Testing the Perey effect

Background: The effects of nonlocal potentials have historically been approximately included by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as the Perey correction factor.Purpose: In this work we investigate the validity of the Perey correction factor for single-channel bound and scattering states, as well as in transfer $(p,d)$ cross sections.Method: We solve the scattering and bound state equations for nonlocal interactions of the Perey-Buck type, through an iterative method. Using the distorted wave Born approximation, we construct the T matrix for $(p,d)$ on ¹⁷O, ⁴¹Ca, ⁴⁹Ca, ¹²⁷Sn, ¹³³Sn, and ²⁰⁹Pb at 20 and 50 MeV.Results: We found that for bound states, the Perey corrected wave function resulting from the local equation agreed well with that from the nonlocal equation in the interior region, but discrepancies were found in the surface and peripheral regions. Overall, the Perey correction factor was adequate for scattering states, with the exception of a few partial waves corresponding to the grazing impact parameters. These differences proved to be important for transfer reactions.Conclusions: If only local optical potentials are used in the analysis of experimental $(p,d)$ cross sections, without any correction factors, as compared to the analysis with nonlocal potentials, the spectroscopic factors could be affected by approximately 20%. The Perey correction factor does offer an improvement over taking a direct local equivalent solution. However, if the desired accuracy is to be better than 10%, the exact solution of the nonlocal equation should be pursued.