An operational method for the particle slowing-down problem

Abstract

The direct operational method is used to transform the collision integral in the transport equation to a polynomial in derivatives with respect to lethargy. This polynomial is approximated by the Padé approximation technique. Different orders of the Padé approximation give the well-known synthetic kernel. This procedure reduces the integro-differential form of the transport equation to differential form. It also gives us the chance to consider the energy-dependent cross-section and to obtain the solution without using the integral transform method. We shall consider here the solution for an infinite homogeneous medium and calculate the energy deposition factor for different orders of the Padé approximation.