Calculation of the higher order eigenvalues for a slab with forward-backward scattering using F-N method

The transport of monoenergetic neutrons with anisotropic scattering and vac uum boundary conditions is studied in plane systems. First, a simple formal equivalence between the transport equations for a critical and for a time- decaying system is established Then, the stationary transport equation is c onverted into one in which the scattering kernel is completely isotropic an d the resulting equation is solved by using the FN method. Numerical result s for the higher order criticality eigenvalues and the corresponding time-d ependent ones are tabulated for various scattering parameters and dimension s of the bodies. Some selected results are compared with those already avai lable in the literature. It is shown that the FN method yields results with an accuracy of four to six significant figures over a wide range of scatte ring parameters Finally we make a few remarks about the behaviour of the cr iticality and time-eigenvalue spectrum of the neutron transport equation wi th forward and backward scattering.