NONLOCAL SEPARABLE SOLUTIONS OF THE INVERSE SCATTERING PROBLEM

We extend the nonlocal separable potential solutions of Gourdin and Martin for the inverse scattering problem to the case where sin δ0 has more than N zeroes, δ0 being the s-wave scattering phase shift and δ0(0) − δ0(∞) = Nπ. As an example we construct the solution for the particular case of 4 He and show how to incorporate a weakly bound state. Using a local square well potential chosen to mimic the real 4 He potential, we compare the off-shell extension of the nonlocal potential solution with the exactly solvable square well. We then discuss how a nonlocal potential might be used to simplify the many-body problem of liquid 4 He .