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

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 (e,e ′ p) and (p,2p) data.

Forging the Link between Nuclear Reactions and Nuclear Structure

“…F and employ the subtracted form of the dispersion relation calculated at this energy [5,8] Re Σ ℓj (r, r…”

“…The solution of the Dyson equation below the Fermi energy was introduced in Ref. [8]. The scattering wave functions are generated with the iterative procedure outlined in Ref.…”

“…The main stumbling block so far has been the need to utilize the approximate expressions for the properties of nucleons below the Fermi energy that were developed by Mahaux and Sartor [5] to correct for the normalizationdistorting energy dependence of the Hartree-Fock (HF) potential. By restoring the proper treatment of nonlocality in the HF contribution, it was possible to overcome this problem [8] although the local treatment of the absorptive potentials yielded a poor description of the nuclear charge density and particle number.In the present work we have for the first time treated the nonlocality of these potentials for the nucleus 40 Ca with the aim to include all available data below the Fermi energy that can be linked to the nucleon single-particle propagator [9] while maintaining a correct description of the elastic-scattering data. The result is a DOM potential that can be interpreted as the nucleon self-energy constrained by all available experimental data up to 200 MeV.…”

“…The main stumbling block so far has been the need to utilize the approximate expressions for the properties of nucleons below the Fermi energy that were developed by Mahaux and Sartor [5] to correct for the normalizationdistorting energy dependence of the Hartree-Fock (HF) potential. By restoring the proper treatment of nonlocality in the HF contribution, it was possible to overcome this problem [8] although the local treatment of the absorptive potentials yielded a poor description of the nuclear charge density and particle number.…”

Effects of nonlocal potentials on(p,d)transfer reactions

“…Because the local version of the DOM still contains an energy-dependence related to non-locality of the real part, it distorts the normalization of the spectral strength and requires a correction for the proper normalization of spectroscopic factors. A non-local Hartree-Fock-like and energy-independent potential was introduced in [22] to avoid this issue. While this step allows the interpretation of the optical potential as representing the nucleon self-energy, it was also shown that observables like the nuclear charge density cannot be described in detail.…”