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.

Recently a variety of studies have shown the importance of including non-locality in the description of reactions. The goal of this work is to revisit the phenomenological approach to determining non-local optical potentials from elastic scattering. We perform a χ 2 analysis of neutron elastic scattering data off 40 Ca, 90 Zr and 208 Pb at energies E ≈ 5 − 40 MeV, assuming a Perey and Buck [1] or Tian, Pang, and Ma [2] non-local form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parameterization. Independently of the starting point in the minimization procedure, an energy dependence in the imaginary depth is required for a good description of the data across the included energy range. We present two parameterizations, both of which represent an improvement over the original potentials for the fitted nuclei as well as for other nuclei not included in our fit. Our results show that, even when including the standard Gaussian non-locality in optical potentials, a significant energy dependence is required to describe elastic-scattering data.

We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, $(d,N)$ or $(N,d)$, including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of $A(d,N)B$ or $B(N,d)A$. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of $E_d=10-70$ MeV, and provides cross sections with $4\%$ accuracy.Comment: 35 pages, 6 figure

Assuming that the ratio between asymptotic normalization coefficients of mirror states is model independent, charge symmetry can be used to indirectly extract astrophysically relevant proton capture reactions on proton-rich nuclei based on information on stable isotopes. The assumption has been tested for light nuclei within the microscopic cluster model. In this work we explore the Hamiltonian independence of the ratio between asymptotic normalization coefficients of mirror states when deformation and core excitation is introduced in the system. For this purpose we consider a phenomenological rotor + N model where the valence nucleon is subject to a deformed mean field and the core is allowed to excite. We apply the model to 8 Li/ 8 B, 13 C/ 13 N, 17 O/ 17 F, 23 Ne/ 23 Al, and 27 Mg/ 27 P. Our results show that for most studied cases, the ratio between asymptotic normalization coefficients of mirror states is independent of the strength and multipolarity of the couplings induced. The exception is for cases in which there is an s-wave coupled to the ground state of the core, the proton system is loosely bound, and the states have large admixture with other configurations. We discuss the implications of our results for novae.

Background: In the last year we have been exploring the effect of the explicit inclusion of nonlocality in (d,p) reactions.Purpose: The goal of this work is to extend previous studies to (d,n) reactions, which, although similar to (d,p), have specific properties that merit inspection.Method: We apply our methods (both the distorted wave Born approximation and the adiabatic wave approximation) to (d, n) reactions on 16 O, 40 Ca, 48 Ca, 126 Sn, 132 Sn, and 208 Pb at 20 and 50 MeV. Results:We look separately at the modifications introduced by nonlocality in the final bound and scattering states, as well as the consequences reflected on the differential angular distributions. The cross sections obtained when using nonlocality explicitly are significantly different than those using the local approximation, just as in (d,p). Due to the particular role of Coulomb in the bound state, often we found the effects of nonlocality to be larger in (d,n) than in (d,p). Conclusions:Our results confirm the importance of including nonlocality explicitly in deuteron induced reactions.

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