Variational correction to the FERMI beam solution

We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab with a pencil beam of nuclear particles impinging upon one surface. 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 backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. A number of modifications of Fermi theory, aiming at improved accuracy, have been proposed. Here, we show that the classic Fermi solution (or any approximate solution) can I be improved via a variational formalism