The Milne Problem for a Large Plane Slab with Constant Source and Anisotropic Scattering

Formulas are derived for the asymptotic neutron density and the neutron current emerging from an infinite plane slab whose thickness is large compared to the scattering mean free path. It is supposed that the slab sustains a uniform source of neutrons. The neutrons suffer capture in addition to scattering. The scattering is assumed to take place in accordance with the law: $\left(\frac{1}{4\pi }\right)(1+3\mathrm{}{f}_1\mu )$ where $f_1$ is a constant, and $\mu$ is the cosine of the angle of scattering. Expressions for the asymptotic neutron density in the slab and the emerging current, in the limiting case of isotropic scattering, are also given.