’
a
Reprinted from NUcLEAR SCIENCE AND ENGINEERING, Vol. 3, No. 1, January 1958
Academic Press Ine.
Printed in C.Su1.
NUCLEAR SCIENCE AND ENGINEERING: 3, 77-84 (1958)
A Semiempirical Method of Calculating the Energy
Absorption Buildup Factor with an Application
to a Uniformly Contaminated Space
Having Spherical Boundaries
Ikeran O’Brtex, Wayne M. Lowber, axp Leonarp R. SOLON
wan
Health and Safety Laboratory, New York Operations Office, U.S. .ltomic Energy Conunission,
New York 23, New York
Received April 18, 1957
A formfor the point-source gamma-ray energy absorption buildup function
valid for a material in the energy range where it is essentially a Compton
scatterer is suggested as a modification of the asymptotic forms derived by U.
.
Fano. Its parameters are evaluated by means of an energyequilibrium con-
dition and a fit to experimental data. The results are compared with those ob-
tained by other methods, and an application to the problem of uniformly and
continuously distributed point sources is discussed.
“
>
.
Co arn
Pew
The point-source energy absorption buildup factor, as conventionally defined,
is the ratio of the energy absorption rate from the total-radiation flux to that
from the primaryflux at some point in the material surrounding the point source.
This material is assumed to be uniform and infinite in extent. The buildup funetion for a given source energy describes the variation of the buildup factor as a
function of mean free path and will be designated by b(¢).
If we assume a form of the buildup function consistent with the considerations
of Fano (7), it is possible to compute buildup factors for Comptonscatterers by
using an energy-equilibrium condition (2-6) in combination with a fit to experimental data (7-9).
The dose rate in uw uniformly contaminated medium ofinfinite extent, when
the contaminant is a monochromatic gamma emitter, is given by
(1)
Ku, [?"
.
.
” dt b(te'
de | do sino | Oe”
Pir +o
-0
0
4
p= Phe f
where J is the dose rate in Mev, sec-gram, # the energy emitted by the contaminant in Mev,’sec-em’, », the energy absorption coefficient for the mediumcorre-
sponding to the source energy in cm ', u, is the total attenuation coefficient for