The Infinite Medium Green’s Function of Monoenergetic Neutron Transport Theory via Fourier Transform

In 1960, Ken Case published his seminal work on the singular eigenfunction expansion for the Green’s function of the monoenergetic neutron transport equation with isotropic scattering. Previously, the solution had been found by Fourier transform as pole and branch cut contributions. It was apparent the two solutions were equivalent; however, showing equivalence for general anisotropic scattering was an unresolved challenge—until now. The motivation for revisiting the Green’s function solution is to resolve this issue by constructing a moments solution through analytical recurrence and application of Christoffel-Darboux formulas. While nothing more than Case’s singular eigenfunction expansion will result, the approach is new and follows Case’s original reasoning in applying separation of variables common to partial differential equations to solve the transport equation; that is, an equivalence to the singular eigenfunction expansion by Fourier transforms should indeed exist.