Theory of deuteron stripping and pick-up reactions for nuclear structure studies

Background: Given the importance of including nonlocality in the effective interactions in reaction models, a recent phenomenological study focusing on neutron-target nonlocal optical potentials suggests the need for the inclusion of explicit energy dependence [Lovell et al., Phys. Rev. C 96, 051601 (2017)].Purpose: In this work, we inspect whether the same is true for proton nonlocal optical potentials.Method: Similarly to the earlier work, we perform a ${\ensuremath{\chi}}^{2}$ analysis of proton elastic scattering data on $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ at energies of $E\ensuremath{\approx}10--45$ MeV, assuming the Tian, Pang, and Ma nonlocal 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 parametrization.Results: No matter which starting point is used, or whether we include backward angles in the fitting procedure, our results show the emergence of a strong energy dependence in the potential. We also show that while our parametrization represents only a modest improvement over the original energy-independent potential for those cases included in the fit, our new energy-dependent potential extrapolates much better for nuclei not included in the fit and for energies above those included.Conclusions: As for the neutron case, we conclude that nonlocality alone cannot provide a complete description of proton elastic scattering data and that a significant energy dependence is required.

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Exploration of the energy dependence of proton nonlocal optical potentials

Transfer reaction code with nonlocal interactions

A widely accepted practice for treating deuteron breakup in A(d,p)B reactions relies on solving a three-body A+n+p Schrodinger equation with pairwise A−n, A−p and n−p interactions. However, it was shown in Phys. Rev. C 89, 024605 (2014) that projection of the many-body A+2 wave function into the three-body A+n+p channel results in a complicated three-body operator that cannot be reduced to a sum of pairwise potentials. It contains explicit contributions from terms that include interactions between the neutron and proton via excitation of the target A. Such terms are normally neglected. We estimate the first-order contribution of these induced three-body terms and show that applying the adiabatic approximation to solving the A+n+p model results in a simple modification of the two-body nucleon optical potentials. We illustrate the role of these terms for the case of 40Ca(d,p)41Ca transfer reactions at incident deuteron energies of 11.8, 20, and 56 MeV, using several parametrizations of nonlocal optical potentials.

Effects of an induced three-body force in the incident channel of ( d,p ) reactions

Calculations of the direct radiative capture reactions are made for the $^{48}\mathrm{Ca}(n,\ensuremath{\gamma})^{49}\mathrm{Ca}$, $^{7}\mathrm{Li}(n,\ensuremath{\gamma})^{8}\mathrm{Li}$, and $^{12}\mathrm{C}(p,\ensuremath{\gamma})^{13}\mathrm{N}$ reactions with the Perey-Buck-type nonlocal potentials using a potential model. Our results reproduce the experimental data reasonably well. From comparisons to results obtained by using local potentials, it is found that the cross sections of direct capture reactions may change by around 25% due to the nonlocality of nuclear potentials.

Effects of nonlocality of nuclear potentials on direct capture reactions

Based on the Perey–Buck nonlocal optical model potential, F. Perey and B. Buck, Nucl. Phys. 32 (1962) 353, we obtain a new set of nonlocal optical model potential (NLOMP) parameters for proton and neutron scattering off nuclei. The experimental angular distributions of nucleon scattering off nuclei ranging from 27Al to 208Pb with incident energies around 10 MeV to 30 MeV are adopted in the fitting procedures. This NLOMP is energy independent. The chi-squares χ2 obtained in the fittings are comparable to those from the KD03 phenomenological local optical model potentials (OMP) A. Koning and J. Delaroche, Nucl. Phys. A 713 (2003) 231. Good agreement is found in comparisons between optical model calculations using this NLOMP and KD03 in their reproduction to the experimental angular distributions of elastic scattering cross-sections and analyzing powers.

Systematic nonlocal optical model potential for nucleons

This paper presents the results of a study that compares CTOM, a microscopic optical model potential (OMP), which is an optical model co-created by the China Nuclear Data Center & Tuebingen University, to CH89, which is a typical phenomenological OMP. The respective OMPs were tested by applying them to the modelling of nucleon elastic scattering and (d, p) transfer reactions involving 14C, 36S, and 58Ni targets at both low and relatively high energies. The results demonstrated that although both potentials successfully accounted for the angular distributions of both the elastic scattering and transfer cross sections, the absolute values of the transfer cross sections calculated using CTOM were approximately 25% larger than those calculated using CH89. This increased transfer cross sections allowed CTOM to produce single particle strength reduction factors for the three reactions that were consistent with those extracted from (e, e′ p) reactions as well as with more recent (p, 2p) and (p, pn) reactions. Notch tests suggested that nucleon elastic scattering and transfer reactions are sensitive to different regions of the OMP; accordingly, phenomenological OMPs, which are constrained only by elastic scattering cross sections, may not be sufficient for nucleon transfer reactions. Therefore, we suggest that microscopic OMPs, which reflect more theoretical considerations, should be preferred over phenomenological ones in calculations of direct nuclear reactions.

Zhong-Yu Ma

Papers

Systematic nonlocal optical model potential for nucleons

What kind of optical model potentials should be used for deuteron stripping reactions