We present an account of the current status of the theoretical treatment of inclusive (d, p) reactions in the breakup-fusion formalism, pointing to some applications and making the connection with current experimental capabilities. Three independent implementations of the reaction formalism have been recently developed, making use of different numerical strategies. The codes also originally relied on two different but equivalent representations, namely the prior (Udagawa-Tamura, UT) and the post (Ichimura-Austern-Vincent, IAV) representations. The different implementations have been benchmarked, and then applied to the Ca isotopic chain. The neutron-Ca propagator is described in the Dispersive Optical Model (DOM) framework, and the interplay between elastic breakup (EB) and non-elastic breakup (NEB) is studied for three Ca isotopes at two different bombarding energies. The accuracy of the description of different reaction observables is assessed by comparing with experimental data of (d, p) on 40,48 Ca. We discuss the predictions of the model for the extreme case of an isotope ( 60 Ca) currently unavailable experimentally, though possibly available in future facilities (nominally within production reach at FRIB). We explore the use of (d, p) reactions as surrogates for (n, γ) processes, by using the formalism to describe the compound nucleus formation in a (d, pγ) reaction as a function of excitation energy, spin, and parity. The subsequent decay is then computed within a Hauser-Feshbach formalism. Comparisons between the (d, pγ) and (n, γ) induced gamma decay spectra are discussed to inform efforts to infer neutron captures from (d, pγ) reactions. Finally, we identify areas of opportunity for future developments, and discuss a possible path toward a predictive reaction theory.

A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in 48 Ca. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator resulting from these self-energies, we have determined the charge and neutron matter distributions in 48 Ca. A best fit neutron skin of 0.249±0.023 fm is deduced, but values up to 0.33 fm are still consistent. The energy dependence of the total neutron cross sections is shown to have strong sensitivity to the skin thickness.A fundamental question in nuclear physics is how the constituent neutrons and protons are distributed in the nucleus. In particular, for a nucleus which has a large excess of neutrons over protons, are the extra neutrons distributed evenly over the nuclear volume or is this excess localized in the periphery of the nucleus forming a neutron skin? A quantitative measure is provided by the neutron-skin thickness ∆r np defined as the difference between neutron and proton rms radii, i.e., ∆r np = r n − r p .The nuclear symmetry energy which characterizes the variation of the binding energy as a function of neutronproton asymmetry, opposes the creation of nuclear matter with excesses of either type of nucleon. The extent of the neutron skin is determined by the relative strengths of the symmetry energy between the central near-saturation and peripheral less-dense regions. Therefore ∆r np is a measure of the density dependence of the symmetry energy around saturation [1][2][3][4]. This dependence is very important for determining many nuclear properties, including masses, radii, and the location of the drip lines in the chart of nuclides. Its importance extends to astrophysics for understanding supernovae and neutron stars [5,6], and to heavy-ion reactions [7].Given the importance of the neutron-skin thickness in these various areas of research, a large number of studies (both experimental and theoretical) have been devoted to it [8]. While the value of r p can be determined quite accurately from electron scattering [9], the experimental determinations of r n are typically model dependent [8]. However, the use of parity-violating electron scattering does allow for a nearly model-independent extraction of this quantity [10]. The present value for 208 Pb extracted with this method from the PREX collaboration yields a skin thickness of ∆r np =0.33 +0.16−0.18 fm [11]. Future electron-scattering measurements are expected to reduce the experimental uncertainty.In this work we present an alternative method of determining r n using a dispersive-optical-model (DOM) analysis of bound and scattering data to constrain the nucleon self-energy Σ ℓj . This self-energy is a complex and nonlocal potential that unites the nuclear structure and reaction domains [12,13]. The DOM was originally developed by Mahaux and Sarto...

The nonlocal implementation of the dispersive optical model (DOM) provides all the ingredients for distorted-wave impulse-approximation (DWIA) calculations of the (e, e ′ p) reaction. It provides both the overlap function, including its normalization, and the outgoing proton distorted wave. This framework is applied to describe the knockout of a proton from the 0d 3 2 and 1s 1 2 orbitals in 40 Ca with fixed normalizations of 0.71 and 0.60, respectively. Data were obtained in parallel kinematics for three outgoing proton energies: 70, 100, and 135 MeV. Agreement with the data is as good as, or better than, previous descriptions employing local optical potentials and overlap functions from Woods-Saxon potentials -both with standard nonlocality corrections -whose normalization (spectroscopic factor) and radius were fitted to the data. The present analysis suggests that slightly larger spectroscopic factors are obtained when nonlocal optical potentials are employed than those generated with local potentials. The results further suggest that the chosen kinematical window around 100 MeV proton energy provides the best and cleanest method to employ the DWIA for the analysis of this reaction. The conclusion that substantial ground-state correlations cannot be ignored when describing a closed-shell atomic nucleus is therefore confirmed in detail. To reach these conclusions, it is essential to have a complete description of the nucleon single-particle propagator that accounts for all elastic nucleon-scattering observables in a wide energy domain up to 200 MeV. The current nonlocal implementation of the DOM fulfills this requirement.

A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in 208 Pb. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, the charge distribution, and the binding energy have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we have determined the charge and matter distributions in 208 Pb. The predicted spectroscopic factors are consistent with results from the (e, e p) reaction and inelastic-electron-scattering data to very high spin states. Sensible results for the high-momentum content of neutrons and protons are obtained with protons appearing more correlated, in agreement with experiment and ab initio calculations of asymmetric matter. A neutron skin of 0.250 ± 0.05 fm is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a non-negligible role in the formation of the neutron skin in finite nuclei.