radioisotopes of interest give rise to stable daughters.
From Equations 1.2 and 1.3
Tm Ast
I, = Nooje
tg ¢X) £,(X) k;(X) dx
(1.4)
For a particular soil and incident neutron spectrum, the integral is a constant, and
Ii = NgKipie
—At
+
(1.5)
where Kj is a constant. When a number of gamma-emitting radioisotopes are formed,
the dose rate above the surface is given by
I = Ng ferkye
—Ayt
—At
-
+ po Ky e Mt, + py, Kne nt]
(1.6)
This equation describes the dose rate at any time only for a given soil and incident
neutron spectrum. Different K values may be expected for each different soil and
spectrum combination.
1.4.2 Neutron Spectra. Although neutron spectra vary both with slant range and
weapon type, spectra from all weapons nevertheless seem to approach the same equilibrium spectrum as slant range increases, so that for slant ranges greater than 900
yards there is invariance with slant range and weapon type.
Before this equilibrium spectrum is established, the spectrum is always softer
(relatively more goid neutrons). In general, both the degree of softness and the slant
range necessary to establish the equilibrium condition are greater for weapons having
the largest amounts of high explosive. In this method, corrections are made for changes
in spectrum when they occur.
1.4.3 Soil Differences. To establish those characteristics of soils which must be
considered to give a reasonable degree of prediction accuracy, extremes in the amounts
of important soil elements were considered.
The influence of each element on the over-
all moderating or slowing-down power of soil was assessed, as was the importance of
each element for absorption of thermal neutrons. Gold neutron measurements versus
depth in Nevada soil served to evaluate the importance of build-up caused by moderation, so that relative dose rates could be calculated for extreme cases.
The moderating power of a soil is determined by its amount of hydrogen, the main
source of hydrogen being the moisture content of soil. However, a compensating effect
Causes dose rates measured above the surface of soil to be fairly insensitive to the
actual amount of hydrogen (over the expected range of hydrogen abundance or moisture
content).
When the hydrogen content is high, build-up of low-energy neutrons occurs
closer to the surface, but the diffusion length (L) of thermal neutrons thus formed is
Correspondingly shorter, a factor which causes faster decay with depth. For a low
hydrogen content, build-up near the surface is less; but the decay of thermal neutrons
With depth is also less (larger L). However, activity produced near the surface must
be considered more important than like amounts at greater depths, since emitted gamma rays must penetrate the soil overburden. Thus, without caiculation, it is not ob-
vlous to what extent such a compensating effect operates.
Figure 1.1, reproduced from Reference 4, shows the extremes expected in relative
dose rates for soils with differing amounts of hydrogen. These extremes were calcu11