Scattering by Spherically Symmetrical Objects

Abstract

The solutions of vector potentials in the presence of spherically symmetric objects are expressed in terms of two auxiliary functions, related respectively to the phase and amplitude of the resulting field. It is shown that these auxiliary functions satisfy first-order differential equations of the radial coordinate, and the scattered field is described by the phase functions alone. Furthermore, the differential equations satisfied by the phase functions are found to be independent of the amplitude functions and are solved numerically by using the well-known initial phase shifts readily obtained from the boundary conditions.