Relativistic inelastic scattering using a logarithmic grid (Q1075026)

This paper describes a method of obtaining approximate solutions of a spherically symmetric non-relativistic or relativistic inelastic scattering problem. The model consists of a pair of coupled, complex, first order differential equations so that it can be regarded as a set of 4 coupled equations using the real and imaginary parts of the equations. From the asymptotic region the solution is approximated inwards and matched, at a point near the classical turning point of the solutions, with the approximations obtained by outward integration. To deal with the asymptotic region the transformation \(p=\log_ er\) has been used so that the grid used covers the whole radial distance. This technique is shown to be efficient and not subject to the same problems of a small step size of the conventional method.