The eigenvalues of one-speed neutrons in a slab with forward and backward scattering

Abstract

The eigenvalue spectrum is studied for one-speed neutrons in a slab with forward and backward scattering. First, the transport equation describing the interaction of neutrons in a system with general geometry is given. Then, the scattering function in transport equation is chosen as the forward-backward-isotropic (FBI) scattering model. The resultant transport equation is solved using the Legendre polynomials expansion (PN method) and the Chebyshev polynomials of second kind expansion (UN method) in neutron angular flux. Then, the PN and UN moments of the equations are obtained using the properties of the Legendre and the Chebyshev polynomials of the second kind. Finally, the eigenvalues for various values of the collision and scattering parameters are calculated using different orders of the presented methods and they are given in the tables for comparison.