Isovector and isoscalar proton-neutron pairing in $N>Z$ nuclei

TL;DR

This paper introduces a particle number conserving formalism for treating isovector and isoscalar proton-neutron pairing in N>Z nuclei, demonstrating its accuracy and significance of these correlations away from the N=Z line.

Contribution

The authors develop a novel quartet condensate formalism that accurately describes proton-neutron pairing in nuclei with N>Z, improving upon previous models.

Findings

Ground state correlation energies match exact diagonalization results.

Both isoscalar and isovector pairing correlations remain significant away from N=Z.

Models based solely on proton-neutron pair condensates are insufficient.

Abstract

We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess. The quartets are built by two isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for $N>Z$ nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. The calculations are done with two pairing interactions, one state-independent and the other of zero range, which are supposed to scatter pairs in time-revered orbits. It is proven that the ground state correlation energies calculated within this approach are very close to the exact results provided by the diagonalization of the pairing Hamiltonian. Based on this formalism we have shown that moving away of N=Z line, both the isoscalar and the isovector proton-neutron pairing correlations remain significant and that they cannot be treated accurately by models based on a proton-neutron pair condensate.