Microscopic optical potentials from a Greens function approach

TL;DR

This work develops a microscopic, nonlocal, dispersive optical potential derived from the Feshbach formalism, linking a nucleon–target interaction to underlying nuclear structure through a dynamic polarization potential $V_{dpp}$ computed with a Green's function $G^Q$ in the $Q$-space. An iterative, self-consistent scheme updates the optical potential $\\mathcal{V}$ with a diagonal, weak-coupling approximation for $G^Q$, enabling absorption to arise from virtual population of excited states. The method is demonstrated by constructing a neutron optical potential for $^{24}$Mg using a $^{25}$Mg shell-model spectrum, yielding nonlocal, energy-dependent $V_{dpp}$ that reproduces elastic cross sections without phenomenological absorption terms, and by benchmarking against $p+^{40}$Ca in a collective model to validate the approach. The results indicate a promising path toward unified, structure-based reaction descriptions and motivate future work on nonlocal static inputs, transition densities, and energy-averaged treatments to explore direct versus compound reaction mechanisms and the limits of Hauser-Feshbach theory in exotic nuclei.

Abstract

Optical potentials are a standard tool in the study of nuclear reactions, as they describe the interaction between a target nucleus and a projectile. The use of phenomenological optical potentials built using experimental data on stable isotopes is widespread. Although successful in their dedicated domain, it is unclear whether these phenomenological potentials can provide reliable predictions for unstable isotopes. To address this problem, optical potentials based on microscopic nuclear structure input calculations prove to be crucial and are an important current line of research. In this work we present an explicit implementation of the Feshbach formalism for the systematic derivation of optical potentials using input from nuclear structure models. Numerical tools for the derivation of Green's functions associated with nonlocal potentials are presented. The new optical potential, based on the valence shell model, is applied to the calculations of n+24Mg elastic scattering and yields a close agreement with the experimental data.

Figures (9)

• Figure 1: Angular differential cross sections as functions of the center-of-mass scattering angle for $^{40}$Ca$(p,p)$ at 30.3 MeV, divided by Rutherford cross sections. The red curve is the calculation from our current work, the green crosses are the results of RaoRS1973, and the black points correspond to experimental data from RidleyT1964. The dotted blue line, which shows the calculation results employing only the static optical potential in Eq. (\ref{['eq112']}), demonstrates the impact of neglecting the coupling to the excited states.
• Figure 2: Angular differential cross sections as functions of the center-of-mass scattering angle for $^{40}$Ca$(p,p)$ at 30.3 MeV, divided by Rutherford using only the real part of the static potential (\ref{['eq112']}), for 1 (dotted blue line), and 30 (red line) iterations.
• Figure 3: Angular differential cross sections as functions of the center-of-mass scattering angle for $^{40}$Ca$(n,n)$ at 30.3 MeV. The blue dashed line corresponds to one iteration of the optical potential, and includes the phenomenological imaginary term $W(r)$ from RaoRS1973, while the red curve shows results with converged OP (30 iterations) and without $W(r)$. The black points are experimental data from DeVitoASB1981.
• Figure 4: Single-neutron spectroscopic factors of the $^{25}$Mg states versus $^{25}$Mg excitation energy, calculated using the PSDPF interaction BouhelalHCN2011. The gray vertical line shows the experimental neutron separation threshold in $^{25}$Mg. Inset: same but in logarithmic scale.
• Figure 5: Real and imaginary parts of the $n+^{24}$Mg dynamic polarization potential (see Eq. \ref{['eq:100']}) for $E=$3.4 MeV, calculated for the $\ell=1$ partial wave.