Solution of the inverse scattering problem at fixed energy with nonphysical S matrix elements - art. no. 064605

The quantum mechanical inverse elastic scattering problem is solved with th e modified Newton-Sabatier method. A set of S matrix elements calculated fr om a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved b y including nonphysical S matrix elements to half, quarter, and eighth valu ed partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be ve ry sensitive to the choice of those nonphysical S matrix values both with t he analytic potential model and in a real application in which the experime ntal cross section for the symmetrical scattering system of C-12+C-12 at E= 7.998 MeV is analyzed.