Application of Laguerre Polynomials in the Analysis of Neutron-Wave Propagation

An energy-dependent transport theory solution for the infinite medium neutron-wave propagation problem is obtained by applying a Laguerre polynomial expansion to represent the flux energy dependence. Integral transform methods are utilized to determine solutions appropriate for a general isotropic scattering kernel and general cross sections. Detailed calculations are performed for a two-term polynomial expansion and an energy-dependent cross-section model. Although the polynomial expansion approximation appears to be quite satisfactory for low modulation frequencies, serious inadequacies exist for higher frequencies where continuum effects are important. A critical frequency is not predicted, and the two-dimensional continuum of eigenvalues is approximated by a series of cuts, the number of which depends on the number of terms in the expansion.