A Genuine Analytical Solution for the SN Multi-group Neutron Equation in Planar Geometry

The analytical solution program for the time-dependent neutron transport equation has undergone a significant evolution since the work of Case [CaZw67], where the one-dimensional stationary problem in a slab was solved analytically. There exists a relevant literature concerning the issue of solving the time-dependent neutron equation in a planar geometry for an unbounded domain. We mention the works of Ganapol and Filippone [GaFi82], Ganapol and Pomraning [GaPo83], Ganapol [Ga86], Ganapol and Matsumoto GaMa86], and Abdul [Ab06]. On the other hand, regarding the literature for bounded domains, we cite the works of Windhofer and Pucker [WiPu85], Warsa and Prinja [WaPr98], Oliveira et al. [OlCaVi02], [OlEtAl02], El-Wakil et al. [ElDeSa05], [ElDeSa06], Tureci et al. [TuGuTe07], Tureci and Tureci [TuTu07], Hadad et al. [HaPiAy08], Coppa et al. [CoEtAl08], [CoDuRa10], and Cargo and Samba [Ca10].