THESE NOMOGRAMS permit rapid esti- 
mation of the photon flux reflected 
from a thin object; this is often re- 
quired in shield design. 
A photon flux J; (y/em?/sec) of en- 
ergy E; (Mev) per photon, incident 
upon a scatterer thin with respect to 
the relaxation length of the incident or 
scattered photon (¢ < A), will scatter 
through an angle @ to a receiver FR at 
distance D (cm) with an intensity Ir 
(y/cm?2/sec/steradian) and energy Er 
(Mev) per photon and an intensity 
given by 
Ir = NopD-4I; = KI; 
The energy flux, ¢ (Mev/cm?/sec/ 
steradian), at F is 
* Knolls Atomic Power Laboratory is op- 
erated by the General Electric Co. for the 
U. S. Atomic Energy Commission. 
) Ne 0D 
90° — 90° 
g0° —100° " 
10 
10°? 
8 
70° toe 6 
1078 
60° —1120° 
= 2 
gz rs 
@ a & 
= "ar 
2 50° —\130° = 
5 : 
2 ° 
Q 2 
a c 
§ = 
= 1026 $ 
§ 3 
2 40°—1140° ° 
& r-) 
i s 
2 e 
z 1028_| 21 
30° —J150° 
4 
102% : 
20° 160° 
2 
10° —l1702 
oe —igoe 10%] 10% 
de = Erle = PE;KI; 
The scattered photon energy, Ep, 
is given by the Compton equation 
P= hs/E; 
E, a 
~ [! os Oe | 
The probability per electron of scat- 
tering the incident photon through 
angle @ is given by the Klein-Nishina 
equation 
op = do/dQ 
= (P — P* sin? 6 + P3)r,2/2 
where the classical electron radius 
r. = 2.82 X 10-3 cm and gp is in cm?/ 
steradian per electron. One must mul- 
tiply by the number of electrons in the 
scattering medium, N, = 6.02 x 1073 
MZ/A, to get the total scattering prob- 
ability. 
Large objects must be subdivided 
into pieces of such size that J; and 6 
can be assumed constant over each 
region of subdivision. Each region is 
then considered to be a point scatterer 
defining a new set of parameters M, D, 
and 6, and the scattered intensities from 
all subdivisions are summed. 
If sma]] values of M are used, K may 
go off-scale; in this case N, can be mul- 
tiplied by a convenient factor of 10 and 
K divided by the same factor to obtain 
the corrected value of K. 
The value of K is not particularly 
sensitive to Z/A. However, the aver- 
age value Z/A for Z = 2-80 is plotted 
at Z < 30 and for Z/A for Z = 31-91 
at Z > 31. This provides for scatter- 
ing media for which only an approxi- 
mate composition is known. 
* * * 
I wish to acknowledge the assistance of 
Miss Joyce Berger, who drew the nomograms. 
R K TH 
1072 8 8 
7 
: 6 
Key: @-P-QOp (left) 5 
Op (right) — R— Ne te 
D-R-K 4 
4 
3 
3 6 
Py 2 
= “ 
oe c 
~~ °o 
a at) 
o KJ 
2 
s e 
= 3 
7 - - 
= 5 10° 
3 8 
$ 8 
2 
1 
fe 6 
@ 
= 
o 
ve 
72) 
. 
5) 
Ip=KIi 
2 
10-4 
Differential Klein—Nishina cross section (cm@) 
221 
