# Isovector and isoscalar pairing in odd-odd $N=Z$ nuclei within a quartet approach

## TL;DR

This paper extends the quartet condensation model to accurately describe isovector and isoscalar pairing in odd-odd N=Z nuclei, revealing coexistence of pairing correlations with isovector pairing being dominant.

## Contribution

The paper introduces an extended QCM approach that effectively models pairing correlations in odd-odd N=Z nuclei, combining isovector and isoscalar pairs variationally.

## Key findings

- The extended QCM predicts low-lying state energies with high accuracy.
- Isovector and isoscalar pairing correlations coexist in these nuclei.
- Isovector pairing plays a more dominant role than isoscalar pairing.

## Abstract

The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axial symmetry. The accuracy of the trial functions is tested for realistic pairing Hamiltonians and odd-odd N=Z nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. It is shown that the extended QCM approach is able to predict with high accuracy the energies of the lowest T=0 and T=1 states. The present calculations indicate that in these states the isovector and the isoscalar pairing correlations coexist together, with the former playing a dominant role.