The Extrapolation Distance for a Black or Grey Cylindrical Neutron Absorber by the Spherical Harmonics Method

The linear extrapolation distance, extrapolated endpoint, and effective radius of grey and black cylindrical neutron absorbers imbedded in an infinite moderator have been calculated using Kofink's formulation of the P_N method, with N odd up to 13. These parameters were determined as functions of the absorption of the moderator and of the linear anisotropic scattering component of the moderator, for two source distributions: 1) uniform isotropic sources; or 2) no sources with a current from infinity. The results are given both in tabular form and in simple formulas that are sufficiently accurate for most purposes. In addition, various kinds of P_N boundary conditions are compared and new calculations are given for the blackness of homogeneous grey rods.