Localization of a nonlocal interaction

Abstract

A simple method for the localization of a separable nonlocal interaction is formulated in terms of Green'sfunctions and the solutions with regular and irregular boundary conditions. The constructed energy{momentum-dependent local potential with regular boundary condition is real while that for the irregular boundary condition iscomplex in nature. The phase function method is exploited to compute elastic scattering phases for the nucleon{nucleonand alpha{nucleon systems. Reasonable agreements in scattering phase shifts with experimental data are obtained,particularly, in the low energy range for the systems under consideration. The phase shifts for the imaginary parts of thepotentials derived from the irregular solutions for the alpha{nucleon systems, however, give indications of resonances atvery low energies.