84
O'BRIEN, LOWDER, AND SOLON
The case of the dose rate in air at some height ¢, (mean free paths in air) over
a uniformly contaminated half-space is of some interest. Here, g = * and f =
fp sec 8, @) = 2a and 6 = 22. Thesolution is
(11)
= SE Unit) + OM Bo+ Bi + Bat? + ---)]
where
By = «10
SA
B= ey
i=1,2,---,n—-1
and
-—HY(-o -|
t
(e*/x) de.
APPENDIX
An integral equal to Eq. (4) and containing an exponential is
(12)
2
I edt = y.
Clearly the integrands of Inqs. (12) and (4) intersect at some one point other
than é = 0. A comparison of Eq. (4) and of the equations formed bysetting the
integrands equal indicates that this point is nearly / = y. If we assumeit is
exactly y, Eq. (6) follows immediately. For a wide range of values of a, 8, and y,
Eqs. (4) and (6) are very close. All parameters are positive here, of course.
It is possible to better this approximation in the region about 8 = 1 by noting
from Eq. (4) that 8 = 1 implies a = y — 1. We substitute fo = y + hy (y -— 1)
and, only in the last stages letting 4 go to zero Iq. (5) follows.
A comparison of Tnqs. (4), (5), and (6) is shown in Fig. 5 for the particular
case of a = 1/y.
AAR we
REFERENCES
U. Fano, J. Research Natl. Bur. Standards 61, 91 (1953).
W.F. Linsy, Science 122, 3158 (1955).
Com
jas)
L. D. Marinxewul, .tm. J. Roentgenol. Radium Therapy 47, 210 (1942).
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R. Loxvineer, J. G. Hott, anp G. J. Hiwe, in “Radiation Dosimetry”, (G. J. Hine and
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