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. -4-