Nonlocal extension of the dispersive-optical-model to describe data below the Fermi energy

TL;DR

This paper introduces a nonlocal dispersive optical model that overcomes limitations of local energy-dependent potentials, enabling comprehensive analysis of nucleon properties below the Fermi energy using elastic scattering data.

Contribution

The paper develops a nonlocal, energy-independent dispersive optical model that accurately describes nucleon behavior below the Fermi energy and aligns with various experimental data.

Findings

Charge radius fit leads to excessive charge near the origin.

High-momentum components are underrepresented, indicating missing correlations.

Deeply-bound hole states are correctly positioned with the nonlocal model.

Abstract

Present applications of the dispersive-optical-model analysis are restricted by the use of a local but energy-dependent version of the generalized Hartree-Fock potential. This restriction is lifted by the introduction of a corresponding nonlocal potential without explicit energy dependence. Such a strategy allows for a complete determination of the nucleon propagator below the Fermi energy with access to the expectation value of one-body operators (like the charge density), the one-body density matrix with associated natural orbits, and complete spectral functions for removal strength. The present formulation of the dispersive optical model (DOM) therefore allows the use of elastic electron-scattering data in determining its parameters. Application to ${}^{40}$Ca demonstrates that a fit to the charge radius leads to too much charge near the origin using the conventional assumptions of the functional form of the DOM. A corresponding incomplete description of high-momentum components is identified, suggesting that the DOM formulation must be extended in the future to accommodate such correlations properly. Unlike the local version, the present nonlocal DOM limits the location of the deeply-bound hole states to energies that are consistent with (\textit{e,e}$^{\prime}$\textit{p}) and (\textit{p,2p}) data.