BAECS ATaT aa are IT. ADAPTATION OF THE POLYNOMIAL EXPANSION MATRIX EQUATION METHOD TO THE AIR-SOIL INTERFACE PROBLEM Calculational details for solving the two media transport problem by the P-~3 and DP-1l polynomial expansion matrix equation method appear in a previous report ‘??, In general, the method consists of separating the spatial and angular dependencies of the angular flux in a truncated series of orthogonal polynomials and making use of the orthogonality properties to reduce the Boltzmann equation to a set of coupled integro-differential equations for each spatial component of the flux. These equations are solved by dividing the energy range into a number of groups and replacing the integration over energy by a summation over these groups. The integro-differential equations are rewritten as a set of differential matrix equations‘*?. These equations have relatively simple exponential solutions. The solution for a given energy group constitutes the source term for the next lower group. Thus, starting at the source energy, the differential energy and angle spectrum can be constructed stepwise down to any desired energy. Total exposure rates and angular exposure rates are obtained by weighting the differential spectra by the appropriate energy absorption coefficient and integrating over the energy and angular intervals of interest. All cross section data used for these calculations were taken from Hubbell‘*?. The calculations discussed in this report are for a given set of soil and air densities, soil moisture content, and soil composition. However, as this section points out, our data can be applied to other soil and air conditions. A. Exposure Rate Dependence on Soil Density The calculated exposure rates are for a soil in situ density of 1.6 gm/cm*. Actual in situ densities of soils can range from less than 1.0 gm/cm® to over 2.0 gm/cm’, although a typical range‘®? would be 1.1 to 1.8 gm/cm’.