The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation

The effect of anisotropic scattering on the eigenvalues of a multiplying (c >1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation is studied. We have made some calculations, not only for the cases c<1 and 0 < g < 1, but also the cases of c >1 and -1<g<0 by using the linear and quadratic approximations of the Henyey-Greenstein scattering kernel. The asymmetry parameter g consists of isotropic, backward and forward bias. An extensive numerical survey is carried out for the eigenvalues in order to provide an accurate evaluation. The numerical results indicate that the discrete eigenvalue increases with forward scattering and decreases with backward scattering in expansions of linear and quadratic anisotropic scattering.