A quantum mechanical inverse scattering method at fixed energy

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Abstract
The authors present a new approach to the quantum mechanical inverse scattering method at fixed energy. The approach employs a polynomial representation for the wavefunction in each partial wave, which contains a number of open parameters. These parameters are determined by the boundary conditions on the wavefunctions (at large radial distances these are imposed by the phase shifts) and the assumption that the wavefunction in each partial wave corresponds to the same local, l-independent, underlying potential. A variational approach is employed. The method is illustrated by inversion of the phase shifts corresponding to a singular potential from electron-atom scattering and a gaussian potential used in nuclear scattering theory.