Pauli nonlocality and the nucleon effective mass

TL;DR

This paper investigates the nucleon effective mass in nuclear matter, emphasizing the role of Pauli nonlocality, and validates a folding model approach through elastic scattering data to understand neutron-proton effective mass splitting.

Contribution

It introduces a method to extract the nucleon effective mass from elastic scattering data using a folding model that accounts for Pauli nonlocality, providing new insights into neutron-proton mass splitting.

Findings

Effective mass depends mainly on exchange term at low momenta.

Nucleon effective mass splitting is linearly related to neutron-proton asymmetry.

Model validation confirms the reliability of the local approximation in folding calculations.

Abstract

A study of the nucleon mean-field potential in nuclear matter (NM) is done within an extended Hartree-Fock (HF) formalism, using the CDM3Y6 density dependent version of the M3Y interaction which is associated with the nuclear incompressibility $K\simeq 252$ MeV. The momentum dependence of nucleon optical potential (OP) in NM at the saturation density $\rho_0$ is shown to be due mainly to its exchange term up to $k\approx 2$ fm$^{-1}$, so that the Pauli nonlocality is expected to be the main origin of the nucleon effective mass at low momenta. Because nucleons in neutron-rich NM at $\rho\approx \rho_0$ are either weakly bound or unbound by the in-medium nucleon-nucleon interaction, the determination of the effective mass of nucleon scattered on targets with neutron excess at low energies should be of interest for the mean-field studies of neutron star matter. For this purpose, the folding model is used to calculate the nonlocal nucleon OP for the optical model analysis of elastic nucleon scattering on $^{40,48}$Ca, $^{90}$Zr, and $^{208}$Pb targets at energies $E<50$ MeV, to probe the model reliability and validate the WKB local approximation to obtain the local folded nucleon OP. The nucleon effective mass $m^*$ is then carefully deduced from the momentum dependence of the local folded nucleon OP which is resulted from the Pauli nonlocality of the exchange term. The neutron-proton effective mass splitting determined at $\rho\approx\rho_0$ from the central strength of the real folded nucleon OP for $^{48}$Ca, $^{90}$Zr, and $^{208}$Pb targets has been found to depend linearly on the neutron-proton asymmetry parameter as $m^*_{n-p}\approx (0.167\pm 0.018)\delta$, in a good agreement with the recent empirical constraints.