed in section 1.5.3, the Allison data differ
from those of Berger in that positron annihilation
in flight was not taken into account. However, at
energies above 10 MeV the approximation involved
in the use of energy-absorption or related coefhi-
cients loses some of its validity because of the com-
parable distances traveled by electrons and photons
(see table 1.-6).

‘2 For a more recent and extensive summary of K-, L-, and M-shell fluorescence
yield data, see Fink et al. [1966].


cent over the entire energy range from threshold
to arbitrarily high energies.

In addition, Jost, Luttinger, and Slotnick [1950]
have extended their derivation to the case of arbi-

trary screening. They obtained a formula differen-
tial in the momentum transfer which includes
screening effects in terms of the atomic form fac-
tor F(g, Z) and which can be numerically inte-
grated to obtain the total cross section Ky.

2.5.3. Pair Production in the Field of an Electron

This effect has a threshold of 4 mc? (=2.044
MeV) as required by the sharing, in this case, of
the photon energy and momentum with the target
electron as well as the created electron-positron
pair. The resulting trajectories of the two electrons
and the positron appear as a three-pronged track
in a cloud chamber or photographic emulsion,
hence the name “triplet production” often given
to the process.

An exact theoretical treatment should include
the following effects:

(1) atomic binding of the target electron,

(2) screening by the other atomic electrons and by
the field of the nucleus,

(3) retardation which occurs when the atomic
electron recoil velocity is not negligible in com-
parison with the velocity of light.

(4) the y—e interaction of the incident photon
with the atomic electron (i.e., virtual Compton
scattering in which the scattered photon gives
rise to an electron-positron pair),

(5) exchange terms resulting from the indistin-
guishability of the two electrons, and

(6) the radiative corrections.

No one treatment has included all six of these
effects, so numerical values are usually obtained
from a combination of one or more of the following
three principal theories, all of which employ the
Born approximation.

Wheeler and Lamb [1939] used the high energy
approximation and included the above effects (1)
and (2). Ghizzetti [1947] and Borsellino 2° [1947]
included only (3), but Suh and Bethe [1959] have
shown that at high energies their neglect of ex-
change (5) is unimportant. Votruba [1948] included
(3), (4) and (5), but his differential cross sections are
so complex that until very recently the required
integrations to obtain the total cross section have
been done only crudely. However, Mork [1967] has
now integrated the Votruba expressions numerically,
and his results are shown in table 2.-14 in the form
of an energy-dependent correction A (triplet) to be

Mi
of the series so
term should rea

gut that th Boraellng rel identifale athe leading terms

1947), and that the last Borsellino
‘ng

fon in eq (2-
21.51, rather than +21.51,

28
ra

li id 28 (2k)
x (Borsellin corrected) =, i tn (2k) —

1 Ths 2 in (2) —
— 7 [fine caky —3 tnt (24) +6.04 In 24) 21.51}

for the cross section per electron.

TABLE 2-14. The Mork [1967] correction to the Borsellino-
Ghizzetti ke result, obtained by numerical integration of the
Votruba differential expressions.

Photon energy .
A triplet
[Mev] (triplet)
2.044 0.215
2.5 0.608
3 0.765
4 0.895
5 0.932
6 0.959
8 0.996
10 1.0

applied to the Borsellino-Ghizzetti result between
threshold and 10 MeV.

Additional theoretical studies of triplet produc-
tion have been made by Watson [1947], Nemirov-
sky [1947, 1948], Reyntjens [1957], Kopylov et al.
[1964], Kaufman [1964], and Knasel [1968]. The
most comprehensive survey of the theory is that of
Joseph and Rohrlich [1958], and more recent results
have been summarized by Gates et al. [1960,
1962], Koch [1964], Davisson [1965], and Olsen
[1968].

In the present tabulation we use values of Ke ob-
tained by combining the Borsellino-Ghizzetti cross
section «2 (using the Ghizzetti expansion which
includes terms through 77), the Mork-Votruba
correction A (triplet), the Wheeler-Lamb screened
cross section x” in the high-energy and Thomas-
Fermi approximations, the Bethe-Heitler un-
screened nuclear-field cross section «8, and the
Mork-Olsen radiative correction here assumed to
have the value 1.01. From threshold to 10 MeV,

where screening is negligible, we used the
combination
ke= «B4 - A(triplet) - 1.01 (2.-38)

for the cross section per electron. At higher ener-
gies, as suggested by Mork, we used the combination

Ke= {ll — [KR (1H) — «89]} + 1.01. (2.-39)

The Ghizzetti [1947] expansion for «2° is repro-
duced here for convenience:

re (28 218
G——£ Jo — t_
Ke mac In Qh) — 37
+4 [-F 1" (2k) +3 In? (2k)
E13
_60+ 16a 5, cy + Hear 168)
3 3
+ (i) 3 Ins (24) —4 In? (2k)
x) |B
+SLt20 4, (2p) Wheto)


2.5. Electron-Positron Pair Production
2.5.1. General Discussion

In this effect, which is the most likely photon
interaction at high energies, a photon disappears in
the field of a charged particle, and an electron-
positron pair appears. The cross section kn for pair
production in the field of a nucleus varies as

ken ~ 22. (2.-26)

The cross section Ke in the field of all the atomic
electrons varies as Z times the square of the unit
charge, or,

ke~Z, (2.-27)

and is of minor importance except for the lowest-Z
materials. The ratio Ke/kn can be set equal to n/Z
where 7 is a slowly varying function of Z and E,
generally close to one, and will be discussed later
in this section.

There have been a number of experimental
studies in which the x, and Ke cross sections have
been isolated to some extent. For x, data see, for
example, the results by Standil and Shkolnik
[1958], Singh et al. [1959], Rao et al. [1968],
Plimpton and Hammer [1963], Yamazaki and Hol-
lander [1965], and Titus and Levy [1966], and for
ke data, the results of Criegee [1960], Sandhu

et al. [1962], and Frei et al. [1964]. Earlier results
for both cross sections have been summarized by
Davisson [1965]. There are additional data which
depend on subtraction of the Compton cross section
of from measured total cross sections Cio (see, for
example, Jones [1959, 1960], Wyckoff and Koch
[1960]), but the recent Mork correction Ac¥ to of
requires slight revisions in these estimates. These
data still leave wide gaps or contain substantial
uncertainties. For tabulations we rely heavily on
theory, as discussed in the remainder of this section.

2.5.2. Pair Production in the Field of the Nucleus

The threshold for this effect is equal to the
combined rest energies of the created pair 2mc?
(=1.022 MeV). The cross section rises monoton-
ically from zero at threshold, varying approximately
linearly with E, until it levels off near 50 MeV for
high-Z materials and at higher energies for low-Z
materials. At 100, 1000 and 10,000 MeV the cross
section is roughly 75 percent, 95 percent, and 99
percent, respectively, of its high-energy limiting
value.

The values of kn we present in table 2.-10 and in
section 3 have been revised to incorporate new
screening calculations by Sérenssen [1965, 1966]
and the Mork-Olsen [1965] radiative correction.
However, it is useful to describe first the procedures
and sources of information for the well-established

TABLE 2-10. Scaled cross section K,/Z* for pair production
in the field of the nucleus, based on x8" (Born) evaluated by
Maximon [1968], screening (Hartree-Fock-Slater) estimates by
Sérenssen [1965, 1966], the Mork-Olsen {1965} radiative correc-
tion, and corrections to the Born approximation by empirical
adjustment of the Coulomb correction.

Units are [b/atomJZ*. For unscaled x» values up to 100 GeV, see tables in section 3.

Photon
energy iH oC wAl Ca 2Fe 29Cu
{MeV}

1,022 0) 0 0 0 0 0

1.5 4.35-1078 437-1075 4,.45-10-8 4.62+10-5 4.81-10°5 4,92+ 10-8

2 1.79-10-4 | 1.79-10- | 1.81-10-4 | 1.84-10-4 | 1,88-10-4 | 1.90-10-4

3 5.12104 | s.1t-10-¢ | 513-1074 | 5.16-10-¢ | 5.19-10-4 | 5.21-10-4

5 1.121073 1.111079 1.11-+10°3 1,41-10°% 1.10+10-% 1,10- 10-8
10 2.15-10-3 | 2.14-10-3 | 2.12-10-8 | 210-1079 | 2.09-10-8 | 2.08-10-2
20 3.30-10-% | 3.28-10-% | 3.23-10-@ | 3.20-10-8 | 3.17-10-3 | 3.15-10-9
30 3.99-10-% | 3.95-10-% | 3,88-10-% | 3.84-10- | 3.79-10-8 | 3.78-10-3
50 487-1079 4.76- 10-8 4.67°10°3 4.60- 10-3 4.54-10°3 4.52- 10-3
100 6.05-10-$ | 5.76-10-8 | 5.61-10-8 | 5.50-10-% | 5.42-10-9 } 5.39-10-3
Photon
energy a2Mo 5080 “uW Pb 2

[MeV]

1,022 0 0 0 ) 0)

15 5.55-10-5 6.01-10-5 7.67-10-® 8.27-10-§ 9.03- 10-5

2 2.02-10-4 | 2.10-10-4 | 2.42-10-¢ | 2.53-10-4 | 2.68-10-4

3 5.33-10-4 | 5.42-10-4 | 5.74-10-4 | 5.86-10-4 ] 6.011074

5 4.10-10-@ } 110-407? | 1.09-10-8 | 1.08-10-8 | 1.08-10-8

10 2,03-10-8 | 1.99-10-? | 1.87-10-8 | 1.83-10-8 | 1.77-10-3

20 3.06-10-? | 3.00-10-9 | 2.79-10-% | 2.72-10-8 } 2.62: 10-8

30 3.67-10-@ | 3.59-19-2 | 3.35-10-3 | 3.27-10-8 | 3,16-10-%

50 4,38-10-% 4.29- 10-3 4.00- 10-3 3.90- 10-3 3.78-10°3
100 5.20-10°3 5.08- 10-8 4.74: 10-8 4.63- 10-3 4.481079

33


Table 3.-2. BERYLLIUM, Z=4

Scattering Pair production Total Total
Photon Photo: =
energy electric
With | Without Nuclear } Electron |} With Without || With | Without
coherent | coherent field field || coherent | coherent |{ coherent | coherent
MeV blatom ——blatom blatom blatom blatom |} bjatom blatom |] cmilg em?|g
1.00-02 |] 3.42+00  2.56+00| 5.46+00 8.88+00  8.02+00 |} 5.93-01 5.3601
1.50-02 |} 3.01400 2.52+00| 1.49+00 4.50+00  4.01+00 |} 3.00-01 268-01
2.00-02 || 2.78+00 2.47400] 6.12-01 3.39400 3.08+00 |] 2.27~01 206-01
3.00-02 |} 2.54400 2.39400] 1.68-01 2.70+00 2.56400 |] 181-01 1.71-01
4.00-02 |] 2.40+00 2.31400] 6.4502 2.47+00 2.38400 || 1.6501 1.5901
5.00-02 || 2.31400 — 2.25+00) 3.06-02 2.34400 — 2.28+00 |] 156-01 -1.52-01
6.00-02 || 2.23+00 2.18+00} 1.6702 2.24400 2.20400 |] 150-01 1.47-01
8.00-02 || 2.09400 2.07400] 6.4403 2.10+00 2.08400 |} 140-01 1.39-01
1,00-01 |] 1.99400 1.97400] 3.04-03 1.99400 1.97400 | 1.33-01 —1.32-01
1.50-O1 |} 1.78400 1.77+00}  8.01-04 1.78+00 1.77400 | 1.1901 1.19-01
2.00-01 1.63+00] 3.15-04 1.63+00 1,09-01
3.00-01 1.41400] 883-05 1.41400 9.4502
4.00-01 1.27400] 3.76-05 1.27400 8.4702
5.00-01 1.16400] 2.01-05 1.16+00 1.7302
6.00-01 1.07+00}  1.26-05 1.07+00 TAS-02
8.00-01 9.40-01| 6.32-06 941-01 6.29-02
1.00+00 845-01} 3.91-06 8.46-01 5.6502
1.50+00 6.87-01| 1.83-06 | 7.10-04 6.8801 4.60-02
2.00400 5.8601) 1.1606 | 2.84-03 5.89-01 3.94-02
3.00+00 4.6101} 6.55-07 | 8.17-03 1.6104 4.70-01 3.1402
4.00+-00 3.8501] 448-07 | 133-02 6.61-04 3.99-01 2.66-02
5.00+00 332-01] 3.44-07| 1.78-02 — 1.30-03 3.51-01 2.3502
6.00+00 2.9401] 2.75-07 | 218-02 — 2.00-03 3.17-01 212-02
8.00+-00 240-01] 1.97-07| 2.86-02 — 3.42-03 2.72-01 1.82-02
2.0501] 1.5507] 341-02 4.67-08 2.43-01 1.63-02
151-01 446-02 7.27-03 2.0301 1.36-02
121-01 5.23402 9.3403 1.83-01 1.22-02
8.8502 6.3202 1.24-02 1.64-01 1.10-02
7.0302 709-02 1.47-02 1.56-01 1.04-02
5.8702 767-02 — 1.66~-02 1.52-01 1.02-02
5.06-02 812-02 1.80-02 1.50-01 1.00-02
3.99-02 881-02 2.0402 1.48-01 9.9103
3.3102 931-02 2.22-02 1.48-01 9.92-03
2.36-02 101-01 2.53-02 1.50-01 1.00-02
1.85-02 107-01 2.7402 152-01 1.0202
1.3102 113-01 3.02-02 156-01 1.04-02
1.0302 LIT-O1 — 3.20-02 159-01 1.06-02
8.49-03 1.20-01  3.33~-02 161-01 1.08-02
7.2703 121-01 3.4302 1.63-01 109-02
5.68-03 1.2401 3.59-02 1.66-01 111-02
4.67-03 1.26-01 — 3.69-02 1.68-01 1.12-02
3.26-03 128-01 3.87-02 1.70-01 1.1402
2.52-03 1.30-01 3.9802 172-01 1.1502
1.76-03, 131-01 4.11-02 1.74-01 1.16-02
1.3503 132-01 4,19-02 1.7501 117-02
111-03 133-01 4.2402 176-01 118-02
9.40-04 133-01 4.28-02 177-01 1.18-02
724-04 1.3401 4.32-02 L701 1.19-02
1.00-+04 5.9104 1.3401 4.35-02 1.7801 1.19-02
1.50+04 4.08-04 134-01 4.38-02 179-01 119-02
2.00+04 3.14-04 135-01 4.40-02 1.7901 1.20-02
3.00+04 217-04 135-01 4.42-02 1.7901 1.20-02
4.00-+04 1.66-04 135-01 4.43-2 1.7901 1.20-02
5.00+04 1.35~04 135-01 4.4402 179-01 120-02
6.00-+04 114-04 135-01 4.44-02 1.80-01 1.20-02
8.00-+04 8.7805 135-01 4.44--02 180-01 1.20-02
1.00-+05 7.14-05 135-01 445-02 1.80-01 1.20-02

(atom) «066890 emt}

42



TanLe L-4. Values of the mass attenuation coefficient lp {em*/gl, excluding Rayleigh (coherent) scattering, the effect of binding on
Compton scattering, and the photonuclear effect, for a number of elements.
That is, values here are (tye+ oe + ku + Ke) b/atom + (N4/M) + 10-**{(cm?g~)/(b/atom)] using values of Tp, 7c, Kn and Ke discussed in
section 2 and tabulated in section 3. For coefficients extrapolated to absorption-edges, see sec. 3 tables.

| HYDRO- BERYL-
PHOTON GEN LIUM | BORON | CARBON | NITROGEN | OXYGEN | SODIUM | MAGNESIUM
ENERGY Z=1 zZ=4 Z=5 Z=6 Z=7 Z= Z=11 Z=12
Mev om'lg

1.00 —02 2.17+ 00 3.57+ 00 5.58+00 1.514 01 2.03+ 01

1.5002 7.22—01 | 1.09+00 1.62+ 00 4.37+ 00 5.98+ 00

2.00 —02 | 3.88—01 | 541-01 7.54—01 1.884 00

3.00-02 2.30—-01 2.76—O1 3.35—01 6.39—

4.00 —02 1.93—O1 2.12—01 2.36—01

5.00 —02 1.79-01 1.87—01 1.99-01

6.00 — 02 1.70—O1 1.74—01 1.81 —O01

8.00 —02 1.58—01 1.60—01 1.62—O1

100-01 | 1.50-01 1.50-01

1.50—01 134-01 ) 134-01

2.00 —01 1.23—01 1.23-O01

3.00-01 107-01 1.06—01

4.00—01 9.55 — 02 9.54 —02

5.00-O1 8.72 —02

6.00 — 01

8.00—01

1,00+00

1.50 +00

2.00 + 00

3.00+ 00

4.00 +00 2.66 —02 2.80 —02 5.04 —

5.00 + 00 2.35 — 02 2.48—02 76 —

6.00 + 00 2.12—02 2.2502 56 —

8.00+ 00 1.82—02 32—

1.00+ 01 1.63 — 02

1.50+01 1.36 -02

2.00+01 1,22—02

3.00 +01 1.10-02 !

4.00401 | 104-02

5.00 +01 1.02 —02

6.00+01 1.0002 1.57—02

8.00401 9.91 —03 1.60—02

1.00 + 02 9.92 — 03 1.19-02 | 1.63 — 02

1.50 + 02 1,00 —02 1.22—02 1.68 — 02

2.00 +02 1.02 —02 1.24—02 | 12 1,72 —02 02

3.00 +02 1.04—02 1.28—02 1.59—02 1.78—02 02

4.00 + 02 1.06 — 02 130-02 1,62 —02 02

5.00 + 02 1.08 — 02 1.32 —02 1.64 — 02 02

6.00 + 02 1.09 —02 1.34-02 1.66 — 02 02

8.00 +02 111-02 1.69-02 02
112-02 1.71 —02 02
114-02 1,73 -—02 02
1,15 —02 1.75 —02 96 — 02

3.00 +03 1.16—02 1.77—-02 98 — 02

4.00 +03 117-02 1.78—02 3.00—02

5.00 +03 118-02 1.79—02 3.01 -02

6.00 — 03 1.1802 1.79 —02 3.02 —02

8.00 +03 1.19-02 | 1.45—02 1.80—02 3.02 — 02

1.00 + 04 1.1902 1.46 — 02 1.80—02 2.02 — 02 3.03 — 02

1.50-+ 04 | 1.19-02 1.46—02 1.81 —02 2.03-02 | 3.08 — 02

2.00 +04 1.20—02 1.47-02 1.81 —02 2.03 —02 3.04—02

3.00 + 04 1.20—02 1.47-02 182-02 2.03 — 02 3.0402

4.00 +04 1.20-02 1.47—02 1.82—02 2.03 —02 3.05 — 02

5.00 + 04 1.20-02 1.47—02 1,82—02 2.04—02 3.05 — 02

6.00 + 04 1.20—02 147-02 1.82—02 2.04—02 3.05 — 02

8.00404 120-02 | 147-02 | 1-82-02 | 2.04-02 3.05 — 02

1.00 +05 1.20—-02 | 1.47—02 1,82 —02 2.04 —02 | 3.05 — 02

10


Table 3.—30. COMPACT BONE, NBS Handbook 85(1964) Composition

Scattering Pair production Total
Photon Photo
enerey With Without electric Nuclear Electron With Without
coherent | coherent field field coherent | coherent
MeV emg cme emg emg ent lg emg enti
1.00-02 || 4.90-01 2.05-01 | 1.98+01 2.03401 2.00+01
1.50-02 |] 3.67-01 —2.01-01 | 5.95+00 6.32+00  6.15+00
2.00-02 |} 3.05-01 1.97-01 | 2.49+00 2.79+00 — 2.68+00
3.00-02 || 2.46-01 1.9101 | 7.16-01 9.6201 9.07-01
4.00-02 |} 2.18-01 1.85-01 | 2.93-01 512-01 4.78-01
5.00-02 || 2.02-01 1.7901 | 1.47-01 3.49-01  3.27-01
6.00-02 || 1.90-01 1.7401 | 8.39-02 2.74-01 2.5801
8.00-02 |} 1.75-01 —1.65-01 | 3.45-02 2.09-01 —_2.00-01
1.00-01 |] 163-01 1.57-01 | 1.70-02 1.80-01 —1.74-01
1.50-01 |] 1.45-01 1.42-01 | 4.86-03 149-01 1.47-01
2.00-01 |} 1.31-01 1.3001} 2.01-03 133-01 1.32-01
3.00-01 |] 1-14-01 1.13-01 | 5.93-04 1.1401 1.14-01
4.00-01 || 1.02-01 1.0101 | 259-04 102-01 1.01-01
5.00-01 |] 9.26-02 9.24-02 | 1.40-04 9.27-02 9.2502
6.00-01 || 8.56-02 8.5502 | 8.79-05 857-02 8.5602
8.00-01 || 7.52-02 7.51-02 | 4.46-05 7.5202 7.5102
1.00+00 || 6.75-02 6.7502 | 2.77-05 6.1602 6.7502
1.50+00 5.49-02 | 1.29-05 | 1.2704 5.50-02
2.00-+00 4.68-02 | 8.15-06 | 5.01-04 4.7302
3.00-+00 3.68-02 | 4.48-06 | 1.4303 1.29-05 3.83-02
4.00+00 3.07-02 | 3.02-06 | 231-03  5.28-05 3.3102
5.00+00 2.65-02 | 2.30-06 | 3.10-03 1.0404 2.9702
6.00+00 2.35-02 | 1.83-06 | 3.79-03 1.5904 2.74-02
8.00+00 1.92-02 | 1.30-06 | 4.95-03 2.7304 2.4402
1,00+01 1.63-02 | 1.02-06 | 5.90-03  3.73-04 2.2602
1.50+01 1.21-02 7.69-03 5.8104 2.0402
2.00401 9.7103 8.99-03  7.45-04 1,94-02
3.00+01 7.0703 1.08-02  9.93-04 1.89-02
4.00+01 5.62-03 1.2102 1.18-03 1.89-02
5.00+01 4.69-03 130-02 1.32-03 1,90-02
6.00+01 4.04-03 138-02 1.44-03 1,93-02
8.00401 3.18-03 149-02 1.61-03 1.97-02
1.00+02 2.65-03 157-02 1.75-03 2.0102
1.50+02 1,88-03 1.7102 1.98-03 2.10-02
2.00+02 1.48-03 1.7902 2.1403 2.1502
3.00+02 1.0503 1.89-02 2.3503 2.23-02
4.00+02 8.19-04 1.9502 2.48-03 2.28-02
5.00-+02 6.78-04 1.98-02  2.57-03 2.3102
6.00+02 5.8104 2.01-02 2.6503 2.33-02
8.00+02 4.5404 2.05-02 — 2.75-03 2.3702
1.00+03 3.73-04 2.07-02 —2.83-03 2.39-02
1.50+03 2.6104 2.11-02 — 2,95-03 2.4302
2.00+03 2.02-04 213-02 — 3.02-03 2.45-02
3.00+03 1.40-04 2.15-02 — 3.10-03 2.4702
4.00+03 1.0804 216-02 3.15-03 2.49-02
5.00-+03 8.85-05 2.17-02 — 3.18-03 2.49-02
6.00+03 7.51-05 2.17-02 — 3.20-03 2.50-02
8.00+03 5.78-05 2.18-02 — 3.23-03 2.5102
1.00+04 2.18-02  3.25-03 2.5102
1.50+04 2.19-02  3.28-03 2.52-02
2.00+04 219-02 — 3,29-03 2.52-02
3.00+04 2.19-02 3.3103 2.5302
4.00+04 2.20-02 — 3.32-03 2.53-02
5.00+04 2.20-02 — 3.32-03 2.53-02
6.00+04 2.20-02 — 3.33-03 2.5302
8.00-+04 2.20-02 3.3303 2.5302
1.00+05 2.20-02  3.33-03 2.5302

70


Table 3.-12.

SULFUR, Z=16

Scattering

Pair production

Total

Photon — | Photo.
energy electric
With — | Without Nuclear | Electron
coherent | coherent field field
MeV blatom —_blatom bjatom bfatom bfatom
100-02 [4.52401 1.02401 | 2.67+03
1.50-02 |] 3.03+01 —1.01+01 | 8.00+02
2.00-02 |] 2.28+01 9.89400 | 3.32402
3.00-02 |) 1.62+01 9.56+00] 9.40401
4.00-02 }]1.33+01 —9.26+00}  3.82+01
5.00-02 |} 1.17401 8.9800} 1.91401
6.00-02 |] 1.07+01 8.73400} 1.08+01
8.00-02 || 9.41+00 8.28+00| 4.40+00
1.00-01 |} 8.61400 —7.88+00} 2.16+00
1.50-01 7.10+00 | 6.10-01
00-01 6.50400 | 2.51-01
3.00-01 5.66+00 | 7.3502
4.00-01 5.07+00 | 3.1902
5.00-01 4.63+00| 1.7302
6.00-01 4.28+00] 1.0802
8.00-01 3.76400 | 5.48-03
1.00+00 3.38+00 | 3.39-03
1.50+-00 2.75+00 | 1.59-03 | 1.18-02
2.00+00 2.34400 | 1.00-03 | 4.62—02
3.00+00 1.84+00 | 5.5304 | 131-01 6.44-04
4.00+00 1.54400 | 3.74-04 | 2.12-01 2.6403
5.00+00 1.33+00 | 2.86-04 | 2.83-01  5.19-03
6.00+00 1.17+00 | 2.27-04 | 346-01 7.99-03
8.00-+00 9.6101 | 1.62-04 | 4.52-01 1.3702
1.00+01 8.18-01 | 1.2604 | 5.38-01 —1.87-02
1.50+01 6.06—01 7.0001 2.9102
2.00+01 4.8601 8.18-01 3. 7302
3.00+01 3.5401 9.83-01  4.98-02
4.00+01 2.8101 1.10+00  5.88-02
5.00+01 2.35-01 1.18+00 6.5702
6.00+01 2.02-01 1.25400 7.11-02
8.00+01 1.60-01 1.35+00 7.95-02
1.00+02 1.33-01 1.42400 8.58-02
1.50+02 9.43-02 1.53400 9.6702
2.00+02 7.39-02 1.60+00 1.0401
3.00+02 5.2402 1.68400 1.1301
4.00+02 4.10-02 1.73400 1.19-01
5.00+02 3.40-02 1.77400 1.23-01
6.00+02 2.9102 1.79400 1.26-01
8.00+02 2.27-02 1.82400 1.31-01
1,00+03 1.87-02 1.84400 1.3401
1,50+03 1.30-02 1.87400 1.3901
2.00+03 1.01-02 1.89400 1.42-01
3.00+03 7.0203 1,90+00  1.45-01
4.00+03 5.42-03 1.91400 1.47-01
5.00+03 4.4303 1.92400 149-01
6.00+03 3.7603 1.92400 1.49-01
8.00403 2.90-03 1.93400 1.50-01
1,00+04 2.37-03 1.93400 1.51-01
1.50404 1.63-03 1.94400 -1.52-01
2.00+04 1.26-03 1.94400 1.53-01
3.00+04 8.66-04 1.94400 1.53-01
4.00-+04 6.6504 1.94400 1.54-01
5.00+04 5.42-04 1.94+00 — 1.54-01
6.00-+04 4.58-04 1.94400 1.54-01
8.00+04 3.51-04 1.94400 1.5401
1.00+05 2.86-04 1.94400 1.54-01

coherent

With |

blatom

2.72403
8.30-+02
3.55-+402
1.10+02

5.15+01
3.08+01
2.15+01
1.38+01

1.08+01
8.04+00
6.94+00
5.81400

5.14400
4.67+00
4.31400
3.77400

3.40+00
2.76400

Without
coherent

blatom

2.68+03
8.10-+02
3.42402
1.04-+02

4.75+01

9.68-01
5.79-01
4.04-01
250-01

2.02-01
151-01
1.3001
1.001

9.6602
8.78-02
8.10-02
7.09-02

6.38-02
5.18-02

(bjatom) x 018780 = entle



Table 3.—10.

SILICON, Z=14

a
Seattering Pair production Total Total
Photon Photo-
energy electric
With Without Nuclear Electron With Without With Without
coherent | coherent field field |] coherent | coherert || coherent | coherent
MeV blatom —bfatom | bfatom | blatom ——bfatom |} b/atom bjatom || emg em*Ig
1.00-02 |] 3.50+01 8.97400] 1.56+03 1.59403 342401 3.36401
1.50-02 |] 2.34401 8.80+00]  4.56+02 4.79402 1.03401 9.97+00
2.00-02 |] 1.78401 8.65400) 1.87402 2.05402 4.39400 4.19400
3.00-02 |] 1.31401 8.36400] 5.29+01 6.60+01 1.41400 1.31400
4.00-02 |] 1.10401 8.10+00) 2.15401 6.96-01
5.00-02 |] 9.79+00 7.86+00) —1.06+01 4.3701
6.00-02 |] 9.01+00 7.64400) —6.00-+00 3.22-01
8.00-02 |] 8.04400 7.24400] 2.42+00 2.24-01
1.00-01 |] 7.41400 6.90+00) —1.19+00 1.8401
1.50-01 |} 6.44+00 6.21400] 3.29-01 145-01
2.00-01 || 5.82+00 5.69400] 1.34-01 1.28-01
3.00-01 || 5.01400 4.95+00] 3.9102 1.08-01
4.00-01 || 4.47400 4.43+00| —1.69-02 9.62-02
5.00-01 || 4.07+00 4.05400] 9.15-03 8.75-02
6.00-01 |] 3.76400 3.75+00| 5.7203 8.08-02
8.00-01 |] 3.29400 3.29400] 2.8903 7.0702
1.00+00 2.96+00]  1.79-03
1.50+00 2.40+00]  8.36-04] 8.9403
2.00400 2.05+00} 5.30-04]  3.52-02
3.00+00 1.61+00|  2.93-04) 1.00-01 5.6304.
4.00-+00 1.35+00] 1.99-04} 1.62-01 —-2.31-03
5.0000 1.16+00] 1.4204] 217-01 4.5403
6.00+00 1.03+00] 1.2104] 267-01 6.99-03,
8.00+00 841-01] 8.61-05| 3.47-01 —1.20-02
1.00+01 7.1601] 6.74-05| 4.13-01 1.6302
1.50+01 5.30-01 538-01 2.55-02
2.00+01 4,25-01 628-01 3.27-02
3.00401 3.1001 755-01 4.35-02
4.00401 2.4601 843-01 5.16-02
5.00+01 2.05-01 913-01 5.76-02
6.00401 177-01 961-01 6.25-02
8.00401 140-01 1.04+00  6.99-02
1.00+02 1.16-01 1.09400 7.55-02
1.50402 8.25-02! 1.18+00  8.51-02
2.00402 6.47-02 1.24400 9.1602
3.00+02 4.58-02 1.30+00 9.9802
4.00+02 3.59-02 1.34400 1.05-01
5.00402 2.97-02 1.36400 1.09-01
6.00+02 2.55-02 1.38+00 112-01
8.00+02 199-03 1.40400 1.16-01
1.00-+03 1.63-02 1.42400 1.19-01
1.50403 1.14-02 1.44400 1.23-01
2.00-+03 8.84-03 1.45400 1.26-01
3.00+03 6.1503 1.47400 1.29-01
4.00+03 4.7408 1.47400 1.31-01
5.00+03 3.88-~03 1.48400 1.32-01
6.00403 3.29-03 1.48+00 1.33-01
8.00403 2.53-03 1.49400 1.34-01
1.00+04 2.07-03 1.49400 1.34-01
1.50+04 143-03 1.49400 1.35~01
2.00404 110-03 1.49400 1.36-01
3.00+04 758-04 1.50400 1.36-01 1.63+00
4.00+04 5.82-04 1.50400 1.37-01 1.64+00
5.00+04 474-04) 1.50+00 — 1.37-01 1.64+00
6.00404 4.01-04 1.50400 1.37-01 1.64+00
8.00+04 3.07-04 1.50400 1.37-01 1.64400
| _ 1.00405 2.50-04 1.50400 1.37-01 1.64400

(atom) x 021440 =emg

50



Table 3.-16. IRON, Z=26

Scattering Pair production Total Total
Photon — || — Photo-
energy electric
With | Without Nuclear | Electron |} With Without |] With} Without
coherent | coherent field field |] coherent | coherent |] coherent | coherent
blatom ——blatom blatom blatom blatom |} blatom blatom omg emg
1.23402 1.67+01]  1.59+04 1.60404 1.59404 |] 1.73402 1.72402
8.05+01 5.15+03 5.23403 5.17403 || 5.64401 5.57401
5.98+01 2.31403 2.37403 2.33403 |] 2.55+01 2.51401
3.89+01 7.15+02 7.54402 7.31402 |{8.13+00 7.88400
2.94+01 1.50401] 3.06+02 3.35402 3.21402 ]|/3.62+00 3.46400
2.43401 1.46401] 1.56402 1.80+02 1.71402 |}1.94+00 1.84400
2.12401 1.42401] 9.04401 1.12+02 1.05402 |} 1.20400 1.13+00
1.76401 1.34401] 3.76+01 5.52401 5: 5.9501 5.50-01
1.54401 1.28+01} 1.89+01 3.43401 3.4201
1.27+01 1.15401] 5.52+00 1.82+01 1.8401
1.12+01 1.06+01]  2.33+00 1.35401 1.3901
9.50+00 9.19+00] 6.98-01 1.02+01 1.0701
8.41400 8.24400] 3.09-01 8.72+00 8.54400 |/ 9.40-02 9.2102
7.62400 7.52400] 1.69-01 7.79400 7.69400 || 8.40-02  8.29-02
7.03+00  6.96+00| 1.07-01 7.14400 — 7.06+00 ||.7.69-02 7.6202
6.15+00 6.11400! 5.4402 6.21400 6.17+00 |/ 6.69-02  6.65-02
5.52+00 5.50+00| 338-02 5.55+00 5.53400 |] 5.99-02 5.9602
4.48+00 4.47400] 1.5602 4.87-02
3.81400] 9.8103 4.2502
3.00+00] 5.3503 3.6202

2.50+00| 3.61-03
2.16+00| 2.73-03
1.91+00| 2.16-03
1.56+00| 1.53-03

1.33+00} 1.19-03
9.84-01} 7.0004
7.90-01| 5.00-04

1.00404 3.8403
1,50+04 2.66-03
2.00+04 2,04-03
3.00-+04 1.41-03

4.00+04 1.08-03
5.00404 8.80-04
6.00+04 744-04
8.00+04 5.70-04

1.00+05 464-04

(bjatom) x 010780 cme

56


Table 3.—20. IODINE, Z=53

Seatterin
Photon {| *
energy

With | Without

coherent | coherent

blatom —_bjatom
6.07402 3.30401
4.05402 3.33401
2.94402 3.28401
1.77402 3.17401
1.56+02 3.13401
1.56402 3.13401
1.23402 3.07+01
9.48401 2.98+01
7.69401 2.89401
5.58+01 2.74401
4.46+01 2.61401
3.21401 2.35401

2.64401 2.15+01
2.09401 1.87+01
1.80+01  1.68+01
1.62401 1.53+01
(48401 1.42401
1.28401 1.25+01
LI3+01 1.12401
9.18+00 — 9.10+00
7.80400 7.77400
6.12400 6.11400
5.12400 5.10+00
4.41400 4.40-+00
3.90400  3.89-+00
3.18400
2.71400
2.01400
1.61+00
1.17400
9.32-01
7.78-01
6.70-01

8.00+01 5.28-01
1.00+02 439-01
1.50+02 3.12-01
2.00+02 2.45-01
3.00+02 174-01
4.00+02 1.3601
5.00-+02 112-01
6.00102 9.63-02
8.00-+02 T5202
1.00+03 6.19-02
1.50+03 432-02
2.00403 3.3502
3.00+03 2.3302
4.00+03 1.80-02
5.00+03 1.47-02
6.00+03 1.24-02
8.00+03 9.59-03
1.00+04 7.83-03
1.50+04 5.41-03
2.00404 416-03
3.00+04 2.87-03
4.00404 2.20-03
5.00+04 1.79-03
6.00404 152-03
8.00404 1.1603
1.00+05 946-04

Photo-
electric

blatom
3.33+04
1.12404

5.18+03
1.65403

1.24403

Pair production

Total

Total

Nuclear
field

blatom

etron

field

With

coherent

blatom

blatom
3.39404
1.16+04

Without
coherent

blatom

+04
1.13404
21403
1.68+03

1.27+03
7.55403
4.69-+03

8.32+00
9.22400
1.00+01
1.13+01
1.22+01
1.29401
1.34401
1.42401
1.48401
1.58+01
1.64401
1.71401

1.75401
1.77+01
1.79401
1.82+01

1.84+01
1.86+01
1.88+01
1.89401

1.90+01
1.90401
1.90+01
1.91401

1.91401
1.9140]
1.92+01
1.92+01

1.92+01
1.92401
1.92401
1.92401

1.92+01

With | Without
coherent | coherent

emg emg

1.61+02 —1.58+02
5.52401 5.34401
2.60401 2.47+01
8.67400 7.98+00

6.62400 6.03400
3.64401 3.58+01
2.27401
1.26401
7.78+00
3.65+00

2.00+00
7.1401
3.72-01
1.78-01

1.22-01
9.7602
8.35-02
6.1602
5.8102
4.64-02
4.1102
3.20-02

3.59-02
3.59-02
3.6402

8.30-02
8.4202
8.5102
8.6402

8.7102
8.8402
8.90-02
8.9602
9.00-02
9.0202
9.0402
9.0502

9.0602
9.0802
9.10-02
9.1102

9.1102
9.1102
9.12-02
9.12-02

9.12-02

(baton) x 004786 = em? he

60


Table 3.—8.

MAGNESIUM, Z=12

Scattering Pair production ‘Total Total
Photon Photo-
energy electric

With | Without Nuclear | Electron || With Without |} With | Without

coherent | coherent field field |] coherent | coherent |] coherent | coherent

MeV blatom ——_blatom blatom bfatom blatom || blatom blatom cml omg
1.00-02 |] 2.60+01 —7.68+00] 8.13402 8.39+02 8.21402 |] 2.08401 2.03+01
1,50-02 }} 1.75401 7.55+00| 2.34402 2.52402 — 2.42+02 || 6.23+00 — 5.98+00
2.00-02 }] 1.37+01 7.41400} 9.60+01 1.10+02 —1.03+02 |] 2.72+00 — 2.56+00
3.00-02 |} 1.03401 7.17+00} = 2.67+01 3.70+01 3.39401 || 9.18-01 —-8.39-01
4.00-02 || 8.87+00 6.94400] 1.07+01 1.96+01 —1.76+01 |] 485-01 4.37-01
5.00-02 |] 8.02+00 6.74400] 5.28+00 1.33401 1.20401 |] 3.29-01 — 2.98-01
6.00-02 |] 7.46+00 6.55400] 2.97+00 1.04401 9.52400 |} 258-01 — 2.36-01
8.00-02 |] 6.73+00 6.21400] 1.19+00 7.92400 — 7.40+00 || 1.96-01— 1.83-01
1.00-01 || 6.25+00 5.91400] 5.81-01 6.83400 — 6.49+00 |} 1.6901 1.61-01
1.50-01 |} 5.48+00 5.32400} 160-01 5.64400 5.48+00 || 140-01 1.36-01
2.00-01 || 4.96+00  4.88+00] 648-02 5.03+00 4.94400 || 1.25-01 — 1.22-01
3.00-01 |] 4.28+00  4.24+00] —1.87-02 4.30+00 4.26400 || 1.0601 1.06-01
4.00-01 |} 3.82+00 —3.80+00| 8.0803 3.83+00 3.81400 || 9.49-02 9.4402
5.00-01 || 3.48+00 3.47400] 4.35-03 3.49+00 — 3.48+00 || 8.64-02 8.6102
6.00-01 || 3.22+00 3.21400] 2.72-03 3.22400 3.21400 || 7.97-02 7.9602
8.00-01 || 2.83+00 2.82400] 1.3703 2.83+00 2.82400 || 7.01-02 6.9902
1.00+00 |} 2.54+00  2.54+00]  8.50-04 2.54400 2.54400 || 6.28-02  6.29-02
1.50+00 2.06400] 3.9904] 6.52-03 2.07+00 5.12-02
2.00+-00 1.76+00| 2.5304] 2.58-02 1.79400 4.42-02
3.00+00 1.38+00|  1.40-04] 7.36-02  4.83-04 1.46+00 3.6102
4.00+00 1.15+00} 9.53-05}  1.19-01 —1.98-03 1.28+-00 3.16-02
5.00-+00 9.97-01| 7.27-05| 160-01 3.80-03 1.16+00 2.87-02
6.00+00 8.81-01| 5.79-05] 1.9501 5.99-03 1.08+00 2.68-02
8.00+00 721-01] 4.14-05]  2.55-01 102-02 9.8601 244-02
1.00+01 6.14-01] 3.23-05] 304-01 1.40-02 9.32-01 2.31-02
1.50401 454-01 3.96-01 2.1802 8.73-01 2.1602
2.00+01 3.6501 463-01 -2.80-02 8.56-01 2.12-02
3.00+01 2.6601 5.5701 3.73-02 8.60-01 2.13-02
4.00+01 211-01 6.22-01 4.4202 8.77-01 2.17-02
5.00+01 1.7601 6.7101 4.9502 8.97-01 2.22-02
6.00+01 152-01 710-01 5.37-02 9.15-01 2.27-02
8.00+01 1.20-01 7.6701 6.0202 9.47-01 2.3502
1.00+02 9.9302 8.09-01 6.5002 9.7301 2.41-02
1.50+02 7.07-02 8.7601 7.3402 1.02+00 253-02
2.00-+02 5.5402 9.1601 7.9102 1.05+00 2.60-02
3.00+02 3.93-02 9.6401  8.63-02 1.09+00 2.70-02
4.00+02 3.08-02 9.91-01 9.1002 1.11400 2.7602
5.00+02 2.55-02 1.01400 . . 2.80-02
6.00+02 2.18-02 1.02+00 2.83-02
8.00-+02 1.70-02 1.04400 2.87-02
1.00+03 1.40-02 1.05+00 2.90-02
1.50-+03 9.79-03 1.07400 2.9302
2.00+03 7.58-03 1.08+00 2.9602
3.00+03 5.27-03 1.09400 2.98-02
4.00+03 4.07-03 1.09+-00 3.00-02
5.00+03 3.33-03 1.10+00 3.0102
6.00+03 2.82-03 1.10+00 3.02-02
8.00-+03 2.17-03 1.10400 3.0202
1.00+04 1.77-03 1.10+00 3.03-02
1.50+04, 1.23-03 1.11400 3.03-02
2.00+04 9.42-04 1.11400 3.04-02'
3.00+04 6.50-04 1.11400 3.04-02
4.00+04 4.99-04 1.11400 3.05-02
5.00+04 4.06-04 1.11400 3.05-02
6.00+04 3.43-04 1.11400 3.0502
8.00+04 2.63-04 1.11400 3.05-02
1.00+05, 214-04 1.11400 3.05-02

(bjetom) x .024770=emte

48



‘TABLE 1.-7 (Continued)

Photon Air H,O
energy
[MeV] Hale | Hxle | Henl@ Hale | Uxle | Henl@
0.01 4.63 4.61 4.61 4.79
0.015 1.27 1.27 1.27 1.28
0.02 0.512 0.511 0.511 0.512
0.03 0.148 0.149
0.04 0.0669 0.0678
0.05 0.0406 0.0419
0.06 0.0305 0.0320
0.08 0.0243 0.0262
0.10 0.0234 0.0256
0.15 0.0250 0.0277
0.2 0.0268 0.0297
0.3 0.0258 0.0319
0.4 0.0295, 0.0328
0.5 0.0297 0.0296 0.0330
0.6 0.0296 0.0295 0.0329
0.8 0.0289 0.0289 0.0321
1.0 0.0280 0.0278 0.0311 0.0309
1.5 0.0257 0.0254 0.0285 0.0282
2 0.0235 0.0236 0.0234 0.0264 0.0262 0.0260
3 0.0212 0.0207 0.0205 0.0234 0.0229 0.0227
4 0.0194 0.0189 0.0186 0.0214 0.0209 0.0206
5 0.0182 0.0178 0.0174 0.0200 0.0195 0.0191
6 0.0174 0.0168 0.0164 0.0190 0.0185 0.0180
8 0.0162 0.0157 0.0152 0.0176 0.0170 0.0166
10 0.0156 0.0151 0.0145 0.0168 0.0162 0.0157

TABLE 1.-8. Values of ualp, p/p, and fex/p extrapolated to the absorption edges from the low-energy and high-energy
‘sides, respectively. Units are cm*lg.

Absorption edge soSn «Pb fe «U
[keV] Halp Hnlp benlp fkeV] Holp — pxlp — Menlp [keV] palp  walp Henlp
1.081 ep apa |S Raa
1820613 wo 663
185535 p5 as | Ms 0
135 ToT eT | Taam |S ET

20


+ (7) [ine 33 In (24) — 2215 he
+) , (2k) — rl

+(Z) [5 Ein ek) + Fe |

+(7)' [-S00 24) + $500}

+() [-Ta00 " 2 + 376000)

+.. | (2-40)

in which the constants

a=— 2.46740 and

6=— 1.80310
are evaluations of definite integrals over a series
expansion given by Ghizzetti. In addition, to make

the results join smoothly and to correct for the
Wheeler-Lamb high-energy approximation, we mul-

TABLE 2-15.

tiplied the results from eq (2-39) by the ratio of
thege two results for hydrogen. This ratio [eq
(2.-38) divided by eq (2.-39)] varies from 0.857
at 10 MeV to 0.997 at 100 MeV.

Values of Ke from eqs (2.-38) and (— 39), given ex-
plicitly in the tables in section 3, are also given in
table 2.-15 in terms of the scaled ratio

n=Z° (Kelkn) (2.-41)
for purposes of interpolation. The total pair pro-
duction cross section can thus be reconstructed
from tables 2.-10 and -15 as

K=Kntke=Z(Z+7)(KilZ?). (2.42)

The values in table 2.-15 can be represented to
within 5 percent from 10 to 100 MeV and within
+2 percent from 20 to 80 MeV by the empirical
formula

— 0.00635 In* (5). (2-43)

in which
a=Z/137,

Values of n=Z + (Kel ky) relating the triplet cross section ke to that

for nuclear-field pair production.

Here, ie is the Borsell
Mork [1967], for screening
(total) = Z(Z +) (x12

[1947}Ghizzetti [1947] unse
ising the Wheeler-Lamb [193
explicit values of ae up to 100 Ge

d result corrected for exchange and for y—e interaction near threshold by
| results, and includes a radiative correction factor of 1.01. Using table 2.-10,

sce tables in section 3.

Photon
energy 1H c Al Ca Fe aC
{MeV}
9 = 2: (xel%n)
2.044 0 0 0 0 0 0
3 0.0786 0.0787 0.0785 0.0781 0.0775 0.0773
4 0.199 0.200 0.199 0.199 0.199 0.199
5 0.292 0.292 0.293 0.293 0.294 0.294
10 0.543, 0.545 0.550 0.555 0.559 0.562
20 0.707 0.711 0.721 0.729 0.737 0.741
30 0.779 0.787 0.801 0.811 0.819 0.820
50 0.849 0.868 0.883 0.888 0.890 0.891
100 0.920 0.956 0.963 0.966 0.968 0.968
Photon
energy «Mo soSn uW aePb nV
[MeV]
11 = 2: (xel%)
2.044 0 oO 0 0 oO
3 0.0755 0.0742 0.0700 0.0687 0,0669
4 0.198 0.197 0.194 0.193 0,191
5 0.295 0.296 0.298 0.299 0.300
10 0.575 0.586 0.624 0.639 0.658
20 0.761 0.773 0.819 0.837 0.861
30 0.833 0.844 0.886 0.901 0.923
50 0.903 0.912 0.954 0.973 0.994
100 0.983 0.994 1.034 1.048 1.068

38


Table 3.—29. 0.8N H.SO, SOLUTION

Seatterin Pair prduction Total

Photon Photo

enerny With Without electric Nuclear Electron With Without

coherent coherent field field coherent coherent

MeV emg emg omg emg cml emg cml
1.00-02 |] 4.03-01 213-01 | 5.36+00 5.76+00  5.57+00
1.50-02 |] 3.13-01  2.10-01 | 1.45+00 1.76+00 — 1.66+00
2.00-02 |} 2.72-01 2.0601 | 5.78-01 8.49-01 7.8401
3.00-02 |} 2.32-01 1.99-01 | 1.59-01 3.9101 3.58-01
4.00-02 |} 2.13-01 1.93-01 | 6.32-02 2.7601 2.5601
5.00-02 |} 2.00-01 1.87-01 | 3.10-02 231-01 2.18-01
6.00-02 |} 1.91-01 1.8201 | 1.74-02 208-01 1.99-01
8.00-02 |} 1.78-01 1.72-01 | 6.92-03 185-01 1.79-01
1.00-01 |} 168-01 1.64-01 | 3.33-03 171-01 1.68-01
1.50-01 | 149-01 1.48-01 | 9.11-04 150-01 1.49-01
2.00-01 || 1.3601 1.35-01 | 3.6704 137-01 1.36-01
3.00-01 || 1.1801 1.18-01 | 1.05-04 118-01 1.18-01
4.00-01 |} 1.0601 1.06-01 | 4.49-05 1.0601 1.06-01
5.00-01 || 9.65-02 9.64-02 | 2.4305 9.65-02 9.6402
6.00-01 |} 8.93-02 8.9202 | 1.52-05 8.93-02 8.9202
8.00-01 7.83-02 | 7.6406 7.83-02
1.00+00 7.0402 | 4.73-06 7.0402
1.50+00 5.72-02 | 2.22-06 | 1.00-04 5.7302
2.00-+00 4.88-02 | 1.41-06 | 3.99-04 4.9202
3.00-+00 3.84-02 | 7.85-07 | 1.1503 1.34-05 3.96-02
4.00+00 3.21-02 | 535-07 | 186-03 5.51-05 3.40-02
5.00-+00 2.77-02 | 4.08-07 | 249-03 1.08-04 3.0302
6.00+00 2.4502 | 3.25-07 | 3.0503 1.6604 2.77-02
8.00400 2.00-02 | 2.33-07 | 3.99-03 2.8504 2.4302
1.00+01 1.70-02 | 1.82-07 | 4.7603 3.89-04 2.22-02
1.50+01 1.26-02 6.21-03  6.06-04 1.9402
2.00+01 1.01-02 727-03 7.78-04 1.82-02
3.00+01 737-03 8.7703 1.04-03 1.72-02
4.00+01 5.8603 9.78-03—1.23-03 1.69-02
5.00+01 489-03 1.06-02  1.38-03 1.68-02
6.00401 4.2103 112-02 1.50-03 1.69-02
8.00+01 3.32-03 1.21-02 — 1.69-03 1.7102
1.00+02 2.7603 1.28-021.83-03 1.74-02
1.50-+02 1.96-03 130-02 2.08-03 1.80-02
2.00+02 154-03 1.4602 2.25-03 1.84-02
3.00-+02 1.09-03 155-02 2.47-03 1.90-02
4.00+02 8.5504 1.60-02 2.61-03 1.94-02
5.00+02 7.08-04 163-02 2.72-03 1.97-02
6.00+02 6.0604 1.65-02 2.7903 1.99-02
8.00+02 4.7304 168-02 2.91-08 2.02-02
1.00+03 3.89-04 1.70-02 — 2.98-03 2.04-02
1.50-+03 272-04 173-02 3.11-03 2.0702
2.00+03 210-04 1.75-02 — 3.19-03 2.09-02
3.00+03 146-04 177-02 3.28-03 211-02
4.00+03 1.13-04 1.7802 3.33-03 2.12-02
5.00+03 9.23-05 178-02 3.37-03 213-02
6.00403 7.83-05 1.79-02 — 3.39-03 2.1302
8.00+03 6.0305 1.7902 3.42-03 2.14-02
1.00+04 4,92-05 1.79-02  3.44-03 214-02
1.50+04 3.40-05 1.80-02  3.47-03, 2.1502
2.00+04 2.62-05 1.80-02 3.49-03 2.1502
3.00404 1.80-05 181-02 3.50-03 2.1602
4.00404 1.30-05 1.81-02  3.51-03 2.1602
5.00404 1.13-05 181-02 3.52-03 2.1602
6.00404 9.5406 181-02  3.52-03 2.1602
8.00404 7.31-06 181-02 3.52-03 2.1602
1.00+05 5.9506 1.81-02 — 3.53-03 2.1602

69



Photon Cross Sections, Attenuation Coefficients, and Energy Absorption
Coefficients From 10 keV to 100 GeV*

J. H. Hubbell

This report updates and extends previous NBS tabulations. Section 1 contains the information
of most immediate practical use: (a) a tabulation of the attenuation coefficient for 23 elements (H
to 2U) between 10 keV and 100 GeV and (b) a tabulation of the energy absorption coefficient for air,
water, and 18 elements between 10 keV and 10 MeV, and for air, water, and 7 elements up to 100 MeV.
Section 2 contains detailed information on the predominant processes (photoelectric absorption,
Compton scattering and pair production) and a brief discussion of other processes which combine
to give the attenuation coefficient. Theoretical and experimental data are reviewed, and auxiliary

tables and approximation formulas are given. Section 3 contains tabulations of cro:
predominant processes between 10 keV and 100 GeV for 23 elements and for 1.

mixtures.

sections for the
compounds and

Key words: Attenuation coefficient; Compton scattering; cross section; energy absorption coefficient;
gamma rays; pair production; photoelectric absorption; photons; x-rays,

1. Attenuation and Energy Absorption Coefficients

1.1. Introduction

The first modern systematic compilation of
photon! interaction cross sections and attenuation
coefficients, covering the energy range 10 keV to
100 MeV, was done by White ? [1952] and appeared
in NBS Report 1003 (unpublished)? Her tables
were subsequently published in the Handbook of
Radiology [1955] and in the 1955 edition of Beta
and Gamma-Ray Spectroscopy [1955]. Storm, Gil-
bert, and Israel [1958] further extended these
tables by interpolation to include all elements from
Z=1 to 100.

With some revisions the tables from NBS Report
1003 were published in NBS Circular 583 [1957],
and were revised in the 10-100 keV region by
McGinnies [1959] in NBS Circular 583 (Supple-
ment). Davisson [1965] further updated these tables
using more recent theoretical estimates of atomic
photoeffect and electron-field pair production.4

The present compilation, an earlier version of
which has been presented elsewhere (Hubbell and

“Supported primarily by the NBS Office of Standard Reference Data. Support was
ako received from the Defense Atomic Support Agency.

The terms “xray,” “gamma-ray,” and “photon” are used interchangeably through-
out this work.

“Referred to in her later work (1957)

Earlier compilations which are party th
or lower energy ranges, include those of Jones

[1927-8], Vietoreen (1943-9

e

and Sun [1947], Davisson and Evans [1952], and G. Allen [1950-1967]. The ws

Known data of 8, J. M, Allen [1930-1967] appearing in the Handbook of Chemistry
193:

and Physics are experimental and have not been revised

“Davisson's [1965] tables are accompanied by an extensive review article, Other
reviews. include those by Latyshey [1947], Bethe and Ashkin [1953], Fano [1953],
Evans [1955, 1963], Hayward [1958], Fano, Spencer, and Berger [1959], Fano,
Zerby, and Berger [1962]. and Koch, MacGillayry, and Milledge [1962]. For further
references to original data and to other compilations there are available extensive
bibliographies by Glocker (1950] and Stainer [1963] in the low energy region and by
Toms [1965} in the high energy region,

Berger [1968]), is based on a new analysis of all
available information. We were of course guided
strongly by methods and results contained in pre-
vious compilations, particularly those of White
[1952], but have also gone back to the original
experimental and theoretical literature.

We retain the format of White for the main tables
(sec. 3) but we have extended the energy range up
to 100 GeV and have taken into account new data
including the following:

(a) Photoeffect calculations by Hultberg et al.

[1968], Rakavy and Ron [1965-7] and Pratt

and Schmickley [1967].

Calculations of double Compton scattering and

radiative corrections to Compton scattering by

Mork [1968].

Nuclear-field pair-production radiative correc-

tions calculated by Mork and Olson [1965] and

screening effects evaluated by Sérenssen

[1965-6].

(d) Electron-field pair-production calculations by

Mork [1967] which combine Votruba’s [1948]

theory with that of Borsellino [1947] and Ghiz-

zetti [1947], and include the radiative correction.

Calculations of coherent and incoherent scat-

tering by Storm and Israel [1967].

(f) Additional experimental data including, among
others, the total cross section measurements
by Barkan [1956], Wiedenbeck [1962], Barlett
and Donahue [1963, 1965], Heinrich [1966],
Hughes and Woodhouse [1966], Carter et al.
[1967], McCrary, Plassman et al. [1967],
Perkin and Douglas [1967], and Knerr and
Vonach [1967].

(b)

(¢

sz


Table 3.—32.

POLYSTYRENE, (CsHs02)n

Scattering Pair production Total
Photon Photo.

energy With Without electric Nuclear Electron With Without

coherent coherent field field coherent coherent

Mev emg emtlg omg em*lg emtlg emtlg cml
100-02 |] 3.13-01 —_2.08-01 1.82+00 2.13400 — 2.03+00
1.50-02 || 2.64-01 2.0401] 4.91-01 7.55-01 6.9501
2.00-02 || 2.39-01 — 2.00-01 1,86-01 4.24-01  3.86-01
3.00-02 || 2.13-01 1.94-01 | 4.63-02 2.59-01 —-2.40-01
4.00-02 || 1.99-01 1.88-01 1.7602 2.17-01 —2.05-01
5.00-02 |} 1.90-01 1.82-01 8.95—-03 1.99-01 1.91-01
6.00—-02 || 1.83—-01 1.77-01 | 5.33-03 1.88-01 182-01
8.00—-02 || 1.71-01 1.68-01 | 2.09-03 1.73-01 1.70-01
1.00-01 1.62-01 1.60-01 1.00—-03 1.63-01 1.61-01
1.50-01 1.45-01 1.4401 | 2.67-04 1.45-01 1.44-01
2.00~-01 1.32-01 1.06—04 1.32-01
3.00-01 115-01 | 2.99-05 1.15-01
4.00-01 1.03-01 1.28-05 1.03-01
5.00-01 9.38-02 | 6.91—-06 9.38-02
6.00-01 8.68-02 | 4.30-06 8.6802
8.00-01 7.63—02 | 2.17-06 7.6302
1.00+00 6.85—02 | 1.34-06 6.8502
1.50+00 5.57-02 | 6.26-07 | 7.64-05. 5.58-02
2.00+00 4.7502 | 3.99-07 | 3.05-04 4.7802
3.00+00 3.74-02 | 2.23-07 | 8.76-04 —:1.30-05 3.83-02
4.00+00 3.12-02 | 1.53-07 142-03 5.36-05 3.27-02
5.00+00 2.69-02 | 1.17-07 | 1.91-03 _ 1.05—-04 2.90-02
6.00+00 2.38-02 | 9.32-08 | 2.3403 —-1.62-04 2.6302
8.00+00 1.95—-02 | 6.68-08 | 3.06-03 = 2.77-04 2.28-02
1.00+01 1.66—-02 | 5.19-08 | 3.65-03 3.7904 2.0602
1.50+01 1.23-02 4.77-03 — 5.90-04 1.76—-02
2.00+01 9.86-03 559-03 -7.57-04 1.62—02
3.00+01 7.17-03 6.74-03 —-1.01-03. 1.49-02
4.00+01 5.70-03 7.54-03 1.1903 1.4402
5.00+01 4.7603 8.14-03 1.3403 1.42—02
6.00+01 4.10-03 8.62-03  1.46-03 1.42—-02
8.00+01 3.23-03 9.3403 -1.65—-03. 1.42—02
1.00+02 2.69-03 9.87-03 —1.79-03. 1.4402
1.50+02 1.91-03 1.08-02 2.0403 1.47-02
2.00+02 1.50-03 1.13-02 —_2.20-03 1.50-02
3.00+02 1.06—-03 1.20-02—_2.42-03 1.55—02
4.00402 8.32-04 1.2402 2.57-03 1.5802
5.00+02 6.89-04 1.27-02 —_.2.67-03 1.60—02
6.00+02 5.90-04 1.29-02—-2.75—-03 1.62—02
8.00+02 4.61-04 1.31-02 2.8603 1.65—02
1.00+03 3.79-04 1.33-02 2.9403 1.66-02
1.50+03 2.65-04 136-02 —3.07-03 1.69-02
2.00+03 2.05-04 137-02 3.15-03 171-02
3.00+03 1.43-04 1.39-02—-3.25-03 1.7302
4.00+03 1.10-04 139-02 — 3.31-03 1.74-02
5.00+03 8.99-05 140-02 3.3403 1.7402
6.00+03 7.6205 140-02 3.37-03 1.7502
8.00+03 5.87-05 1.41-02 — 3.40-03 1.75—-02
1.00+04 4.79-05 141-02 3.42-03 1.76-02
1,50+04 3.31-05 142-02 -3.45-03 1.76-02
2.00+04 2.55-05 142-02 3.47-03 1.77-02
3.00+04 1.76-05 1.42-02 349-03 1.77-02
4.00404 1.35-05 142-02 3.50-03 1.77-02
5.00+04 1.10-05 1.42-02 3.51-03 1.77-02
6.00+04 9.28-06 142-02 3.51-03 1.77-02
8.00+04 7.12-06 142-02 3.52-03 1.78-02
1.00+05 5.79-06 142-02 3.52-03 1.78-02

72



Table 3.-31. MUSCLE, Striated,

S Handbook 85(1964) Composition

Scattering Pair production Total
Photon Photo.
energy With Without electric Nuclear Electron With Without
coherent coherent field field coherent coherent
emt cmtle emt emtlg emtlg em*lg emt
3.89-01__2.12-01 | 4.88+-00 5.27400 — 5.09+00
3.05-01 —-2.08-01 1.32+00 1.63+00 = 1.53+00
2.6601 -2.05-01 |_ 5.26-01 7.93-01 — 7.31—-01
2.29-01 1.98-01 1.44-01 3.73-01 — 3.42-01
2.10-01 1.92-01 | 5.73-02 2.68-01 = -2.49-01
1.98-01 1.86-01 | 2.81—-02 2.27-01 2.1401
1.90-01 1.81-01 1.58-02 2.05-01 1.97-01
176-01 1.71-01 | 6.31-03 1.83-01 1.78-01
1.67-01 1.63-01 3.0403 1.70-01 1.66—-01
1.49-01 1.47-01 8.32—-04 149-01 1.48-01
1.35-01 1.35-01 | 3.35—-04 1.36-01 1.35-01
1.18-01 117-01 9.59-05 1.18-01 1.17-01
_ 1.05—01 1.05-01 | 4.11—05 1.05-01 1.05-01
5.00-01 9.59-02 9.58-02 | 2.22-05 9.60-02 9.5902
6.00-01 8.88-02  8.87-02 | 1.39-05 8.88-02 = 8.8702
8.00-01 7.79-02 | 6.99-06 7.71902
1.00+00 7.00-02 | 4.33-06 7.00—-02
1.50+00 5.69-02 | 2.03-06 | 9.69-05 5.70-02
2.00+-00 4.86-02 | 1.29-06 | 3.86-04 489-02
3.00+00 3.82-02 | 7.18-07 1.11-03 —1.33-05 3.9302
4.00+00 3.19-02 | 4.89-07 180-03 5.47-05 3.37-02
5.00+00 2.75-02 | 3.73-07 | 2.41-03 _—-1.08-04 3.00-02
6.00+00 2.43-02 | 2.97-07 | 2.95-03 1.6504. 2.7402
8.00+00 1.99-02 | 2.13-07 | 3.86-03 283-04 2.40-02
1.00+01 1,69-02 | 1.66-07 | 4.60-03  3.87-04 2.19-02
1.50+01 1.25—-02 6.00-03 6.0304. 1.92—02
2.00+01 1.01—02 7.03-03 7.73-04 1.79-02
3.00+01 733-03 8.4703 —1.03-03 1.6802
4.00+01 5.82-03 9.46-03 — 1.22-03 1.65—-02
5.00+01 4,86—-03 1.02-02—-1.37-03. 1.6402
6.00+01 4.19-03 1.08-02—-1.49-03. 1.65—02
8.00+01 3.30-03 117-02 _——-1.68-03. 1.67—-02
1.00+02 2.75-03 1.24-02 1.8203 1.70-02
1,50+02 1,95—-03 135-02 2.07-03 1.75—-02
2.00+02 153-03 142-02 2.2403. 1.79-02
3.00+02 1.09-03 150-02 _2.46-03 1.85—-02
4,00+02 8.50-04 154-02 2.60-03. 1.89-02
5.00+02 7.0404. 158-02 2.70-03. 1.92-02
6.00+02 6.02—04 1.60-02—.2.78-03. 1.9402
8.00+02 4.70-04 1.63-02 —.2.89-03. 1.97-02
1.00+03 3.87-04 1.65-02—-2.97-03. 1.99-02
1.50+03 2.70-04 1.68-02—-3.10-03. 2.02-02
2.00403 2,09-04 1.69-02-3.18-03. 2.03—-02
3.00+03 1.46-04 171-02 3.27-03. 2.05—-02
4.00+03 1.12-04 1.72-02 2.06—-02
5.00+-03 918-05 1.73-02 2.07-02
6.00+03 7.79-05 1.73-02 2.08-02
8.00+03 6.00-05 1.7402 3.41-03. 2.08-02
1.00+04 4,.90-05 1.7402  3.43-03 2.09-02
1.50+04 3.38-05 1.7402 3.46-03 2.09—-02
2.00+-04 2.60-05 1.75-02 — 3.48-03. 2.10-02
3.00+04 1.79-05 175-02 3.49-03 2.10-02
4.00+-04 1.38-05 1.7502 3.50-03 2.10—-02
5.00+04 112-05 1.75-02  3.51-03 2.10-02
6.00+04 9.48—-06 1.7502 3.51-03 2.10-02
8.00+04 7.27-06 1.7502 —-3.52-03 2.10-02
1.00+05 5.91-06 1.75-02-3.52-03 2.11-02

71


Table 3.-34. POLYETHYLENE, (CH:)
Scattering Pair production Total
Photon Photo.

enerey With Without electric Nuclear Electron With Without

coherent coherent field field coherent coherent

MeV emtlg ctl emily emt ently emtlg cml
1.00-02 || 3.18-01 — 2.20-01 1.69+-00 2.01400 —1.91+00
1.50-02 || 2.72-01 2.16-01 | 4.56-01 7.28-01  6.72-01
2.00—-02 || 2.48-01—2.13-01 1.73-01 4.20-01—-3.85-01
3.00-02 |} 2.23-01 —-2.06-01 |_ 430-02 2.66-01 —-2.49-01
4.00-02 }} 2.10-01 1.99-01 1.6302 2.2601 -2.15-01
5.00—-02 || 2.00-01 1.93-01 | 8.30-03 2.0901 .2.01-01
6.00—-02 |} 1.93-01 1.88-01 | 4.95-03 1.98-01 1,93-01
8.00-02 1.81-01 L78-01 1.9403 1.83-01 1,.80-01
1.00-01 1.7101 1.69-01 | 9.29-04 1.72-01 1.70-01
1.50-01 154-01 1.53-01 2.47-04 1.54-01 153-01
2.00-01 1.40-01 | 9.85—-05. 1.40-01
3.00-01 1.22-01 | 2.78-05. 1.22-01
4.00-01 1.09-01 1.19-05 1.09-01
5.00-01 9.95-02 | 6.41—-06 9.95—-02
6.00-01 9.21-02 | 3.99-06 9.21-02
8.00-01 8.09-02 | 2.01-06 8.09-02
1.00+00 7.27-02 | 1.2406 7.27-02
1.50+00 5.91-02 | 5.81-07 | 7.28-05 5.9202
2.00+00 5.04-02 | 3.70-07 | 2.91-04 5.0702
3.00+00 3.9602 | 2.07-07 | 8.35-04 —-1.38-05 4.05—02
4.00+00 3.31-02 | 1.42-07 | 1.35-03 5.6805 3.45—-02
5.00+00 2.86-02 | 1.08-07 | 1.82-03_—1.12-04. 3.05—-02
6.00+00 2.53-02 | 8.65-08 | 2.23-03 1.7204. 2.77-02
8.00+00 2.07-02 | 6.20-08 | 2.92-03 2.9404 2.39-02
1.00+01 1.7602 | 4.82-08 | 3.48-03 4.02-04 2.1502
1.50+01 1.30-02 455-03 6.2604 1.82-02
2.00+01 1.05-02 5.33-03 8.0304 1.66—-02
3.00+01 7.61-03 6.42-03 —-1.07-03 1.51-02
4.00+01 6.05-03 7.19-03 — 1.27-03 1.45-02
5.00+01 5.0503 7.7603 1.42-03 1.42-02
6.00+01 4.35-03 8.22-03 —-1.55-03 1.41-02
8.00+01 3.4303 8.91-03 —-1.75-03 1,41-02
1.00+02 2.8503 9.42-03 —-1.90-03 1.42-02
1.50+02 2.03-03 1.03-02_—-2.17-03 1.45—02
2.00+02 1.59-03 1.08-02 2.3403 1.47-02
3.00+02 1.13-03 115-02 2.58-03 152-02
4.00+02 8.82-04 119-02 —_2.73-03 1.5502
5.00+02 7.30-04 1.21-02 = 2.85—-03 1.57-02
6.00+02 6.25—-04 1,.23-02 —-2.93-03 1,.59-02
8.00+02 | 4.88-04. 1.26-02-3.05-03 1.61-02
1.00+03 |) 4.02-04 1.27-02 3.1403 1.6302
1.50403 2.8104 1.30-02 — 3.28-03 1.65-02
2.00+03 { 2.17-04 1.31-02 — 3.36-03 1.67—02
3.00+03 151-04 1.3302 3.46-03 1.69-02
4.00-+-03 117-04 133-02 3.52-03. 1.70-02
5.00+03 9.5305 134-02 3.56-03 1.70-02
6.00+03 8.08-05 1.3402 — 3.59-03 1.71-02
8.00+03 6.23-05 135-02 3.62-03 1.72-02
1.00+04. 5.08-05 1.352 3.6403 1.72-02
1.50+04 3.51-05 1.35-02 3.6803 1.73-02
2.00+04 2.70-05 136-02 -3.70-03 1.7302
3.00+04 1.86-05 1.36-02 —3.72-03 1.73-02
4.00404 1.43-05 136-02 3.73-03 1.73-02
5.00+04 1.16-05 1.36-02 — 3.73-03 1.73-02
6.00+04 9.8406 1.36-02 3.7403 1,.74-02
8.00+04 7.5506 1.36-02 3.7403 1.74-02
1.00+05 6.14-06 136-02 3.75-03 1.74-02

74



Storm and Israel [1967] have used S(q, Z) values
of Cromer and Mann (and additional data from
Cromer) and F(q, Z) values from Hanson et al.
to calculate o2? and op (integrating over equa-
tions (2-18) and (2.-22), respectively) for all
elements Z=1 to 100 and energies ranging up from
1 keV. Figure 2.-3 shows ratios of these values of
oP (excluding interpolated-values) to values given
by the Klein-Nishina formula [eq (2.-8)] for photon
energies of 1, 10, and 100 keV.

Cumulative angular distributions of or, based
on values of F(g, Z) from Nelms and Oppenheim
[1955], are displayed in figure 2.-4 forC, Fe, and
Hg. At high energies it is seen that Rayleigh scat-
tering is confined to small angles (at 1 MeV more
than half the photons are scattered by less than
5°), At low energies, particularly for high-Z ma-
terials, the angular distribution is much broader.
Here, however, the Rayleigh scattering cross
section is small in comparison with photoelectric
absorption. On the basis of these considerations,
Rayleigh scattering is frequently disregarded in
gamma ray transport theory and shielding calcu-
lations (Fano, Spencer, and Berger [1959], Gold-
stein and Wilkins [1954)).

Rayleigh scattering can, however, be of im-

ple criterion for judging the angular spread of Ray-
leigh scattering is (Moon [1950], Evans [1958]):

(2.-23)

0.013328
6¢=2 arcsin [ Z |

E[MeV]

where 6 is the opening half-angle of a cone con-
taining at least 75 percent of the Rayleigh-scattered
photons (see also fig. 2.-4).

The sum (o?+p), rather than oP? and ox
individually, has been tabulated in previous compila-
tions (White-Grodstein [1957] and Davisson [1965]),
because this sum is less sensitive to errors from
approximations in the theory. In this report, since
present theory still relies on the impulse approxima-
tion and neglects initial motion of the electrons, we
retain the White-Grodstein format in our tables in
section 3. That is, in tables 3-1 to 3.-36 we list
the sum (of + op) (or “scattering, with coherent”
in the notation of White-Grodstein and Davisson),
in which o% and ox are the values given by Storm
and Israel [1967]. Also, in table 2.-9 we give these
results in the form of a percentage correction to
the total “without coherent” cross section, Got,
given in table 1.-4, viz

portance in interpreting “narrow beam” attenu- (oP? + on) —ok®
ation coefficient measurements, depending on the sv, X 100%. (2.-24)
angular resolution of the apparatus. A useful sim- tot
1.0) —
WH one me wee [ee wee le ee tw Te. den 4
100 keV |
. -
| ~ |
}— wee oe ee
oo ae |
}— o 8 we we .
10 keV
z OP —
Ne [2 8 a
So [ee ¢ . . I kev 4
° . ° . . ° |
. . . oe
IL . oe
0.01 | | | \ | | i | !
ce) 20 40 60 80 100
Zz

FIGURE 2-3. Ratio of the bound-electron Compton collision cross section, 0?
calculated by Storm and Israel [1967] to that for free electrons, of", evaluated from

the Klein-Nishina formula.

31


TABLE 1-7. Values of (a) the mass absorption coefficient j1q/p; (b) the mass energy-transfer coefficient jux/p; and
(0) the mass energy-absorption coefficient Hen)p.

Units are em/g (see footnote a).

Photon ,H 6c N
energy
[MeV] Hale Axle Henle Hale Bxle Henle Hale Bxle Henle
0.014 0.00991 1.98 3.38
0.015 0.0110 0.538 0.908
0.02 0.0136 0.208 0.362
0.03 0.0186 0.0596 0.105
0.04 0.0231 0.0307 0.0494
0.05 0.0271 0.0234 0.0319
0.06 0.0305 0.0212 0.0256
0.08 0.0362 0.0205 0.0223
0.10 0.0406 0.0216 0.0224
0.15 0.0481 0.0246 0.0248
0.2 0.0525 0.0266 0.0267
0.3 0.0569 0.0288 0.0287
0.4 0.0586 0.0296 0.0295
0.5 0.0590 0.0298 0.0297 0.0296
0.6 0.0587 0.0297 0.0295 0.0296 0.0295
0.8 0.0574 0.0290 0.0288 0.0289 0.0289
1.0 0.0555 0.0280 0.0279 0.0280 0.0279
1.5 0.0507 0.0257 0.0255 0.0257 0.0255
2 0.0465 0.0464 0.0238 0.0235 0.0234 0.0238 0.0236 0.0234
3 0.0400 0.0399 0.0398 0.0210 0.0206 0.0204 0.0211 0.0207 0.0205
4 0.0355 0.0353 0.0352 0.0191 0.0187 0.0185 0.0194 0.0189 0.0186
5 0.0320 0.0319 0.0317 0.0178 0.0174 0.0171 0.0181 0.0177 0.0173
6 0.0294 0.0292 0.0290 0.0169 0.0164 0.0161 0.0172 0.0167 0.0163
8 0.0255 0.0253 0.0252 0.0156 0.0151 0.0147 0.0161 0.0156 0.0151
10 0.0229 0.0227 0.0225 0.0147 0.0143 0.0138 0.0154 0.0149 0.0143

4) Values for ug/e and Henle given only if different from ugle.

Photon 0 nNa Mg

energy

[MeV] Hale Hxle Henle? Hale | Bxle | Henle Hale | Bxle | Henle
0.01 5.39 14.9 20.1

0.015, 1.44 4.20 5.80

0.02 0.575 1.70 2.38

0.03 0.165 0.475 0.671

0.04 0.0734 0,199 0.276

0.05 0.0438 0.106 0.144

0.06 0.0322 0.0669 0.0888

0.08 0.0249 0.0382 0.0475

0.10 0.0237 0.0297 0.0346

0.15 0.0251 0.0260 0.0279

0.2 0.0268 0.0265 0.0277

0.3 0.0288 0.0278 0.0288

0.4 0.0296 0.0284 0.0294

0.5 0.0298 0.0285 0.0294

0.6 0.0296 0.0284 0.0293

0.8 0.0289 0.0277 0.0275 0.0286 0.0285
1.0 0.0280 0.0278 0.0268 0.0266 0.0277 0.0275
1.5 0.0257 0.0254 0.0246 0.0245 0.0243 0.0254 0.0253 0.0251
2 0.0239 0.0236 0.0234 0.0230 0.0227 0.0225 0.0238 0.0234 0.0232
3 0.0213 0.0208 0.0206 0.0208 0.0202 0.0199 0.0216 0.0210 0.0206
4 0.0196 0.0191 0.0188 0.0195 0.0188 0.0184 0.0204 0.0196 0.0191
5 0.0185 0.0179 0.0175 0.0186 0.0179 0.0174 0.0196 0.0187 0.0181
6 0.0177 0.0171 0.0166 0.0181 0.0173 0.0167 0.0190 0.0182 0.0175
8 0.0166 0.0160 0.0155 0.0174 0.0167 0.0159 0.0185 0.0177 0.0168
10 0.0160 0.0154 0.0148 0.0171 0.0164 0.0155 0.0183 0.0176 0.0165

17


The remaining small effects (resonance scattering
and Thomson scattering by the nucleus, Compton
scattering by nucleons, meson production, reso-
nance scattering associated with meson production,
Delbriick scattering and nucleon-antinucleon
production) will not be treated here. For a general
discussion of these effects, including order of magni-

tude estimates, see Bethe and Ashkin [1953].
Recent photomeson data have been summarized by
Crouch et al. [1964], Allaby et al. [1966], Panofsky
[1968], and Joos [1968]. We have reproduced in
table 2.-2 the photomeson cross section compilation
by E. Lohrmann in the review by Joos [1968].

TABLE 2.-2. Meson photoproduction cross sections in ub(10-*°cm*), as summarized by
E. Lohrmann in the article by Joos [1968].

Reaction Photon energy
Po 7 References

1GeV | “2GeV | 3GeV |4.5 GeV

pr? 0.6 | 70, 71, 72, 74

nz? 1.0 | 70, 72, 73, 75, 76

Pp? 17 | 45, 47, 52,55

Pwo 3 | 46,51, 55

Po ~0.2 | 55

Pn <0.2 | 51,55, 78, 79, 80

PX°(959) ~0.2 | 51,55

Pee ~0.3 | 52,55

At+ (1238) a> 2 | 50, 55, 77, 81, 82

Ant 55, 77

Attp- 52) 55, 77

AK* ~ 0.25 | 53, 73, 83, 84

SK+ ~O.1 73

Stk <0.2

Y*°(1385) K~ ~0.2

Y** (1385) K° ~0.1

[45] Brown-Harvard-MIT-Weizman Institute Bubble Chamber group (CEA-Bubble
Chamber Group) Phys. Rev. 146 (1966), 994.
[46] CEA-Bubble Chamber Group, Phys. Rev. 115 (1967), 1468, Contribution No. 278 to

this Conference. (See Joos [1968].)
[47] CEA-Bubble

chamber Group, Phys. Rev. 155 (1967), 1477.

[50] DESY-Bubble Chamber Collaboration, Phys. Letters 23 (1966), 707.

[51] DESY-Bubble Chamber Collaboration, Nuovo Ci
[52] DESY-Bubble Chamber Collaboration, Nuovo Ci
(53) DESY-Bubble Chamber Collaboration, Nuovo C

ento 46 (1966), 795.
nento 48 (1967), 262.
nento 49 (1967), 504.

[54] DESY-Bubble Chamber Collaboration, Nucl. Phys. B1 (1967), 668.
{55} DESY-Bubble Chamber Collaboration, Contribution No. 8 to this Conference. (See

Joos [1968].)
{70} Data Comp:
Report CTSL~42 CALT 68-108.

‘ion below 1.5 GeV: J. T. Beale, S. D, Ecklund, and R. L. Walker,

(71] Braunschweig, M., Husmann, D., Liibelsmeyer, K., and Schmitz, D., Phys. Letters
22 (1966), 705: Braunschweig, W., Contribution No. 140 to this Conference. (See

Joos [1968].)

[72] Alvarez, R., Bar-Yam, Z., Kern, W., Lukey, D., Osborne, L. S., and Tazzari, S.,

Phys. Rev. Letters 12 (1964), 707.

[73] Elings, V. B., Cohen, K. J., Garelick, D. A., Homma, S., Lewis, R. A., Luckey, P. D.,
and Osborne, L. S., Phys. Rev. Letters 16 (1966), 474.

[74] Bolon, G. C., Garelick, D., Homma, S., Lewis, R., Lobar, W., Luckey, D., Osborne,
L. , Switters, R., and Uglum, Je, Phys. Rev. Letters 18 (1967), 926."

(75] Buschhorn, G., Carroll, J., Eandi, R.D. , Heide, P., Hiibner, R., Kern, W., Kitz, U.,
Schmiiser, P., and Skronn, H. I, Phys. Rev. Letters 17 (1966), 1037; Phys. Rev.

Letters 18 (1967), 571.

[76] Boyarski, A., Bulos, F., Busza, W., Diebold, R., Ecklunk, S., Fischer, G., Rees, J.,
B.

and Richter,
Photon Intera
(77) CEA-Bubble Chamber Group,

Results presented at the Stanford Conference on Electron and
ions at High Energies (1967), by B. Richter.
ntribution to the Stanford Conference on Electron

and Photon Interactions at High Energies (1967).
[78] Bacci, C., Penso, G., and Salvini, G., Nuovo Cimento 44 (1966), 983.

[79] Prepost, R., Lundquist, D., and Quinn, D.
(80} Heusch, C. A., Prescott, C. Y., Bloom,
Letters 17 (1966), 573, and Contribution No. 284 to this Conferen

[1968},)
{81} Allaby, J. V.. Lynch
[82] Hauser, M. G., CAL

68-123.

Phys. Rev. Letters 18 (1967), 82.
. D., and Rochester, L. S., Phys. Rev.
- (See Joos

L., and Ritson, D. M., Phys. Rev. 142 (1965), 887.

[83] Anderson, R. L.. Gabathuler, E., Jones, D., MacDaniel, B. C., and Sadoff, A., Phys.

Rev. Letters 9 (1962), 131.

[84] Peck, C. W., Phys. Rev. 135B (1964), 830.

23


TABLE 1-7 (Continued)
Photon ca aeFe 29Cu
energy
(MeV] | Hale | axle | Henle | Hale | #xle | Henle | Hale | uxle | Henle
0.01 95.4 91.6 91.6 171. 142, 142, 223. 160. 160.
0.015 29.4 28.6 28.6 55.5 49.3 49.3 73.2 59.4 59.4
0.02 12.4 12.2 12.2 24.9 22.8 22.8 32.8 28,2 28.2
0.03 3.65 3.60 3.60 7.72 7.28 7.28 10.5 9.50 9.50
0.04 1.51 1.50 1.50 3.31 3.17 3.17 4.56 4.24 4.24
0.05 0.770 0.764 0.764 1.69 1.64 1.64 2.35 2.22 2.22
0.06 0.447 0.444 0.444 0.989 0.961 0.961 1.39 1.32 1.32
0.08 0.197 0,196 0.196 0.422 0.414 0.414 0.593 0.573 0.573
0.10 0.109 0,223 0.219 0.219 0.311 0.302 0.302
0.15 0.0498 0.0821 0.0814 0.0814 0.108 0.106 0.106
0.2 0.0371 0.0498 0.0495 0.0495 0.0602 0.0597 0.0597
0.3 0.0318 0.0342 0.0335 0.0335 0.0371 0.0370 0.0370
0.4 0.0309 0.0308 0.0318
0.5 0.0304 0.0295 0.0298
0.6 0.0300 0.0299 0.0287 0.0286 0.0287 0.0286
0.8 0.0291 0.0289 0.0275 0.0273 0.0273 0.0272 0.0271
1.0 0.0281 0,0280 0.0278 0.0264 0.0262 0,0261 0.0261 0.0258
1.5 0.0259 0.0257 0.0254 0.0243 0.0241 0.0237 0.0240 0.0237 0.0233
2 0.0245 0.0240 0.0236 0.0233 0.0225 0.0220 0,0230 0.0222 0.0217
3 0.0231 0.0220 0.0214 0.0225 0.0212 0,0204 0.0225 0.0211 0.0202
4 0.0226 0.0213 0.0205 0.0225 0.0209 0.0199 0.0228 0.0211 0.0200
5 0.0224 0.0211 0.0200 0.0228 0.0211 0.0198 0.0233 0.0214 0.0200
6 0.0225 0.0211 0.0198 0.0232 0.0215 0.0199 0.0239 0.0220 0.0202
8 0.0229 0.0215 0.0198 0.0242 0.0226 0.0204 0.0251 0.0234 0.0209
10 0.0234 0.0222 0.0201 0.0252 0.0238 0.0209 0.0264 0.0248 0.0215
Photon Sn Pb 2
energy
[MeV] Hale | uxle | Henle Hale | uxle | Henl@ Hale | Ble | Henl@
0.01 139. 136, 136. ize 127. 127, | 173. 171, 170.
0.015 J 45.2 43.7 43.6 112.0 91.7 91.7 | 60.2 59.6 59.4 Lo
0.02 20.0 19.8 19.8 [| 833 69.2 69.1 | 683 35.5 35.5 int
0.03 40.5 16.2 16.2 28.2 24.6 24.6 39.4 33.0 33.0
0.04 18.8 9.97 9.96 13.0 11.8 11.8 18.6 16.3 16.3
0.05 10.2 6.25 6.24 710 6.57 6.54 10.3 9.30 9.25
0.06 6.20 4.20 4.19 4.31 4.11 4.08 6.34 5,82 5.78
0.08 2.78 219 2.18 1.96 1.87 1.86 2.94 2.76 2.73
0.10 1.49 1.26 1.25 5.12 2.28 2,28 1.61 1.54 1.52 K
0.15 0.485, 0.446 0.442 1.80 1.16 115 2.39 T.12 1.19
0.2 0.226 0.211 0.209 0.869 0.637 0.629 1.15 0.712 0.704
0.0892 0.0853 0.0843 0.322 0.265 0.259 0.425 0,322 0.315
0.4 0.0550 0.0536 0.0530 0.168 0.147 0.143, 0.222 0.184 0.178
0.5 0.0428 0.0423 0.0416 0.108 0.0984 0.0951 0.140 0.122 0,118
0.6 0.0361 0.0358 0.0353 0.0793 0.0737 0.0710 0.100 0.0902 0.0864
0.8 0.0302 0.0301 0.0294 0.0525 0.0503 0.0481 0.0640 0.0599 0.0569
1.0 0.0271 0.0270 0.0264 0.0407 0.0396 0.0377 0.0479 0.0458 0.0432
15 0.0239 0.0233 0.0226 0.0303 0.0288 0.0271 0.0337 0.0317 0.0295
2 0.0234 0.0220 0.0210 0.0286 0.0259 0.0240 0.0310 0.0278 0.0255
3 0.0243 0.0219 0.0205 0.0300 0.0260 0.0234 0.0322 0.0276 0.0246
4 0.0259 0.0232 0.0212 0.0324 0.0281 0.0245 0.0346 0.0298 0.0256
5 0.0275 0.0247 0.0221 0.0350 0.0306 0.0259 0.0372 0.0324 0.0270
6 0.0290 0.0262 0.0230 0.0372 0.0331 0.0272 0.0394 0.0348 0.0281
8 0.0319 0.0292 0.0245 0.0411 0.0378 0.0294 0.0423 0.0392 0.0298
10 0.0344 0.0319 0.0258 0.0446 0.0419 0.0310 0.0468 0.0432 0.0312

19



‘At energies above 100 keV the sum (of?+ 02)
given by Storm and Israel (based entirely on the
Hartree model) is within 1 percent of that given by

180°

Lo

0.1
PHOTON ENERGY, Mev

Ficure 2-4. Opening half-angle, @, of cone containing 25
percent, 50 percent, 75 percent, and 95 percent, respectively,
of photons Rayleigh-scattered from C, Fe, and Hg.

The function 6 (Eq. 2.23) is included for comparison.

TABLE 2-9. Percentage by which ow or ylp is increased if coherent scattering
Based on data by Storm and Israel {1967} taking into account Rayleigh scattering and the effect of electron bi

White-Grodstein and Davisson (based mostly on the
Thomas-Fermi model). However, between 10 and
100 keV there are differences of as much as 10
percent in either direction.

2.4.3, Radi:

‘ive Corrections. Double Compton Effect

The radiative correction (of the order 1/137) is
associated with emission and reabsorption of vir-
tual photons whereas in the double Compton effect
an additional real photon, usually very low in energy,
is emitted.

Because of the predominance of pair production
at high energies, experimental data on these effects
are difficult to obtain and the existing experiments
by Cavanagh [1952], Bracci et al. [1956], Theus
and Beach [1957], and Burdet [1963] have large
uncertainties. Hence, the information is primarily
theoretical and has only recently become sufh-
ciently quantitative for inclusion in tabulations.
We have relied on the recent theoretical results of
Mork [1968] who made a calculation combining the
radiative correction o(rad. corr.) with the cross
section o(double Compt.) for the double Compton
effect.

The differential formulas (Brown and Feynman
[1952], Mandl and Skyrme [1952]) for the two
effects each contain an “infrared divergence.”
These divergencies are of opposite sign, and in the
combined calculation they cancel each other to
give a physically meaningful result.

The Mork correction, which must be added to
the Klein-Nishina cross section,

Ao¥= (double Compt.) + o(rad. corr.)
(2.-25)

is given in table 2.-8 separately and in the com-
bination with of. It is seen that the contribution
of Ac¥ to ac is ~ 0.25 percent at 4 MeV, rising to
~1 percent at 100 MeV and ~5 percent at 1000
MeV.

fects are included.
on Compton scattering

Photon Absorption
energy iH oC wAl 2oCa Fe avCu | Mo | soSn aW Pb aU edges
[MeV]
0.01 | —.2 5.2 1.9 0.9 0.7 0.6 2.6 18 48 3.8 3.1
Luedge
oor) -1 | 107} ss} 27| 19) 17 [so] sat 307 27] 37] rr
0.03 | 0 90 | 84] 46] 32] 28] 18 16) 52} 45 [ 37f
00} of} 47] 16 | 79) 57] 51] 32] 28 Lot] 81} 66
a1] o| 14] 58} 84} 82] 80] 59] so] 34] 33 | 117
K-edge
020} 0} os | 20] 38] so] 60] 72] 69] 53] 49 | 44
030} 0] <o5] 10} 20] 32} 36] 58] 62] 58] 54] 50
0.50 0 <05 <0.5 0.9 1.3 17 2.8 3.8 5.0 48 4.7
1.0 0 | <05 | <05 | <05 | <05 | 05] 11 12| 22] 26] 28
2.0 0} <035 | <05 | <05 | <05 | <05 |] <05|<05| 08 | 11 0.9
3.0 0 <05 | <05 | <05 | <05 | <05 | <05 | <05 | <05 | 06

<05



100 ee a T -YPERIMENTALD
FE Tp TTT) 71 TT aR
Uy —) © BROOKES, et a! [i967]
ay D sones [i959, 960]
[> = eg2Pb ) v be wire, et a! (i95i)
all KENNEY, et al [i954]
E 73107 —| & ANDERSON, et al [i986]
Xe | a cooPER [i958]
| a ¥ MALAMUD [1959]
Sat © NICHIPORUK [i967]
a bad ‘6 WALKER, et al [i966]
a2Mo © FIDECARO, et al [1962]
10 ca, | ORNASEL 8 WALKER [1966]
eae sR THEORETICAL:
tT THIS COMPILATION
ze)
|g ae ah

I o 0-104 z |
[La arg eee ——
Ol v —£r |
F |
C 7
pao r) |
Pr ae bi) i
10? 10° 1o* 10°
PHOTON ENERGY, MeV
Ficure 1.-3.

Comparison of present total cross sections Oy(= Tet O¢+ kat ke) (see tables in

section 3) above 100 MeV with available experimental data.

1.5.2. Conditions Under Which the Coefficients
are Useful

At high energies the range of secondary elec-
trons tends to become comparable with the gamma-
ray mean free path, as indicated by the ratios in
table 1-6. Under such conditions the compu-
tation of gamma-ray energy deposition in a medi-

um requires a cascade calculation involving
coupled electron and photon transport equa-
tions,!°

However, at energies below 10 MeV where the
travel of electrons is of less significance, it may
be sufficient to treat the problem in terms of the
gamma-ray flux and either the ‘mass energy-
absorption coefficient” or one of the various ap-
proximations such as the “mass energy-transfer
coefficient” or ‘‘mass absorption coefficient” dis-
cussed in the following section 1.5.3.

** For a calculation of this type see, for example, that of Brysk 1954)

14

The amount of energy, €, absorbed per unit time
in a “volume of interest,” AV, at a point r in the
medium, can be expressed as the sum of two terms.
The first term describes the conversion of photon
energy to electron kinetic energy and involves the
mass energy-absorption coefficient, The second
term describes the migration of energy into and out
of the volume of interest in the form of kinetic
energy of electrons. Thus one can set up the energy
balance equation:

=[,, dntetr) [ ae ote, ne HB)

+ [ein ~ €oue] (a.-9
in which €, in, and €w are in MeV s~, p(r) is the
density of the medium in g cm~3 at r, E is the pho-
ton energy in MeV, and pen/p(E) is in cm? g. The
quantity $(E, r), with dimensions MeV-! cm~ s—,
represents the flux per unit energy interval (inte-
grated over all directions) of photons, including
secondaries, with energies between E and E+ dE.


U.S. DEPARTMENT OF COMMERCE
WASHINGTON, D.C. 20230

OFFICIAL BUSINESS POSTAGE AND FEES PAID
U.S. DEPARTMENT OF COMMERCE



Table

3.—33. POLYMETHYL METHACRYLATE (Lucite), (Cs;H:02),

Photon
energy

Seat

Photo

Pair production

Total

With Without Nuclear Electron With Without
coherent coherent field field coherent coherent
MeV cml omtlg emily emilg cml emtlg em*lg

1.00-02 || 3.42-01 2.0801 | 2.90+00 3.25+00 — 3.11+00
1.50-02 || 2.79-01 2.0401 7.78-01 1.06+00 = 9.82-01
2.00-02 || 2.48-01 2.01-01 | 3.03-01 5.5101 -5.03-01
3.00—-02 |} 2.18-01 1.94-01 7.9802 2.98-01 = 2.7401
4.00—-02 || 2.03—-01 1.88-01 | 3.12-02 2.34-01 —-2.19-01
5.00-02 1.92-01 1.83-01 1.5402 2.08-01 1.98-01
6.00-02 |] 1.8401 1.77-01 |_ 8.86-03 1.93-01 —_-1.86-01
8.00-02 || 1.72-01 —-1.68-01 | 3.50-03 1.76-01_—1.72-01
1.00-01 |} 1.63-01_—-1.60-01 |_ 1.68-03 1.64-01 — 1.62-01
1.50-01 1.46-01 1.44-01 | 4.52-04 1.46-01 1.45-01
2.00-01 1.33-01 1.32-01 1.81-04 1.33-01 1.32-01
3.00-01 1.15-01 1.15-01 | 5.14-05 1.15-01 1.15-01
4.00-01 1.03-01 1.03-01 | 2.19-05 1.03-01 1.03-01
5.00—-01 |} 9.41-02 9.4102 |_ 1.18-05 9.4102 9.41—-02
6.00—-01 |} 8.71-02 8.7002 |__7.39-06 8.7102 8.70-02
8.00-01 7.6502 | 3.72-06 7.6502
1.00+00 6.87—-02 | 2.30-06 6.87—-02
1.50+00 5.59-02 | 1.08-06 | 8.49-05 5.59-02
2.00+-00 4.77-02 | 6.85-07 | 3.38-04 4.80—-02
3.00+00 3.75-02 | 3.83-07 | 9.72-04 —-1.31-05 3.85—-02
4.00+00 3.13-02 | 2.62-07 1.58-03 -5.37-05 3.29-02
5.00+-00 2.70-02 | 2.00-07 | 2.12-03 1.0604 2.92—-02
6.00+00 2.39-02 | 1.59-07 | 2.59-03 1.6204 2.66—-02
8.00+00 1.95-02 | 1.14-07 | 3.39-03 2.7804 2.32-02
1.00+01 1.66—-02 | 8.92-08 | 4.05-03 = 3.80—-04 2.11-02
1.50+01 1.23-02 5.29-03 5.9104 1.82—-02
2.00+01 9.88-03 6.19-03 —-7.59-04 1.68-02
3.00+01 7.19-03 7.46-03 —-1.01-03 1.57-02
4.00+01 5.72-03 8.34-03 —-1.20-03 1.53-02
5.00+01 4.77-03 9.00—-03 1.35—03 151-02
6.00+01 4.11-03 9.5403 1.47-03 151-02
8.00+01 3.2403 1.03-02 1.6503 152-02
1.00+02 2.69-03 1.09-02_—1.79-03. 1.5402
1.50+02 1.92-03 1.19-02 2.0403 1.59-02
2.00+02 1.50-03 1.25-02 —.2.20-03 1.62—02
3.00+02 1.06-03 1.32-02—-2.42-03 1.67—-02
4.00+02 8.3404 1.37-02 —.2.56-03. 1,71—-02
5.00402 6.90-04 140-02 2.67-03 1.73—-02
6.0002 5.91-04 142-02 2.7403 1,75—02
8.00+02 4.62—-04 145-02 2.86-03 1.78-02
1.00+03 3.80-04 1.46-02 2.9403. 1.80-02
1.50+03 2.65-04 1.49-02 -3.06~-03. 1.82-02
2.00+03 2.05~-04 1.51-02 3.1403 1.8402
3.00+03 1.43-04 152-02 3.24-03 1.86-02
4.00+03 1.10-04 153-02 3.29-03. 1.87-02
5.00+03 9.01-05 1.5402 — 3.33-03 1.88-02
6.00+03 7.6405 154-02 3.35-03 1.88-02
8.00+03 5.89-05 155-02 3.38-03. 1.89-02
1.00+04 4.81-05 1.55-02 3.40-03 1.89-02
1.50+04 3.32-05 155-02 —-3.43-03 1.90-02
2.00+04 2.55-05 1.5602 3.45-03 1.90—-02
3.00+04 1.76-05 1.5602 = 3.47-03 1.91-02
4.00+04 1.35—-05 156-02 3.48-03 1.91—02
5.00+04 1.10-05 156-02 3.48-03 1.91-02
6.00+04 9.31-06 1.5602  3.49-03 1.91-02
8.00+04 7.14-06 156-02 3.49-03 1.91-02
1.00+05 5.80-06 1.56-02 —-3.50-03 1.91-02

73



Photon
energy

With
coherent

Scattering

Without
coherent

7 blatom
3.77+02
46+02
1.74402
1.74402
1.07+02

7.64+01
5.94401
4.90+01
3.71401

3.06+01
2.32+01
1.97401
1.60+01

1,39+01
1.25+01
1.16+01
1.00+01

8.97+00
7.25+00
6.17+00
4.84400

4,05-+-00
3.50+00

blacom

Photo.

blatom

1.34404
4.24403
1.84403
1.28+04
4.48+03
2.04403
1.09+03
6.54402
2.85402
1.47402
4.50+01
1.93+01
6.02+00

2.74400
1.53+00
9.80-01
5.04-01

3.1301
143-01
8.8402
4.7702

3.18-02
2.3002
1.88~02
1.31-02

1.0202
6.39-03
4.65-03
3.0103

2.2203
1.7603
1.46~03
1.08-03

8.65—04

Table 3.—18. MOLYBDENUM, Z=42

Pair production

Total

Total

Nuclear
field

bfatom

9.99-02
3.5401
9.40-01

1.21401

1.21401
1.22401
1.22401
122401
1.22401
1.22401
1.22401
1.22401
1.22401

Electron
field

bfatom

With Without
coherent | coherent

bfarom

1.37404
4.49-+03
2.01403
1.30+04
4.59403

2.12403
1.15403

1.12401

1.14401
1.16+01
L.17+01
1.19+01

1.20+01
1.21401
1.22+01
1.23+01

1.24401
1.24401
1.24401
1.24401

1.25+01
1.25+01
1.25+01
1.25+01

1.25+01
1.25401
1.25401
1.25+01

1.25+01

With | Without
coherent

“oherent
emé |g cme |g
8.62+01 8.40401

2.68+01

1.17+01
8.08+01

2.83401

1,30+01

6.97400

4.25400

1,92+00

1.05+00

3.99-01

2.28-01

131-01
1.0501 1.01-01
8.83-02  8.50-02
7.8802 7.6702
6.61-02 6.5202
5.83-025.77-02
4.70-02 468-02
415-02 4.14-02
3.6602
3.49-02
3.44-02

7.0002

7.1602
127-02
7.3502
7.4502
7.5302
7.6202
7.6702
1.7302

1.7702
7.79-02
7.80-02
7.81-02

7.8302
7.85-02
7.8502
7.8602
7.8602
7.86-02
7.87-02
7.88-02

7.8802

(bjatows) x 006277 = emg

58


The mass attenuation coefficient p/p is propor-
tional to the total photon interaction cross section
per atom, Cio, i-e., to the sum of the cross sections
for all the elementary scattering and absorption
process. This relation is

atoms
[el [4]-— gaiom
ple tt atom u—s ’

g-atom

b
= wt [al +NalM-10-*4, (1.-5)

where N, is Avogadro’s number (6.02252-10
atoms/g-atom) and M is the atomic weight of the
absorber material. Table 1.-1 lists values of
(Na/M)-10-4 for a number of elements, in addition
to typical values for p, and similar information is
given in table 1.-2 for some mixtures. The cross
section per atom, Oy, should be used in prefer-
ence to p/p as a basis for interpolation vs. Z be-
cause of the dependence of «/p on the atomic
weight, M. Not only does M vary irregularly from
element to element, but values of M can differ
from those given in table 1-1 depending on the
isotopic composition of a given sample. The effects
of isotopic variation on oy (excluding photo-
nuclear interactions) are negligible in comparison
with effects on a/p.

TABLE 1-1. Values of the atomic weight M, the factor (Na/M)
10" for converting attenuation data from blatom to cng”,
and typical densities p for converting from cm?g-! to cm.

M,* Nay ave
Element | gromie we, | 4px 10%" ps
| ; b
Z |Sym- om /
pol | gle—atom |g / atom glem®
1) H 1.00797 0.5975 0,00008988 g,
(H:)
2) He 4.0026 1505 0001785
3) Li 6.939 ‘08679 | ‘534
4| Be 9.0122 ‘06683 | 1.85
5| B 10.811 05571 2.535,
6| Cc 12.0115 05014 2.25 (graph-
ite)****
7|N 14.0067 04300 -001250 g, (Nz)
3} 0 15.9994 103764 | .001429 «, (O2)
9| F 18.9984 £03170 | 1001696 g: (Fs)
10/ Ne | 20.183 “02984 | 10008999 4
11] Na | 22.9898 02620 971
12| Mg 24.312 02477 1.74
13] Al 26.9815, 02232 2.70
14] Si 28.086 ‘02144 | 2.42
15| P 30.9738 ‘01944 | 1.8—2.7
16| $ 32.064 01878 | 1.96 —~2.07
17| Cl 35.453 ‘01699 | 1003214 g, (Cl)
18) Ar | 39.948 (01508 | .001784
19| K 39.102 ‘01540 87
201 Ca | 40.08 01503 | 1.55

TABLE 1-1. Values of the atomic weight M, the factor (Ns/M)
X 10° for converting attenuation data from blatom to cmtg*,
and typical densities p for converting from cm®g to cm, —
Continued

Element | stone we, % x 19-20 pe
Z | Sym- cm? / b
bol | g/g—atom % / atom glem*
21| Se 44.956 01340
22| Ti 47:90 101257
23| Vv 50.942 01182
24) Cr 01158
25| Mn “01096
26 | Fe 01078
27) Co -01022
28 | Ni -01026
29) Cu 009478
30) Zn 009213
31| Ga 69.72 008638
32| Ge 72.59 008297
33| As 74.9216 008038
34) Se 78.96 007627
35 | Br 79.909 007537
007187
1007046
006873
006774
006602
006482
006277
(.006083)
005959
45| Rh 102.905 005853.

46 | Pd 106.4 005660 | 12.25

47| Ag 107.870 .005583 | 10.49

48 | Cd 112.40 8.65

49\ In 114.82 7.43

50| Sn 118.69 5.75 — 7.29
$1|Sb | 121.75 6.62
52|Te | 127.60 6.25,

53| 1 126.9044 4.94
54|Xe | 131.30 2005896 g
55|Cs | 132.905 1.873

56 | Ba | 137.34

57| La | 138. cis
58|Ce | 140.12 6.90

59| Pr | 140.907 6.48

60} Nd | 144.24 | 7.00

61| Pm | (145) (.004153)} [7.22] ******
62] Sm | 150.35 004006 | 7.7-7.8
63| Eu | 151.96 003963 | [5.259]
64) Gd | 157.25 003830 | [7.948]
65|Tb | 158.924 -003790 | [8.272]

66 | Dy 162.50 0.003706 [8.536}

67| Ho | 164.930 -003652 | [8.803]
68) Er | 167.26 1003601 | [9.051]*#***
69} Tm | 168.934 2003565 | [9.332]
70| Yb | 173.04 2003480 | [6.977]

71] Lu | 174.97 .003442 | [9.872]
72/ Ht | 178.49 2003374 | 13.3
73/Ta | 180.948 003328 | 17.1
74/W | 183.85 2003276 | 19.3

751 Re 186.2 -003234 | 20.53



TABLE 2.-8. Compton scattering cross section o¢ for a free electron.

These values were evaluated using eq. (2.~8) and modified by the Mork [1968] combined radiative and double-Compton corrections AoTM here listed,

The average fraction of photon energy transferred to the electron, fc, is also listed.

Photon hot oc= of" ff! Photon on dof oc= oft fe
energy + dol energy + Ack
MeV | bjelectron | bjelectron | blelectron MeV | bjelectron |" blelectron | bjelectron
0.010 0.64039 (0.00000) | (0.6404) | 0.01876 40 |0.017462 | 0.00012 0.01758 0.76004
2015, 162888 (00001) (.6289) 50 | .014565 00011 201468 76922
02 161791 (00001) (6179) 60 | .012541 00010 201264 177624
03 59742 (,00002) (5974) 80 | :0098806 | .000090 :009970 -78650
04 57867 (.00002) (.5787) . 100 | .0081976 | .000082 .008280 79385,
‘05 "56144 (00003) (5615) “8071 150 | .0058182 | .000075 2005893 80600
“06 134555 (00003) (5456) 09363 200 | -0045506 | .000070 2004620 81379
“08 151722 (00004) (5173) “11713 300 | 0032086 | .000067 003276 82378
. 400 | 0024992 | .000066 .002565 83024
Jo | -s5369 | onoos) apa, | tsago $99 | tosses | toouet | toatse | aos
3 “40643 (00008) (4065) "91635 600 | 0017531 2000065 2001818 83858
00 | 0013609 | .000059 2001420 184402
3 35340 (00010) (3535) 126965 8 :
| stess | cosy | sus | some |} ue | gus, | comer, | canes, | ge
‘5 18913 (00014) (2893) 34136 2000 | ‘00060303 | (-0000283) | (.0006314) | 85913
6 6747 (00016) (2676) | 36751 3000 | ‘00041929 | (0000197) | (004390) | ‘86492
3B -23493 (.00018) (.2351) -40866 . (i ) ( 000: 389) ‘36874
4000 | .00032365 | (.0000152) | (.0003 4
1.0 21118 (,00020) (2114) 44004 5000 | .00026462 | (.0000124) | (.0002771) | .87156
15 -17156 (00023) (.1718) -49468 6000 | .00022439 | (.0000105) | (.0002349) 87378
2.0 14634 (00024) (1466) 53084 8000 | .00017288 | (.0000081) | (.0001810) | .87713
3.0 £11508 (.00024) (1153) ‘57732
10000 | .00014115 | (.0000066) | (.0001478) | .87960
4 095963 00024 09620 -60693 15.000 | ,000097550 | (.00000458) | (.0001021) -88386
5 -082856 -00022 -08308 62799 20000 | .000074997 | (.00000352) | (.00007852) | .88670
6 073221 00020 207342 64400 30000 — | 000051721 | (.00000243) | (00005415) | .89047
8 +0597 00018 06006 072 40000 | .000039708 | (.00000187) | (.00004157) | .89300
10 050983 -00017 05115 68356 50.000 .000032335 | (.00000152' } (.00003385) 89488
15 037708 00015, 03786 | .71004 60000 | .000027333 | (00000128) | (00002862) | .89637
20 030246 00014 -03039 | .72656 80000 | 000020958 | (00000099) | (.00002194) | 89864
30 021995, 00013 202212 | .74713 100.000 | .000017051 | (.00000080) | (00001785) | 90033

elements the K-shell binding energies are low in
comparison with the photon energies considered,
while for high-Z materials with substantial K-shell
binding energies these electrons are a small frac-
tion of the total.

The scattering of 0.662-MeV photons by K-shell
electrons of various heavy atoms has been measured
by Motz and Missoni [1961], Sujkowski and Nagel
[1961], and Varma and Eswaran [1962]. The ratio
of the observed differential cross section dof(@)/dQ,
to the Klein-Nishina differential cross section
da '*(0)/dQ. [eq (2.-6)] for tin and gold is given in
figure 2.-2, based on data of Motz and Missoni.
It is seen that for small angles the effect of binding
is to decrease the cross section, whereas for large
angles an increase occurs. The decrease and in-
crease tend to compensate each other, so that for
the cases shown in figure 2.2 the integrated cross
sections oc and of" [eq (2.-8)] agree within ex-
perimental error. Similar measurements by Dowe
{1965] on thallium K-shell electrons suggest such
compensation may extend down to 0.122 MeV.

The usual Klein-Nishina cross section, which
assumes that the target electron is free and at rest,
has been generalized by Jauch and Rohrlich [1955]
to the case where the electron is free but in motion.

Motz and Missoni used this generalized theory to
interpret their data at large angles. Their results,
obtained by averaging over the appropriate elec-
tron velocity distributions, are shown as the solid

curves in figure 2.-2.
|
| y i pe electron
iz
Aes

{ E662 kV
He Fags | |

i rau

if T
Electron (empirical) \

(0)

KN
(

ldo

Compton cross section ratio. dors (0)/
S
8

0° x 120°
Photon scattering angle

FIGURE 2-2. Ratio of observed Compton scatter-
ing from K-shell electrons (Motz and Missoni
[1961]) to Klein-Nishina theory, eq. (2-6).

Jes are extrapolations (by Motz and Missoni) to
yeary of Jauch and Robrlich [1955] which considers

180° 760°



Table 3.—25. SILICON DIOXIDE, SiO,

Scattering Pair production Total
Photon Photo-
enersy With Without electric Nuclear Electron With Without
coherent coherent field field coherent coherent
Mer entle emtla entle cmtig ont entle entle
1.00-02 || 5.6401 1.93-01 1.85+01 1.90+01 1,87+01
1.50-02 |} 3.95-01 1.89-01 | 5.33+00 5.73+00 — 5.52+00
2.00—-02 |} 3.16-01_-:1.86—-01 | 2.18+00 2.49400 — 2.36+00
3.00-02 || 2.46-01 1.80-01 | 6.13—-01 8.59-01 —-7.93-01
4.00-02 || 2.1401 1.74-01 | 2.48-01 4.63-01  4.22-01
5.00-02 |] 1.96-01 1.69-01 | 1.22-0i 3.18-01 —-2.91-01
6.00—-02 {| 1.83~01 1.64-01 | 6.91-02 2.52-01 —-2.33-01
8.00—-02 |} 1.67—-01 1.56-01 | 2.78-02 1.94-01 1.83-01
1.00-01 1.55-01 1.48-01 136-02 1.6901 _——-1.62-01
1.50-01 1.3701 1.33-01 | 3.76-03 1.40-01 1.37-01
2.00-01 1.2401 1.22-01 1.53-03 1.26-01_ 1.2401
3.00-01 1.07-01 1.06—-01 4.45—04 1.08-01 107-01
4.00-01 9.5702 9.5202 | 1.92-04. 959-02 9.5402
5.00-01 8.7302 8.7002 |__1.04-04 8.74-02  8.71-02
6.00-01 || 8.07-02 = 8.05-02 | 6.50-05 8.08-02 8.0502
8.00-01 7.0702 | 3.28-05 7.0702
1.00+00 6.36—-02 | 2.03—-05 6.3602
1,50+-00 5.16-02 | 9.49-06 | 1.47-04 5.18-02
2.00+00 4.41—02 | 6.02-06 | 5.81-04 4.47-02
3.00+00 3.47-02 | 3.33-06} 1.66-03 1.2105 3.63-02
4,00+00 2.89-02 | 2.26-06 | 2.69-03 4.97-05 3.17-02
5.00+00 2.50-02 1.63-06 | 3.60-03 —9.76—-05 2.87-02
6.00+00 2.2102} 1.38-06 | 4.42-03 — 1.50-04 2.66-02
8.00+00 1.81-02 | 9.81-07 | 5.76-03 2.57-04 2.4102
1.00+01 1.5402 | 7.68-07 | 6.86-03 3.51-04 2.26-02
1.50+01 1.1402 8.9403  5.47—-04. 2.09-02
2.00+01 9.1403 1.05-02_7.02—-04 2.0302
3.00+01 6.65-03 1.2602 = 9.35-04 2.02—-02
4.00+01 5.28-03 1.40-02 | 1.11-03 2.0402
5.00+01 4.41-03 152-02 1.2403 2.08-02
6.00+01 3.80-03 1.60-02—-1.35-03 2.12-02
8.00+01 3.00-03 1.73-02—1.51-03. 2.18-02
1.00+02 2.49-03 1.83-02 1.6403. 2.2402
1.50+02 1.77-03 1.98-02 1.8503 2.3402
2.00402 1.39-03 2.07-02 —-:1.99-03 2.41-02
3.00+02 9.85—-04 2.19-02 = 2.18-03 2.50-02
4.00+02 7.7104 2.25-02 = 2.30-03 2.5602
5.00+02 6.39-04 2.29-02 2.3803 2.60-02
6.00+02 5.47-04 2.33-02 = 2.4503 2.62-02
8.00+02 4.27-04 2.37-02 2.5403 2.6602
1.00+03 3.51-04 2.39-02 = 2.6103 2.69-02
1,50+03 2.45—-04 2.43-02 = -2.71-03 2.73-02
2.00+03 1.90-04 2.45-02 —2.78-03 2.75-02
3.00+03 1.32-04 2.48-02 = 2.8503 2.7802
4.00+03 1.02-04 2.49-02 —-2.89-03 2.79-02
5.00+03 8.33-05 2.50-02 = -2.92-03 2.80-02
6.00-+03 7.06-05 2.50-02 2.9403 2.81-02
8.00+03 5.4405 2.51-02 = -2.97-03 2.8102
1.00+04 4.4405 2.52-02 — 2.98-03 2.82-02
1.50+04 3.07-05 2.52-02 3.0103 2.83—-02
2.00+04 2.36-05 2.53-02  3.02-03 2.83-02
3.00+04 1.63-05 2.53-02 3.03-03 2.8302
4.00+04 1.25-05 53-02 3.0403 2.8402
5.00+04 1.02-05 2.53-02 3.0403 2.8402
6.00+04 8.60-06 2.538-02 — 3.05-03. 2.8402
8.00+04 6.60—-06 2.53-02 3.05-03 2.8402
1.00+05 5.3706 2.5402 —3.05-03 2.8402



Table 3.-27. AIR, NBS Handbook 85(1964) Composition

Scattering Pair production Total
Photon Photo.
eneriy With Without electric Nuclear Electron With Without
coherent coherent field field coherent coherent
MeV emilg emit cmt emilee omtla om'lg cmtlg
1.00-02 |} 3.64-01 1.93-01 | 4.63+00 4.99+00  4.82+00
1.50-02 |) 2.85-01 1.89-01 1.27+-00 1.55+00 —-1.45+00
2.00—-02 |} 2.47-01 1.86-01 5.05-01 752-01 6.91-01
3.00—02 || 2.11-01 1.80-01 1.39-01 3.49-)1 — 3.18-01
4.00-02 |} 1.93-01 1.74-01 5.5302 248-01 — 2.29-01
5.00-02 || 1.81-01 1.69-01 | 2.70-02 2.08-01 1.96-01
6.00—-02 || 1.73-01 1.64-01 1.52-02 1.88—-01 1.79-01
8.00-02 || 1.61-01 156-01 | 6.06—03 1.67-01 1.62-01
1.00-01 151-01 1.48-01 | 2.9403, 1.54-01 151-01
1.50-01 1.35-01 1.33-01 | 8.05-04 136-01 1.3401
2.00-01 1.23-01 1,22-01 | 3.2404 1.23-01_—-1.23-01
3.00-01 1.07-01 1.06-01 9.30-05 1,07-01 1.06-01
4.00-01 9.53-02  9.52-02 | 3.99-05 9.5402 9.5302
5.00-01 }} 8.70-02 8.70-02 |_ 2.15-05 8.70-02 —8.70--02
6.00-01 8.05-02 8.0402 | 1.34-05 8.0502 — 8.05-02
8.00-01 7.0702 | 6.79-06 7.0702
1.00+00 6.3602 | 4.20-06 6.3602
1.50+00 5.17-02 1.96—-06 | 9.89-05 5.1802
2.00+00 4.41—02 | 1.25-06 | 3.9404 4.45—-02
3.00+00 3.47-02 | 6.97-07 | 1.13-03 — 1.21-05 3.58-02
4.00+00 2.89-02 | 4.73-07 | 1.83-03 4.9705 3.0802
5.00+-00 2.50-02 | 3.61-07 | 2.46-03  9.76-05 2.75-02
6.00+00 2.21—-02 | 2.88-07 |} 3.01-03 1.5004. 2.52-02
8.00+00 1.81-02 | 2.06-07 | 3.94-03 2.5704 2.23-02
1.00+01 1.5402 1.61-07 | 4.70-03 3.5104. 2.0402
1.50+01 1.1402 6.14-03  5.47-04 1.81—-02
2.00+01 9.1403 7.18-03 — 7.02—04 1.70-02
3.00+01 6.65—-03 8.65-03 9.3504 1.62-02
4.00+01 5.28-03 9.67-03 1.1103 161-02
5.00+01 4.41—03, 1.04-02 1.2403 1.61—-02
6.00+01 3.80-03 111-02 — 1.36-03 1.62—02
8.00+01 3.00-03 1.20-02, 1.5303. 1.6502
1.00+02 2.55-03 1.26-02 —-1.65~03 1.68-02
1.50+02 1.77-03 1.38-02 1.8703. 1.7402
2.00+02 1.39-03 1.45-02—2.02~-03. 1.7902
3.00+02 9.85-04 1.53-02—2.22-03. 1.85-02
4.00+02 7.7104 1.58-02 2.3403 1.89-02
5.00+02 6.38-04 1.6102 2.43-03 1,92-02
6.00+02 5.47-04 1.63-02 — 2.50-03 1.9402
8.00+02 4.27-04 167-02 —_2.60-03 1.97-02
1.00+03 3.51-04 1.69-02 — 2.67-03 199-02
1.50+03 2.45-04 1.72-02 —.2.79-03. 2.02—02
2.00+03 1.90-04 1.73-02—.2.86-03 2.0402
3.00+03 132-04 1.75-02—.2.95~-03 2.06—02
4.00+03 1.02-04 1.76-02 —.2.99-03 2.07-02
5.00+03 8.33-05 1.77-02 —-3.02—03 2.0802
6.00+03 7.07-05 1.77-02— 3.05-03. 2.08-02
8.00+03 5.44-05 1.78-02— 3.08-03 2.0902
1.00+04 4.4405 1.78-02 —-3.10-03 2.09—-02
1.50+04 3.07-05 1.78-02—-3.12-03 2.10-02
2.00+04 2.36-05 1.79-02 3.1403 2.10-02
3.00+04 163-05 1.79-02 3.1503 2.11-02
4.00+04 1.25-05 1.7902 3.16—-03 2.11-02
5.00+04 1.02-05 1.79-02 -3.17-03 2.11-02
6.00+04 8.60-06 1.79-02 -3.17-03 2.1102
8.00+04 6.60-06 1.79-02 3.1803 2.11-02
1.00405 5.37-06 1.79-02 3.1803. 2.11-02



Table 3.—28. CONCRETE, Grodstein—McGinnies Composition

Scattering Pair production Total
Photon Photo
enerny With Without electric Nuclear Electron With Without
coherent | coherent field field coherent | coherent
Mev onelg cme cle emg onl ome emg
1.00-02 |} 6.00-01_—:1.93-01 | 2.63+01 2.69+01 = 2.65+01
1.50-02 || 4.21-01_—-1.89-01 | 7.82+00 8.24400 8.01400
2.00-02 || 3.34-01 —-1.86-01 |_ 3.26+00 3.59400 — 3.45+00
3.00—-02 |} 2.56-01 —-:1.80-01 | 9.38-01 1.19400 1.12400
4.00-02 |} 2.20-01 = 1.74-01 | 3.8401 6.0501 5.59-01
5.00—-02 || 2.00-01 = 1.69-01 | 1.92-01 3.92-01_ 361-01
6.00—-02 || 1.86-01 -1.64-01 | 1.09-01 2.95-01 — 2.73-01
8.00-02 |} 1.69-01—1.56-01 | 4.45-02 2.13-01 —_2.00-01
1.00-01 157-01 —-1.48-01 | 2.19-02 1.79-01 —1.70-01
1.50-01 |} 1.37-01 —1.34-01 | _ 6.20-03 1.44-01 1.40-01
2.00-01 || 1.25-01_—-1.22-01 | __2.56-03 1.27-01_—:1.25-01
3.00-01 |} 1.07-01_—-1.07-01 |_7.52-04 1.08-01_——-:1.07-01
4.00-01 || 9.60-02 9.5402 | 3.27-04 9.63-02 9.58-02
95.00—-01 |] 8.75-02 8.72-02 |_1.77-04 8.77-02 8.7302
6.00-01 |} 8.09-02  8.06-02 |_1.11-04 8.10-02 8.0702
8.00-01 || 7.09-02 7.08-02 | 5.6405 7.09-02 —7.09-02
1.00+00 6.37-02 | 3.50-05 6.37-02
1.50+00 5.18-02 | 1.63-05 | 1.58-04 5.19-02
2.00+00 4.42-02 | 1.03-05 | 6.22-04 448-02
3.00+00 3.47-02 | 5.67-06 | 1.77-03_—1.21-05 3.6502
4.00+00 2.90-02 | 3.84-06 | 2.87-03  4.98-05 3.19-02
5.00+00 2.50-02 | 2.86-06 | 3.8403 9.78-05 2.90-02
6.00+00 2.21-02 | 2.32-06 | 4.70-03 1.5004. 2.70-02
8.00+00 1.81-02 | 1.65-06 | 6.13-03 _2.57-04 2.45—-02
1.00+01 154-02 | 1.29-06 | 7.31-03 3.52-04 2.31-02
1.50+01 114-02 | 9.21-08 | 9.52-03 5.4804. 2.15-02
2.00+01 9.1503 | 658-08 | 1.11-02 7.0304 2.10-02
3.00+01 6.67—-03 134-02 9.37-04 2.10-02
4.00+01 5.30-03 1.49-02_—1.11-03 2.13-02
5.00+01 4.42-03 1.61-02 1.2403 2.18-02
6.00+01 3.81-03 1.70-02——-1.35-03. 2.22-02
8.00+01 3.00-03 184-02 1.51-03 2.29-02
1.00+02 2.49-03 1.9402 1.6403 2.3502
1.50+02 1.78-03 2.11-02 — 1.85-03 2.47-02
2.00402 1.39-03 2.20-02 =: 1.99-03 2.5402
3.00+02 9.87-04 2.32-02—-2.18-03 2.64-02
4.00+02 7.7304 2.39-02 =. 2.30-03 2.69-02
5.00+02 | 6.40—-04 2.43-02 — 2.38-03 2.73-02
6.00402 5.48-04. 2.47-02 2.4403 2.76—-02
8.00+02 4.28-04 2.5102 2.5403 2.8102
1.00+03 | 3.52-04 2.54-02 = 2.60-03 2.83-02
1.50+03 2.46-04 2.58-02 = 2.71-03 2.87-02
2.00+03 1.90-04 2.60-02—_.2.77-03 2.90-02
3.00+03 132-04 2.63-02 = 2.85-03 2.92-02
4.00+03 1.02-04 2.6402 —-2.89-03 2.9402
5.00+03 8.35-05 2.65-02 —_2.92-03 2.95-02
6.00+03 7.08-05 2.65-02 = -2.93-03 2.95-02
8.00+03 |) 5.45-05 2.66-02 = 2.96-03 2.96-02
1.00+04 4.45-05 2.67-02 = 2.97-03 2.97-02
1.50404 3.08-05 2.67-02 = 3.00-03 2.9802
2.00+04 2.37-05 2.68-02 —3.01-03 2.98-02
3.00+04 1.63-05 2.68-02 —3.02-03 2.98-02
4.00+04 1.25-05 2.68-02 —3.03-03 2.99-02
5.00+04 1.02-05 2.68-02 — 3.03-03 2.99-02
6.00+04 8.62-06 2.68-02 3.0403 2.99-02
8.00+04 6.61-06 2.68-02 3.0403 2.99-02
1.00+05, 5.38-06 2.69-02 3.0403 2.99-02

68



TABLE 2.-5. Scaled values of the total photoelectric cross section Tye

Photon
energy ie oC Al woCa woke awCu
[MeV]
Toe {b/atom] - (E[MeV})* - Z~** « 10®
0.01 913 | 124 il 8.87 6.17
0.02 671} 101 10.6 9.25 727
0.03, 5.59 8.50 | 10.1 9.13 7.83
0.05 4.45 7.60 9.29 8.79 8.1
0.10 3.32 6.80 8.21 8.23 8.09
0.20 2.62 5.77 7.40 791 7.98
0.30 244 5.49 724 7.92 8.15
05 2.56 5.88 780 8.70 9.22
Tye{b/atom] - E[MeV] - Z-*8 - 10°
T
05 10.2 23.5 31.2 34.8 36.3 36.9
1.0 3.98 910 | 123 13.8 146 14.8
2 2.36 5.42 T: all 8.42 8.56
3 1.99 4.55, 03 6.67 6.89 7.00
5 15 3.97 5.22 5.70 5.86 5.91
10 1.58 3.53 4.64 5.02 bl 5.12
100 1.43 3.19 4.01 4.41 4.45 4.46
oe 141 3.15 ¥ 4.33 4.37 439
~ T
Photon Absorp-
energy | 42Mo soSn »W Pb a tion
[MeV] edges
Toe [bfatom] - (E[MeV))s 2-45 - 10°
0.01] 0.663 | 0.108 | 0.108] 0.0995
0.02|__0730| o7i4] 0.615 | 0.500] 0.314"
0.03 6.00 4.88 0.693 0.640 |" 0.612 — 7!
0.05| 6.74 5.70 0.779 | 0.744 0.740
0.10! 7.29 6.57 793 429 |_0.919_ |.
0.20| 7.66 7.28 6.06 5.70 | 5.21
0.30| 8.06 7.83 691 6.79 | 6.25
05 9.50 9.91 8.77 892 | 8.44
Tye (b/atomn] - E[MeV] - 2-45 + 10°
05 | 38.0 39.6 35.1 35.7 | 33.8
Lo | 15.5 15.6 15.0 15.6 | 15.1
2 8.77 8.73 8.25 8.64 | 8.26
3 7.10 7 6.49 6.70 | 651
5 5.92 5.86 5.19 530 | 5.11
10 5.04 4.93 4.28 435 | 4.19
100 4.30 4.16 3.56 344 | 3.49
os 4.22 411 | 350 330 | 344

*,H has only one K-shell electron, hence values in this column contain an
additional factor of two to allow smooth interpolation to adjacent elements.

26


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1.2.2. Notation and Units

Symbol Name or definition Units Where used
“ “narrow beam” linear em Table 1.-5;
attenuation coefficient Eqs (1.-1) to (-4)
p absorber density gem-3 Tables 1-, 2
ulp mass attenuation coefficient om? gt Tables 1.~4; 3.~1 to 36;
= om [b/atom] + (Na/M) » 10-* Eqs (1.5) to (-7)
[(em*g~)/(b/atom)]
mfp mean free path cm Eq (14a)
gem? Fig 1.-2
tus Half-value laye: .69315/ pu, em Eq (1.-4b)
.69315/ (n/p) gem-* Fig 1.-2
tyro 1/10—value layer=2.3026/p1, cm Eq (1.4)
3026] (n/p) gem? Fig 1-2
av “volume of interest” in a medium, cm? Eq (1-9)
for photon energy transfer estimates
Penlp mass energy-absorption coefficient, allowing for cm? g-! Fig 1.-3; Tables 1.-7, 8, 9;
escape from the volume of interest of all secondary Eq (1-10)
photons, including bremsstrahlung, as given in
definition (17) in NBS Handbook 85 (ICRU Rep. 10b)
[1964]
Bxlp mass energy-transfer coefficient allowing only cm? g-! Tables 1.-7, 8
for the escape of Compton-scattered, fluorescence
and annihilation photons, as given in definition
(16) in NBS Handbook 85 (ICRU Rep. 10b) [1964]
bal mass absorption coefficient allowing for escape of em? g? Tables 1-7, 8, 9
Compton scattered photons only, as defined in
eq (8f-48) of Evans [1963]
ti average fraction of photon energy transferred dimensionless Eq (1.-10)
to the medium as a result of photoelectric
absorption
fi average fraction of photon energy transferred dimensionless Eqs (1-10), (2-13)
to the medium as a result of a Compton collision Table 2-8
Se average fraction of photon energy transferred dimensionless Eq (1.-10)
to the medium as a result of a pair production event
Re electron range (here used in the gem? Table 1.6
“continuous-slowing-down-approximation”)
ow total photon interaction cross section per atom b/atom Eqs (1-5), (2.-24);
(defined in this paper to include only photoelectric Fig 2-1
absorption, Compton collision, and pair production)
The total photoelectric absorption cross section per b/atom Sec. 2.3.; Tables 2.~4, 5,
atom= tht T+* + 3.-1 to 3
Fig 2-1
Help Tye [b/atom] - (N4/M) + 10-* [(em*g-!)/(b/atom ] cm? go? Eq (1-10)
Thy Thos photoelectric absorption cross section per atom b/atom Table 2-6;
for K-shell electrons, L-shell electrons, etc. Eq (2.-1)
Tel TK ratio of total photoelectric to K-shell dimensionless Table 2.-6
Eq (2.-2)

photoelectric cross section (above the K-edge)
_tkttmtmt: +: 8

TK Vv
where 6 is the K-edge “jump ratio”
tettt tts .
pa 8s defined by Kirchner [1930]


In addition, we tabulate various related coeffi-
cients that can be used to compute the transfer
of energy to the medium, namely: (a) the mass
energy-absorption coefficient, (b) the mass energy-
transfer coefficient, and (c) the mass absorption
coefficient. These coefficients were obtained by
updating and extending the work of R. Berger
[1961] and Allison [1961].

In the present work we have taken 10 keV as a
lower limit on the energy range considered. Tabu-
lations which extend to lower energies include
those by Brown [1966] (Z=1 to 100; 1 keV-10
MeV), McMaster et al. [1967] (87 elements Z=1 to
94; 1 keV—1 MeV), and by Storm and Israel [1967]
(Z=1 te 100; 1 keV-100 MeV). For light elements
at lower energies, Henke et al. [1967] have used
their own experimental data and those of others to
provide a compilation of attenuation coefficients
versus energy for the 17 elements He through Ar
over the energy range 0.030 to 6.0 keV. Additional
low-energy attenuation coefficient tabulations for
use by electron microprobe analysts (the coefficients
are given at characteristic x-ray emission wave-
lengths) include, among others, those by Birks
[1963], Heinrich [1966], Frazer [1967], and
Theisen and Vollath [1967].

1,2. Physical Constants; Units; Notation

1.2.1, Physical Constants and Conversion Factors

Zz atomic number,

M atomic weight in g/g-atom,

m electron rest-mass= 9.1091-10~28 g,

me? electron rest-mass energy=5.11006-105 eV,
c velocity of light =2.997925-10" cm s“',

For definitions of these coefficients see Secs. 1.2. and 1.5. A great variety of names
and symbols have been used for these coefficients, and readers interested in the
nomenclature used by various authors should consult R. Berger [1961].

"Note: Numerical values given here are those recommended ji by the Com
mittee on Fundamental Constants of the National Academy of Sciences — National
Research Council [1964] are based on the atomie weight scale in which
M= 12.0000 for C¥

e elementary charge= 1.60210-10-" Coulomb
= 4,80298-10-" emil2gt?2s—1

Te classical electron radius
81777-10- cm,
re cm’,
or cross section for classical Thomson scat-

from an electron=87r,2/3= 6.6516

teri
10-5 cm?,

Na Avogadro constant= 6.02252-10°3= atoms/
mole,

@ fine structure constant
= 7.29720-10°3= 1/137.0388 ~ 1/137,

E photon energy in eV units (e.g: keV,

MeV or GeV),
photon energy in units of the electron rest-
mass energy (i.e., mc? units)=E[MeV]/
0.511006,
q momentum transfer to an atom or electron
in units of me,
oN photon wavelength in Compton units
= 1/k=0.511006/E [MeV],
(A) photon wavelength in angstroms
(1 angstrom= 10°* em}=1.23981-10-2/
E[MeV]?

b barn= 10-4 cm?.

"In additioy to the angstrom, which is based on the centimeter, two photon wave
length Units, A"and aay are in use which are based on chamuctesate Rigs emseanen
wavelengths. The recently-inteoduced A*unit (Bearden (1967) is presently identical
with the angstrom within an uncertainty of 5 ppm. ie

At = 14-5 ppm,

The tungsten Ka; emission line has been recommended by Bearden as the “ray
wavelength primary standard with the value

ACWKay) = 0.209010 A*

and hence
AUPKay) =0.2090100A +5 ppm.

The xunit (), used in much of the older literature and occasionally in the present

literature, was intended to be 10-A hot has taken on a variety of values because of

errors and inconsistencies in the various wave
num Key, emission line is taken as a referent

th standards used. If the molybde-
ith the value (Bearden (1967):

(Mo Kay) = 707.831 xu

then

1 x= 1,002056-10-9 A*

A(aw) = 12.37/E(MeV).


Fhofon

Annihilation in Right, Bremsstrahlung

fest mass of pairs

Kinetic energy of electrons

| t Tonization and excitation J

Photvelecions, Auger electrons

Ficure 1-4.

Flow diagram of conversion of energy from one form to another in

the course of photon energy absorption in a medium.

the diagram should also contain a box labelled “excitation energy of nuclei,” as well as
ting the emission of secondary neutrons, charged particl

der to prevent the diagram from becoming unduly com
jents presented here do not take into account photonuc

and gamma rays. This box has been

TABLE 1-6. Ratios of the electron range," Ry, to the photon mean-free-path, (1/4), based on electron data of Berger and
Seltzer (1964 and photon data from tables 1.-4 and 3.~24, -26, -27, and -28.
Photon c
energy | ,H 6c Al asFe | g9Sn  g2Pb Air H,O ote Nal
[Mev crete
Rew
0.01 |0.000041{ 0.00058] 0.0091 | 0.076 [2.987 fot L-cdges | 9014 | 9.0012 | 0.0074 || 0.085 | Iodine
a ie K-ed,
0.1 }0.0020  } 0.0024 | 0.0030 | 0.0073 | 0.043 0.17 | *-®48*} 9.0025 | 0.0023 | 0.0029 | 0.041 eee
1.0 |0.027 0.031 0.034 0.036 0.040 0.053 0.031 0.030 0.033 0.039
10.0 {0.077 O11 0.13 0.18 0.23 0.29 O11 O11 0.12 0.22
100.0 ]0.22_ } 0.55 081 f 14 1518 0.53 | 0.56 | 0.69 1.4

4) Here we use the mean range as calculated in the continuous-slowing-down approximation,

Under conditions of electronic equilibrium,”
€in=€ouw, and the second term vanishes. When the
size of the volume of interest, AV, is large compared
with the ranges of the secondary electrons involved,
the term [€in—€ow] is small compared with the
integral term and may be disregarded.

1 Electronic equilibrium prevails if the gamma-ray flux distribution is effectively
constant over a region having dimensions of the order of the range of the secondary
electrons. Discussions of this concept and its application are given in NBS Handbook
85 [1964] and in a number of dosimetry texts (see, for example, Whyte [1959] and
Johns [1961)).

1.5.3. Evaluation of the Coefficients From
the Cross Sections

The ‘mass energy-absorption coefficient,” en/p,
as specified in definition (17) in Appendix I of NBS
Handbook 85 [1964], takes into account all the
modes of energy transfer to electrons shown in
figure 1-4. The other coefficients treated here,
namely the ‘‘mass energy-transfer coefficient”
bx/p as specified in definition (16) in Appendix I of


1.3. Definition and Significance of Narrow-
Beam Attenuation Coefficient

The most important quantity characterizing the
penetration and diffusion of gamma radiation in
extended media is the attenuation coefficient, 1.
This quantity depends on the photon energy E and
on the atomic number Z of the medium, and may
be defined as the probability per unit pathlength
that a photon will interact with the medium.

Consider, as a typical situation, a slab of material
of thickness t located between a narrowly col-
limated source of monoenergetic gamma ray photons
and a narrowly collimated detector, as indicated in
figure 1-1. In a layer dx within the slab there will
occur a reduction of the intensity, J, of the gamma
ray beam, due to:

(1) outright absorption, or

(2) scattering out of the beam.

The resulting fractional reduction of the beam
intensity, —d//J, is proportional to the “narrow
beam” attenuation coefficient, 4, and to the layer
thickness, dx, ice.,

—dl|I= ps dx. (1-1)

Integrating this equation and assuming that the
beam intensity incident on the slab has the value
Io, one obtains for the intensity transmitted through
the slab the value

/
1(0)= 10 exe {[- f w(x)dr} 2)
F
For a homogeneous medium this reduces to
I(t)=Io e#*. (1-3)

For situations more complicated than the narrow-
beam experiment, the attenuation is still basically
exponential but is modified by two additional fac-
tors. The first of these, sometimes called a “‘geom-
etry factor,” depends essentially on the source
geometry and involves, for example, the insertion
of the inverse square law in eq (1.-3) for a point
isotropic source. The other factor, often called the
“buildup factor,” takes into account secondary
photons produced in the absorber (mainly as the
result of one or more Compton scatters) which

reach the detector. The determination of such
a
yo Y)
id 4 Detector
A ae
Collimator Absorber Collimator
Ficure 1-1. Arrangement for experimental determination of

narrow-beam attenuation coefficients.

buildup factors constitutes a large part of gamma
ray transport theory.

In the narrow-beam equation (1.—3), the absorber
thickness ¢ in which the beam intensity is reduced
by a factor e (i.e., [/[o=1/e= 0.36788), is called
the mean-free-path. One mean-free-path (mfp) also
represents the average distance traveled by a photon
between successive interactions. Analogous quan-
tities are the half-value layer and one-tenth-value
layer, ¢:2 and tio, in which the intensity is re-
duced by } and ,,, respectively." These quantities
can be evaluated graphically from an experimental
narrow beam attenuation curve, as indicated in
figure 1-2 for 7Cs (E=0.662 MeV) gamma rays
in concrete and lead. They are related to the at-
tenuation coefficient according to

1 mfp=1/p, (14a)
tin = (—In d)/m=0.69315/n, (1-4b)
and

tino = (—In 4s)/m= 2.3026]. (1.-4c)

From the above discussion it is apparent that
the attenuation coefficient 2 has dimensions of an
inverse length. Hence, if t is in cm, in, ft, etc., the
corresponding values of 4 must be in units or
em", in~!, ft“, etc., and as such are called “linear
attenuation coefficients”. However, although
linear attenuation coefficients are convenient for
engineering application, they are proportional to
the absorber density, p, which usually does not
have a unique value but depends to some extent
on the physical state of the material. Therefore, it
is common practice, for purposes of tabulation, to
remove this density dependence and to use the
“mass attenuation coefficient” u/p which, if wu is
in cm and p is in g/cm, will be in the customary
units of cm~?/g.

1 wr Tr T
08 {Cs y-ray, 0662 MeV
2 a6
§ T
ala _
2 Par
q a
3S ai |_|
i
Ss Pb:
8 oy 4 =——

Baad mfp—4 |
206| {{ ‘oye lye — 1
0 0 6 wo & wD
Thickness [g/om?]

FIGURE 1-2. Semilog plot of narrow-beam attenuation of

'3"Cs (0.662 MeV) gamma rays in lead and concrete.

Graphical determinations of the mean-free-path and of the 1/2- and 1/10-value layers

should be noted that the ICRU (see, for example,
@ half-value layer (HVL) in terms of exposure 1
ability of the radiation to produce ion pairs in air) rather than intensity. The difference
between these definitions can lead to different half-value layer thicknesses if the source
is not monoenergetic,

NBS Handbook 85 [1964]
intensity weighted by the

defin


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TABLE 1.-9. Values of the mass absorption coefficient jtalp and mass energy-absorption coefficient * penlp for photon energies

10 to 100 MeV.

Units are em'/e,

Photon iH N 0 ysAl yAr
energy
(MeV] Hale | Henle | Hale | Henle | Hale | Henle | Hal@ | Henle | Hale | Henle
10 0.0229 | 0.0222 | 0.0154 }| 0.0143 | 0.0160 | 0.0148 | 0.0185 | 0.0164 | 0.0201 | 0.0176
15 0.0188 | 0.0179 | 0,0145 | 0.0131 | 0.0153 | 0.0136 | 0.0187 | 0.0163 | 0.0211 | 0.0183
20 0.0166 | 0.0156 | 0.0142 | 0.0128 | 0.0152 | 0.0135 | 0.0192} 0.0162 | 0.0222 | 0.0187
30 0.0141 | 6.0130 | 0.0142 | 0.0123 | 0.0153 | 0.0131 | 0.0203 | 0.0164 | 0.0240 | 0.0192
40 0.0129 | 0.0116 | 0.0144 | 0.0121 | 0.0156 | 0.0130 | 0.0212 | 0.0166 | 0.0254 | 0.0192
50 0.0121 | 0.0107 | 0,0146 | 0.0119 | 0.0160 | 0.0129 | 0.0220 | 0.0164 | 0.0266 | 0.0192
60 0.0117 | 0.0102 | 0.0149 | 0.0118 | 0.0163 | 0.0129 | 0.0227 | 0.0161 | 0.0276 | 0.0190
80 0.0111 | 0.0095 | 0.0153 | 0.0118 | 0.0169 | 0.0127 | 0.0238 | 0.0159 | 0.0290 | 0.0188
100 0.0109 | 0.0092 | 0.0158 | 0.0119 | 0.0174 | 0.0127 | 0.0246 | 0.0156 | 0.0301 | 0.0184
Photon asFe mPb Air Water
energy
[MeV] Hal@ | Henle | Hole | Henle | Hale | Henle | Hale | Henle
10 0.0252 | 0.0212 | 0.0446 | 0.0324 | 0.0156 | 0.0145 | 0.0168 } 0.0155
15 0.0277 | 0.0223 | 0.0522 | 0.0352 | 0.0148 | 0.0132 |] 0.0157} 0.0141
20 0.0298 | 0.0230 | 0.0587 | 0.0367 | 0.0145 | 0.0131 | 0.0153 | 0.0136
30 0.0330 | 0.0236 | 0.0682 | 0.0375 | 0.0146 | 0.0126 | 0.0152 | 0.0131
40 0.0354 | 0.0235 | 0.0747 | 0.0372 | 0.0148 | 0.0124 | 0.0153 | 0.0128
50 0.0372 | 0.0234 | 0.0796 | 0.0366 | 0.0151 | 0,0122 | 0.0156 | 0.0126
60 0.0387 | 0.0230 | 0.0834 | 0.0357 } 0.0154 | 0.0122 | 0.0158 } 0.0125
80 0.0410 | 0.0233 | 0.0890 | 0.0334 | 0.0159 ] 0.0121 | 0.0163 } 0.0125
100 0.0427 | 0.0217 | 0.0930 | 0.0301 | 0.0163 | 0.0121 | 0.0167 | 0.0124

*Values of en/p in this table are taken directly from Allison [1961]. Hence the input cross-section data are those of
White-Grodstein [1957], and positron annihilation in flight is not taken into account.

2. Photon Cross Sections

2.1. Scope

This section contains descriptions and tabulations
of the individual atomic cross sections for scattering,
absorption, and pair production that enter into the
computation of the attenuation, energy absorption,
and other related coefficients. The information
in this report is confined primarily to total cross
sections, although some angular distribution
information for Compton and Rayleigh scattering
is included."4

2.2. Classification of Interactions

Interactions of photons with matter, by which
individual photons are removed or deflected from
a primary beam of x- or y-radiation, may be classi-
fied according to:

(1) The kind of target, e.g., electrons, atoms, or
nuclei, with which the photon interacts, and

(2) The type of event, e.g., scattering, absorption,
pair production, etc., which takes place.

'* For further angular distribution data and formulas, reference for Compton scatter-
ing can be made to Compton and Allison (1935), Davisson and Evans [1952], Ne
{1953}, Burton [1953], Evans [1958], Curien [1962], Stinner et al. (1965), and Veigele
{1965}; for the atomic photoeffect to Hultberg et al. (1968] and Pratt et al (1964); and
for electron- positron pair production to Heitler (1954).

Possible interactions are summarized in table
2-1 (adapted from Fano, Spencer, and Berger
[1959)). The relative magnitudes of cross sections for
these interactions as functions of energy are shown
in figure 2.—1, in which the vertical distance between
curves represents the percent contribution of an
indicated cross section to the total “electronic”
cross section (i.e., excluding photo-nuclear effects).

It is apparent from figure 2-1 that for attenua-
tions of photons in this energy range the most
important interactions are:

(1) The photoelectric effect, Tpe,
(2) Compton scattering, ac, and
(3) Electron-positron pair production, (kn+ Ke).

Rayleigh scattering, op, is usually of minor im-
portance for the broad beam conditions typically
found in shielding but must be known for inter-
pretation of experimental attenuation coefficient
data. Two-photon Compton scattering, together with
the radiative correction, amounts to less than
1 percent of oc below 100 MeV and is included in
the total Compton cross section oc in figure 2.1.
The photonuclear effect, Gpn.n., is mostly restricted
to the region of the giant resonance around 10 to
30 MeV where, at the resonance peak, it may
amount to as much as 10 percent of the total
“electronic” cross section.

21


UNITED STATES DEPARTMENT OF COMMERCE
Maurice H. Srans, Secretary,
NATIONAL BUREAU OF STANDARDS» A. V. Astin, Director

Photon Cross Sections, Attenuation Coefficients,
and Energy Absorption Coefficients
From 10 keV to 100 GeV

J. H. Hubbell

Center for Radiation Research
National Bureau of Standards
Washington, D.C, 20234

NSRDS-NBS 29

Nat. Stand. Ref: Data. Ser., Nat. Bur. Stand. (U.S.), 29, 85 pages (August 1969)
CODEN: NSRDA

Issued August 1969

For sale by the Superintendent of Documents, U.S. Government Printing Office
‘Washington,D.C., 20402 — Price 75 cents




Photon
energy

Total

j

Table 3.—4. CARBON, Z=6
Scattering Pair production
| Photo- —
electric
With | Without Nuclear | Electron || With
rent | coherent field field |} coherent
blatom —blatom bJatom blatom bjatom |} blatom
6.11400 3.84400} 3.93+01 4.54401

3.77400] 1.06+01
3.71400] 4.01400
3.58+00} 9.99-01
2.12400
1.90+-00
1.74400
1.61+00
1.41400
1.27400
1.03+00 1.60-03
8.79-01 6.40-03
6.92-01 1.8402 _2.41-04
5.7701 2.98-02  9.91-04
4.98-01 4.00-02 —1.95-03
4.40-01 4.90-02 — 3.00-03
3.60-01 6.4202 5.12-03
3.07-01 766-02 7.01-03
227-01 1.00-01 1.0902
1.82-01 117-01 1.40-02
1.33-01 141-01 1.87-02
1.05-01 158-01 — 2.21-02
8.80-02 L.71-0l — 2.48-02
750-02 181-01 2.71-02
5.98-02 1.9601 3.06-02
4.97-02 2.07-01 331-02
3.5402 2.26-01 3.7602
2.77-02 237-01 4.06-02
1.9602 251-01 4.46-02
1.54-02 260-01 4.72-02
1.27-02 2.6501 4.9102
1.09-02 269-01 — 5.05-02
8.5203 2.7501 5.26-02
7.01-03 2.78-01  5.40-02
4.89-03 2.84-01 5.6402
3.79-03 2.87-01 5.7902
2.6403 2.90-01 5.9802
2.0303 2.92-01 6.0802
1.6603 2.93-01 6.1502
1.41-03 2.93-01  6.20-02
109-03 2.94-01  6.26-02
8.87-04| 2.95-01 — 6.30-02
6.13-04 2.96-01  6.36-02
4.7104,
3.25-04
2.49-04 297-01 645-02
2.0304 297-01 6.4602
1.72-04 2.97-01 6.4702
1.32-04 2.9801 6.48-02
107-04 2.98-01  6.49-02

=>
Total
Without {} With — | Without
coherent || coherent | coherent
bfatom cm’ om?lg
4.31401 |] 2.28+00 — 2.17+00
1.44401 || 787-01 7.22-01
7.72400 || 4.29-01 — 3.88-01
4.58+00 |} 2.51-01 — 2.30-01
3.85+00 || 2.06-01 — 1.93-01
3.56+00 |} 187-01 1.79-01
3.39+00 |/ 1.7601 1.70-01
161-01 1.58-01
1.5201 1.50-01
135-01 1.3401
1.2301 1.23-01
1.0701 —1.07-01
9.5702 9,55-02
8.7202
8.0702
709-02
6.3702
5.19-02
4.4502
3.5702

3.61-01
3.6201

3.62-01
3.62-01
3.62—01
3.6301

3.63-01

05-02
2.71-02
2.47-02
2.16-02

1.9602
1.70-02
1.58-02
1.4702

1.44-02
1.42-02
1.4302
1.44-02

1.4602
50-02
53-02
59-02
62-02
64-02
66-02
69-02

71-02
73-02
-75-02
1.7702

1.78-02
1.79-02
1.79-02
1.80-02

1.80-02
1.81-02
1.81-02
1.82-02

1.82-02
1.8202
1.82-02
1,82-02

1,82-02

{atom x 050240 ene

44


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TABLE 1-1. Values of the atomic weight M, the factor (Na/M)
10° for converting attenuation data from blaiom to cm’g-,
and typical densities p for converting from cm2g-' to cm-.—
Continued

Me
My 2a
Element | atomic wt. x 104 pt
Z | Sym- emt /: U
bol | g/g—atom & / atom elem

76| Os | 190.2 003166

77| Ir 192.2 003133

78| Pt 195.09 :003087

79| Au | 196.967 003058

80| He | 200.59 2003002

81| TI 204.37 002947

82/ Pb | 207.19 2002907

83 | Bi 208.980 002882

84| Po | (210) (002868),

85| At | (210) (.002868)}.....

86} Rn | (222) (.002713)} 00996 g
87| Fr | (223) (002701) fee
a8| Ra | (226) (-002665)| 5(?)

89) Ac (227) (.002653)} [10.07]
90 | Th 232.038 -002595 | 11.00
91! Pa (231) (.002607)] [15.37]
92; U 238.03 002530

18.7
(-002541)] [19.36]
(002489)| [19.84]

93| Np | (237)
94] Pu | (242)

95| Am | (243) (002478)| [11.7]
96 | Cm | (247) (.002438){[~ 7]
97] Bk | (249) (-002419)}.
9g]}cr | (251) (.002399)|.
99| Es | (254) (002371)
100 | Fm | (258) (002380)|.

ights are those recommended in 1961 by the International Union of Pure
and Applied Chemistry, based on M= 12.0000 for C## (Weast and Selby (1966-1967).
These values are based on average isotopic abundances and ignore natural and arti
ficial variations. In practice, for example, M can vary from 6.01513 for pure ali® to
7.01601 for pure aLi?, with corresponding variation in the conversion factor from
0.1001 to 0.08584,

*W,= Avogad
‘Academy of
Constants (1964).

Densities are for common solids, except as denoted liquid () or gas (e), at 20 C,
from the compilation by Trent, Stone, and Lindsay [1963] and in square brackets (}
from the Handbook of Chemistry and Physics (Hammond (1966-1987). Gas devsiis
are at S.T.P.:0°C, 16

“**Graphite theoretical density, based on x-ray diffraction n data, Commercial wade
pile graphite, according to Loch [1960], has a density rang m
SE penciy values for erbium wary inthe Ricrature fom 477 8 sted by Trent,

number =6.02252 x 10% atoms/gatom, € scale (National
National Research Council Committee on Fundamental

Stone, and Lindsay [1963] to the values 9.05 and 9.16 given in the Handbook of Chem:
istry and Physics (Hammond (1966-1967).
****The density of Pm'® as measured by Wheelwright (1969} is 7.22 g/em~*,

Rau and Fano [1968] have examined the pos-
sible effect of irregularities in atomic shell struc-
ture on interpolation of atomic cross sections with
respect to Z. Their results suggest that irregulari-
ties in the cross sections are most likely at the noble
gases: He, Ne, Ar, Kr, Xe, and Rn, and at the noble
metals (filling of the d-subshells): Cu, Pd and Au.
At low energies (E < 10 keV) where the outer atomic
electrons can play a significant role Manson and
Cooper [1968] predict such irregularities in the
photoeffect (see sec. 2.3) and Storm and Israel
[1967] predict similar effects for Compton scatter-
ing (see fig. 2-3, sec. 2.4.2.). Also Sérenssen
[1965, 1966] predicts irregularities in the nuclear-
field pair production cross section (see sec. 2.5.2)

TABLE 1.-2. Conversion factors and densities, similar to those
in table 1.-1, for a few compounds and mixtures.

Substance Conversion p
factor
gm /: b
« / molecule glem®
H.0 0.03344 | 1.001, 0.917 (ice)
SiO, 01002 | 2.32
Nal 004019] 3.667
Air (20 °C, 76 em Hg) : 0.001205
Concrete 22-24
0.8 N H,SOx soln 1,049 1
Bone 1.7-2.0
Muscle ~1
Polystyrene, (CaHs)n 1.05-1.07
Polyethylene, (CHe)n 0.92
Polymethyl methacrylate
(Lucite), (CsHsO2), 1.19
Bakelite (typical),
CagHseOr 1.20-1.70
Pyrex glass (Corning
No. 7740) | eceseseesssteeeeeseese 2.23

for energies above 100 MeV where screening of
the nuclear charge by the atomic electrons becomes
important. Experimental evidence for such irregu-
Jarities is still inconclusive for photon energies
between 10 keV and 100 MeV.

If the absorber is a chemical compound or a mix-
ture, its mass attenuation coefficient /p can be
approximately evaluated from the coefficients ui/pi
for the constituent elements according to the
weighted average

uip=>, wigilpi, (1-6)

where w; is the proportion by weight of the ith

constituent. For example, for water (H2O:

My= 1.00797; My= 15.9994),

Hay 2° 1.00797 pe 15.9994.

7 thO)= 5.0153 p + Te.0153 p >
=0.1119& (H)+0.888 4 (0). 7)

Values of w; for some additional compounds and
mixtures are given in table 1.-3.

The limitations of the “mixture rule” in eq (1-6)
are that it ignores changes in the atomic wave-func-
tion resulting from changes in the molecular, chem-
ical or crystalline environment of an atom. Above
10 keV errors from this approximation are expected
to be less than a few percent (except in the fine-
structure regions just above absorption edges which
are most sensitive to such changes), but at very low
energies (10-100 eV) errors of as much as a factor
of two can occur. A survey of present knowledge of
limitations of the mixture rule is given by Des-
lattes [1969].


Table 3.-17. COPPER, Z=29

[ . - ~
Scattering Pair production Total Total
Photon Photo- a
energy electric
With | Without Nuclear } Electron With — | Without |] With | Without
coherent | coherent field field coherent | coherent {| coherent | coherent
dlatom —bjatom | blatom | blatom ~—Bfatom |} bfatom —bJatom || emg cml
1.66+02 1.86+01| 2.35+04 2.37+04 2.35+04 |] 2.24402 2.93402
1.06+02 1.82401] 7.72403 7.83403 7.74403 |] 7.42+01 3+01
7.70401 1.79401} 3.46+03 3.54403 3.48403 || 3.35+01
4.92401 1.73401 | 1.11403 1.15403 1.12403 |] 1.09401
3.64401 1.68+01| 4.80+02 5.16+02 4.89+00
2.96+01 — 1.63+01| 2.47402 2.77402 2.62400
2.55+01 1.58401 | 1.45402 1.71402 1.62400
2.07+01 1.50401] 6.08401 8.14401 172-01
1,79+01 1.43401} 3.08+01 4.87401 461-01
1.45401 1.29401 | 9.04400 2.36+01 2.23-01
1.27401 1.18401} 3.80400 1.65+01 157-01
1.07+01 1.02401 | 1.15+00 1.18401 11201
9.42400 9.19400] 5.1201 9.93+00 941-02
8.54400 8.39400] 2.81-01 8.82+00 8.36-02
7.86+00 7.76+00| 1.77-01 8.04400 7.62-02
6.87+00 6.82+00] 9.11-02 6.96+00 6.60-02
6.16400 6.13400} 5.65—02 6.22400 5.89-02
4.99400 4.98400 | 2.6102 5.06+00 4.80-02
4.25400 4.25400] 163-02 4.43400 4.20-02
3.35400 3.34400] 888-03 3.79400 3.60-02
2.79+00 | 5.9603,
2.41400 | 4.50-03
2.13400 | 3.56-03
1.74400 | 2.52-03
1.48+00 | 1.95-03
1.10+00 | 1.20-03
8.81-01 | 9.00-04
6.41-01 | 6.00-04
5.10-01 | 400-04
4.25-01
3.67~0L
2.8-01
240-01
171-01
1.34-01
9.50-02
7.44-02
6.16-02
5.27-02
4.12-02
3.39-02
237-02
1.83-02
1.2702
9.83-03
8.03-03
6.81-03
5.25-03
429-03
2.96-03
2.28-03
157-03
1,21-03
9.82-04
8.30-04
6.36-04
5.18-04



Manowitz et al. [1964] and DeProost et al. [1966])
as well as in shielding is the radioactivity which
results from the photodisintegration of the nucleus
in which the photon was absorbed or from the cap-
ture in other nuclei of the reaction products.

An initial attempt at a systematic photonuclear
cross section compilation (in the form of graphs)
has been made by Hunt et al. [1963] for use in food
irradiator design studies. Parameters describing
gross features of measured cross sections for photo-
nuclear reactions have been tabulated by Goryachey
[1964].

However, the best source of data for individual
nuclei is at present the technical literature. Avail-

able data in the literature can be located by means
of the NBS Photonuclear Data Index (Baggett et al.
[1966] and Collins et al. [1967]) which is an anno-
tated index and bibliography of references contain-
ing experimental data on photonuclear reactions.
Each index entry gives specific quantitative data
about the type of information available in each
reference. The source of data used to compile this
index is the NBS Photonuclear Data File. This file
consists of data sheets containing abstracts of the
significant data (both numerical and graphical)
from each reference. These data sheets, as well as
a reprint collection of all references abstracted,
are on deposit at the Photonuclear Data Center at
the National Bureau of Standards.

3. Tabulation of Cross Sections for Elements and Compounds

This section contains photon interaction cross
sections and attenuation coefficients as described
in sections 1 and 2. The data are presented by ele-
ment, following the format of White-Grodstein
[1957] and Davisson [1965] except that total cross
sections are given in barns/atom in addition to
the mass attenuation coefficient in cm2/g, Similar
data (all in cm?/g) for some compounds and mix-
tures of interest in dosimetry (Evans [1968]) have
been added.

In tables 3.-1 to 3.-23 the first column lists the
photon energy in MeV. In this and in other columns
the sign and following two digits at the end of
each entry indicate the power of ten by which
the preceding part of the entry is to be multiplied.
A pair of successive identical energies, the second
of which is preceded by K, L,, Ls, or Ls, marks
the presence of an “absorption edge” discon-
tinuity in the photoelectric and total cross sec-
tion columns.

The second column, labeled “scattering, with
coherent,” is the sum (oc®2+ oR) of the Compton
(incoherent) collision cross section corrected
for electron binding and the Rayleigh (coherent)
scattering cross section. This sum is based on
values calculated by Storm and Israel [1967]
(see sec. 2.4.2). The third column, labeled “scat-
tering, without coherent,” is the free-electron
Compton collision cross section (ZX oc) [b/atom]

40

where oc, including the Mork [1968] radiative and
double-Compton corrections Ag¢', is given in table
2-8.

The fourth column, labeled ‘‘photoelectric,”
is the photoeffect cross section Tye derived from
experimental and theoretical values by proce-
dures described in section 2.3. The fifth column,
labeled “pair production in field of nucleus,”
contains values of kn from eq (2.31), and the
sixth column, labeled “pair production in field
of electrons,” contains values of ke from eqs
(2.-38) and (2.-39).

The seventh and eighth columns, labeled “total,
with coherent” and “total, without coherent,”
are sums Oy over columns 2, 4, 5, and 6, and
over columns 3, 4, 5, and 6, respectively. The
conversion factor at the bottom of each page
(also in table 1.-1) has been used to convert the
total cross section values (b/atom) in columns
7 and 8 into the corresponding mass attenuation
coefficients u/p(cm?/g) in columns 9 and 10. Values
of »/p in the last column are identical with those
in table 1—4. Estimates of uncertainties for vari-
ous ranges of E and Z are given in section 1.4.

Tables 3.-24 to 3.-36 for compounds and mix-
tures were derived from values in tables 3.—1 to
3.-23 using eq (1-6) and the fractions-by-weight
w; in table 1.-3. Possible errors from use of the
“mixture rule” as employed here are discussed
in the last paragraph of section 1.3.


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Integration of eq. (2.-6) over all angles gives the
total Klein-Nishina cross section

2(.+k)_ In (1424)
[ 142k k |

1+k
Re

ofv= anf

In (142k) | 13h | om? } 7
+ or A +2k)% [electron] 8)

This formula is not particularly suitable for
evaluation of of at low energies because of near-
cancellation between the logarithmic and purely
algebraic terms. For example, using 8-place arith-
metic, errors of 1 to 2 percent will occur at 10 to
15 keV. Values of of in table 2.-8 were computed
in double-precision arithmetic and we believe them
correct to the 5 significant figures given.

For k <1, eq. (2.-8) can be expanded as

8 1 6 1 2
xv 8 ep — 6 pL ysy 2p
ott=$ art crap (1+ 2+ $ & 44342
— 5 ps4 8 pop 4 yp...) f—om_].
35 +105 #05 ) alectron|) 2-9)

Using only terms through #?, the value of o%*
from eq. (2.9) at 10 keV is within 0.001 percent of
that from eq. (2-8). In the low-energy limit (k > 0)
this expression becomes the classical Thomson
cross section,'®

For k > 1, a useful approximation is (Heitler [1954]):

2
or=8 arr = 0.6652 * 10-4 | om (2.-10)

electron

cm?

[act

which is equivalent to eq (2.-8) as k—> ©, and
gives a result differing by +0.6 percent at 100
MeV and by + 0.09 percent at 1000 MeV.

In addition, Hastings [1955] has fitted eq (2.-8)
by the empirical formula

142 In (24)
‘ 2k

of ~ are (2-11)

Cr€ + cE? + c9€4 em?

(nese te) [acct
2-12)

off ~ of =m

where €=1/(1+5k). The parameters have the
values

b= 0.222037
1.651035 d= 12,501332
9.340220 dy 14.200407

325004 ds 1.699075

For photon energies 0S ES1 MeV values of off
are within 0.1 percent of of%, and for ES 100 MeV
° However, extrapolation to this limit [o§¥]k.0=or is valid only fora free electron;

for bound electrons [oc}-0=0.

28

are within 1.3 percent. However, at 1 GeV values of
o# are less than of by 17 percent, and at 100 GeV

less by 44 percent.
‘Also listed in table 2.-8 are values of the Compton

energy transfer fraction f& (for use in computing
pxlp and fa/p but not pen/p) where

SE = ao'Slo'®. (2-13)
The numerator ao" is obtained by weighting the
right-hand side of eq (2.-6) by the fraction of the
photon energy transferred to the recoil electron.
This fraction is

(2.-14)

where k' is the energy of the deflected photon.
Combining eq (2.-6) with eq (2-12) we have

ag) 2 __Ml—eos 8)
daoiOldN=5 2 + kA — cos OF
ys HA —cos 6 ] [smiltecuon.
x [) tes? 0+ 7 rq —cos #| | steradian
(2-15)

Integration of the right-hand side of eq (2.-15) over
all angles yields: |

2d +h 143k _
k(1+2k) (1+2k?

(1+4)Qk2—2k—1)
T+ 2h?

ook’ = Qrr2 {

4h 1t+k 1,1 }
4h _(1tk 11 Vi ap
30+ 2he (a 2 3B) In@+2h)
em? 9
[acco] 2-16)

At low photon energies eq (2.-16) suffers from
loss of precision similar to that in eq. (2.-8). An
expansion of eq (2-16) useful for k <1 is
3

8 1 9
(N= — ——— = <p
wot =3 me OT ap (e343

13 pay 2 ps gues)
35 M35 ht 35 Bag et

2.4.2. Electron Binding Corrections to Compton Scat-
tering. Rayleigh Scattering

In gamma ray transport theory and shielding
calculations, electron binding effects have usually
been either disregarded or treated very approxi-
mately by combining them with Rayleigh scattering.
The justification for this treatment is that for low-Z


Table 3.-5. NITROGEN, Z=7

Scattering Pair production Total Total
Photon |} — Photo- |
energy electric
With | Without Nuclear | Electron|| With} Withour |] With | Without
coherent | coherent field field |] coherent | coherent || coherent | coherent
MeV dlatom —bjatom | blatom | Bfatom ——Blatom |} blatom —Bfatom |] emg emg
1.00-02 |] 8.03+00 4.48+00 7.86401 8.66401 8.31401 || 3.73400 3.57400
1.50-02 |} 6.38+00  4.40+00f 2.10+01 2.74401 2.54401 |} 1.18+00 — 1.09+00
2.00-02 |] 5.60+00 4.33400] 8.26+00 1.39401 1.26401 || 5.9601 5.41-01
3.00-02 |] 4.83+00  4.18+00 2.23400 7.06+00  6.41+00 |} 3.04-01  2.76-01
4.00-02 |] 4.44+00  4.05+00} 8.7801 5.31400 4.93+00 || 229-01 2.12-01
5.00-02 }] 4.18+00 3.93400] 4.25-01 4.61+00 1.87-01
6.00-02 |] 4.00+00 3.82400] 2.38-01 4.24400 17-01
8.00-02 |] 3.73+00 3.62400] 9.40-~02 3.82400 1.60-01
1.00-01 |} 3.52+00  3.45+00] 4.5402 3.56400
150-01 |} 3.13+00 3.11400} 1.22-02 3.15+00
2.00-01 |] 2.86+00 2.85400] 4.85-03 2.86+00
3.00-01 |} 2.48+00 2.48400} 1.38-03 2.49+00
4.00-01 2.22400} 5.89-04
5.00-01 2.03400] 3.16-04
6.00-01 1.87+00] 1.97-04
8.00-01 1.65+00}  9.94-~05
1.00+00 1.48+00} 615-05
1.50400 1.20400] 2.88-05] 219-03
2.00-+00 1.03+00] 1.8405] 8.71-03
3.00-+00 8.07-01 250-02 2.82-04
4.00+00 6.73-01) 406-02 1.16-03
5.00+00 5.81-01 544-02  2.27-03
6.00+00 5.1401 667-02 3.50-03
8.00400 4.20-01 8.73-02 5.9803 5.14-01 2.21-02
1.00+01 3.58-01 104-01 8.17-03 4.70-01 2.0202
1.50+01 136-01 1.27-02 414-01 1.7802
2.00401 159-01 163-02 3.88-01 1.6702
3.00+01 1.92-01 2.18-02 3.68-01 1.58-02
4.00+01 214-01 2.5802 3.63-01 1.5602
5.00401 232-01 2.9002 3.63-01 1.56-02
6.00+01 245-01 3.16-02 3.65-01 1.57-02|
8.00+01 266-01 3.5602 3.71-01 1.60-02}
1.00+02 281-01 3.8502 3.79-01 163-02}
1,50+02 3.06-01 4.3702 3.91-01 1-68-02
2.00+02 321-01 4.7102 4.01-01 1.7202
3.00402 340-01 5.1702 4.14-01 1.7802
4.00+02 351-01 5.47-02 4.23-01 1.82-02|
5.00+02 358-01 5.68-02 430-01 1.85-02|
6.00+02 3.63-01 5.8402 435-01 1.8702]
8.00+02 3.70-01 6.0802 441-01 1.90-02)
1.00+03 3.75-01  6.24-02 4.46-01 192-02}
1.50403 382-01 6.5102 4.53-01 1.9502]
2.00+03 3.86-01 6.68-02 457-01 1.9602}
3.00+03 3.90-01  6.89-02 4.62-01 1.99-02
4.00+03 392-01 7.00-02 4.64-01 2.00-02
5.00+03 3.93-O1 — 7.07-02 4.66-01 2.00-02
6.00-+03 394-01 7.13-02 4.67-01 2.01-02
8.00-+03 395-01 7.20-02 4.69-01 2.02-02
1.00+04 3.96-O1 7.24~-02 4.70-01 2.0202
1.50+04 397-01 7.31-02 4.71-01 2.03-02
2.00404 3.98-Ol 7.3402 4.72-01 2.03-02
3.00+04 3.99-01 7.3802 4.73-01 2.03-02
4.00404 399-01 7-40-02 4.73-01 2.03-02
5.00+04, 399-01 7.41-02 4.73-01 2.04-02
6.00+04 399-01 7.42-02 474-01 2.04-02
8.00-+04 399-01 7.43-02 474-01 2.04-02
1.00+05 399-01 7.43-02 4.74-01 2.0402

(atom) x 048000 = ene


‘LABLE 2-6. Parameters for empirical fit [eq (2.—1)] to the K-shell photoelectric
cross section 7.

n a bn on Pn
1 1.6268 10-9 -2.683- 10°? 4173+ 10°? 1
2 1.5274 1079 -5.110- 10-188 1.027-10-* 2
3 1.1330+10-9 ~2.177+ 10-22 2.013+1072 3.5
4 -9.12 +1074 _ oO 0 4

TABLE 2.-7. The experimental ratio (TyelTx)x-eage 4S
derived from Kirchner (1930] by Davisson [1965].

Element — | (Tpe/Tx)c-odge| Element | (tpe/Tx) K-edge
iH 1.00 pCa 111
«Be 1,03 Fe 1.12
ec 1.04 29 1.13
7N 1.05 42Mo 1.16
30 1.06 505M 1.18
uNa 1.075 ssl 1.19
Mg 1,08 “aW 1.20
1sAl 1,09 woPt 1.22
Si 1.09 a2Pb 1.22
asAT 1.10 o2U 1.235
pe 1.10

McMaster, Del Grande, et al. For the heavier ele-
ments 74W, s2Pb, and »:U some energy-dependence
in the ratio Tpe/tx is included, based on the Rakavy-
Ron results, from the K-edge to about ] MeV where
the ratio joins smoothly with the values from table
2-7.

Although not truly a smooth function of Z because
of irregularities in the higher electron shell struc-
ture, the ratios in table 2.-7 can be represented
pith an accuracy of + 2 to 3 percent by the empirical

it

Tpelte ~1+0.01481 In?Z — 0.000788 In? Z. (2.-2)

2.4. Scattering
2.4.1. Compton Scattering. Klein-Nishina Formula

In Compton scattering, a photon collides with an
electron, loses some of its energy and is deflected
from its original direction of travel. The basic theory
of this effect, assuming the electron to be initially

free and at rest, is that of Klein and Nishina [1929].

This theory has been well confirmed experimentally
(see, for example, Meitner and Hupfeld [1930],
Hofstadter and McIntyre [1949], Cross and Ramsey
[1950], French [1965], Sahota et al. [1966], and
Gittelman et al. [1968]). Predictions of this theory
have been summarized and extensive tabulations
have been given by Nelms [1953], Burton [1953],
and Evans [1958, 1968].

Over most of the region in which Compton scat-
tering is a major part of the total cross section, the
Klein-Nishina theory is directly applicable. Depar-
tures from it occur at low energies because of elec-
tron binding effects, and at high energies because
of the possibility of emission of an additional pho-

ton (double Compton effect) and radiative cor-
rections associated with emission and reabsorption
of virtual photons. These corrections are discussed
later in this section.

The relation between photon deflection and
energy loss for Compton scattering, assuming the
electron to be initially free and stationary, is de-
termined from conservation of momentum and
energy between the photon and the recoiling elec-
tron (Compton [1923], Debye [1923]). This relation
can be expressed as

EB 1
E 1+ (Ejme?) (1—cos 6)

(2.-3)

where E and E’ are the energies of the photon
before and after the scattering, mc? is the electron
rest energy and @ is the photon deflection angle.

In transport calculations it is often convenient
to use, instead of the energy variable, the wave-
length of the photon in Compton units,

d= me?/E=0.5110/E [MeV]. (2.-4)

The increase in wavelength associated with a
Compton scattering event in these units is
-d’-h=1—cos 8, (2.-5)
where A and X’ are the Compton wavelengths of the
photon before and after the deflection. The maxi-
mum shift in wavelength, occurring for a deflection
= 180°, is two Compton units.
For unpolarized photons the Klein-Nishina
angular distribution function per steradian of solid
angle 2 is

dof" (0)/dO=3r2{1+k(1—cos 6)]* x

x [1+ cos! 94 Hl =cos 8)* | [satistectcon).

1+k(—cos 6) |” steradian
(2.-6)

in which & is the reciprocal of the incident photon
Compton wavelength

k=1/K=E]me?=E[MeV]/0.5110. (2-7)


Table 3.-24. WATER, H.0
Scattering. Pair production Total
Photon Photo
eneray With Without electric Nuclear Electron With Without
coherent | coherent eld feld coherent | coherent
MeV emtlg emg emg omg emilg emg ome
1.00-02 | 3.97-01 2.1401} 4.78+00 5.18+00  4.99+00
1,50-02 |] 3.09-01 2.10-01 | 1.27+00 1.58+00  1.48+00
2.00-02 }} 2.70-01 2.0701] 5.0501 175-01 7.1101
3.00-02 || 2.32-01 2.00-01} 1.38-01 3.38-01
4.00-02 |} 2.13-01  1.93-01] 5.4802 267-01 248-01
5.00-02 |) 200-01 1.88-01 | 2.67-02 227-01 214-01
6.00-02 |] 1-91-01 1.82-01 | 1.50-02 2.0601 1.97-01
8.00-02 |] 1.7801 1.73-01 | 5.9503 1.8401 1.79-01
1.00-01 || 1.68-01 1.6501] 2.85-03 1.7101 1.68-01
1.50-O1 || 150-01 1.48-01] 7.7604 151-01 1-49-01
2.00-01 || 1.37-01 1.3601 | 3.11-04 137-01 1.36-01
3.00-01 |] 1.19-01 1.18-01} 8.86-05 1.1901 1.18-01
4.00-01 || 1.06-01  1.06-01) 3.7805 1.0601 1.0601
5.00-01 |] 9.68-02 9.67-02] 2.0405 9.68-02 9.6702
6.00-01 || 8.96-02 8.9502 | 1.28-05 8.9602 8.95-02
8.00-01 7.8602 | 6.42-06 7.8602
1,00+00 7.06-02 | 3.98-06 7.07-02
1.50+00 5.74-02 | 1.8606} 9.86-05 5.7502
2.00+00 4.90-02 | 1-18-06 | 3.93-04 4.9402
3.00+00 3.85-02 | 6.62-07 | 113-03 1.34-05 3.9702
4.00+00 3.22-02 | 4.51-07 | 183-03 5.5205 3.40-02
5.00+00 2.78-02 | 3.4407] 245-03 1.09-04 3.03-02
6.00400 245-02] 2.75-07] 3.00-03 1.6704 2.77-02
8.00+00 2.01-02 | 1.97-07 | 3.93-03 2.8604 2.4302
1.00+01 1.71-02} 1.5407} 4.69-03 — 3.90-04 2,22-02
1.50401 1.27-02 6.11-03 6.0804 1.94-02
2.00+01 1.0202 7.1603 7.80-04 1.81-02
3.00+01 7.40-03 8.63-03 1.0403 1.7102
4.00+01 5.88-03 9.63-03 1.23-03 1.67-02
5.00401 4.91-03 1.0402 1.38-03 1.67-02
6.00+01 4.22-03 110-02 1.51-03 1.67-02
8.00+01 3.33-03 1.19-02 1.7003 1.70-02
1.00+02 2.77-03 1.26-02 1.8403 1.72-02
1.50402 1.97-03 137-02 2.09-03 1.78-02
2.00+02 154-03 144-02 2.26-03 1.8202
3.00+02 1.09-03 152-02 2.48-03 1.88-02
4,00+02 8.57-04 157-02 2.62-03 1.9202
5.00+02 7.10-04 1.60-02 2.7303 1.95-02
6.00+02 6.08-04 1.63-02 2.8003 1.97-02
8.00-+02 4.7504 166-02 — 2.92-03 2.00-02
1.00+03 3.90-04 1.68-02 3.0003 2.02-02
1.50+03 2.7304 171-02 3.12-03, 2.0502
2.00+03 211-04 172-02 — 3.20-03 2.0602
3.00+03 147-04 1.7402 3.30-03 208-02
4.00+03 1.13-04 1.75-02  3.35-03 2.10-02
5.00+03 9.26-05 1.7602 —3.38-03 2.10-02
6.00+03 7.86-05 1.76-02 — 3.40-03 2.1102
8.00+03 6.05-05 1.7702 3.43-03 2.1102
1.00+04 4.9405, 1.77-02 — 3,45-03 2,12-02
1.50-+04 3.41-05 1.77-02  3.48-03 2.1302
2.00-+04 2.62-05 1.7802 3.50-03 2.1302
3.00404 1.81-05 1.78-02 3.5203 213-02
4.00+04 139-05 1.7802 3.52-03 213-02
5.00+04 1.13-05 1.78-02 3.53-03 213-02
6.00-+04 957-06 1.7802 3.53-03 2.1402
8.00+04 7.3306 1.78-02 3.5403 214-02
1.00+05 5.97-06 1.78-02  3.54-03 2.1402

64



1.2.2. Notation and Units—Continued

Symbol Name or definition Units Where used
oc Compton (“incoherent”) collision cross section b/electron or Sec. 2.4.5 Table 2-8;
b/atom Eq (1-8); Fig. 2-1
I gc[b/atom] « (Na/M) « 10-* om? g"" Eq (1.10)
mop [(em?g-*)/(b/atom)]
of ac as given by the Klein-Nishina formula belectron Table 2.-8; Eqs (2.-8), (-9),
1)
of oc as given by Hasting’s empirical fit to of” bjelectron Eq (2.-12)
ope oc for bound electrons b/electron Sec. 2.4.2; Eq (2.-18); Fig. 2-3
or b/atom
ok ac for a K-shell electron bjelectron Fig 2-2
S(q,Z) incoherent scattering function dimensionless. Eq (2.-18)
oR Rayleigh (“coherent”) scattering cross section b/atom. Sec, 2.4.2; eq (2.-22); Fig. 2-4
per atom
F(q,Z) atomic form factor dimensionless Eq (2.-22)
Ge criterion angle for assessing importance of Rayleigh degrees or Eq (2.23); Fig. 2.-4
scattering radians
o(“scattering, total bound-electron scattering cross section b/atom Sec. 2.4.2; Tables 2-9, 3-1 to
with coherent”) =o2?+on 23
Aoi! Mork correction to c= (double Compton)+o bjelectron Tables 2.-8; Eq (2.-25)
(radiative correction)
o(“scattering, free-electron scattering cross section, including b/electron or Tables 2-8, 3-1 to -23
without radiative corrections = of" + Aot! b/atom
coherent”)
K total pair production cross section=kn+ Ke b/atom Sec. 2.5; Eq (2.-42)
ble «[b/atom]-(Na/M)-10-* [(em? g-")/(b/atom)] cm? g-! Eq (1.-10)
Kn cross section for pair production in the field of b/atom Sec. 2.5.2; Tables 2.-10, 3.-1 to
an atomic nucleus ~23; Eqs (2.-26), (-30), (-31)
Ke cross section for pair production in the field of the b/atom Sec. 2.5.3; Tables 2.-15, 3.-1 to
atomic electrons (““triplet” production) =23; Eqs (2.-27), (-38), (39)
n Z-(KelKn) dimensionless Secs. 2.5.1, 2.5.3; Table 2.-15;
Eqs (2. “41) to (-43)
«84 (Born) nx as formulated by Bethe and Heitler in the Born b/atom Table 2.-11; Eqs (2-30), (-31),
approximation (-33), (-34), (36)
—AKpeM Davies-Bethe-Maximon Coulomb correction to b/atom Table 2.-12; Eqs (2.-28), (-30),
K24(Born) a)
sHtFS Hartree-Fock-Slater screening corrections b/atom Table 2.-13; Eq (2-31)
to Kn
Opn. nj total photonuclear cross section bfatom or
=o(y,n)+o(y, pit > - mb/atom
Ey energy at which the maximum, a», of the opi, ». MeV Table 2.-16; Eq (2-44)
resonance peak occurs
r width at half-max. of the apn.» peak MeV Table 2.16; Eq (2.~44)


TABLE 1-7 (Continued)
Photon wsAl “Si wP
energy
[MeV] Hale Ble Henle Hale | uxle | HenlQ Hale | Bxle | HenlQ
0.01 | 25.6 25.5 25.5 33.4 33.3 33.3 40.4 39.8 39.8
0.015 7.48 VAT 7.47 9.78 9.75 9.75 11.9 11.8 11.8
0.02 3.06 4.02 4,01 4.01 4.93 4.91 4.91
0.03 0.868 1.14 1.14 1.14 1.39 1,39 1.39
0.04 0.357 0.473 0.472 | 0.472 | 0.573 0.572 0.572
0.05 0.184 0.241 0.293
0.06 o.111 0.144 0.173
0.08 0.0562 0.0701 0.0820
0.10 0.0386 0.0459 0.0511
0.15 0.0286 0.0312 0.0323
0.2 0.0276 0.0293 0.0292
0.3 0.0283 0.0294 0.0288
0.4 0.0287 0.0298 0.0291
0.5 0.0288 0.0286 | 0.0298 0.0290
0.6 0.0286 0.0286 0.0296 0.0295 0.0288
0.8 0.0279 0.0277 | 0.0289 0.0288 | 0.0281 0.0278
1.0 0.0270 0.0269 0.0279 0.0277 0.0272 0.0270
15 0.0248 | 0.0247 | 0.0245 | 0.0257 | 0.0255 | 0.0253 | 0.0250 | 0.0248 | 0.0246
2 0.0233 0.0229 0.0226 0.0241 0.0237 0.0234 0.0235 0.0231 0.0228
3 0.0213 | 0.0206 | 0.0202 | 0.0221 | 0.0214 | 0.0210 | 0.0217 | 0.0209 | 0.0204
4 0.0201 | 0.0193 | 0.0188 | 0.0211 | 0.0202 | 0.0196 | 0.0207 | 0.0198 | 0.0192
5 0.0194 | 0.0185 | 0.0179 | 0.0204 | 0.0194 | 0.0187 | 0.0201 | 0.0191 | 0.0184
6 0.0190 0.0181 0.0172 0.0201 0.0191 0.0182 0.0198 0.0188 0.0179
8 0.0186 | 0.0177 | 0.0168 | 0.0197 | 0.0187 | 0.0177 | 0.0197 | 0.0187 | 0.0175
10 0.0185 0.0176 0.0165 0.0197 0.0188 0.0175 0.0197 | 0.0188 0.0174
Photon 1S aeAt wk
energy
[MeV] Hale | uxle | Henle Hale | exile | Henle Hale | Hx/Q | Henle
0.01 | 50.1 49.7 49.7 63.6 62.3 62.3 79.9 71.6 71.6
0.015 15.0 14.9 14.9 19.3 19.1 19.1 24.4 23.9 23.9
0.02 6.24 6.21 6.21 8.10 8.02 8.02 10.3 10.2 10.2
0.03 1.77 1,77 1.77 2.33 231 2.31 2.97 2.94 2.94
0.04 0.729 0.727 0.727 0.967 0.962 0.962 1.23 1.23 1.23
0.05 0.372 0.490 0.488 0.488 0.626 0.623 0.623
0.06 0.218 0.285 0.284 0.284 0.368 0.366 0.366
0.08 0.101 0.128 0.162 0.162 0.162
0.10 0.0610 0.0735 0.0915 | 0.0913 | 0.0913
0.15 0.0357 0.0377 0.0442
0.2 0.0311 0.0304 0.0343
0.3 0.0300 0.0278 0.0304
0.4 0.0301 0.0275 0.0298
0.5 0.0300 0.0273 0.0295 0.0293
0.6 0.0298 0.0270 0.0268 | 0.0292 0.0290
0.8 0.0290 0.0288 | 0.0262 0.0261 | 0.0283 0.0282
1.0 0.0280 0.0278 | 0.0253, 0.0251 | 0.0273 0.0270
15 0.0258 | 0.0256 | 0.0253 | 0.0233 | 0.0232 | 0.0229 | 0.0252 | 0.0250 | 0.0247
2 0.0243 | 0.0238 | 0.0235 | 0.0220 | 0.0215 | 0.0212 | 0.0238 | 0.0233 | 0.0229
3 0.0225 | 0.0216 | 0.0211 | 0.0206 | 0.0198 | 0.0192 | 0.0224 | 0.0214 | 0.0208
4 0.0216 | 0.0205 | 0.0199 | 0.0199 | 0.0189 | 0.0182 | 0.0218 | 0.0206 | 0.0198
5 0.0211 | 0.0200 | 0.0192 | 0.0197 | 0.0185 | 0.0177 | 0.0215 | 0.0202 | 0.0193
6 0.0209 | 0.0197 | 0.0188 | 0.0196 | 0.0184 | 0.0174 | 0.0215 | 0.0202 | 0.0190
8 0.0208 | 0.0197 | 0.0184 | 0.0197 | 0.0186 | 0.0173 | 0.0218 | 0.0205 | 0.0190
10 0.0210 | 06,0200 | 0.0184 | 0.0201 | 0.0190 | 0.0174 | 0.0222 | 0.0210 | 0.0191

18





Table 3.—15. CALCIUM, Z=20

Photon
energy

Scattering

With
coherent

8.00+04
1.00+05

blatom

6.78+01
4.68+01
3.49401
2.36+01

1.87401
1.61+01
1.4401
1.24401

1.12+01
9.47+00
8.47+00
7.22400

Without

coherent

blatom

1,28+01
1.26401
1.24401
1.19401

1.16+01
1.12401
1.09401
1.03401

9.85+00_
8.87400.
8.13400.
7.07+00!

6.33400
5.79+00

Pair production Total Total
Photo. |.
electric
Nuclear Electron With Without With Without
field field |} coherent | coherent |}coherent | coherent
blatom bjatom blatom || bJatom blatom || cmtg ome lg
6.35-+03 6.42+03 9.65401 9.56+01
1.96-+03 2.00+03 3.01401 2.96401
8.27402 8.62402 1.30+01 — 1.26+01
2.42+02 2.66+02 3.99400 3.82+00
9.98+01 1.19402 1.78+00 1.67400
5.03+01 6.64401 998-01 9.25-01
2.87401 4.31401 648-01 5.95-01
1.19401 2.43401 3.6501 3.34-01
5.89+-00 1.71401 256-01 2.37-01
1.70+00 1.12401 1.68-01—1.59-01
7.0901 9.17400 138-01 1.33-01
2.10-01 7.43+00 109-01
9.19-02 6.51400 9.6602
4.9802 5.89+00 8.78-02
3 8.0902
4.72400 7.0902!
4.25400 4.24400 6.37-02
188-02 3.46+00 3.46400 5.2002
7.30-02 3.01400 3.01400 4.5202
206-01 8.05~-04 2.51400 3.7802
3 3.40-02
3.17-02
3.03-02
2.89-02
1.88+00 2.83-02
1.88+00 2.83-02,
2.89-02|
1.52400 6.22-02 3.05—02:
1.70+00 7.3202 3.19-02!
1.83400 8.1602 3.3102,
1.93400 8.83-02 3.42~02)
2.08400 9.8502
2.19400 1.06~01
2.39400 1.20-01
2.48+00 —1.28-01
2.60400 1.39-01
2.67400 1.46-01 4.32-02'
2.72400 1.51-01 4.3802!
2.76400 1.55—01 4.4302)
2.81400 1.60-01 4.50-02|
2.84+00 1.6401 4.5502
2.88+00 — 1.70-01 4.6102
2.90+00 1.7401 4.6402
2.03400 1.7801 4.6802!
2.94400 1.8001 4.70-02
2.95400 1.81-01 4.72-02
2.96+00 — 1.82-01 4.73-02
2.97400 1.83-01 4.74-02
2.97400 1.84-01 4.7502
2.98+00 —1.85~-01 4.7602
2.98400 1.86-01 4.702
2.99400  1.86~01 4.702
2.99400 1.87-01 3.18+00 4.77-02
2.99400 1.8701 3.18+00 4.78-02
2.99400 1.87-01 3.18+00 4.78-02
2.99400 1.87-01 3.18400 4.7802
2.99400 1.8701 3.18+00 4.7802

‘biatom) x 015080= emFhe


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Table 3.—22. LEAD, Z=82
Scattering Pair production
Photon 7 | Photo. | —_ —
energy electric
With | Without Nuclear [* ectron
coherent | coherent field field
blatom blatom blatom blatom blatom
1.73403 4.40404
1.34+03 2.20404
ls 1.34403
1.15+03
1.13403
lL, 1.13+03
1.08+03
Li 1.08+03
8.17402
4.91402
3.36-+02
2.48+02
194-402
1.32402
1.16+02
K 1.16+02
9.93+01
6.39+01
4.92+01
3.61+01
3.00+01
2.63+01
2.37401
2.03+01
1.79401
1.43+01
1.22+01
9.51+00
7.94-00 5.77400 1.3502
6.84400 7.30400 2.66-02
6.04400 8.54400 4.0902
4.93+00 1.05401 7.00-02
1.00+01 || 4.20+00 1.22+01 9.5702
1.50401 1.55401 148-01
2.00+01 1.81401 — 1.86-01
3.00+01 2.18401 242-01
4,00+01 2.43+01 — 2.81-01
5.00401 261401 3.11-01
6.00+01 2.75+01 3.3501
8.00401 2.96401 3.7101
1.00+02 141-02} 3.10401 3.97-01
1.50402 3.33401 441-01
2.00+02 3.48+01 4.6801
3.00-+02 3.64401 — 5.03-01
4.00+02 3.73401 5.25-01
5.00+02 3.79401 5.40-01
6.00+02 3.83401 5.51-01
8.00-+02 3.89401 5.66-01
1,00+03 3.92401 5.76-01
1,50+03 3.98401 5.90-01
2.00403 4.00401 5.98-01
3.00403 4.04401 6.07-01
4.00+03 4.05401 6.1201
5.00403 4.06+01  6.15-01
6.00403 4.07401 6.17-01
8.00403 4.08+01  6.20-01
1.00+04 4.09401 6.21-01
1.50+04 4.09401 6.2401
2.00404 4.10401 6.2501
3.00404 4.10+0]  6.27-01
4.00-+04 4.10401 6.28-01
5.00-+04 4.11401 6.28-01
6.00+04 4.11401  6.28-01
8.00404 4.11401 6.29-01
1.00405 4.11401 629-01

Total Total
With Without With | Without
coherent} coherent {| coherent | coherent
bjatom ——_blatom em'ig cml
4.57404 4.41404 |] 1.33402 — 1.28+02
2.33404 —2.20+04 |! 6.78401 6.41401
5.71404 — 5.59+04 || 1.66402 1.62+02
3.96404 3.85404 |] 1.15402 1.12402
3.86404 — 3.76+04 || 1.12402 — 1.09402
5.01404 4.91404 |] 1.46402 1.43402
4.46404 —4.36+04 |] 1.30402 1.27+02
5.40+04 5.29404 || 1.57402 1.54402
2.95404 2.87+04 || 8.57401 8.34401
1.02+04 —9.76+03 |} 2.97+01 2.84401
4.81403 4.52403 |] 1.40401 1.31401
2.68403 2.48+03 || 7.81400 7.22400
1.67+03 — 1.52+03 |] 4.87400 4.43+00
8.03402 7.13402 }] 2.33400 2.0700
6.31402 — 5.56+02 |] 1.83400 — 1.62+00
2.56+03 2.49403 || 7.45+00
1.86+03 — 1.80+03 |] 5.40+00
6.78+02 6.51402 || 1.97+00
3.41402 3.25+02 |] 9.91-01
1.39402 1.32402 |} 4.04-01
7.96+01 — 7.56+01 || 2.31-01
5.55+01 5.29401 |/ 1.61-01
4.29401 4.11+01 || 1.25-01
3.04401 2.95+01 |} 8.8502
2.43401 — 2.37+01 |] 7.08-02
1.78+01 —1.75+01 || 5.17-02
1.57401 1.55+01 || 4.55-02
1.44401 1.43+01 || 4.18-02
1.43401 1.43+01 |] 4.16-02
1.46+01 — 1.46+01 || 4.24-02
1.50+01 —1.49+01 || 4.35-02
1.58+01 1.58401 |] 4.59-02
1.67401 —1.67+01 |} 4.8402

1.89+01
2.04401
2.30+01
2.60+01
2.77401
2.89+01
3.08+01

1.21-01
1.2101
1.2101
1.21-01

1.2101
1.2101
1.21-01
1.21-01

1.21-01

(b/atom) x 002907 = emg

62


TABLE 2-11. Energy-dependent parameters used for evaluating Kq.

Mork-Olsen i
c Empirical Theoretical
Phot ve hen ©
‘oton BH (Born) radiative | jnuitiplier for | multiplier for
energy 2 correction Coulomb Coulomb
(MeV) Diatom/2 factor correction | correction
[1+ A (rad. corr.) }
1,022 0 1.000 0 0
1.5 4.30 +1078 (1.011) —0.0677 0.2778
2 1,772+10-4 (1.012) —0.1286 0.4359
3 5.055+ 10-4 (1.012) —0.1356 0.6061
4 8.205-10-4 (1.013) — 0.0639 0.6971
5 1.100- 10-8 (1.013) +0.0204 0.7539
6 1,350- 10-8 (1.013) 0.1216 0.7927
8 1.775: 10-8 (1.013) 0.305 0.8425
10 2.127 10-3 1.012 0.450 0.8729
15 2.792+ 10-8 1,012 0.655 0-9144
20 3.278- 10-8 1.011 0.740 0.9354
30 3.977+ 10-8 1.011 0.824 0.9567
40 4479+ 10-3 1.011 0.871 0.9674
50 4.872: 10-8 1.011 0.900 0.9739
60 5.194+ 10-8 1.011 0.924 0.9782
80 5.705+ 10-8 1.010 0.954 0.9837
100 6.102 10-8 1.010 0.976 0.9869
TABLE 2-12. Davies-Bethe-Maximon [)954] high-energy where
Coulomb correction, —Ax?TM, divided by Z?. 4
Units are [b/atoml/Z* u=ft [9 In (183 Z-¥8)J1
Z | —AnpBM|z2 | Zz —AnRBM|Z2 ’
and
1 115 +10°7 18 3.684 10-8 . : 4
4 1.84 -10-6 19 —4.097- 10-8 K=255 Z-1/(15.6 —$ In Z).
5 2.88 - 10-6 20 —4,532+ 10-5
6 4.15 +10°8 26 7.566- 10-8 . . .
7 5.64 + 10-® 29 9.344 10-8 This formula can be integrated analytically to
3 — 7.36 -10°8 42 1.884- 10-4 give the total pair production cross section:
MW ~ 1.388- 10-5 50 —2.591-10-4
12 = 1.651-10-* 53 --2.876- 10-4 29
13 = 1.935- 10-8 74 —5.078+ 10-4 BH, ete Z
14 —2.241-10-5 82 5.977 10-4 1q(Born)~ > 37° In 183 Z
15 —2.569+ 10-8 92 7.119 10-4
__16 —2.919- 10-8
uK
«(148
The differential Bethe-Heitler Born-approxima-
tion cross section, in the high-energy approximation
and for partial screening, can be approximated by 140K
use of a simple and convenient formula derived by as
Bernstein [1950]. In this approximation the Bethe- x (2-33)
Heitler screening functions ¢1 and gs (based on the 144K

Thomas-Fermi atom) are assumed to be equal, and
¢1 is fitted by an analytic expression to better than
2 percent. In terms of the photon energy é and the
outgoing electron kinetic energy T, both in mc?
units, the resulting formula is

dx (Born)/dT

ar: su Lf) _, Pt} (4)
= 137, In (183 Z rab u rs +u k
Kk 4
Kk 2.-32)
«[! aenucT=p| 2 ee?

35

If the Bernstein formula (2-33) is inserted into
eq (2.-31) we obtain values of kn which agree
with those in table 2-10 and with experimental
data to ~5 percent over the energy range
E25 MeV for Z 2 29. For lighter materials this
agreement is restricted to higher energies: e.g.,
for carbon the Bernstein result is lower by ~ 20
percent over the range 5 to 20 MeV but agrees
within ~ 5 percent for E>50 MeV. However, for
these materials the addition of the contribution
of Compton scattering results in total photon inter-


Table 3.-35.

BAKELITE (Typical), (CisH3s07)n

Scattering Pair production Total

Photon Phot

energy With Without eclectic Nuclear Electron With Without

coherent | coherent field field coherent | coherent

MeV entle em*lg ontle entle ont entle entle
1.00-02 |] 3.27-01 2.0401 | 2.43+00 2.76+00 = 2.64+00
1.50-02 || 2.69-01 —_2.00-01 | 6.53-01 9.23-01 8.5401
2.00-02 j} 2.41-01 1.97-01 | 2.52-01 4.92-01  4.48-01
3.00-02 || 2.12-01 1.90-01 | 6.50—-02 2.77-01 2.5501
4.00-02 || 1.98-01 1.84-01 2.51-02 2.23-01 —-2.09-01
5.00-02 || 1.88-01 1.79-01 1.26-02 2.00-01 1.91-01
6.00—-02 |} 1.80-01 1.74-01 7.31-03 1.87-01 181-01
8.00—-02 || 1.68-01 1.65-01 2.88-03 1.71-01 — 1.68-01
1.00-01 1.59-01 157-01 1.38-03 1.61-01 1.58-01
1.50-01 1.42-01 141-01 | 3.70-04 1.43-01 1.42-01
2.00-01 1.30-01 1.29-01 1.48-04 1.30-01 1.30-01
3.00-01 1.13-01 | 4.19-05, 1,13-01
4.00-01 1.01-01 1,79-05 1.01-01
5.00-01 9.21-02 | 9.66-06 9.21-02
6.00-01 8.52-02 | 6.02-06 8.52-02
8.00-01 7.49-02 | 3.0406 7.4902
1.00+00 6.7302 | 1.88-06 6.7302
1.50+00 5.47-02 | 8.78-07 | 8.20-05 5.4802
2.00+00 4.6702 | 5.59-07 | 3.27-04 4.70-02
3.00+00 3.6702 | 3.13-07 | 9.40-04 — 1.28-05 3.77-02
4.00+00 3.06—-02 | 2.13-07 153-03 -5.26-05 3.22-02
5.00+00 2.6402 | 1.63-07 | 2.05-03 — 1.03-04 2.86—-02
6.00+00 2.3402 | 1.30-07 | 2.50-03 1.5904 2.60-02
8.00+00 1.91-02 | 9.32-08 | 3.28-03 2.72-04 2.27-02
1.00+01 1.63-02 | 7.27-08 | 3.91-03  3.72-04 2.06—-02
1.50+01 1.21-02 5.12-03 5.7904 1.78-02
2.00+01 9.6703 5.99-03 —-7.43—-04 1.6402
3.00+01 7.0403 7.22-03  —-9.90-04 1.53-02
4.00+01 5.60-03 8.07-03 —-1.17-03 1.48—-02
5.00+01 4.6703 8.72-03 —-1.32-03 1.47-02
6.00401 4.02-03 9.23-03 1.4403 1.47-02
8.00+01 3.17-03 1.00-02 1.6203 1.48-02
1.00+02 2.64-03 1.06-02_—-1.76-03. 1.50-02
1.50+02 1.88-03 1.15-02 —_2.00-03. 1.5402
2.00+02 1.47-03 1.21-02—_2.16-03 1.57-02
3.00+02 1.04-03. 1.28-02—-2.37-03 1.62-02
4.00+02 8.17-04 1.33-02—-2.51-03 1.66—-02
5.00+02 6.76—-04 1.35-02 —_2.61-03. 1.68—-02
6.00+02 5.7904 1.37-02—-2.69-03 1.70-02
8.00+02 452-04 1.40-02 —_2.80-03. 1.73—-02
1.00+03 3.72-04 1.42-02 — 2.88-03. 1.7402
1.50+03 2.60-04 1.45-02 — 3.00-03 1.77-02
2.00+03 2.0104 146-02 — 3.08-03. 1.79-02
3.00+03 1.40-04 1.48-02 -3.17-03. 1.81-02
4.00+03 1.08-04 149-02 3.23-03 1.82-02
5.00+03 8.82-05 1.49-02 —-3.26-03. 1.83-02
6.00+03 7.48-05 150-02 -3.29-03 1.83—-02
8.00+03 5.76-05 1.50-02-3.32-03 1.8402
1.00+04 4.71-05 1.50-02 3.3403 1,84-02
1.50+04 3.25-05 151-02 -3.37-03. 1.85—02
2.00+04 2.50-05 151-02 3.39-03 185-02
3.00+04 1.72-05. 151-02 3.41-03 1.85-02
4.00+-04 1,32-05 1.51-02  3.42-03 1.86—-02
5.00+04 1.08-05 151-02 3.42-03. 1.86—02
6.00+04 9.11—-06 1.52-02 —-3.43-03. 1,86—02
8.00+04 6.99-06 1.52-02 —3.43-03. 1.86—02
1.00405 5.68-06 152-02 3.44-03 1.86—02

75



TABLE 2-13.

Sérenssen [1965, 1966] screening (Hartree-Fock-Slater) corrections, s""*, to be subtracted from

«84 (Born) divided by Z?.

Since s"*S is not a smoothly varying function of Z near +H, values of s"*S/Z? for 2,3, and 4 are included. Values below 10 MeV are extrapolated. Units are (b/atom|Z*

Photon
energy iH 2He si Be oc asAl oC
[MeV]

1.022 0 0) 0) 0 0 0

15 - = 1.0 +10-7 1,0 -10-7 1.0 +1077 3.0 +10-7

2 - 3.0 + 10-7 3.0 +107? 3.0 +10-7 4.0 +10-7 6.0 +10-7

3 2.0 +10-7 8.0 +1077 9.0 +1077 1,0 +10- 1.1 +10-8 1.6 + 10-8

5 8.0 +10°7 2.1 +10-8 2.3 -10°6 2.6 +1078 3.3 +10-8 5.0 + 10-6

10 4.0 +10-5 6.2 +10-% 6.7 +10-8 7.5 +10- 9.4 910-8 2.01-10-

20 1,51-10-8 1.65- 10-5 1,75- 10-8 2.07- 10-5 3.07-10-5 6.60- 10-4

30 2,87-10°5 2.82- 10-5 311-1078 4,30-10-5 6.60- 10-5 1.20- 10-4

50 5.28-10-8 | 5.46-10-8 | 8.20-10-8 | 1.10-10-4 | 1.57-10-4 | 2.38-10-4
100 1.10-10-# ] 1,82-10-4 | 2.70-10-& | 3,30-10-# | 3.94-10-4& | 5.32-10-4
Photon
energy 2Fe oC «Mo soSn nW aPb UV
(MeV]

1.022 0 0 0)

1 5.0 + 6.0 -10-? 8.0 +1077 9.0 +10-7 1.25 1.4

2 11+ 1.3 -10-$ | 1.9 -10-6 | 2.2 -10-6 | 28 2.9

3 2.9 + 3.2 +10° | 4.3 -10°6 | 4.9 -10°° | 64 6.8

5 8.0 + 8.6 +1078 111-1078 1,25-10-8 1.57+10-5 1.79-10-8
10 3.05- 3.17-10-8 3.85° 1078 4,32-+10-5 5.40- 10-5 5.91-10-5
20 9.10- 9.43-10-8 | 1.14-10-4 | 1.24-10-4 | 1.50-10-4 1,66+ 107-4
30 1.64+ 1,68-10-¢ | 1.98-10-¢ | 2.17-10-4 | 2.55-10-4 2.76- 10-4
50 3.11+ 3 3.73+1074 | 4,00-10-4 | 4.59-10-4 4.96+10-4
100 6.64-10-4 | 6.76-10-4 | 7.76-10-* | 8.20-10-4 | 9.20-10-4 9.74: 10-4

action cross sections Oy which agree with those
in table 1-4 within 5 percent.

This differential Bethe-Heitler Born-approxi-
mate cross section, without the high energy ap-
proximation and with screening disregarded, has
been integrated analytically by Racah [1934, 1936]
and Jost, Luttinger, and Slotnick [1950], but the
resulting expression contains double and single
integrals over elliptic functions. Recently Maxi-
mon [1968] has derived two series expansions
for this expression, which he integrated to give
the total cross section «#"(Born, unscreened).
The resulting two series, which converge rapidly
at low and high energies, respectively, are:

(a) ForE <2 MeV:

Ke"(Born, unsereened)= 4
(1 +h pr 3 pti pt or ptt .. | o-34)
where
SON (2-35)

(b) For E > 2 MeV:
«2(Born, unscreened)= Be In (2k) — =
+ (i) [6 In (2k) 242 ins(2K) — In? (2k)
atin (2k) +2¢(8) +=
-@ lz In (2k) +3]
-() Ee3 256 In (2h) — 55 wont } (2-36)
where

w3)=> A= 1.2020569 see, (2-37)

These two expansions (2-34) and (2.-36), using
only the terms given here, provide values of
«?4Born, unscreened) accurate to within 0.01 per-


Table 3.—11.

PHOSPHORUS, Z=15

Scattering Pair production Total Total
Photon Photo-
energy electric
With Withot Nuclear Electron With Without With Without
coherent | coherei field field || coherent | coherent |} coherent | coherent
blatom blatom blatom blatom blatom || blatom blatom cml emg
3.99401 9.61400] 2.06-+03 2.10403 2.07+03 |] 4.08401 4.02+01
2.66+01 9.43400] 6.10-+02 6.37+02 1.24401 1.20+01
2.02+01 9.27400] 2.53402 2.73402 5.31400 5.10+00
1.46+01 8.96400] 7.10+01 8.56+01 1.66+00 —1.55+00
1.21401 8.68400] 2.89+01 4.10+01 7.97-01 731-01
1.07401 8.42400] 1.44401 51401 489-01 4.44-01
9.84+00  8.18-+00 1.80+01 350-01 3.18-01
8.71400 7.76400 1.20401 234-01 2.1501
8.00400 7.39400 187-01 1.75-01
6.93-+00 1.4401 1.38-01
6.25+00 1.2501 1.22-01
5.38+00 1.06-01 104-01
4.79+00 4.81400 936-02 9.28-02
4.36+00 4.37+00 850-02 8.46-02
4.03400 4.03+00 784-02 7.82-02
3.54400 3.54400 688-02 6.8602
1.03-02
4.0502
115-01 6.04-04
186-01 2.48-03
249-01 4.87-03
3.0401 7.49-03
3.98-01 1.28-02
4.73-01 1.7502
616-01 2.73-02
720-01  3.50-02
8.66-01 4.66-02
967-01 5.5202
1.04400 6.17-02
1.10+00 6.6802
1.19400 7.47-02
1.25400 8.06-02
1.35+00 — 9.09-02
1.41400 9.7802 1.58400
1.49+00 1.06-01 1.64+00
1.53400 1.12-01 1.68+00
1.56+00 — 1.16-01 1.71400
1.58400 1.19-01 1.72400
1.60400 1.23-01 1.75-+00
1.75-02 1.62400 1.26-01 1.77400
1.22-02 1.65400 1.31-01 1.79400
9.47-03 1.66400 1.3401 1.81+00
6.58-03 1.68+00 1. 1.82+00
4.00-+03 5.08-03 1.69+00
5.00403 416-03 1.69+00
6.00+03 3.52-03 1.70400
8.00403 2.7103 1.70+00
1.00+04 2.22-03 1.70+00
1.50404 153-03 1.71400
2.00+04 1.18-03 1.71400
3.00+04 8.12-04 1.71400
4.00404 6.24-04 1.71400
5.00404 5.08-04 1.71400
6.00-+04 4.29-04 1.71400
8.00+04 3.29-04 1.714001. 3.62-02
1.00+05 2.68-04 1.72400 1.46-01 3.62-02

{bjatom) x 019840 em?le

1



The cross section for photoproduction of nucleon-
antinucleon pairs, as discussed by Vdovin [1957],
Bushev and Vdovin [1958], Segré [1958], Bertram
et al. [1966], and Earles et al. [1967], is three orders
of magnitude smaller than that for photomeson
production. The threshold for nucleon-antinucleon
pair production varies from 3.75 GeV (4 nucleon
masses) in the field of a proton at rest down to 3.0
GeV (3.2 nucleon masses) for protons moving in a
complex nucleus.

2.3. Atomic Photoeffect (Photoelectric
Absorption)

In the atomic photoeffect, a photon disappears
and an electron is ejected from an atom. The elec-
tron carries away all the energy of the absorbed
photon, minus the energy binding the electron to
the atom. The K-shell electrons, which are the
most tightly bound, are the most important for
this effect in the energy region considered in this
report. However, if the photon energy drops
below the binding energy of a given shell (see

table 2.-3), an electron from that shell cannot
be ejected. Hence, a plot of tye versus photon energy
exhibits the characteristic “absorption edges”
which are shown for lead in figure 2.—1.

Although there have been a few direct measure-
ments of tye or Tx in the region between 0.1 and
3 MeV (see, for example, Latyshev [1947], Seeman
[1956], Hultberg and Stockendal [1959], Titus
[1959, 1965], Bleeker, Goudsmit, and DeVries [1962],
Dowe [1965], and Parthasaradhi et al. [1966]),
the best information in the high energy region is
at present mostly theoretical.

Most of the theoretical information has been on
the K-shell component tx (see, for example, Bethe
and Salpeter [1957], Erber [1959], Gavrila [1959],
Pratt [1960a], Nagel [1960], Hultberg et al. [1961],

'8 As a note of caution, it should be mentioned that the high-energy side of an absorp:
tion edge exhibits a fine structure (see, for example, Faessler [1955], Sandstrim (19571,
or Azroft[2963)) such that for light elements, where the K-edge is well below 10 ke'
Tye can oscillate by as much as a factor of five near the edge. However, for the region
above 10 keV considered here, the os less than 10 percent and will be
disregarded, for practical purposes, in favor of a smooth extrapolation from the mono-
tonic region back to the theoretical edge,

TABLE 2-3. Energies of absorption edges above 10 keV
Values are taken from Bearden (1964-1967) except numbers in parentheses, which are from Fine and Hendee (1955)
K-edge K-edge Ty - edge Ly- edge | Lay edge
Element [keV] Element [keV] [keV] {keV] ikeV]

Ga 10,368 wDY 53.793

3Ge 11,104 erHo 55.619

aos 11.865 soET 57.487

Se 12.654 stm 59.38 10.121

Br 13.470 20¥b 61.30 10.490

saKr 14.324 nla 63.31 10.874 10,345

Rb 15.202 Ht 65.31 11.274 10.736

3ST 16.107 nla 67.403 11.682 11.132

Y 17.038 Ww 69.508 12.100 11.538 10.200

Wad 17.999 7pRe 71.658 12.530 11.954 10.531

aNb 18.987 2308 73.856 12.972 12.381 10,868

Mo 20.004 air 76.101 13.423 12.820 11.212

Te 21.047 zePt 78.381 13,883 13.272 11.562

Ru 22.119 AU 80.720 14,354 13.736 11.921

Rh 23.219 woe 83.109 14.842 14.212 12.286

Pd 24,348 atl 85,533 15.343, 14,699 12,660

Ag 25.517 Pb 88.005 15.855 15.205 13.041
26.716 Bi 90.534 16.376 15.719 13.426
27.942 PO (93.112) (16.935) (16.244) (13.817)
29.195 gat (95.740) (17.490) (16.784) (14.215)
30.486 oR (98.418) (18.058) (17.337) (14,618)
31.811 Ft (101.147) (18.638) (17.904) (15.028)
33.166 wRa (103.927) 19.236 18.486 15.444
34.59 eeAc (106.759) (19.842) (19.078) (15.865)
35.987 soTh 109.646 20.464 19.683 16,299
37.452 Pa (112,581) (21.102) (20.311) (16.731)
38.934 115.62 20.771 20.945 17.165
40.453 (118.619) (21.417) (20.596) (17.614)
42.002 (121.720) 23.109 22,253 18.054
43.574 (124.876) (23.793) (22.944) (18.525)
45.198 (128.088) (24.503) (23.640) (18,990)
46.849 (131.357) (25.230) (24.352) (19.461)
48.519 (134.683) (25.971) (25.080) (19.938)
50.233 (138.067) (26.729) (25.824) (20.422)
52.002 (141.510) (27.503) (26.584) (20.912)



Table 3.-14.

POTASSIUM, Z=19

Scattering Pair production Total Total
Photon Photo:
energy electric

With | Without Nuclear | Electron || With Without |] With | Without

coherent | coherent field field || coherent | coherent |} coherent | coherent

MeV blatom ——bfatom blatom blatom blatom || blatom blatom || emg om?le.
1.00-02 |] 6.22+01 1.22401} 5.19403 5.25+03 5.20403 || 8.09+01 — 8.01+01
1.50-02 |] 4.25+01 1.19401 | 1.58+03 1.63+03 — 1.60+03 |} 2.50+01 — 2.46+01
2.00-02 || 3.17+01 1.17401] 6.69+02 7.01402 6.81402 |} 1.08401 1.05+01
3.00-02 |] 2.17401 1.13401 1.93+02 2.14402 2.04402 |} 3.30+00 3.14400
4.00-02 |] 1.73+01 1.10+01] 7.94+01 9.67401 9.04401 || 1.49400 1.39+00
5.00-02 |] 1.49+01 1.07401] 3.98+01 5.A7+01 5.05401 || 843-01 7.77-01
6.00-02 |) 1.35+01 1.04401 | 2.29+01 3.64+01 — 3.33+01 || 5.60-0l — 5.12-01
8.00-02 |] 1.16+01 9.83400] 9.40+00 2.10401 1.92401 |) 3.24-01 2.9601
1,00-01 |} 1.05+01 9.36+00| 4.65+00 1.52401 1.40+01 || 2.33-01 216-01
1.50-01 |} 8.95+00  8.43+00) 1.34+00 1.03+01 —9.77+00 || 158-01 1.50-01
2.00-O1 || 8.02400 7.72+00| 5.5701 8.58+00  8.28+00 || 132-01 1.28-01
3.00-01 |] 6.85+00 6.72400] 1.6401 7.01400 — 6.88+00 || 1.08-01_—-1.06—-01
4.00-01 |] 6.09+00  6.02+00] | 7.17-02 6.16+00 6.09400 || 9.49-02 9.3802
5.00-01 || 5.54400  5.50+00| 3.89-02 5.58+00 — 5.53+00 |) 859-02 8,52-02
6.00-01 |] 5.12+00 5.08400 2.4402 5.14400 5.11400 || 7.92-02 7.8702
8.00~01 |] 4.48+00 4.47400 1.2402 4.49400 4.48400 |} 692-02 6.90-02
1,00+00 || 4.03+00 4.02406} 7.68-03 4.04400 6.21-02  6.20-02
1.50+00 |) 3.27+00 3.26400] = 3.58-03. 3.29+00 5.06-02 — 5.06-02
2.00+00 2.78400 | 2.26-03 4.39-02
3.00+00 2.19400 | 1.2403 3.6602
4.00+00 1.83+00| 8.39-04 3.2802
5.00+00 1,58+00 | 6.38-04 3.0602
6.00+00 1.39400 | 5.06-04 291-02
8.00+00 1.14400 | 3.60-04 2.7602
1,00+01 9.72-01 | 2.80-04 270-02
1.50401 719-01 268-02
2,00+01 5.77-01 2.7302
3.00401 4.20-01 2.86-02
4.00401 3.3401 2.99-02
5.00+01 2.79-01 3.1002
6.00401 240-01 3.19-02
8.00401 1.8901 3.34-02
1,00+02 1.5701 3.45-02
1.50402 112-01 368-02
2.00+02 8.78-02 3.77-02
3.00+02 6.22-02 3.9302
4.00+02 4.8702 4.0202
5.00+02 4.0302 408-02
6.00+02 345-02 4.12-02
8.00+02 2.70-02 4.19-02
1.00+03 2.22-02 4.23-02
1.50+03 1.5502 4.29-02
2.00403 1,20-02 432-02
3.00403 8.34-03 4.3602
4.00403 6.M-03 4.3802
5.00403 5.2603 4.39-02
6.00403 446-03 4.4002
8.00+03 344-03 4.41-02
1,00+04 281-03 4.42-02
1.50-+04 1,94-03 443-02
2.00+04 1.49-03 4.43-02
3.00404 1.03-03. 4.44-02
4.00404 7.90-04 445-02
5.00+04 643-04 445-02
6.00404 544-04 445-02
8.00404 417-04 445-02
1.00-+05 3.39-04 445-02

(atom) 015400 ems

54



3.03+01

Table 3.—23. URANIUM, Z=92
Scattering Pair production Total Total
Photon Photo- —
energy electric
With | Without Nuclear | Electron j[ With | Without With | Without
coherent | coherent field field coherent | coherent |} coherent| coherent
Mev blatom —blatom | blatom | bfatom ——bfatom || bJatom —blatom |] cme ent
1,00-02|] 2.17+03 5.89401] — 6.84+041 7.05+04 6.84404 || 1.78+02 — 1.73+02]
1.50-02 || 1.47+03 5.79401] 2.38+04 2.53+04 — 2.38+04 || 6.39401 6.03401
1.72-02|| 1.27403 5.74401] 1.68-+04 1.81404 1.69404 || 4.58401 4.28+01
L,  1.72-02]] 1.27+03 5.74401] 4.06+04 4.07+04 || 1.06402 1.03+02
2.00-02 |} 1.07+03 5.68401) — 2.70+04 2.71404 |] 7.10401 6.85+01
2.09-02 |] 1.01403 5.67401) 2.38+04 2.38+04 || 6.27401 6.03+01
L, 209-02] 1.01403 5.67401] 3.38+04 3.38+04 |] 8.80401 8.56+01
2.18-02 |] 9.61402 5.65401) —3.06+04 7.98401 7.75+01
L, 2.18-02 || 9.61402 S+01] 3.53404 9.18401 8.95+01)
3.00-02 |} 6.36402 5.50401] 1.56+04 4.10+01 3.96401
4.00-02 |) 4.36402 5.32401} 7.35-+03 1.97401 1.87+01
5.00-02 |] 3.22402 5.16401] 4.07+03 111401 1.04401
6.00-02 |] 2.51402 5.02401] 2.50+03 | 6.96+00
8.00-02 |] 1.68402 4.76401} 1.16+03 3.35400
1,00-01 |} 1.25402 4.53401] 6.31402 1.91400
116-01 |] 1-05+02 4.38401] 4.26402 1.34400
K 4.38401] 1.82+03 4.86+00
4.08+01] 9.36+02 2.56+00
3.74401] 4.48-+02 1.28+00
3.25401] 1.59+02 5.09-01
2.91401] 7.87+01 1.13+02 2.86-01
2.66401] 4.64401 7.65+01 1.93-01
2.46401 3.06+01 5.76+01 1.46-01
2.16401] 1.65+01 3.94401 9.97-02
1.94401) 1.04401 3.07401 7.7602
1.58+01| 4.73+00 2.17401 5.48-02
1.35+01) 2.84400 1.88+01 4.7502
1.06+01| 1.49+00 1.73401 4.38-02
8.85400) 9.58-01 1.72401 4,35-02
7.64+00| 7.02-01 1.76401 4.45-02
6.75+00| 5.4301 1.80+01 4.55-02
5.52400} 3.75-01 1.90+01 4.80-02
4.71400] 2.88-01 2.00+01 5.06-02
3.48400] 180-01
2.80400] 1.31—01
2.04400] 850-02
1.62+00| 6,20~-02 3.16+01
1.35+00] 5.0002, 3.36+01
1.16+00] 4-00-02 3.51401
917-01} 3.00-02 3.75+01
7.62-01}  2.40-02 3.89401
4.17+01
4.34401
4.53401 115-01
4.64401 117-01
4.71401 1.19-01
4.76+01 121-01
4.83401 1.22-01
4.88401
4.94401
4.97401
5.01401
4.96+01 6.7401 5.03+01
4.97401  6.78-01 5.04401
4.98+01  6.80-01 5.05+01
5.00+01 6.8301 5.07+01
5.00401 — 6,85-01 5.07+01
5.01401 6.88-01 5.08+01
5.02401 6.8901 5.00401
5.02401 6.9101 5.09401

{ojatom) x .002830= em



Contents

1. Attenuation and energy absorption coefficients.

1.1. Introduction... 1
1.2. Physical constants; units; notation. 2
1.2.1. Physical constants and conversion factor 2
1.2.2. Notation and units... 3

1.3. Definition and significance of narrow-beam attenuation coefficient. 5
1.4. Tabulation of attenuation coefficients. 9
1.5. Definition and significance of energy-absorption coefficients and related quantities. 9
1.5.1. Modes of energy transfer. 9
1.5.2. Conditions under which the coefficients are useful. 14
1.5.3, Evaluation of the coefficients from the cross section: 15

1.6. Tabulation of energy absorption coefficients. 16
2. Photon cross sections... 21
2.1. Scope... 21
lassification of interactions. 21

. Atomic photoeffect (photoelectric absorption). 4
Scattering... 27
2.4.1, Compton scattering. Klein-Nishina formula. 27
2.4.2, Electron binding corrections toCompton scattering. Rayleigh scattering, 28

2.4.3. Radiative corrections. Double Compton effect . 32

2.5. Electron-positron pair production..
2.5.1. General discussion...

2.5.2. Pair production in the field of the nucleus.

2.5.3. Pair production in the field of an electron.

2.6. Photonuclear absorption.

3. Tabulation of eross sections for elements and compounds.
4. References

iv


Table 3.—3. BORON, Z=5
Scattering Pair production Total Total

Photon Photo-

energy electric

With | Without Nuclear | Electron |} With Without |} With | Without
coherent | coherent field field |] coherent | coherent |] coherent | coherent
MeV blatom — bjatom | blatom | blatom ——Bfatom |] bfatom ——blatom || emg emg

1.00-02 |] 4.61400 3.20400] 1.63+01 2.09+01 1.95401 |! 1.16+00 — 1.09+00
1.50-02 |} 3.95400 3.14400] 4.36+00 8.31400 7.50+00 || 463-01 4.18-01
2.00-02 |} 3.61400 3.09400] 1-68+00 5.29400 4.77+00 |} 295-01 2.66-01
3.00-02 |} 3.25+00 2.90400] 4.52-01 3.70+00 3.44400 |] 2-06-01 1.92-01
4.00-02 |} 3.04400 2.89+00| 1.84-01 3.23+00 — 3.08+00 || 1.80-01 — 1.71-01
5.00-02 |] 2.91400 2.81400) 8.80~02 3.00+00  2.89+00 || 1.67-01 1-61-01
6.00-02 |} 2.80+00 2.73+00] 4.86-02 2.85+00  2.78+00 || 159-01 1.5501
8.00-02 |] 2.63+00 2.59400) 1.89-02 2.64+00 2.60400 |] 147-01 1-45-01
1.00-01 |] 2.49400 2.46+00) 8.97~03 2.50400 2.47400 |} 139-01 1.38-01
1.50-01 |] 2.23400 2.22400] 2.38-03 2.23400 2.22400 |] 124-01 1.24-01
2.00-01 |] 2.04400 2.03+00 9.4104 2.04400 2.03400 |} 114-01 1.13-01
3.00-01 |] 1.77400 1.77400] 2.65-04 1.77-00 1.77400 |} 9.8402 9.85~02
4.00-01 1.58400] 1.13-04 1.58-+00 8.83-02
5.00-01 1.45+00] 6.05~05, 1.45+00 8.06-02
6.00-O1 1.34400] 3.77-05 1.34400 7-45-02
8.00-01 1.18400] 1.90-05, 1.18+00 6.55-02
1.00+00 1.06400] 1.18-05, 1.06+-00 5.89-02
1.50+00 850-01] 5.5106 8.60-01 4.79-02
2.00-+00 7.3301] 3.51-06 737-01 4.1102
3.00-+00 5.77-01| 1.97-06 5.90-01 3.28-02
4.00+00 5.03-01 2.80-02
5.00-+00 4.45-01 2.48-02
6.00+00 4.04-01 2.25-02
8.00-+00 349-01 1.95-02
1.00+01 1.7502
1.50401 149-02
2.00+01 137-02
3.00401 1.25~02
4.00401 1.21-02
5.00401 119-02
6.00+01 118-02
8.00+01 1.18-02
1.00+02 1.19-02
1.50+02 1.22-02
2.00-+02 1.24-02
3.00-+02 1.28-02
4.00-+02 130-02
5.00402 132-02
6.00-+02 1.3402
8.00402 136-02
1.00+03 1.37-02
1.50+03 140-02
2.00+03 141-02
3.00-+03 143-02
4.00+03 144-02
5.00+03 1.44-02
6.00+03 1.45—02
8.00403 1.4502
1,00+04 146-02
1.50-+04 1.46-02
2.00404 1.47-02
3.00404 1.47-02
4.00404 147-02
5.00-+04 147-02
6.00-+04 147-02
8.00+04 1.47-02
1.00405 1.47-02

(biatom) x 085710 emg

43



fable 3.-1. HYDROGEN,
Scattering Pair production Total Total
Photon Photo- —
energy electric
With Without Nuclear | Electron With Without With Without
coherent | coherent field field coherent | coherent || coherent | coherent
blatom —batom blatom blatom blatom || blatom blatom cm*|g cm]

639-01 6.40-01] 4.57-03 6.45—01 || 3.85-01 3.8501
6.28-01 1.13-03 6.30-01 || 3.76-01 — 3.76~01
617-01 4,19-04 6.18-01 || 3.69-01 3.6901
1.03-04 5.98-01 357-01

79-01 3.4601

3.35-01 |

3.26-01

3.0901

2.94-01

2.6501

2.4301

211-01

1.8901

1.73-01

1.60-01

1.40-01

211-01 1.2601

1.72-01 1.03-01

1.46-01 8.7502

1.15-01 4.0205 6.9102

9.6202 1.65-04 5.8102

8.31-02 3.25-04 5.0502

7.3402 499-04 4.5002

6.0102 8.5404 3.7502

5.1102 117-03 3.2502

3.00-+04

4.00-+04
5.00-+04
6.00-+04
8.00+04

1.00+05

8.57-03

8.71-03
8.93-03
9.04-03
9.1603

9.2403
9.27-03
31-03
9.3503

9.37-03
9.4103
9.43-03
9.4503

9.4603
9.47-03
9.47-03
9.48-03

9.48-03

503
8.8203
9.2103
9.47-03
9.88-03
1.0102
1.04-02

1.06~02
1.06-02
107-02
1,08-02

1.09-02
109-02
1.10-02
1.10-02

1.1102
1.1102
1.1102
1.1102

1.1102

2.01-02
2.02-02
2.0302
2.03-02

2.0402
2.0502
2.0502
2.0602

2.0602
2.0602
2.0602
2.0602
2.0602

1.22-02
1.22-02
1.23-02
1.23-02

Dato) x SOTSO0= Emile

41


Table 3.—26. SODIUM IODIDE, Nal

Scattering Pair production Total
Photon Photo

enerey With Withour electric Nuclear Electron With Without

coherent coherent field field coherent coherent

Mev emily emtla omfg onl ontle entle entle
1.00-02 |} 2.53+00 =1.65-01} = 1.36+02 1.39402 — 1.36+02
1,50-02 |] 1.69+00 1.62-01|  4.57+01 4.74401 4.59+01
2.00—-02 || 1.23+00 = 1.59-01} 2.11401 2.23+01 = 2.12+01
3.00-02 |} 7.48-01 1.5401} 6.70+00 7.45+00 — 6.86+00
3.3202 |} 6.60-01 1.52-01 | 5.03-+00 5.69400 — 5.19+00
*3.32-02 || 6.60-01 1.52-01 | 3.03+01 3.09+01 3.04401
4.00-02 |} 5.28-01  1.49-01} = 1.88+01 1.93+01 1.89+01
5.00—02 |} 4.10-01 144-01 1.03+01 1.07+01 —1.05+01
6.00-02 |} 3.36-01 1.40-01 | 6.28+00 6.62400  6.42+00
8.00—02 |} 2.49-01 133-01 | 2.87+00 3.12400 — 3.00+00
1.00-01 || 2.02-01 1.27-01| 1.52+00 1.72+00 — 1.64+00
1.50-01 149-01 1.1401] 4.76-01 6.25-01 —5.90-01
2.00-01 }} 1.24-01 —-1.05-01]  2.09-01 3.34-01 3.1401
3.00-01 || 9.99-02 9.09-02] 6.68-02 167-01 1.58-01
4.00-O1 || 864-02  8.15—-02| 3.10-02 117-01 1.12-01
5.00-01 || 7.78-02 7.4402} 1.77-02 955-02 9.2102
6.00-01 |} 7.12-02 6.88-02) 1.1402 8.26-02 8.0202
8.00-01 |} 6.17-02 6.0502 5.88—-03 6.7602 — 6.63-02
1.00+00 |} 5.49-02 5.43-02| = 3.66-03 5.86-02 — 5.80-02

4.69-02 4.6602
413-02 4.1202
1.0305 || 3.66-02 3.66—-02

4.25-05 |] 3.51-02 3.5002

1.50+00 |} 4.45-02  4.42—02 1.66—-03
2.00+00 || 3.78-02  3.77-02|_—-1.02-03
3.00+00 || 2.97-02 2.97-02}  5.46-04

4.00+00 || 2.48-02 2.47-02} 3.61—-04

5.00+00 2.14—02| 2.70-04 8.35-05 3.4602
6.00+00 1.89-02] 2.1104 1.28-04 3.47-02
8.00+00 1.5402] 1.47—04 2.20-04 3.5502
1.00+01 1.32-02 1.13-04 3.0004 3.68-02
1.50+01 9.73-03 | 7.08-05 4.68—-04 4.02-02
2.00+01 7.81-03 | 5.14-05 5.97-04 4.3302
3.00+01 5.69-03 | 3.31—-05 7.82-04 4.8402
4.00+01 4.52-03 | 2.45—-05 9.13—-04 5.20-02
5.00+01 3.77-03 1.94-05 1.01-03 5.4802
6.00+01 3.25—-03 | 1.60—-05 1.09-03 5.7102
8.00+01 2.56-03 | 1.19-05 1.2203 6.0502
1.00+02 2.13-03| 9.52-06 1.31-03 6.29-02
1.50+02 1.5203 1.46-03 6.7002
2.00+02 1.19-03 1.5603 6.9502
3.00+02 8.42-04 1.69-03 7.2402
4.00+02 6.59-04 1.77-03 7.4102
5.00+02 5.4604 1.82-03 7.5202
6.00+02 4.6804 1.87—03 7.60-02
8.00+02 3.6504 1.92-03 7.7102
1.00+03 3.00—-04 1.9603 7.7802
1,50+03 2.10-04 2.02—03 7.8902
2.00+03 1.6204 2.06—-03 7.9402
3.00+03 113-04 2.09-03 8.00-02
4.00+03 8.71-05 2.11-03 8.0302
5.00+03 7.1205 2.13-03 8.05—02
6.00+03 6.04—-05 2.1403 8.07-02
8.00403 4.65~-05 2.15-03 8.08-02
1.00+04. 3.80-05 2.16—-03 8.09-02
1.50+04 2.63-05 2.17-03 8.11-02
2.00+04 2.0205 2.18-03 8.1202
3.00+04. 1.30-05 2.18-03 8.13-02
4.00+04 1.0705 7.9102 -2.19-03 8.13-02
5.00+04 8.7006 7.9202 2.19-03 8.1402
6.00+04 7.3606 7.92-02 2.1903. 8.1402
8.00+04 5.64~06 7.93-02 2.1903 8.15—02

1.00+05 4.59-06 7.93-02 — 2.19-03 8.15—-02

6A



TABLE 1-4,

(Continued)

PHOTON |ALUMINUM| SILICON SULFUR | ARGON | PorassiuM | CALCIUM IRON
ENERGY | Z=13) | Z=14 Z=16 2=18 2-19 Z=20 2%

Mev omile
1.00 —02 2.58+ 01 3.36401 4.02+ 01 5.03+ 01 8.01 + 01 9.56+ O1 1.72+ 02
1.50 —02 7.66 + 00 9.97 +00 -20+01 | 1.52+01 .' 2.46+01 2.96+ 01 5.57+01
2.00 —02 3.24400 4.19400 | 5.10+00 6.42 + 00 8.274 00 1.05+ 01 1.26401 2.51401
3.00 -02 1.03 +00 1.31400 1.55 +00 1.94-+ 00 2.48+ 00 3.14+00 3.82+ 00 7.884 00
4.00 —02 5.14—-01 731-01 8.91—01 1.11+ 00 1.39+ 00
500-02 | 334-01 | 3. au—01 | 527-01 | 630-01 | 7.77-01
6.00 — 02 2.55-01 2.92—01 3.18—-01 3.67—OL 4.20—01 5.12-01
8.00 —02 1.89—01 2.07—O1 215-01 2.38-01 2.52-01 2.96 —O1
1.00—01 1.6201 1.7301 1.75-01 1.89-01 1.89-01 2.16—01
1.50-01 1.34—01 140-01 1.38-01 136-01 150-01
2.00-01 1.20~01 1,.25-01 1,22-01 117-01 1,28—01
3.00-01 | 103-01 1.07—01 1.04-01 9.79 —02 1.06 —O1

|

4.00 —01 9,22 —02 9.28—02 8.68 — 02 9.38—02 9.66 — 02 9.21 —02
500-01 8.41—02 8.46 — 02 7.90 —02 8.52 —02 8.78—02 8.29—02
6.00—01 7.77 —02 7.82 —02 7.29 -02 7.87 —02 8.09—02 7.62 —02
800-01 | 6.8302 6:86 —02 640-02 | 690-02 | 709-02 6.65
1,00 +00 6.14—02 6.17 —02 5. 6,20—02 6.37 —02
1.50+ 00 5.00—02 5.03 —02 4.69—02 5.06 — 02 5.20—02
2.00+ 00 4.3202 4.36 —02 4.07 —02 4.39—02 4.52 — 02
3.00 +00 3.54-02 3.59-02 3.38—02 3.66 — 02 3.78 — 02
4.00 +00 3.11—02 3.02 —02 3.28—02 3.40—02
5.00 +00 2.84—02 2.80 —02 3.06 — 02 3.17—02
6.00 + 00 2.66 —02 2.67—02 2.91 —02 3,03 — 02
8.00+ 00 2.44—02 2.51—02 2.76 —02 2.89—02
1,00+ 01 2.31 —02 2.44— 2.70-02 2.83 — 02
1.50401 2.19—02 2.41— 2.68—02 2.83 —02
2.00401 2.16—02 | 244-02 | 2.73~02 2.89—02
3.00401 2.19-02 2.42—02 2.55 — 0: 2.86 — 02 3.05 — 02
4.00401 2.2402 2.50 —02 2.70—02 2.66—02 2.99—02 x
5.00401 2.30 —02 2.57—02 2.78—02 2.75— 02 3.10—02 z 02
6.00 +01 2.35 —02 2.64—02 2.86 - 02 2.84—02 3.19—02 . 02
8.00401 2.44—02 2.74—02 2.98 — 02 2.96 — 02 3.34—02 4. 02
1.00 + 02 2.51 —02 2.83 — 02 3.06 3.45 — 02 4.32 — 02
1.50 +02 2.63 — 02 2.98 —02 3. 3.68 —02 4.58—02
2.00 +02 2.71—02 3.07 -02 3. 3.77—02 4.75 — 02
3.00 + 02 2.82 —02 3.1902 3. 3.93 — 02 4.94 — 02,
4.00 + 02 2,88 —02 3. 4.02 — 02 5.06 — 02,
5.00 + 02 2.92 -02 3. 4.08 —02 5.14—02
6.00 +02 2.95 —02 3. 4.12—02 5.19—02
8.00 +02 3.00 -02 . 4.19—02 5.27-02
1,00 +03 3.02 —02 4 02
1,50 + 03 3.07 -02 4.29—02 02
2.00 +03 3.09 —02 4.32 — 02
3.00 +03 3.12—02 4.36 02
4.00 + 03, 3.13 —02 4.38—02 — 02
5.00 +03 3.1402 4.39—02 —02
6.00 + 03 3.15—02 4.40—02 —02
8.00 +03 3.16—02 4.41 —02 -02
1.00 + 04. 3.16 —02 3.59 -02 | 4.42 -02 5 — 02
1.50 + 04 3.17—02 3.60—02 4.43 — 02 6 — 02
2.00 + 04 3.17-02 3.61—02 4.43 —02 6 — 02
3.00 + 04 3.18 —02 3.61 —02 4.44—02 7 — 02
4.00+04 | 3.18—02 3.61 — 02 4.45 — 02 4.77—02 5.57 —02
5.00+ 04 3.18—02 3.62 —02 4.45 — 02 4.78—02 5.58—02
6.00 + 04 3.18—02 3.62 —02 4.45 — 02 4.78—02 5.58— 02
8.00 + 04 3.18—02 3.62 —02 | 4.45—02 4.78—02 5.58 — 02
1.00 +05 3.19-02 3.62—02 | | 4.45 —02 4.78—02 8 — 02

iW



Table 3.-13.

ARGON, Z=18

Scattering Pair production Total Total
Photon Photo: -
energy electric
With Without Nuclear Electron With Without With Without
coherent | coherent field field |] coherent | coherent |] coherent | coherent
MeV |) blatom —bfatom | blatom | blatom ——bfatom |} b/atom dlatom || emg emg
1.00-02 |} 5.66+01 1.15401] 4.22403 4.28403 4.23403 |} 6.45+01 6.38401
150-02 |] 3.84401 1.13401 1.28+03 1.32403 1.29403 |] 1.99401 1.95+01
2.00-02 |] 2.87+01 1.11401] 5.37+02 5.66402 5.48+02 |] 8.53+00 8.27400
3.00-02 |] 1.97401 1.08401] 1.54402 1.74402 1.65+02 |] 2.62400 2.48+00
4.00-02 |] 1.59401 1.04401] 6.34401 7.93+01 — 7.38+01 |] 1.20+00 — 1.11+00
5.00-02 | 1.38401 1.01401] 3.17401 4.55401 4.18401 |] 687-01 — 6.30-01|
6.00-02 |} 1.25+01 9.82400] 1.80+01 3.05+01 — 2.78+01 |] 4.60-01 4.20-01
8.00-02 |} 1.09401 9.31+00| | 7.40-+00 1.83+01 1.67401 |) 2.75-01  2.52-01
8.87400] 3.65+00 1.35+01 2.0401 1.89-01
7.98+00| 1.05+00 9.49+00 143-01 1.36-01
7.32400] 4.34-01 8.01400 121-01 1.17-01
6.36400] 1.28-01 6.61400 9.96~02 9.79-02
5.70+00] 5.5702 5.82+00 8.78-02 8.6802
5.21400] 3.0102 5.27400 7.95-02 —7.90-02
4.82400] 1.8902 4.86+00 733-02 7.29-02
4.23400] 9.60-03, 4.25400 641-02 6.40-02/
3.80+00|  5.95—03 3.82+00 5.7602 5.7502
3.09400] 2.77-03 3.11400 4.70-02  4.69-02
2.64400) 1.75—03 4.0702
2.08+00]  9.66-04 3.38-02
1.73+00] 6.52-04 3.0202
1.49400] 4.9604 2.80-02
1.32400] 3.9404 2.67-02
1.08+00]  2.81—04 251-02
921-01] 219-04 2,44-02
681-01 2-41-02
5.4701 244-02
3.98-01 2.55-02
3.16-01 2.66-02
2.64-01 2.7502
2.28-01 : 2.8402
1.79-01 : 2.96-02
1.49-01 1.78+00  9.60-02 3.06~02
1.06~01 1.94400 — 1.08-01 3.25-02
8.32-02| 2.02+00  1.16-01 3.34-02
5.8902 2.12400 1.26-01 3.48-02
4.6202 2.18400 1.3301 3.56-02
3.82-02 2.22400 1.37-01 3.61-02
3.27-02 2.25+00 1-41-01
2.56-02 2.29400  1.46-01
2.10-02 2.31400 1.49-01
147-02 2.35+00  1.55-01
114-02 2.37+00  1.58-01
7.90-03 2.39400 1.62-01
6.10-03 2.40400 1.64-01
4.99-03 2.41400 1.65-01
423-03 2.41400 1.66-01
3.26-03 2.42400 —1.67~01
2.66-03 2.42400 1.68-01
1.84-03 2.43+00 1.69-01
141-03 2.43400 1.69-01 :
9.75-04 2.44400 1.70-01 3.93-02
7.48-04 2.44400 1.70-01 3.93-02
6.09-04 2.44400 1.71-01 3.93-02
5.15-04 2.44400 1.71-01 3.94-02
8.00+04 3.9504 2.44400 1.71-01 3.94-02
1.00+05, 3.21-04 2.44400 1.71-01 3.9402

{jatom) 015080 omg



Table 3.-19. TIN, Z=50

Scattering Pair production Total Total
Photon —_ Photo: —________} —
energy electric
With Without Nuclear Electron With Without With Without
coherent } coherent field field coherent | coherent {| coherent — coherent

Mev blatom ——blatom blatom bjatom bjatom |} blatom —bfatom omg cm}

1.00-02 |[ 5.38402 3.20+01 2.79404 2.74404 |} 1.41402 1.39+02
1.50-02 |] 3.60+02 3.14401 9.27403 8.94403 ]] 4.70401 4.53+01
2.00-02 |} 2.59402 3.09401 4.21403 — 3.98+03 }) 2.13401 2.02+01
2.92-02 |} 1.61402 2.99401 1.49403 1.36+03 || 7.54+00 — 6.88+00.
K  2.92-02 |] 1.61+02 2.99401 8.73403 8.60+03 |] 4.43401  4.37+01

3.00-02 |] 1.56+02 2.99401) 7.98403 8.14403 8.01403 |] 4.13401 — 4.07+01
4.00-02 }} 1.10402 2.89401) —3.70+03 3.81403 —3.73+03 |) 1.94401 1.89+01
5.00-02 |] 8.44+01 2.81401] 2.02403 2.10+03 — 2.04+03 |} 1.07+01 1.04401
6.00-02 |] 6.85+01 2.73401) 1.22403 1.29403 1.25+03 || 6.53400 6.32+00
8.00-02 |} 5.02+01 2.59401) 5.45402 5.95402 5.71402 || 3.02+00 — 2.90+00
1.00-01 |] 4.05+01 — 2.46+01] —2.90+02 3.31402 —3.15+02 |] 1.68+00 — 1.60+00
150-01 |} 2.96+01  2.22401{ 9.15+01 1.21402 1.14402 |] 6.14-01 5.7701
2.00-01 |] 2.45+01 2.03401] 4.02401 6. 3.28-01 3.07-01

164-01 1.55-01

116-01 1.10-01
9.46-02 9.1102
8.1602 7.9102

3.00-01 |} 1.96+01 1.77401] 1.28+01

4.00-01 |] 1.69401 —1.58+01| 5.93400
5.00-01 |] 1.51401 1.45401! 3.50400
6.00-01 || 1.39401 1.34401] 2.20400
8.00-O1 }} 1.20+01  1.18+01] —1.15+-00

1.00+00 |} 1.07+01 5.7802

1,50+00 |} 8.65+00 4.6302

2.00+00 |] 7.36+00 4.10-02

3.00+00 |} 5.77+00 3.6702

4.00+00 |} 4.82+00 4.81400] 6.93-02| 2.10400 3.5502

5.00+00 |] 4.16400  4.15+00]  5.18-02] 2.74400 3.5402

6.00+00 |] 3.68+00 3.67+00] 4.05-02} 3.2900 3.5702

8.00+00 3.00+00|  2.83-02| 4.21400

1.00+01 2.56400] 2.1802] 4.95+00

1.50+01 1.89+00] 1.37-02| 6.38+00

2.00+01 1.52+00| 9.94-03| 7.44400

3.00+01 1.11+00| 6.41-03| 8.92400 1.52-01

4.00+01 8.79-01| 4.73-03 | 9.92400 1.77-01

5.00+01 7.3401 1.07+01

6.00+01 6.3201 1.12401

8.00401 4.98-01 1.21401

1,00+02 1.27401 6.7702
1.50+02 1.36401 7.21-02
2.00+02 1.42401 7.48-02
3.00402 1.49401 7.80-02
4.00+02 1.53+01 7.98-02
5.00+02 1.55401 8.10-02
6.00-+02 1.5701 8.19~-02
8.00+02 1.59401 8.3102
1.00+03 1.61401 8.38-~-02
1.50+-03 1.63401 8.4902
2.00-+03 1.64401 8.56-02
3.00+03 1.66401 8.6202
4.00+03 1.66+01 8.65-02
5.00+03 1.67+01 8.67-02
6.00+03 1.67+01 8.68-02
8.00+03 1.67401 8.7002
1,00+04 1.68401 8.7102
1.50+04 1.68+01 8.73-02
2.00:+04 1.68+01 8.74-02
3.00+04 1.68401 8.7502
4.00+04 1.68401 8.7602
5.00+04 1.69401 8.77-02
6.00+04 1.69401 8.77-02
8.00-+04 1.69401 8.7702
1.00405 1.69+01 8.77-02

(ator) x 005074=em#l=



TABLE 1.-5. Gamma-ray linear attenuation coefficients w[cm~], for various materials of interest in shielding.

Except for slight revisions for air. this is the compilation by Hungerford [1960] from data in the Hogerton-Grass Reactor Handbook (1955).

A Linear attenuation coefficient fem~]
Material Density @ Sent atom
{g/em*] 1 MeV 3 MeV 6 MeV

Air*) (20 °C, 76 cm Hg pressure) 0.001205 0,0000765 0.0000431 0.0000304
Aluminum 2.7 0.166 0.0953 0.0718
Ammonia (liquid) 0.771 0.0612 0.0322 0.0221
Beryllium 1.85 0.104 0.0579 0.0392
Beryllium carbide 1.9 0.112 0.0627 0.0429
Beryllium oxide (hot-pressed blocks) 23 0.140 0.0789 0.0552
Bismuth 9.80 0.700 0.409 0.440
Boral 2.53 0,153 0.0865 0.0678
Boron (amorphous) 2.45 0.144 0.0791 0.0679
Boron carbide (hot pressed) 25 0.150 0.0825 0.0675
Bricks

Fire clay 2.05 0.129 0.0738 0.0543

Kaolin 21 0.132 0.0750 0.0552

Silica 1.78 0.113 0.0646 0.0473
Carbon 2,25b) 0.143 0.0801 0.0554
Clay 2.2 0.130 0.0801 0.0590
Cements

Colemanite borated 1.95 0.128 0.0725 0.0528

Plain (1 Portland cement: 3 sand mixture) 2.07 0,133 0.0760 0.0559
Concretes

Barytes*) 3.5 0.213 0.127 0.110

Barytes-boron frits*) 3.25 0,199 0.119 0.101

Barytes-limonite®) 3.25 0.200 0.119 0.0991

Barytes-lumnite-colemanite*) 31 0.189 0.112 0.0939

Tron-Portland¢) 6.0 0.364 0,215 0.181

MO (ORNL mixture) 5.8 0.374 0.222 0.184

A 2.2 0.141 0.0805 0.0592

Portland®) (1cement: 2sand: 4 gravel mixture) { 24 0.154 0.0878 0.0646
Flesh) 1.0 0.0699 0.0393 0.0274
Fuel oil (medium weight) 0.89 0.0716 0.0350 0.0239
Gasoline 0.739 0.0537 0.0299 0.0203
Glass

Borosilicate 2,23 0.141 0.0805 0.0591

Lead (Hi-D) 6.4 0.439 0.257 0.257

Plate (avg) 2.4 0.152 0.0862 0.0629
Iron 7.86 0.470 0.282 0.240
Lead 11.34 0.797 0.468 0.505
Lithium hydride (pressed powder) 0.70 0.0444 0.0239 0.0172
Lucite (polymethyl methacrylate) 1.19 0.0816 0.0457 0.0317
Paraffin 0.89 0.0646 0.0360 0.0246
Rocks

Granite 2.45 0.155 0.0887 0.0654

Limestone 2.91 0.187 0.109 0.0824

Sandstone 2.40 0.152 0.0871 0.0641
Rubber

Butadiene copolymer 0.915 0.0662 0.0370 0.0254

Natural 0.92 0.0652 0.0364 0.0248

Neoprene 1.23 0.0813 0.0462 0.0333
Sand 2.2 0.140 0.0825 0.0587
Type 347 stainless steel 7.8 0.462 0,279 0.236
Steel (19% carbon) 7.83 0.460 0.276 0.234
Uranium 18.7 1.46 0.813 0.881
Uranium hydride 11.5 0.903 0,504 0.542
Water 1.0 0.0706 0.0396 0.0277
Wood

Ash 0.51 0.0345 0.0193 0.0134

Oak 0.77 0.0521 0.0293 0.0203

White pine 0.67 0.0452 0.0253 0.0175

* From table 3.-27,
» Graphite theoretical density. See table 1.~1, footnote ****,
© Concrete mixtures for shielding reported by Gallaher and Kitzes (1953},
4 Elemental composition, wt %: hydrogen, 1.0; oxygen, 52.9; silicon, 33.7; aluminum, 3.4; iron, 1.4; calcium, 4.4; magnesium, 0
: potassium, 1
* Composition, wt %: oxygen, 65.99; carbon, 18.27; hydrogen, 10.15; nitrogen, 3.05; calcium, 1.52; phosphorus, 1.02.

sarbon, 0.1; sodium,

13


Foreword

The National Standard Reference Data System is a Government-wide effort to provide for the
technical community of the United States effective access to the quantitative data of physical
science, critically evaluated and compiled for convenience, and readily accessible through a
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The responsibility to administer the System was assigned to the National Bureau of Stand-
ards and an Office of Standard Reference Data was set up at the Bureau for this purpose. Since
1963, this Office has developed systematic plans for meeting high-priority needs for reliable ref-
erence data. It has undertaken to coordinate and integrate existing data evaluation and compilation
activities (primarily those under sponsorship of Federal agencies) into a comprehensive program,
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Government agencies, academic institutions, and nongovernmental laboratories. The independent
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that are components of the NSRDS produce compilations of critically evaluated data, critical
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The NSRDS —NBS series of publications is intended primarily to include evaluated reference
data and critical reviews of long-term interest to the scientific and technical community.

A. V. Astin, Director.

iii


White-Grodstein [1957] compilation, and then note
how the present evaluation differs.

White-Grodstein used as an initial approxi-
mation the Bethe-Heitler theory done in the Born
approximation (Bethe and Heitler [1934], Heitler
and Sauter [1933], and Racah [1934, 1935]). In the
energy region E <5 MeV, where screening effects
are negligible, cross section values for an un-
screened nucleus were obtained from a formula of
Hough [1948], which fits the Bethe-Heitler results
to 0.1 percent. For E>>5 MeV the differential
Bethe-Heitler formula, including screening based
on the Thomas-Fermi model of the atom (Bethe
and Heitler [1934, eq (36)], also Bethe and Ashkin
(1953, eq (114)]), was integrated numerically
over the energy distribution between the pair
particles to obtain «2#(Born).

Corrections to the Born approximation values
were applied at all energies. These corrections were
derived from:

(1)Calculations of Jaeger and Hulme in the energy
range E < 5 MeV,

(2) Calculations of Davies, Bethe and Maximon
for E >5 MeV, and

(3) Experimental data.

The results of Jaeger and Hulme [1936] and
Jaeger (1936, 1941] were obtained by numerical
solution of the Dirac equation and indicate consid-
erable departures from the Born approximation near
threshold, especially for high-Z elements. For ex-
ample, for tin at 3 mc? (~1.533 MeV) the ratio of
their result to that from formulas based on the
Born: approximation is 1.30, while for lead at 3mc
this ratio is 1.97, dropping to 1.24 at 5.2mc?
(= 2.66 MeV).18

The calculation of Davies, Bethe, and Maximon
[1954] for an unscreened nucleus went beyond the
Born approximation, using Sommerfeld-Maue
[1935] wave functions rather than plane waves.
Their results lead to the appearance of a negative
Coulomb correction

28 22

— ‘DBM — — —s! Z =
Akn 9 7/4)» (2.-28)
where f(Z) may be evaluated from the sum
F(Z) = a2[(1 + a2) 1 + 0.20206 — 0.0369 a?
+0.0083 a4—0.002a8+---], 2-29)

in which
a=Z/137.

In their approximation (neglect of terms of order
In k{k and 1/k) the Coulomb correction remains the
same whether screening is absent, partial, or com-
plete.

“Recently Overbp [1967] has extended the Jaeger-Hulme results to include 8 ele-
rents a through ye and energies ranging from 2.001 mc® (1.0225 MeV) to 65 met
(3.32 MeV).

34

In her tabulations in the energy range E < 5 MeV,
White-Grodstein used the Hough formula to cal-
culate «8(Born) and then applied graphically-
interpolated values of the Jaeger-Hulme correction.
In the range E>5 MeV she fitted the relevant
corrections by a semi-empirical formula

kn(White-Grodstein) = «2#(Born) — Ax2#M

ink
ak

where the terms «#(Born) and—Ax?2" were
computed as explained above. The additional
term J?(In k)/k was adjusted to give better agree-
ment with experimental data, particularly those of
Colgate [1952] and Paul [1954] and to provide a
smooth transition to the low-energy results of
Jaeger and Hulme.

In the present revision, use was made of a slightly
different semiempirical formula

+B (2-30)

kn= [x24 (Born, unscreened) — s#"5]
*[1+A (rad. corr.)] — A (empirical) « Ax?TM,
(2-31)

which, although not necessarily more accurate than
eq. (2.-30), covers the entire energy range from
threshold to the high energy limit. Values of kn
computed using eq (2-31) are presented in table
2-10 in the scaled form x,/Z? for ease of
interpolation.

New data taken into account in this revision are:
(a) the near-threshold expressions by Maximon
[1968] of x8" (Born, unscreened) as given in
equations (2-34) and (2.-36),
the screening correction s#S (in table 2.-13)
calculated by Sérenssen [1965, 1966] using
Hartree-Fock-Slater wave functions (Hanson
et al. [1964]) for 0<q<0.3 and the Thomas-
Fermi model of the atom for 0.3<q<8.0
where g is momentum transfer in me units,
the radiative correction of Mork and Olsen
[1965] given in table 2.-1]1, and
an empirical correction to the Born approxi-
mation entered as ar energy-dependent cor-
rection factor (given in table 2.-11) applied to
the high-energy Coulomb correction AK?5
given in table 2.12, since both corrections vary
approximately as Z* and are large and of op-
posite sign near threshold.'® The latter correction
takes into account additional x, experimental
data including measurements by Standil and
Shkolnik [1958] and Titus and Levy [1966],
and total attenuation data by Barkan [1956],
Hiibel, Roh, and Scheer [1959] and Barlett and
Donahue [1965].

(b)

(d)

' Maximon has derived an energy dependence (see table 2-11) for the Coulomb
correction, giving the modified correction [1— (2/7)(9k'—6k-*-+4k-*) ] - Ax28!,
as quoted by Koch [1964] and Sirenssen [1965, 1966], which goes to zero at threshold.
However, this improved Coulomb correction stil resulis in a negative theoretical cross
section near threshold if no empirical correction term is added.


Table 3.—36.

PYREX GLASS, (Corning 7740)

Seattering Pair production Total

Photon Photo

energy With Without electric Nuclear Electron With Without

coherent | evherent eld feld coherent | coherent

MeV emg cml cml emt) cmlg cme emg
1.00-02 |} 5.36-011.92-01 } 1.65+01 1.71401 1.67+01
1.50-02 |} 3.79-01 1.88-01 | 4.76+00 5.14400 4.95+00
2.00-02 |} 3.06-01 1.8501 | 1.94400 2.25+00 2.13400
3.00-02 |] 240-01 1.79-01) 5.46-01 786-01 7.24-01
4.00-02 |] 2.10-01 1.73-01 | 2.21-01 4.3101 3.94-01
5.00-02 |] 1.93-01 1.6801 | 1.09-01 302-01 -2.77-01
6.0002 |] 1.81-01 1.6301 | 6.1502 242-01 2.25-01
8.00-02 |) 1.65-01 1.55-01 | 2.47-02 1,90-01 — 1.80-01
1.00-01 || 154-01 1.47-01 | 1.21-02 1.6601 1.60-01
1.50-01 || 136-01 1.33-01 | 3.3403 139-01 1.36-01
2.00-01 |} 1.2301 1.22-01] 1.3603 1.2501 1.23-01
3.00-01 |] 107-01 1.06-01 | 3.9504 1.0701 1.06-01
4.00-01 |] 953-02 9.48-02 | 1.71-04 954-02 9.5002
5.00-01 |} 869-02 8.66-02| 9.23-05 8.70-02 8.6702
6.00-01 |} 803-02 8.01-02 | 5.7705 8.04-02 8.0202
8.00-01 7.04-02 | 2.9105 7.0402
1.00+00 6.33-02 | 1.80-05 6.33-0z
1.50+00 5.14-02 | 843-06 | 1.40-04 5.1602
2.00+00 4.30-02 | 5.35-06 | 5.53-04 4.44-02
3.00+00 3.45-02 | 2.96-06 | 1.58-03  1.20-05 3.6102
4.00+00 2.88-02 | 2.01-06 | 256-03 4.95-05 3.14-02
5.00+00 2.49-02 | 1.46-06 | 343-03 9.72-05 2.8402
6.00+00 2.20-02 | 1.22-06 | 4.20-03 1.49-04 2.63-02
8.00+00 1.8002] 8.71-07 | 5.49-03 2.5604 2.37-02
1,00+01 153-02] 6.82-07 | 654-03 3.50-04 222-02
1.50+01 1.13-02 852-03 5.44-04 2.04-02
2.00+01 9.10-03 9.9603 6.99-04 1.9802
3.00401 6.6203 1.20-02  9.31-04 1.9502
4.00+01 5.26-03 134-02 — 1.10-03, 1.9802
5.00+01 4.39-03 145-02 1.2403 2.01-02
6.00+01 3.78-03 153-02 1.3403 2.04-02
8.00+01 2.98-03 1.6502 1.51-03 210-02
1.00+02 2.48-03 1.7402 1.63-03 2.15-02
1,50+02 1.76-03 189-02 1.84-03 2.25-02
2.00:+02 1.3803 1.9802 1.99-03 2.32-02
3.00+02 9.80-04 2.09-02  2.17-03 2.40-02
4.00+02 768-04 2.1502 2.29-03 2.4502
5.00+02 6.36-04 219-02 2.3803 2.49-02
6.00+02 5.44-04 222-02 2.44-03 2.52-02
8.00+02 4.2504 2.2602 254-03 2.56-02
1.00+03 3.50-04 2.29-02 — 2.60-03 2.58-02
1.50+03 244-04 232-02 2.71-03 2.62-02
2.00+03 1.89-04 234-02 2.78-03 2.64-02
3.00+03 1.31-04 2.37-02 — 2.85-03 2.67-02
4.00+03 1.01-04 2.38-02 — 2.90-03 2.68-02
5.00+03 8.29-05 2.39-02 2.9203 2.69-02
6.00+03 7.0305 239-02 —2.94-03 2.69-02
8.00+03 5.42-05 2.40-02 2.97-03 2.70-02
1.00+04 442-05 240-02 2.9803 2.71-02
1.50404 3.06-05 241-02 3.01-03 2.7102
2.00+04 2.35-05 2.41-02 — 3.02-03 2.72-02
3.00+04 1.62-05 242-02 — 3.04-03 272-02
4.00+04 1.24-05 2.42-02 — 3.04-03 2.72-02
5.00-+04 1.01-05 2.42-02 — 3.05-03 2.72-02
6.00-404 8.57-06 2.42-02 — 3.05-03
8.00404 6.57-06 242-02 — 3.06-03 2.73-02
1.00+05 5.34-06 2.42-02 — 3.06-03 2.73-02

16



Solid-line boxes indicate the major effects contribu

1 percent over particular energy ranges.

TABLE 2-1. Classi

‘ation of elementary photon interactions.
0 photon attenuation in matter. Dotted-ine boxes indicate additional effects which contribute more than

Type of interaction . Scattering Multi-photon
Absorption Elastic Inelastic effects
Interaction with: (coherent) (incoherent)
(a) (b) {c) (a)
(1) Atomic electrons Photoelectric effect Rayleigh Compton i ‘Two-photon
scattering, scattering, Compton
{ 724 dow energy) op ~Z? oonZ scattering,
pe | ~Z® (high energy) I Z
(2) Nucleons ‘Photonuciear reactions Elastic nuclear Inelastic
(y, n), (y, p), Photo- scattering, nuclear
fission, etc. (yn y)~Z? scattering,
Diam Z wr’)
(E = 10 Mev)
(3) Electric field (i) Electron-positron Delbrick
surrounding pair production in scattering,
charged particles field of nucleus, ~Zt
Hy ~ZP
(E = 1.02 MeV)
(2) Blectron-positron
pair production in
electron field,
Xe ~Z
(E = 2.04 MeV)
(3) Nucleon-antinucleon
pair production
(E = 3 GeV)
(4) Mesons Photomeson production, Modified
(E = 150 MeV) (yy) —
‘at T
700
j
Ficune 2-1, Relative contributions of the various
- Photon interactions as functions of energy for carbon,
0 iron, and lead.
In these plots the vertical distance betueen curves represents the percent
contibution of the indicated process tothe sum "eta eoce wie ee
% | tables in section 3)
&
SL tht See)
}—
0 it | Ss
sana:
% 1% +
9 mel
at Pol \ |
inl iL
a tail Ltt wee
We 07 M2

7
Photon energy [MeV]


Library of Congress Catalog Card No. 73-600412


Table 3.—6. OXYGEN.

Scattering Pair production
Photon —
energy
With Without Nuclear Electron Without
coherent | coherent field field coherent
Mev bjatom —bJatom | bjatom | bfatom ——blatom || blatom ——blatom || emt/g emg
1.00-02 |] 1.06+01 — 5.12+00 1.54402 1.48402 |] 5.78400 5.58+00
1.50-02 || 8.00+00 —5.03+00 4.61401 4.31401 | 1.74+00 — 1.62+00
2.00-02 |} 6.84400 4.94-+00 2.19401 2.00401 |] 826-01 7.54-01
3.00-02 || 5.74400 4.78+00 9.87400 8.91400 || 3.72-01 3.3501
4.00-02 |{ 5.20+00 4.63400 6.84400 6.27400 2.3601
5.00-02 |] 4.87+00 4.49400 5.67+00 5.29400 |] 213-01 1.99-01
6.00-02 |] 4.63+00  4.36+00 5.08400 4.81400 || 1.91-01— 1.81-01
8.00-02 |] 4.29400 4.14400 4.47400 4.32400 |] 168-01 1.62-01
1.00-01 |} 4.05+00 4.13400 4.03400 || 1.56-01
1.50-01 |} 3.60+00 3.62400 1.3601
2.00-01 |} 3.27+00 3.28-+00 1.2401
3.00-01 2.84-+-00 1.07-01
4,00-01 2.54400 957-02 9.5402
5.00-01 2.32400 873-02 8.7102
6.00-01 2.15+00 808-02 8.06-02
8.00-01 7.08-02
1.00+00 z 1.69+00 6.37-02
1.50+00 : 1.38400 5.1802
2.00+00 : 1.18+00 446-02
3.00-+00 9.23-01 3.22-04 9.5601 3.60-02
4.00+00 7.69-01 32-03 8.24~01 3.10-02
5.00+00 6.65-01 2.60-03 738-01 2.78-02
6.00+00 5.87-0L 3.99-03 6.7801 2.55-02
8.00400 480-01 6.83-03 6.01-01 2.26-02
1.00+01 4,09-01 934-03 5.5401 2.09-02
1.50401 3.03-01 1.4502 4.95~01 1.8602
2.00+01 2.43-01 1.87-02 4.69-01 1.77-02
3.00401 177-01 2.4902 4.52-01 1.70-02
4.00+01 1.41-01 2.95-02 4,49-01 169-02
5.00+01 117-01 ; 3.31-02 452-01 1.70-02
6.00+01 1.01-01 - 3.6102 4.56-01 1.72-02
8.00+01 7.9802 346-01 4.05-02 4.66-01 1.7502
1.00+02 6.62-02 365-01 4,39-02 4.75-01 1.79-02
1.50+02 4.72-02 397-01 497-02 4,94-01 1.8602
2.00-+02 3.70-02 4.17-01 5.3602 5.08~01 1.91-02
3.00+02 2.6202 440-01 5.8702 5.25~01 1.98-02
4.00+02 2.05-02 454-01 6.21-02 5.3701 2.02-02
5.00402 1.70-02 6.44-02 2.05-02
6.00+02 145-02 6.62-02 2.07-02
8.00+02 114-02 6.88-02 210-02
1.00+03 9.3403 7.0702 2.12-02
1.50+03 6.53-03 737-02 2.16-02
2.00-+03 5.05-03 756-02 2.18-02
3.00-+03 3.51-03 7.78-02 2.2002
4.00+03 2.71-03 7.90-02 2.21-02
5.00+03 2.22-03 7.98-02 2.22-02
6.00+03 1.88-03 2.22-02
8.00+03 145-03 2.23-02
1.00+04 1.18-03 2.23-02
1.50404 8.17-04 2.24-02
2.00404 6.28-04 224-02
3.00+04 433-04
4.00+04 3.33-04 2.25-02
5.0004 2.71-04
6.00404 2.29-04
8.00+04 1.7504
1.00+05 143-04 2.25-02

(byatom) x 037690)

‘ewe

46


The binding corrections have usually been treated
in the impulse approximation, taking into account
not only the K-shell, but all the atomic electrons.
This involves applying a multiplicative correction,
the so-called “incoherent scattering function,”
S(q, Z), to the differential Klein-Nishina formula
leq. (2.-6)]

doc (0)/dO. =S(q, Z)dok* (6) /dQ. (2.-18)

The momentum transfer q is related to the photon
energies and deflection angle @ according to

q= VE+K?—2kk cos 6, (2-19)

or, using eq (2-3),
Oo ap a) .

q=2k sin 5° V1+ (22+ 2k) sin? 6/ (1+ 2k sin? 6),

(2.-20)

where q is in mc units and & and k’ are the photon
energies (in mc® units) before and after the deflec-
tion. Since binding effects are important mainly
for small momentum transfers, the approximation
k—k' ~0 is usually made, so that

q~ 2k sin $ (2-21)

The incoherent scattering function S(q, Z) repre-
sents the probability that an atom be raised to any
excited or ionized state as a result of a sudden im-
pulsive action which imparts a recoil momentum
q to an atomic electron. For K-shell electrons only,
S(q, Z) would correspond to the ratios shown in
figure 2.-2.

Rayleigh scattering is a process by which photons
are scattered by bound atomic electrons and in
which the atom is neither ionized nor excited. The
scattering from different parts of the atomic charge
distribution is then “coherent,” i.e., there are
interference effects.

This process occurs mostly at low energies and
for high Z materials, in the same region where
electron binding effects influence the Compton
scattering cross section. Indeed, if each atomic
electron contributed independently to the cross
section, the onset of Rayleigh scattering for low
momentum transfer would exactly compensate for
the reduction of Compton scattering due to binding.
However, the various atomic electrons contribute
coherently to Rayleigh scattering, greatly increas-
ing the probability for the process.

We shall restrict the following discussion to Ray-
leigh scattering in the narrower sense, in which the
coherence extends only over the Z electrons of
individual atoms. This coherence can also extend
to electrons of different atoms to give more striking

interference effects, such as Bragg-law diffraction
by crystal lattices.

Experimental studies of Rayleigh scattering have
been made by Moon [1950], Storruste [1950], Wilson
(1951), Mann [1956], Schopper [1957], Storruste and
Tjom [1958], Anand, Singh, and Sood (1963, 1964],
and Nath and Ghose [1964]. In interpreting these
measured data, one must also take into account
other, much less probable, elastic or quasi-elastic
scattering processes, such as Thomson scattering
by the nucleus, nuclear resonance scattering, and
Delbriick scattering (see sec. 2.2.), in addition
to Rayleigh scattering. Theoretical information on
these processes, including constructive interfer-
ence effects between the different processes, has
been summarized by Moon [1950] and by Jauch and
Rohrlich [1955].

Detailed Rayleigh scattering calculations have
been made by Levinger [1952] for K-shell electrons
of tin, and by Brown et al. [1954-1957] for K-shell
electrons of mercury. In practice, it is necessary to
consider the charge distribution of all Z electrons
at once. This can be done approximately through
use of an “atomic form factor” F(q, Z) based on
the Thomas-Fermi, Hartree, or other model of the
atom. The square of this form factor, [F(q, Z)P,
is the probability that the Z electrons of an atom
take up a recoil momentum, g, without absorbing
any energy. In this process q is well-represented
by (eq (2.21) since it is assumed that k—k'=0.
The above probability [F(q, Z)F, is combined
with the low-energy limiting form of the Klein-
Nishina differential formula [eq (2.—6)] to give the
differential Rayleigh scattering cross section for
unpolarized photons:

fd “m2;
dox(0)/d0 = (1+ cos *0)[F(q, 2)? [aver
(2-22)

Calculations of S(q, Z) and F(q, Z) depend
on knowledge of the atomic wave functions; they
can be done analytically for hydrogen and, for
other atoms, in various approximations based on
the Thomas-Fermi, Hartree, or other models. The
procedures used in such calculations have been
discussed by White-Grodstein [1957] for S(q, Z)
and by Nelms and Oppenheimer [1955] for F(q, Z)-

Evaluations of o8? have until recently used
S(q,Z) values based on the Thomas-Fermi model.'7
However, Cromer and Mann [1967] have now pro-
vided Hartree-Fock S(q, Z) data for the 39 spher-
ically symmetric atoms. Corresponding Hartree-
model tabulations of F(q, Z) have been given by
Hanson et al. (1964] and by Cromer and Waber
[1965].

"In addition to the Grodstein [1957] (and Davisson [1965}) results, extensive evalu:
ations of a based on the Thomas-Fermi model have been given by Brown (1966b]
1€Z=100, 1 keV to MeV and by Veigele [1965]: 1<Z<106, 0.1 keV to 1 MeV.

30


and k is the photon energy in mc? units. Below
10 MeV, ke is less than 2 percent of a, and experi-
mental estimates (see, for example, the recent
results of Frei, Staub, and Stiissi [1964]) still con-
tain uncertainties too large for confirmation of
present theory.

2.6. Photonuclear Absorption

This effect consists of nuclear interactions ini-
tiated by the absorption of a photon. The most likely
result of such an interaction is the emission of a
single neutron, but one must also consider the emis-
sion of charged particles, gamma rays, or more than
one neutron. Available experimental and theo-
retical information on such interactions is discussed
in review articles by DeSabbata [1957, 1959],
Levinger [1960], Fuller and Hayward [1962], Hay-
ward [1963], Brenig [1965], and Danos and
Fuller [1965].

The most characteristic feature of the cross sec-
tion for nuclear absorption of photons is the “giant
resonance.” This is a broad peak in the absorption
cross section centered at about 24 MeV for light
nuclei, decreasing in energy with increasing mass
number to about 12 MeV for the heaviest stable
nuclei. The width “I” (energy difference between
the points at which the cross section drops to one
half its maximum value) varies from about 3 MeV
to 9 MeV depending on the detailed properties of
individual nuclei.

When studied with finer resolution the gross
“resonance” is found to have considerable sub-
structure, A prominent feature of this sub-structure,
for nuclei having large permanent deformations, is
a splitting of the giant resonance into two main
peaks. In general, those nuclei having either large
permanent deformations or large “dynamic deforma-
tions” (resulting from the vibrational nature of the
nuclear ground state) have their giant resonances
spread over the widest energy range.

Table 2-16 gives the gross parameters of the
giant resonance for a representative group of nuclei
throughout the periodic table. From these para-
meters the giant resonance can be approximately
reconstructed by assuming that it has the shape of
a Lorentz line (see, e.g., Fuller and Hayward
[1962], eg. (2.5), p. 117):

Er?
© °° Ch? BE?) + BT?

Opn. n.(E) (2.-44)

As indicated in table 2.-16, the magnitude of
the photonuclear absorption cross section, even at
the resonance peak energy, Eo, is small in compari-
son with the sum of the competing “electronic”
cross sections discussed in sections 2.3 to 2.5, and
in no case contributes more than 10 percent to the
total cross section. However, photonuclear absorp-
tion can be of considerable importance in shielding
and irradiation technology whenever photon energies

are present which exceed reaction threshold
energies such as those indicated in table 2.16.

In shielding technology (see, e.g., NBS Handbook
97 [1964] and Hubbell and Spencer [1964]) nuclear
absorption of photons is important because neutrons

are produced in a large fraction of the reactions
(about 40 to 100 percent probability depending on
the photon energy and the mass number of the
particular nucleus). These neutrons are usually
far more penetrating than the incident photons.
Of importance in irradiation technology (see, e.g.,

TaBLe 2-16. Photonuclear giant resonance cross section
parameters.!

| |

Threshold Percent

energies | ou,value | I, peak fof “elec
Nucleus —| Sfamie [widtrai{teone”| Refs!

anpeak |"half- | cross

om) (pb | max. | section

Mey Mev | Mey | bfatom | Mev | 9%
2 18.7 16.0] #23, | 40.018] 3.6| 5.9 | 63Bu3
Al 13.1 83) #215 | 4.038) 9.0| 3.9 | 64Do2
“Ca 15.7 83] 2205 4.100) 45] 5.2 | 66Do2
Cu 10.8 61] 17.0) 5.070] 80| 20) 64Ful
Zp 120 84! 170] 5.180] 45| 3.0 |67Be2
pall 91 62) 152) §.210| 5.7! 23 |66Brl
15Ho, 80 6.1 | #140] *.220) 85| 1.7 )65Am1
Ta 76 62} 2140 *.280| 65| 1.8 |63Brl
28Ph 74 80] 136] $495! 38] 27 )6¢Ha2
235) 61 76 | %122] 7.500] 7.0] 2.4 |64Bo3

' This table was supplied by E. G. Fuller.
*References (as given in the Photonuclear Data Inde:
63 Br1 Bramblett, R. L., Caldwell, J. T., Auchampaugh, G. F.,
Fultz S. C.; Phys. Rev. 129, 2723 (1963).

63-Bu 3 Burgov, N. A., Danilyan, G. V., Dolbilkin, B. S.,
Lazareva, L. E., Nikolaev, F. A.; Zhur. Eksp. i Teoret.
Fiz. 45, 1693 (1963); Soviet Phys. JETP 18, 1159
(1964).

64.Bo 3 Bowman, C. D., Auchampaugh, G. F., Fultz, S. C.
Phys. Rev. 133, B676 (1964).

64Do 2 Doibilkin, B. S., Zapevalov, V. A., Korin, V. L, Laza-
reva, L. E., Nikolaev, F. A.; PICNS-64' 1060 (1964).

64Ful Fultz, S. C.; Bramblett, R. L., Caldwell, J. T., Harvey,
R. R.: Phys. Rev. 133, B1149 (1964).

64Ha2 Harvey, R. R., Caldwell, J. T., Bramblett, R.
Fultz, S. C.; Phys. Rev. 136, B126-131 (1964).

65Am1 Ambler, E., Fuller, E. G., Marshak, H.; Phys. Rev.
138, 117 (1965)

66Br1 Bramblett, R. L., Caldwell, J. T., Berman, B. L.
Harvey, R. R., Fultz, S. C.; Phys. Rev. 148, B1198
(1966).

66 Do2 Dolbilkin, B. S., Zapevalov, V. A., Korin, V. 1., Laza-
reva, L. E., Nikolaev, F. A’; Izv. Akad. Nauk fiz. 30,
349 (1966); Bull. Acad. Sci. USSR—Phys. 30, 354
(1966).

67 Be2 Berman, B. 1. Caldwell J T.. Harvey, R. R.. Kelly

‘Bramblett, R. L., Fultz, S.
162. 1098 (1967).

®Cross section has structure, Energy
mean energy for photon absorption.

4Total nuclear absorption cross section at Ev.

5 Maximum absorption cross section resulting in production
of neutrons. For these nuclei this is a good approximation to the
total nuclear absorption cross section.

®Deformed nuclei. Absorption cross section has two peaks.
Comments under footnote 5 apply.

TIncludes photofission cross section. Comments under foot-
notes 5 and 6 apply.

Phys. Rev.

given is approximate


Pratt et al. [1964], Hall and Sullivan [1966], Gorshkov
[1967], Forssner [1968], and Hultberg et al. (1968),
but some calculations including L- and higher-shell
contributions are now available (see, for example,

Pratt [1960b], Gavrila [1961], Alling and Johnson
[1965], Matese and Johnson [1965], Schmickley and
Pratt [1967], Brysk and Zerby [1968], and the ex-
tensive results by Rakavy and Ron [1967] which in-
clude almost all the higher shells and cover the range
1 keV to 2 MeV). Uncertainties in 7x due to screening
and other effects are probably about 2 percent over
the region from 0.2 to 100 MeV. However, the un-
certainty of the total tpe(=tx+7.+7+" * +) is
probably more like 3 to 5 percent because of much
poorer knowledge of the outer shell contribution,
which amounts to as much as $ of 7x for the heavier
elements.

Extensive theoretical results for the photoeffect
in the soft x-ray region (0.1 to 2 keV) are now be-
coming available (Cooper [1962, 1964], Fano and
Cooper [1965], Manson and Cooper [1968], and
Fano and Cooper [1968]). The work of these authors
is based on the solution of the Schrodinger equation
in the dipole approximation, using self-consistent-
field wave functions. Numerical results are given
for the photoelectric absorption in various outer
atomic subshells, with emphasis on the detailed
structure of the cross section near threshold. These
papers also provide a survey of recent experimental
results in the soft x-ray region obtained with syn-
chrotron light and other soft x-ray sources.

In the energy range 10 keV to 0.2 MeV, although
the Rakavy-Ron calculations are in considerably
better agreement with experiments than are pre-
vious theoretical results, present estimates of Tpe in
this region still rely heavily on high-precision total
attenuation coefficient measurements such as those
of Hahn [1934], Cuykendall [1936], Jones [1936],
Laubert [1941], Bearden [1958, 1966], Deslattes
[1958], Wiedenbeck [1962]; McCrary, Plassmann
et al. [1967], and others.

From these measurements “experimental”
values of Tpe are obtained by subtracting theoretical
estimates of the scattering cross sections o#?+or
from the observed values of oye.

In the present tabulation in the region 10 keV =
=E=100 keV, we follow the subtraction proce-
dure, using re-evaluated experimental oj, data and
scattering cross sections (o#?+ or) from Storm and
Israel [1967], except for uranium for which 7p. is
taken directly from Rakavy and Ron. Values of
Tye for tin, tungsten and lead in this energy were
taken from a computer-assisted subtraction and
analysis in progress (McMaster, Del Grande et al.)
and hence constitute a further updating of Tpe, Ttot
and related quantities from values given by Hubbell
and Berger [1968].

At higher energies we present revised values for
Tpe Which take into account not only the numerical
calculations of tx by Pratt et al. [1964] used by
Davisson, but also the extensive 7x calculations by
Hultberg et al. [1968]. Although we use the results

25

of Gavrila [1959] and Pratt [1960a] in the high energy
limit, we ignore, on the advice of Pratt, the extrapo-
lated values of 7x in table 2 in Pratt [1960a] for
Z/137=0.4 and 0.6 at energies E=2, 3, 5 and 10
MeV.

‘As can be seen in table 2.—4, tye varies over a
wide range of magnitudes, decreasing with in-
creasing energy except at the edges and increasing
with atomic number. To make interpolation more
reliable and convenient, it is important to scale
these values in some way. It was found that the
product Tye‘ (E[MeV])?-Z-45 (above or between
absorption edges) varies by less than a factor. of
three over the range Z=1 to 92 and E= 10 to 500
keV, and the product tye E[MeV]-Z-** by less
than a factor of ten for Z=1 to 92 and E=500 keV
to 100 MeV. Values of these products are presented
in table 2.-5.

For some purposes, particularly in machine com-
putations, simple empirical formulas are desirable.
An empirical formula for the K-shell photoeffect
above 0.2 MeV is

aes Ee

A

ant bb bad

b
Tte2 ° | QT)

atom,

TABLE 2-4. Total atomic photoeffect cross section Ty. (blatom),
indicating the range of magnitudes
Photon Te
energy _
[MeV]
oC aFe oePb
0.01 | 3.93-10' | 1.59- 108
0.10 | 2.16-10-? | 1.89- 10! K,, Ledges
1.0 | 2.89-10-| 3.38- 10-2
10 1.12-10-° | 1.19- 10-8
100 1.01 -10-7 | 1.04- 10-4

for which the parameters ap, bn, Cn and pn are given
in table 2.-6. This formula goes to the Pratt [1960a]
numerical values in the high energy limit and
reproduces the combined experimental and theo-
retical data fairly well. Deviations from these data
over most of the range 0.2 MeVSE<~o and
13 SZ = 92 are less than 1 to 2 percent, and in no
case do they exceed 5 percent over this range.
For other empirical formulas see Biggs and Light-
hill [1967].

Total tpe values, such as those given in tables
2-4 and —5, can be obtained approximately by
multiplying tx by the ratios tpe/tx from table 2-7.
Hultberg [1959] suggested that, for practical pur-
poses, this ratio is energy-independent, and the
values. in table 2-7 are those derived by Davisson
[1965] from the compilation by Kirchner [1930]
of experimental K-edge data.

For elements ,H through 531 the Davisson-Kirchner
ratios agree within 2 percent with the latest K-
edge ratios in the compilation in progress by


1.4. Tabulation of Attenuation Coefficients

Table 1.—4 contains mass attenuation coefficients,
wip [cm2/g], obtained by inserting in eq (1.-5)
values of Ns/M-10-* [(cm?g)/(b/atom)] from
table 1-1 and yalues of oo: combined from individ-
ual cross sections quantitatively discussed in sec-
tion 2. Specifically, we have used for oy, the sum

Sto ~ Tre + Oo +K (1.-8)
of the photoelectric absorption (tpe), Compton col-
lision (ac) and pair production () cross sections per
atom. For reasons discussed in section 2.4.2. the
Rayleigh scattering cross section, or, is omitted
from the sum in eq (1.—8) in table 1.—4. Hence, our
resulting values of y/p correspond to the columns
“total, without coherent (scattering) of White-
Grodstein [1957] and Davisson [1965].

Values of the attenuation coefficient including
coherent scattering and the effect of electron bind-
ing on incoherent scattering are given in the tables
in section 3. The relative importance of these effects
is indicated in table 2-15. The photonuclear effect
has been omitted from the tables in section 3 but
could be included using information in section 2.6.
Values of u/p extrapolated to the absorption edges
can be found in the tables in section 3.

For convenience, we have reproduced in table
1-5 the Hungerford [1960] compilation of linear
attenuation coefficients, u [cm-'], at 1, 3, and 6
MeV for a number of common materials associated
with shielding. With the exception of air, these
values have not been revised, but agreement with
table 1.—4 is within 1 to 2 percent.

Estimated uncertainties:

Due to gaps in available experimental data, and
the various approximations and ranges of appli-
cability of different theories, the accuracy of the
Bip entries in table 1-4 is not the same for all
values of E and Z. In the regien dominated by the
Compton effect, we estimate the uncertainty to
be about ] percent. Estimates of uncertainties for
low-, medium- and high-Z materials are as follows:

(1) Low-Z materials:

For elements hydrogen through oxygen this 1
percent uncertainty estimate extends from 100
MeV down to about 30 keV. Below 30 keV uncer-
tainties of as much as 5 to 10 percent may be
present because of (a) poor knowledge of the photo-
effect for low Z’s, (b) corrections to experiments for
high-Z impurities and (c) departures of the Compton
cross section from Klein-Nishina theory. Above
100 MeV the contribution of the triplet cross section
(see sec. 2.5.3) is increasingly important and strongly
affected by screening. The theory of the triplet
cross section has, except for hydrogen (Wheeler and
Lamb [1939]) and for results for He by Knasel[1968],
so far only been worked out with the Thomas-Fermi
model of the atom. Uncertainties in y/p from this
source may be 5-10 percent.

(2) Medium-Z materials:

For elements sodium through copper uncer-
tainties of 1 to 2 percent are present at low ener-
gies (10 keV to 1 MeV) because of uncertain par-
titioning of experimental totals into photoeffect
and scattering totals. At medium energies (1 to
100 MeV) uncertainties of 2 to 3 percent are pres-
ent because of uncertainties in the pair produc-
tion cross section, particularly in the 10 to 30
MeV photonuclear giant resonance region. Above
100 MeV the pair production in the field of both
nucleus and electrons is better-known theoreti-
cally than at lower Z. Uncertainties in p/p in
this region are estimated to be 1 to 2 percent.
(3) High-Z materials:

For elements molybdenum through uranium the
uncertainties at low energies (10 keV to 1 MeV)
range from 1 to 2 percent far from an absorp-
tion edge to 5 to 10 percent in the vicinity of an
edge. In the range 1 to 100 MeV uncertainties
from pair production estimates are 2 to 3 per-
cent and above 100 MeV 1 to 2 percent.

The high-energy data from 100 MeV to 100
GeV in this report are based completely on theory.
As shown in figure 1—3, they are in general agree-
ment with available experimental data up to
13.5 GeV.

1.5. Definition and
Absorption
Quantities

ignificance of Energy-
Coefficients and Related

1.5.1. Modes of Energy Transfer

The effects of gamma rays on irradiated media
are largely indirect, i.e., they occur via electrons
(or positrons) which are set in motion as a result
of gamma ray interactions with matter, and then
dissipate their energy as they are brought to
rest. The relation between electron (or positron)
energy deposition in a medium and the various
physical, chemical, and biological effects is com-
plicated and, in most cases, not well understood.
However, it is commonly assumed that the amount
of energy absorbed per unit mass of the medium
(absorbed dose) is a significant parameter which
provides a basis for discussing radiation effects.

The transfer of energy from photons to elec-
trons, and vice versa, takes place in a complex
chain of events with feedbacks as indicated in the
flow diagram in figure 1.-4.8 Following this flow
diagram, a complete treatment of an energy depo-
sition problem should take into account all indi-
cated energy transfer routes leading to electron
collision losses and associated typical effects
such as are listed in the bottom triangle.®

* Although the diagram in fig. 1-4 treats electrons and positrons alike, there are

actually small differences in the rates by which they lose energy (see Nelms [1956,
1958) and Berger and Seltzer (1964).
* Additional energy transfer routes, not shown in fig. 1.~4,

of nuclear absorption. The neutrons, charged particles and gami
such an event will, in turn, either directly or indirectly transfer
energy to electrons. These additional routes were disregarded by
Allison [1961] and in the present work.

reer (1961),


Table 3.-21. TUNGSTEN.

Scattering Pair production
Photon Photo. [-____
energy electric
With | Without Nuclear | Electron
coherent | coherent field field
MeV blatom ——_blatom blatom blatom blatom
1.00-02 ]]1.38+03 4.74401 | 2.78+04
1.0202 ||1.35+03 4.74401 | 2.63404
Ls 102-02 ]}1.35+03 — 4.74+01 7.04404
1.1502 |!1.20+03 4.71401 | 5.06+04
LT, —1.15-02]/1.20+03 4.71401 | 7.05+04
1.2102 |}1.14+03 4.70401 | 6.17404
L, — 1.21-02/]1.14+03 4.70401 | 7.45+04
1.50-02 || 8.99+02
2.00-02 || 6.39+02
3.0002 |] 3.88+02
4.00-02 || 2.65+02
5.00-02 |} 1.96-+02
6.00-02 || 1.54402
6.9502 || 1.28+02
K 6.9502 ||1.28+02
8.00-02 || 1.07+02
1.00-01 |] 8.13+01
150-01 || 5.38+01
2.00-01 || 4.20+01
3.0001 |] 3.15+01
4.00-01 |] 2.65+01
5.00-01 |] 2.34+01
6.00—01 |] 2.12+01
8.00-01 |] 1.82+01
1.00+00 |] 1.61+01
1.50+-00 |] 1.30+01
2.00+00 |] 1.09+-01
3.00+00 |] 8.57+00 2.98-03
4.00+00|]7.16+00 7.1200 1,22-02
5.00+00|]6.17+00 6.1500 2.40-02
6.00+00|]5.45+00  5.43+00 3.69-02
8.00-+00 ||4.45+00 4.4400 6.32-02
1.00+01 |} 3.80+00 — 3.78+00 8.6402
1.50+01 2.80+00 1.34-01
2.00+01 2.25+00 16-01
3.00+01 1.64400 219-01
4.00+01 1.30+00 2.55-01
5.00+01 1.09+00 2.83-01
6.00+01 9.3501 3.05—01
8.00+01 7.38-01 3.38-01
1.00+02 6.13-01 3.6201
1,50+02 4.3601 4.02-01
2.00+02 3.42-01 4.27-01
3.00+02 2.42-01 459-01
4.00+02 1,90-01 4.80-01
5.00+02 1.5701 4.94-01
6.00+02 1.3401 5.04-01
8.00+02 1.05-01 5.18-01
1.00+03 8.64-02 5.27-01
1.50+03 6.0402 5.40-01
2.00+03 4.67-02 5.48-01
3.00:+03 3.25-02 5.5601
4.00:+03 2.51-02 3.38401 5.60-01
5.00-+03 2.05-02 3.30401 5.6301
6.00+03 1.74-02 3.40+01 — 5.65-01
8.00+03 1.34-02 3.40401 5.6801
1.00+04 1.0902 3.41401 5.70-01
1,50+04 756-03 3.41401 5.72-01
2.00+04 5.8103 3.42401 5.73-01
3.00-+04 4.01-03 3.42401 5.75-01
4.00+04 3.08-03 3.42401 5.7601
5.00+04 2.51-03 3.43401 5.76—-01
6.00+04 2.12-03 3.43+01 5.7601
8.00+04 1.62-03 3.43401 5.77-01
1.00+05 1.32-03 3.43401 5.77-01

Total

With

coherent

blatom

2.92404
2.77+04
7.18+04
5.17404
1.17404
6.29404
1.56404
4.34404
2.05+04
7.01403

3.2603
1.80403
1.12403
7.60-+02
3.46403
2.41403

1.35403
4.80402
2.37+02
9.75401

5.79+01
4.15+01
3.29401
2.44+01

2.00+01
1.52401
1.33401
1.23401

1.22401
1.24401
1.27401
1.34401

1.42401

Total

7.05-+04
6.18-+04
7.45404
4.251404
1.99+04
6.67403

3.0403
1.65+03
1.00+03
6.71402
3.37403
2.34403

1.31403
4.59-+02
2.25-+02
9.22401

5.48+01
3.95+01
3.15+01
2.36+01

1.95+01
1.49401
1.32401
1.22+01

1.22401
1.24401
1.27+01
1.34401

1.41401
1.60+01
1.76+01
2.01+01

2.19+01
2.32+01
2.42+01
2.58+01

2.69+01
2.87401
2.98+01
3.11401

3.18+01
3.23+01
3.26+01
3.31401
3.34401
3.38+01
3.40+01
3.43+01
3.44401
3.45+01
3.45+01
3.46+01

3.47+01
3.47+01
3.48+01
3.48+01

3.48+01
3.48+01
3.48+01
3.48+01

3.48401

With) Without

lcoherent_| coherent

emg om*/g

9.55+01 9.12401
9.07+01

(iat) x 008276=

carla


The author is particularly indebted to M. J. a number of other including F. Biggs, A. B. Chilton,
Berger and U. Fano for suggestions and comments J. W. Cooper, R. D. Deslattes, R. D. Evans, S.
on the manuscript, and to E. G. Fuller for supply-  Meshkov, and R. H. Pratt. The author also thanks
ing material presented in section 2.6. Helpful in- S. Seltzer for computational assistance.
formation and corrections were also received from

77


Table 3.—7.

SODIUM, Z=11

Scattering Pair production Total Total
Photon Photo-
energy, electric
With | Without Nuclear | Electron || With Without || With — | Without
coherent | coherent field field |] coherent | coherent |{ coherent | coherent
Mev blatom ——_bjatom blatom blatom blatom || blatom blatom cm?|g cm?|g
1.00-02 }} 2.19401 7.04400] 5.69+02 5.76+02 |} 1.55+01 1.51401
2 1.49401 — 6.92+00| 1.60-+02 1.67402 |] 4.58+00 — 4.37+00
. 1.18+01  6.80+00| 6.48+01 7.16+01 |] 2.01400 — 1.88+00
3.00-02 |} 9.11400 6.57400] 1.78+01 2.44401 || 7.05-01 6.3901
4.00-02 |} 7.90+00  6.37+00| 7.18+00 1.35+01 || 3.95-01
5.00-02 |} 7.19+00 3.53+00 9.71400 || 2.81-01
6.00-02 || 6.73+00 1.99400 7.99+00 || 2.28-01
8.0002 || 6.11+00 7.92-01 6.48+00 || 1.81-01
1.00-01 |} 5.69+00 3.85-01 5.80+00 |] 1.59~01
1,50-01 |] 5.01400 1.06-01 4.99+00 |] 1.3401
2.00-01 |} 4.5400 4.29-02 4.51400 |] 1.20~01
3.00-01 || 3.92+00 1.24-02 3.90+00 || 1.03~01
4.00-01 || 3.50+00 5.3103 3.49400 || 9.1802
5.00-01 |} 3.19+-00 2.86-03 3.18+00 || 8.36--02
6.00-01 |] 2.95+00 1.78-03 2.95+00 || 7.7402
8.00-01 9.0104 2.59+00
1.00+-00 2.33+00|  5.58-04 2.3300
1.50+00 1.89+00} 261-04 1.90+00
. 1.63+00
4.43-04 1.33400
1.82-03 1.16+00
3.57-03 1.05+00
5.4903 9.7701
9.40-03 8.85-01
1.28-02 8.31-01
2.00-02 7.70-01
2.57-02 7.50-01
3.4202 7.4701
4.0502 758-01
4.5502 7.72-01
4.9402 7.87-01
5.5302 8.12-01
5.98-02 8.33-01
6.7502 8.72-01
7.27-02 8.9701
7.95-02 9.30-01
8.38-02 9.50-01
8.69-02 9.64-01
8.9202 9.74-01
9.26-02 9.87-01
9.50-02 9.9601
9.89-02 1.01+00
1.01-01 1.02+00
1.04-01 1.03+00
1.05-01 1.03+00
1.06-01 1.04400
1.07-01 1.04400
1.08-01 1.04+00
1.08-01 1.04400
1.09-01 1.04-+00
1.10-01 1.05+00
1.1001 1.05+00
1.10-01 1.05400
111-01 1.05+00
1.1101 1.05-++00
1.11-01 1.05+00
1-01 1.05+00

Plato) x 026200= enh

47



Table 3.-9. ALUMINUM, Z=13

Photon
energy

Scattering

With

coherent

Without

coherent

Photo:
electric

Nuclear
field

Pair production

Total

Total

Electron
field

With

coherent

Without
coherent

With

coherent

ithout

coherent

8.00401

1.00+02
1.50+02
2.00+02
3.00+02
4.00+02
5.00+02
6.00-+02
8.00+02

1.00+03

3.00+04

4.00+04
500-04
6.00+04
8.00-+04

1.00405

blatom

3.04401
2.03+01
1.57+01
1.17401

9.89+00
8.88+00
8.22+00
7.38+00

6.83+00
5.96+00

blatom

8.32400
8.17+00
8.0300
7.77400

7.52400
7.30+00
7.09+-00
6.72400

6.41400

blatom

1,15+03
3.35+02
1,37+02
3.85+01

1,55+01
7.65+00

bjatom

1.13-+00

1.16+00
1.18-+00
1,19+00
1.22+00

1.23400
1.2500
1.26+00
1.27400

1.28+-00
1.28+00
1.28+00
1.29400

1.29+00
1.29400
1.29400
1.30400

1.30400
1.30+00
1.30400
1.30400

1.30400

bfatom

5.2304

2.1503
4.22-03
6.49-03
111-02
1.52-02
2.3602
3.03—-02
4.04-02

4,79-02
5.3602
5.8102
6.5102

7.03-02

bjatom

1.18+03
3.55+02
1.53402
5.02+01
2.54+01
1.65+01
1.25401
9.11400

7.67+00
6.19+00
5.49+00
4.67+00

4.15+00
3.78+00
3.49+00
3.06-+00

2.75+00

bfatom

1.16-+03
3.43+02

A5+02
4.63+01

2.30+01
1.49+01
1.14401
8.4500

7.25+00

2.75+00
2.24400
1.94400
1.59400
1.39+-00
1.27400
1.19+00
1.09+00

1.04400
9.80—01
9.68-01
9.81-01

1.01400
1.03+00
1.05+00
1.09+-00

1,12+00
1.18+00
1.21400
1.26+00

1.29400
1.31+00
1.32+00
1.34400

1.35+00
1.37+00
1.38+00
1.40+00

1.40+00
1.41400
1.41400
1.41400

1.42+00
1.42400
1.42400
1.42+00

1.43+00
1.43400
1.43+00
1.43+00

1.43+00

em*le

2.63+01
7.93400
3.41400
1.12400

5.67-01
3.69-01
2.80-01
2.03-01

171-01
1.38-01
1.2201
1.04-01
9.27-02
8.44-02
7.80-02
6.84-02

6.1302

cm*}g

2.58+01
7.66+00
3.24400
1.03+00

5.1401
34-01
501

2.3102
2.19-02
2.1602
2.19-02

2.24-02
2.30-02
2.3502
2.44-02

2.51-02
2.6302
2.7102
2.8202

2.88-02

(Bjatom) x 022320 emg

49



TaBLE 1.-4. (Continued)

MOLYB-
PHOTON | COPPER | DENUM TIN TUNGSTEN URANIUM | ABSORPTION
ENERGY Z=29 Z=42 Z=50 z= Z=92 EDGES
Mev omg
100-02 | 2.23402 | 84o+o1 | 1.39402 | 1s8+02  fffaiz+o1 1.28-+02 1.73 +02
150-02 | 7.33+01 | 2.68+01 | 4.53+01 | 5.34+01 139402] [1.12402 6.03 +01 Ln EDGE
ee BT
200-02 | 3.30+01 | 1.17401 | 2.02401 | 2.47401 6.51401 StF 01 6.85 +01
. L, EDGES
300-02 | 1.06407 | 2.83+01 | 4.07+01 {7.98400 2.18+01 2.84401 3.96-+ 01
4.0002 1.30+01 | 1.89+01 | 2.23401 9.97 +00 1.31401 1.87401
5.0002 6.97+00 | 1.04401 | 1.23401 5.40400 7.22 +00 1.04401
6.0002 4.25-+00 | 6.32400 | 7.55400 3.28400 4.43400 6.45+00
8.00—02 11,9240 | 2.90400 | 3.52+00 7.66-+00 2.07 +00 3.04 +00
100-01 1.05+00 ] 1.60+00 | 1.91+00 4.29400 5.23+00 1.71400
K EDGE
150-01 3.9901 | 5.77-01 | 6.74—01 1.50+00 1.89-+00 2.47+00
2.00-01 2.28-01 | 3.07—01 | 3.49-01 7.38—01 9.4501 1.23 +00
3.00—01 131-01 | 153-01 | 168-01 3.0201 3.8301 4.85 —01
4.0001 1.0101 1.80—01 2.7301
5.00—01 8.59—02 1.2901 1.85—01
6.00—01 7.6702 1.0301 140-01
8.0001 652-02 1.7302 9.64—02
1,00+ 00 5.7702 6.3902
150-405 4.68 —02 4.88 ~02
2.00400 4.1402 4.34—02
3.00+00 3.66 —02 4.01 02
4.00+00 3.4802 3.98 —02
5.00400 3.4302 4.06 ~02
6.00+ G0 3.4302 4.16 —02
8.00400 3.5002 4.3902
1.00401 3.62—02 4.63 —02
1.50401 3.9302 5.2402 |
2.00401 4.2302 5.7702
3.00+01 4.7002 6.5902
4.00+01 7.1602
5.00401 7.60 —02
6.00401 7.94 ~02
8.00401 8.45 —02
1,00-+02 8.81—02
1.50402 9.3902
2.00402 9.76 --02
3.00-+ 02 1.02~01
4.00+02 1.0401 117-01
5.00+02 1.06 ~01 119-01
6.00-+ 02 1.07~01 121-01
8.00402 1.0801 1.22-01 |
1.00+03 1.09~01 123-01 |
1.50-+ 03 Lu-01 1.25-01 |
2.00-+ 03 Lol 1.26—01
3.00-+ 03 112-01 1.27-01
4.00-+03 9,00 —02 113-01 1.27-01
5.00-+ 03 9.0202 113-01 1.28-01
6.00-+ 03 9.04 —02 113-01 128-01
8.00-+ 03 9.05 —02 1.13 ~01 1.28-01
1.00+ 04 9.06 —02 114-01 1.28-01
1.50-+04 9.0802 114-01 120-01
2.00+ 04 9.10—02 114-01 1.2901
3.00-+04 9.1102 114-01 1.29-01
4.00-+04 9.1102 1.1401 1.29-01
5.00404 9.1102 Lld~O1 1.29-01
6.00-+ 04 9.1202 114-01 129-01 |
8.00+04 | 912-02 114-01 129-01 |
1.00405 9.12—02 114-01 121-01 129-01 |
|