The problem of describing steady-state transport of a perpendicularly
incident particle beam through a thin slab of material is considered F
or a scattering kernel sufficiently peaked in momentum transfer to all
ow a Fokker-Planck description of the scattering process in both energ
y and angle, an approximate closed form solution to this problem was o
btained almost 50 yr ago and is referred to as the Fermi-Eyges formula
. It is shown that a Fermi-Eyges-like formula can be derived for a bro
ader class of scattering kernels. This class consists of scattering de
scribed by the continuous slowing-down approximation (the Fokker-Planc
k description in energy), but not sufficiently forward peaked in angle
to allow an angular Fokker-Planck representation. This generalized fo
rmula reduces to the classic Fermi-Eyges result for scattering operato
rs,vith a valid Fokker-Planck limit and also describes problems that,
while involving a forward-peaked scattering kernel, do not possess a F
okker-Planck description. A classic example of such a kernel is the He
nyey-Greenstein kernel, and the Fermi-Eyges-like solution in this case
exhibits more beam spreading than that predicted by the classic Fermi
-Eyges formula. In particular, the scalar flux is non-Gaussian in the
radial coordinate, as contrasted with the Gaussian Fermi-Eyges result.