Pade approximation method in neutron slowing - down problems

The method for approximate solution of neutron slowing-down equations based on the Pade approximation of the scattering operator by a function of the differentiation operator with respect to lethargy is formulated. A simple approximate analytical solution describing self-simulating asymptotic conditions of neutron slowing-down from a monochromatic pulse source in the spatially uniform medium without absorption and at power dependence of scattering cross section on neutron rate is found and analysed on the base of a more complicated approximation. It is shown that in the most trivial particular cases the realization of the approximate approach leads to some generalizations of the known Wigner and Grueling-Hertzel approximations and permits in a compact form to reproduce a series of the slowing-down theory analytical results