Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (SN) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is ʹnewʹ, are presented for determining the eigenvalues and eigenvectors of such SN problems. In the first method, separation of variables is directly applied to the SN equations. In the second method, common characteristics of the SN and PN-I equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Greenʹs functions (transmission and reflection factors) are known. Numerical results for S4 test problems are given to compare the new method with the existing methods