On the analytical solution of the one-dimensional two energy group neutron diffusion equation with source in cylinder geometry by the Hankel Transform

In this work we solve the one-dimensional diffusion equation for neutrons of General Perturbation Theory, in a two energy group model and in homogeneous cylinder geometry by the Hankel Transform. The analytical solution of the transformed problem in matrix form is diagonalized and the scalar neutron flux for two energy groups is obtained by inversion of the Hankel transform. We show as results the fast and thermal flux and compare them with findings from the literature. (author)