INVERSE SCATTERING PROBLEM FOR RANK-2 SEPARABLE POTENTIALS AND OFF-SHELL EFFECTS

In this article an exact solution is given for the inverse scattering problem for rank-two separable potentials. It is shown that one of the form factors can be chosen arbitrarily, in practice the attractive one. If we require that the potential in addition to phase shift and binding energy also reproduces an arbitrary bound state wave function, a special and unique solution is obtained. This special potential is shown to be promising as a first order approximation to a local potential. The arbitrariness of the attractive form factor is used to investigate off-shell effects in the simplest and most direct way, by calculating the half-off-shell R-matrix. By only changing the strength and the range of an attractive form factor of the Yamaguchi type, we already obtain large differences in the half-off-shell R-matrix. On the other hand it is found that two rank-two separable potentials having the same bound state wave function in addition to the same phase shift and binding energy also have nearly the same half-off-shell R-matrix, in spite of their having rather different form factors. © 1969.