# Symmetry restoration in the mean-field description of proton-neutron pairing

## TL;DR

This paper demonstrates that restoring symmetries in mean-field models accurately captures isoscalar and isovector proton-neutron pairing, showing equivalence of pair- and quartet-based descriptions in nuclear physics.

## Contribution

It introduces a symmetry-restoration approach within a simple SO(8) model to accurately describe proton-neutron pairing, bridging pair- and quartet-based frameworks.

## Key findings

- Symmetry restoration accounts for pairing properties.
- Pair-condensate and quartet-condensate descriptions are equivalent.
- Method can be extended to realistic nuclear models.

## Abstract

We show that the symmetry-restored paired mean-field states (quasiparticle vacua) properly account for isoscalar versus isovector nuclear pairing properties. Full particle-number, spin, and isospin symmetries are restored in a simple SO(8) proton-neutron pairing model, and prospects to implement a similar approach in a realistic setting are delineated. Our results show that, provided all symmetries are restored, the pictures based on pair-condensate and quartet-condensate wave functions represent equivalent ways of looking at the physics of nuclear proton-neutron pairing.