A method for determination of the potential from the reaction matrix at fixed energy

Abstract

The inverse problem at fixed energy, in the case of a central potential with finite range, is transformed to a form that is similar to the inverse problem for the S-wave scattering. Using a rational-function representation of the input data for the reaction matrix for different partial waves and a modified Gel'fand–Levitan formulation, one can construct the potential from the partial-wave phase shift at a given energy. In this formulation of the inverse problem the properties of the Cauchy matrix have been used to perform a number of operations analytically, thus reducing the sources of numerical round-off and truncation errors. The method has been applied to construct the potential for some simple scattering problems.