Study of Equivalent Local Potentials Obtained from Separable Two-Nucleon Interactions

A method of equivalent local potentials is applied to separable interactions which fit the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ two-nucleon phase shifts. The method of generating equivalent local potentials used in this paper is independent of the boundary conditions imposed on the solutions of the nonlocal equation; consequently, all solutions of the nonlocal equation lead to the same equivalent local potential. The uniqueness of the equivalent local potential obtained by the present method is considered to be useful for the purpose of understanding nonlocal interactions. The Yamaguchi, the one- and two-term Tabakin, and the case-IV Mongan potentials are studied. The equivalent local Yamaguchi potential is similar to low-energy local two-nucleon interactions which do not have short-range repulsion. The two-term Tabakin potential results in an equivalent local potential with short-range repulsion. The occurrence of spurious states in the one-term Tabakin potential is related to a class of zeros of this separable interaction in coordinate space. The case-IV Mongan potential results in an equivalent local potential with strong short-range attraction. Further study of this interaction revealed a spurious state at 19.6 BeV which causes the wave function to have an additional node at experimentally relevant energies. The paper is concluded with an examination of the problem of constructing separable interactions which have short-range repulsion. It is shown that such interactions have a pronounced tendency to produce spurious states.