Since in our calculations we are dealing with a one-
dimensional medium in the sense that only the direction
perpendicular to the soil-air interface enters into the yray transport equation and then only in terms of the y-ray
mean free path (mfp), the effect of changing the soil
density is equivalent to a changing scale factor in this
This is because the y-ray mean free path is
direction.
equal to the
inverse of the total
attenuation coefficient,
a quantity directly proportional to the density of the
Medium.
Therefore, the soil density can affect calculations
with certain source distributions.
For a source distributed exponentially with depth
(S = Soe%%, where S is the activity at depth z, So is the
surface activity, and a is the reciprocal of the relaxation
length), changing the density, pe, is equivalent to changing
the effective source distribution such that a’ = 1.6 a/p
(In each case the total source activity inal em? column
= 1 y/sec).
Thus, increasing the soil density effectively
buries the source more deeply, decreasing the flux and exposure rate at the detector
in the
air half space.
Therefore,
in order to use the data given at certain relaxation lengths
in this report for a density other than 1.6 gm/cm’, one
would have to apply the above transform, a’ = 1.6 a/o’, to
determine which relaxation length to use.
Since a 7- »
corresponds to an infinite plane source it follows that the
soil density has no effect for this case.
When our calculations are for a uniformly distributed
source of one y-ray emitted per cm® at 1.6 gm/cm*, the
calculated exposures and fluxes are valid for a uniformly
distributed source of intensity 1.6/p gammas emitted/cm®sec where p is the actual in situ soil density.
This is so
because changing the density by some factor is equivalent to
changing the source intensity in the mean free path interval
(dt, which is t mfp from the interface) by this same factor.
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