A Grey Radiative Transfer Procedure For Gamma-ray Transfer in Supernovae
  The gamma-ray transfer in supernovae for the purposes of energy deposition in the ejecta can be approximated fairly accurately as frequency-integrated (grey) radiative transfer using a mean opacity as shown by Swartz, Sutherland, & Harkness (SSH). In SSH's grey radiative transfer procedure (unoptimized) the mean opacity is a pure absorption opacity and it is a constant aside from a usually weak composition dependence. In this paper, we present a variation on the SSH procedure which uses multiple mean opacities which have both absorption and scattering components. There is a mean opacity for each order of Compton scattering. A local-state (LS) approximation permits an analytic solution for the gamma-ray transfer of scattered gamma-ray fields. The LS approximation is admittedly crude, but the scattered fields are always of lesser importance to the energy deposition. We call our procedure the LS grey radiative transfer procedure or LS procedure for short. For a standard Type Ia supernova (SN Ia) model the uncertainty in gamma-ray energy deposition is estimated to be of order 10 % or less. The LS procedure code used for this paper can be obtained by request from the author.   For completeness and easy reference, we include in this paper a review of the gamma-ray opacities important in supernovae, a discussion of the appropriate mean opacity prescription, and a discussion of the errors arising from neglecting time-dependent and non-static radiative transfer effects. 
David J. Jeffery