Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method

Abstract

One speed, time independent neutron transport equation in slab geometry can be solved with the triplet anisotropic scattering for the criticality problem with the reflected boundary condition. The value of the critical slab thickness is investigated numerically by using the Modified F-N (H-N) method. Case's eigenfunctions, normalization relation and orthogonality relations must be derived for this scattering in order to use the Modified FN method. Some selected values, which can be calculated from the criticality equation, can be tabulated. Also the term which comes from the Poincare-Bertrand formula may be added to the orthogonality formula of the continuum eigenfunction.