Background: The effects of non-local 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 non-local 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 17 O, 41 Ca, 49 Ca, 127 Sn, 133 Sn, and 209 Pb 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 non-local 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: 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 non-local equation should be pursued.

Background: Although local phenomenological optical potentials have been standardly used to interpret nuclear reactions, recent studies suggest the effects of non-locality should not be neglected. Purpose: In this work we investigate the effects of non-locality in (p, d) transfer reactions using non-local optical potentials. We compare results obtained with the dispersive optical model to those obtained using the Perey-Buck interaction. Method: We solved the scattering and bound-state equations for the non-local version of the dispersive optical model. Then, using the distorted wave Born approximation, we calculate the transfer cross section for (p, d) on 40 Ca at Ep=20, 35 and 50 MeV. Results: The inclusion of non-locality in the bound state has a larger effect than on the scattering states. The overall effect on the transfer cross section is very significant. We found an increase due to non-locality in the transfer cross section of ≈ 30 − 50% when using the Perey-Buck interaction and ≈ 15 − 50% when using the dispersive optical potential. Conclusions: Although the details of the non-local interaction can change the magnitude of the effects, our study shows that qualitatively the results obtained using the dispersive optical potential and the Perey-Buck interaction are consistent, in both cases the transfer cross sections are significantly increased.

Background: Traditionally, nucleon-nucleus optical potentials are made local for convenience. In recent work we studied the effects of including nonlocal interactions explicitly in the final state for (d,p) reactions, within the distorted wave Born approximation.Purpose: Our goal in this work is to develop an improved formalism for nonlocal interactions that includes deuteron breakup and to use it to study the effects of including nonlocal interactions in transfer (d,p) reactions, in both the deuteron and the proton channel.Method: We extend the finite-range adiabatic distorted wave approximation to include nonlocal nucleon optical potentials. Results: We find that nonlocality in the deuteron scattering state reduces the amplitude of the wave function in the nuclear interior, and shifts the wave function outward. In many cases, this has the effect of increasing the transfer cross section at the first peak of the angular distributions. This increase was most significant for heavy targets and for reactions at high energies.Conclusions: Our systematic study shows that, if only local optical potentials are used in the analysis of experimental (d, p) transfer cross sections, the extracted spectroscopic factors may be incorrect by up to 40% due to the local approximation.