Discrete eigenvalues of the neutron transport equation with anisotropic scattering

Based on two properties of the discrete eigenvalues of the one-speed neutron transport equation with anisotropic scattering, the number and mathematical character of these discrete eigenvalues are discussed when the scattering function can be expanded into a finite series of Legendre polynomials. Such special cases as linearly and quadratically anisotropic scattering are studied in detail, and our results are plotted in parameter space. The two physically interesting problems of isotropic scattering and linearly anisotropic scattering in the center-of-mass system are also discussed. The discrete eigenvalues of these two problems are obtained numerically