A large deflection Fermi–Eyges pencil beam formula

In the 1940s, Fermi and Eyges derived an approximate closed form solution for the energy- dependent scalarflux for the finite slab steady-state pencil beam problem. This solution is based upon the assumption that the Fokker±Planck scattering representation is valid in both energy and angle. It further assumes that the beam remains nearly collimated as it passes through the slab. In this paper, we relax this near-collimation assumption and obtain a mod- ified Fermi±Eyges formula which is significantly more accurate for large beam de¯ections. The modern interest in this beam problem is in connection with radiation oncology treatment planning.