Computation of higher spherical harmonics moments of the angular flux for neutron transport problems in spherical geometry

The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coecients are obtained by solving their singular integral equations. It is shown that these expansion coecients provide a representation of all sphe- rical harmonics moments of the angular ¯ux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precau- tions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Arons- son.