NUCLEONICS DATA SHEET No. 16 
Shielding 
Gamma-Ray Streaming Through an Annulus 
By DAVID G. CHAPPEL 
Knolls Atomic Power Laboratory* 
General Electric Co. 
Schenectady, New York 
PRACTICAL DESIGN of biological shields 
for reactors often involves accounting 
for the gamma flux that streams through 
the annular space between a pipe and 
the shield. This nomogram permits 
rapid and accurate determination of the 
geometrical attentuation of the gamma- 
ray flux from an emitting surface onto 
which the annulus abuts perpendicu- 
larly. Scattering effects are not ac- 
counted for. The formula for the 
attenuation isf 
A = KD,“AD*L-? 
where K is 2.8/8, 5.6/8 and 7.2/8 
for spherical, cosine, and Fermi emit- 
ters{ respectively. The other symbols 
are shown in the diagram accompanying 
the nomogram. The formula is valid 
only if L > AD, the usual situation. 
Example: Annulus with D, = 4.5in., 
AD = 0.02 in. (AR = 0.01 in.), and 
L = 10 in. abuts perpendicularly onto 
a gamma-emitting surface. As shown 
the nomogram gives A = 7.0 X 107° 
for a spherical emitter, 1.8 X 10-5 for 
a Fermi emitter. Attenuation for a 
cosine emitter is twice that for a spheri- 
cal or 14 X 10-°. 
* Under Contract No. W-31-109-ENG-52. 
+C. W. Wende. The computation of 
radiation hazards. TNX Report 7, p. 465. 
t When source density increases with 
depth and there is self-absorption the radi- 
ation passing through the interface will be 
enhanced in the forward direction. A good 
approximation to the distribution is given by 
the Fermi formula, 
N(8) = ~ cos 0 — 1/3 cos? 0. 
D, A 
‘0 
L 
50 10° te Do =| 80 
40 AD 70 
10° G20 
30 iB 60 
i 50 
20 107! Ale 
40 
107! 
10 30 
8 . 1072 
@ 
6 = 
5 E io~2 20 
= AD 
ar 8 < 
Ss & 1S 
. 3 2 10-5 é \ 
o a © = 
- o - o 
4 = c 
§ 2 s < lo? € se = 
5) 3 = 10 6 
a E s 
a s o ae 
2 -4 u 8 4 
E + 10 
(3 I 2 Ol - ie: 
3 os : 5 
2S S 05 © 6 
06 = e 
f =) o 5 
z 5 
wees E 10-8 3 
0.4 Ss 4 
oo § 
0.3 2 
0005 § 3 
0.2 
10-6 
2 
0.001 
0.1 
0.0005 
10-7 
222 
