Nuclear Science and Engineering / Volume 180 / Number 2 / June 2015 / Pages 224-246
Technical Paper / dx.doi.org/10.13182/NSE14-55
In 1960, Ken Case published his seminal work on the singular eigenfunction expansion for the Greenâ€™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 challengeâ€”until now. The motivation for revisiting the Greenâ€™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 Caseâ€™s singular eigenfunction expansion will result, the approach is new and follows Caseâ€™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.