The Relative Abundance of Correlated Spin-zero Nucleon Pairs

TL;DR

This paper combines the generalized contact formalism with a mean-field model to analyze the prevalence of spin-zero short-range correlated nucleon pairs in nuclei, revealing isospin-dependent variations especially in nuclei with more than 50 nucleons.

Contribution

It introduces a novel approach integrating the generalized contact formalism with Woods-Saxon mean-field theory to study short-range correlations across different nuclei.

Findings

Neutron-neutron pair probability increases in heavy nuclei.

Proton-proton pair probability decreases in heavy nuclei.

Neutron-proton pair probability remains stable across nuclei.

Abstract

We utilize the generalized contact formalism in conjunction with the Woods-Saxon mean-field description of the long-range part of the nuclear wave function to assess the relative prevalence of short-range correlation pairs within atomic nuclei. We validate our approach by fitting experimental charge density results and electron scattering experiments to a very good agreement. Applying our model, we calculate the spin-zero short-range correlations contact ratios. Interestingly, for nuclei with $A>50$, we observe a notable dependence on the neutron-to-proton ratio $N/Z$. Specifically, the probability per nucleon to find neutron-neutron pairs increases, while that of proton-proton pairs decreases, whereas the probability of finding neutron-proton pairs remains relatively constant. To interpret this isospin symmetry breaking effect, we employ a simple model based on generalized Levinger constants, linking it to differences in nuclear proton and neutron radii.