Variationally improved Fermi beam solutions

The time-independent. transmission problem for a purely scattering, homogeneous slab of finite thickness is considered. This problem corresponds to a planar beam of radiation impinging perpendicularly upon one surface of a source-free slab. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that radiation backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. By using the recently reported solution for an obliquely incident pencil beam. we show that the Fermi solution (or any other approximate solution) can be improved via a variational formalism