Applicability of Phase-Equivalent Energy-Dependent Potential. Case Studies

Energy-momentum dependent phase-equivalent local potential to the Graz separable one is constructed following the method of Arnold and MacKellar. The scattering phase shifts for the nonlocal potential are computed via the Fredhlom determinant and for equivalent local potential the same are calculated through the phase function method for nucleon-nucleon and alpha-nucleon systems. We achieve excellent agreement with the standard data up to partial wave l = 2. However, it is observed that this method of constructing equivalent local potentials works satisfactorily for few lower partial waves. It is also examined that beyond l = 2 our local potential is unable to reproduce the proper phase parameters. This may be caused due to the high momentum components (l > 2) of the nonlocal wave function that are not equivalent to those generated by the energy-momentum dependent local potential.