Localization of a nonlocal interaction

A simple method for the localization of a separable nonlocal interaction is formulated in terms of Green’s functions and the solutions with regular and irregular boundary conditions. The constructed energy–momentumdependent local potential with regular boundary condition is real while that for the irregular boundary condition is complex in nature. The phase function method is exploited to compute elastic scattering phases for the nucleon–nucleon and 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 the potentials derived from the irregular solutions for the alpha–nucleon systems, however, give indications of resonances at very low energies.