Forging the link between nuclear reactions and nuclear structure

W H Dickhoff

doi:10.1051/epjconf/201612209003

Abstract

A review of the recent applications of the dispersive optical model (DOM) is presented. Emphasis is on the nonlocal implementation of the DOM that is capable of describing ground-state properties accurately when data like the nuclear charge density are available. The DOM, conceived by Claude Mahaux, provides a unified description of both elastic nucleon scattering and structure information related to single-particle properties below the Fermi energy. We have recently introduced a nonlocal dispersive optical potential for both the real and imaginary part. Nonlocal absorptive potentials yield equivalent elastic differential cross sections for ${}^{40}$Ca as compared to local ones but change the $\ell$-dependent absorption profile suggesting important consequences for the analysis of nuclear reactions. Below the Fermi energy, nonlocality is essential for an accurate representation of particle number and the nuclear charge density. Spectral properties implied by $(e,e'p)$ and $(p,2p)$ reactions are correctly described, including the energy distribution of about 10\% high-momentum protons obtained at Jefferson Lab. The nonlocal DOM allows a complete description of experimental data both above (up to 200 MeV) and below the Fermi energy in $^{40}$Ca. It is further demonstrated that elastic nucleon-nucleus scattering data constrain the spectral strength in the continuum of orbits that are nominally bound in the independent-particle model. Extension of this analysis to $^{48}$Ca allows a prediction of the neutron skin of this nucleus that is larger than most predictions made so far.

Highlights

A review of the recent applications of the dispersive optical model (DOM) is presented
The nonlocal DOM potential generated in Ref. [15] was motivated by theoretical calculations of the self-energy for 40Ca which either emphasized long-range correlations (LRC) [17] or short-range correlations (SRC) [18]
In Ref. [17] the results of the ab initio Faddeev random phase approximation (FRPA) which emphasizes the coupling of nucleons to low-lying collective states and to giant resonances, were compared with local DOM results

Summary

Introduction

Playing a role in the properties of nuclei and play a very important role in the success of ab initio methods to describe nuclei that rely on interactions with substantial repulsive cores. The link between nuclear reactions and nuclear structure is possible by considering these potentials as representing different energy domains of one underlying nucleon self-energy provided by the framework of Green’s function theory [5] This idea was implemented in the DOM by Mahaux and Sartor [6]. A compact formulation for the propagator leads to the Dyson equation which relates the propagator to a noninteracting one used as a starting point and the so-called self-energy The latter acts as the potential in a Schrödinger-like equation derived from the Dyson equation with solutions that identify the properties of nucleons that are either removed or added to a ground-state nucleus.

Green’s functions and the dispersive optical model

Results for 40Ca

Results for 48Ca

Conclusions and outlook