Quasi-elastic electron scattering with KIDS nuclear energy density functional

TL;DR

This study investigates how isoscalar and isovector effective masses influence quasi-elastic electron scattering in nuclei using the KIDS density functional, showing good agreement with experimental data and highlighting the impact of effective mass variations.

Contribution

It introduces a detailed analysis of effective mass effects in electron scattering within the KIDS functional framework, including parameter adjustments and spectroscopic factor estimations.

Findings

Cross sections increase with smaller isoscalar effective masses.

Isovector effective mass has negligible effect on scattering cross sections.

Spectroscopic factors align with existing literature.

Abstract

Isoscalar and isovector effective masses of the nucleon in nuclear medium are explored in the quasi-elastic electron scattering of nuclei with KIDS (Korea-IBS-Daegu-SKKU) density functional model. Effective masses are varied in the range (0.7 ~ 1.0)$M$ where $M$ is the mass of the nucleon in free space. Parameters in the KIDS functional are adjusted to nuclear matter equation of state, energy and radius of selected nuclei, and effective mass of nucleons. Hartree-Fock equation is solved to obtain the wave functions of the nucleon in target nuclei, and they are plugged in the calculation of electron-nucleus scattering cross sections at the energies of incident electrons 300 MeV ~ 2.5 GeV. Theoretical prediction agrees well with measurement. Dependence on the effective mass is evident: cross section tends to increase with small isoscalar effective masses. However, effect of isovector effective mass is negligible. Spectroscopic factors are estimated for the protons in the outermost shells of $^{16}$O, $^{40}$Ca, and $^{208}$Pb. Results are consistent with the values in the literature.