# Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states

## TL;DR

This paper presents an exact shell-model solution for nuclear pairing correlations, including proton-neutron pairs, using a minimal parameter Hamiltonian, and demonstrates its effectiveness in reproducing experimental data and elucidating pairing effects.

## Contribution

It introduces a novel exactly solvable shell-model Hamiltonian with only two parameters that accurately captures pairing correlations, including proton-neutron interactions, across a range of nuclei.

## Key findings

- Accurately reproduces experimental 0+ state energies for isotopes A=10 to 62.
- Isolates effects of like-particle and proton-neutron pairing.
- Provides estimates for pairing gaps and explains N=Z irregularity.

## Abstract

We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector $T=1$ pairing interaction and an average proton-neutron isoscalar $T=0$ interaction, where the $T=0$ term describes the average interaction between non-paired protons and neutrons. This Hamiltonian is exactly solvable, where, utilizing 3 to 7 single-particle energy levels, we reproduce experimental data for 0$^+$ state energies for isotopes with mass $A=10$ through $A=62$ exceptionally well including isotopes from He to Ge. Additionally, we isolate effects due to like-particle and proton-neutron pairing, provide estimates for the total and proton-neutron pairing gaps, and reproduce $N$ (neutron) = $Z$ (proton) irregularity. These results provide a further understanding for the key role of proton-neutron pairing correlations in nuclei, which is especially important for waiting-point nuclei on the rp-path of nucleosynthesis.