Energy-Dependent Potentials Obtained by IP Inversion

Abstract

The iterative-perturbative (IP) algorithm allows real or complex, central and spin-orbit potentials to be determined by inversion from the elastic S-matrix for both spin 0 and spin-1/2 scattering [1]. The procedure can also be applied to incomplete data sets, to data sets for a range of energies (“mixed case inversion”) and to data sets containing experimental errors [2], [3]. Simple regularisation techniques are used to obtain the smoothest possible potentials where the data sets are incomplete. Although the method does not represent a rigorous mathematical solution of the inverse scattering problem, a considerable improvement over model independent fitting methods is obtained by using the Born approximation to obtain a rapidly convergent and computationally efficient solution. Similar techniques have been used by Kukulin, [4].