A solution of the inverse problem in quantum mechanical scattering theory using the distorted born and other approximations

Abstract

In this thesis, we extend previous work where it was shown how one can use the Simple Born Approximation and special mathematical techniques in order to extract the interaction from the phase shifts it produces. In particular we use the Distorted Born Approximation and Auxiliary Potential to extract the potential from the phase shifts it produces. Our approach includes, as a special case, the previous work. Our results are much more accurate than those in previous work. Moreover, we obtained very good results for strong potentials which the previous work could not. Finally, in the course of this research, we obtained some useful and relevant mathematical expressions. Some of these involve new results.