  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.
