130
MATHEMATICAL AIDS IN UNDERSTANDING OF BIOLOGICAL HAZARDS
THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD
showing that at about 6 feet above a con-
taminatedfield
e
droppedoff to about 13013.
Y
This result was the cause of a great deal of
uneasiness within the Radiological Safety group
during Operation Greenhouse because the
instruments were, as usual, measuring and
recording gamma dose only.
It was suggested
that if reference 2 had included the effect of
Compton scattering of gamma rays in air,
perhaps the beta/gamma dose ratio would be
less alarming. For this reason, in reference 4
an atiempt to include buildup or multiple
seattering factors was made during Operation
Greenhouse.
Simple analytical treatments
are not possible if buildup factors are to be
considered. The approach used in reference 3
was a laborious numerical integration using
certain empirical measurements of a buildup
factor (4) that had become available.
An
example of how gamma dose at point 7 was
obtainedis given in Table J.
The contaminated ground was divided into
unequal ring increments as in column 1.
¢ in column(2) is the net geometrical attenuation factor.
Column (4) is the good geometry, narrow
beam absorption factor.
Column (5) was obtained from White [4].
In that work White used a Co” source and a
water absorber, but the results were used in [3]
without modification.
nteremet
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(6)
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garding the beta/gamme dose ratio.
Comparison of columns (4) and (5) shows
how buildup only partially compensates for
absorption.
Beta dose in reference 4 was calculated using
increment.
meter of radius
numerical integration method using, this time,
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game, aeemear| Maui| Bensageor| eantre| eins
din om.
equal ring increments. Distances greater than
6 meters were not considered significant. The
distance for each ring is taken as d,, the distance to the midpoint(see fig. 4).
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45
. 50
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1.03
97
.37
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602
608
618
632
650
671
922
1081
1616
2571
0, 94
94
94
194
94
204
91
. 90
. 86
79
10
10
10
10
1.0
190
10
Li
Lt
1.2
0. 08
24
2385
42
47
49
. 94
~ 96
3. 50
2, 28
0. 08
.24
. 35
42
47
49
47
- 48
35
. 24
0. 72
2.16
3. 15
3. 78
423
442
8 46
8. 64
3L 5
20, 5
Pp
2.09
6059
- 56
15
176
- 09
15.8
Rog wo. OO
18
14
L. 67
1, 80
1,42
Lid
a7
3551
4540
8022
10479
13514
16511
10509
1. 09
1,44
24007
27500
. 84
37500
97
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450-500... ee ee eee eee
w
show that inclusionof multiple scattering makes
a militarily significant change in the total
gamma dose but does not radically change the
conclusions of Condit, Dyson, and Lamb re-
the method of Parker [5]. This is again a
Tasty L—-GAMMA DOSE h=6 meters
ay
Column(7) takes into account the fact that
the increments chosen are not of equal width.
In column (7) note that for a height of 6
meters, maximum dose delivering efficiency
occurs at about the 6-metor radius.
In column (8) about half of the dose comes
from inside the circle r==30 meters. For h=1
meter 50 percent comes from inside {2 meters
(see fig. 2). Thus the net result of [8] was to
. 66
32500
42500
47500
71
. 65
47
387
- 28
13
L4
L7
2.0
23
1, 66
1,27
1,25
1. 33
, 89
24
16
26
30
. 62
47
. 05
4.8
28
.10
07
. 08
. 02
OL
3.5
40
5.4
57
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~32
14
. 08
. 04
Total. ..-----~.----..f--------- |e eee ee fen eee wee eee [ewe nee eee eee
A sluilar table 1s necessary for each height desired.
Comparison of column (5) with column (8) indicates that scatter secountsfor about 30 pereentof the total dose at P.
. 16
14
14.9
114
. 06
- 04
13
12.0
02
. 009
5.6
42
- 03
- 006
. 005
. 003
he ( meter
fluxes in air at points above a plane, in a foxhole,
and so forth.
This work continues even now,
and the writer has the impression that the
theories used are fundamentally powerful
enough to give satisfactory mathematical solutions for any foresecable military medical
problems due to fallout: hazard.
In 1955 the multiple scattering theory was
applied to beta particles [6] and another theoretical treatmentof the same subject. appeared
(7}.
These later, and professionally competent
mathematical approaches yield results which
agree with the physical measurements that have
been made to date.
So far as comparison is
possible the results are notin disagreement with
the conclusions reached in the crude attempts
NBS groupinclude the use of anelectronic com-
4m
9
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6
G
Beta dose at point P
gamma dose as in Table I, gave beta/gamma
ratios which were not significantly different
av
has been applied to the calculation of gamma
a wide spectrum of opinion regarding the operational implications of these conclusions.
The mathematical methods evolved by the
3.4
2.9
4
in cooperation with, the AFSWP mathemati-
cians, the NBS theory of multiple scattering
their theoretical conclusions and field measurements are essentially the same as ours. There is
Fraure 4.—~Beta dose at point P,
13
For some years prior to 1952, the National
Bureau of Standards group (Fano, Spencer,
et al.) had been developing a mathematical
theory concerning the penetration of X-rays
through thick barriers. At the request of, and
previously discussed.
British and Canadian documents have become available in recent years which show that
80
21
131
Calculating beta dose in this manner, and
from those in reference 2.
Operation Greenhouse marked the end of
what might be called the primitive era, since
immediately afterward the AFSWP staff in
Washington began to expend greater effort on
the mathematics of fallout radiation.
puter and, on the whole, appear to be beyond
the ken of anybiologist or physician now available to work on fallout hazard. In this situation, any progress on medical problems will
require that:
A. The biologists concerned will have to
accept. on faith mathematical conclusions
which they do not really understand.
B. The mathematician and the radiological
physicist will have to be patient and endure
diffuse and frustrating discussions of what
really needs to be calculated and measured in
order to develop an adequate medical policy.