A method for solving the quantum inverse scattering problem for coupled channels at fixed energy

This paper describes the inversion of a scattering problem with coupled channels at fixed energy. The coupling potential matrix is obtained from the S-matrix with the modified Newton-Sabatier method with a special expansion of the integral kernel and a determination of the potential matrix by using the coupled radial equations. The method is applied to problems restricted to two channels and with a monopole, dipole and quadrupole coupling (lambda = 0, 1, 2) between the channels. The inversion is shown to work quite satisfactorily and is useful for heavy ion scattering in nuclear physics.