Mark and Marshak boundary conditions in surface harmonics method

Abstract

In the surface harmonics method (SHM) as a boundary condition it can be used a link of even angular momentum vector of the neutron distribution with odd momentum vector to obtain a finite difference equations. On the border with the vacuum such boundary conditions are called Mark or Marshak boundary conditions. Instead of odd angular momenta the SHM uses their linear combinations (so called neutron levels), so in this paper it is obtained the matrix of connection between odd angular momentum vector and the neutron levels vector (such as Marshak boundary conditions) and matrices of connection between odd angular momentum vector and the neutron levels vector(such as Mark boundary conditions). In present article connection matrix is used in SHM and for computation of the reference neutron distributions in PN - approximation (up to N = 97).