Appendix A
DERIVATION of ALTITUDE ABSORPTION
of GAMMA RADIATION
Keran O’Brien, Radiation Branch, Health and Safety Laboratory
where j is the disintegration per second per cubic centirneter and Ey is the average source energy.
The equation giving the dose rate above a hole in an
finite half-space that subtends an angle 6°, when the
half-.pace is uniformly contaminated with a gamma
Ej
y
|
Bay Eh 8)
eanitter, is described in Reference 10 and is:
E 4he 9")
6
—~—
soy
1
Where:
A.l
(A.1)
The constants may be converted to appropriate units
to relate contamination density to gamma dose rate by:
E is the gamma eneigy emitted per cubic centimeter by the contaminant
K
cas the density of the absorbing medium
CdHe (3,600) E
=
Wee
his the height of the detector, in meters, and
Y
Where:
Mt the ratio of the total attenuation co-
He
efficient to the energy absorption coefficient
of the medium, corresponding to the source
(
6
A.9)
c = 3.7.x 10' (photons/sec)/m*
= 4.8x 10 "esu
Me = 3.54 10 %cm™(for water)
W = 3.25 x 10% Mev (32.5 ev)
energy
3,600 sec/hr
Por A:
Ath, 6°) = X {tui (—tu) + e B(tu)}
10° cm?/m!?, and
(A.2)
E,) is assumed to be 0.5 Mev
t = y,h, u > sec 6°, and B(tu} is a polynomial
Then:
The dose rate above a plane, similarly contaminated,
can be obtained bythe partial derivative of Equation A.1
v
to obtain an infinitesimal thickness of slab:
aly,
ap dh = Ip
Ip Pp= ou,
2aY Be dh Mit
(tu)
0.3
=
S48 L(h, 6 R/hr
2
v
(A.10)
where Cc, = curies per cubic meter.
(A.3)
CASE Il.
This is
A.4
Land Contamination:
J(h, 6) = M(h, 6°)—M(h, 6)
(A.11)
uyEdh
gEoK
(A.12)
20Y
20
and
(A.4)
with M(tuy = —E, (-tu) +e” [B(tuy—B? (tu)-1)(A.3)
y
se:
Where:
(A.B)
dB
B to= atu)
where k represents disintegrations per second per
Square centimeter.
The clearing on the surface also subtends on angle @.
This reduces Equation A.4 to:
For the case of radiation from water or land con~
I
taminated with fission products, seen by an aireraftmounted detector, a finite diameter of contamination
p
=
HeE,k
2a
J(h, 6°)
13
{A-13)
on the surface is described by a half-angle sensitivity,
With the constants converted to appropriate units as in
é.
Case I, and 104 cm?/m’.
CASE !.
Water contamination from Equation A. l.
Lih, 4) - Ath, @*)—A(h, 8)
and
E
~n
25¥
Eo)
= 29
20¥
(A.6)
A.7
k Eo
K = SmhelS
(A.14)
Ip = 3.4427 C, Sth, 6°)R/br
{(A.15)
where Cp = curies per square meter.
(A-7)
62