P-N solutions of the time-dependent neutron transport equation with anisotropic scattering in a homogeneous sphere

In an earlier paper, the spherical harmonics method for the solution of the time-dependent transport equation with the Marshak boundary conditions was presented in order to investigate the effect of a strongly anisotropic sca ttering law on the slab thickness. Here, the previous work is extended to t he study of the time-dependent problems in a homogeneous sphere with the sa me scattering function as used in the previous work. The time-dependent neu tron transport equation is solved in the manner used for a critical sphere and all radii for a given time-dependent system are determined by finding t he critical radii for the corresponding critical system. The P-N calculations of the critical radii were carried out for various com binations of the anisotropy parameters and the fundamental time eigenvalues . Some indications of the accuracy of the method were given for the problem of interest and the variation of the radius with anisotropic scattering wa s studied. We also obtained numerical values of the critical radii in the r ange of (1 - Lambda) less than or equal to alpha, beta less than or equal t o 1. Finally, some results were discussed and compared with those already o btained by various methods.