Exact T=0 Eigenstates of the Isovector Pairing Hamiltonian

TL;DR

This paper derives exact T=0 seniority-zero eigenstates of the isovector pairing Hamiltonian, revealing their structure as superpositions of T=1 pairs grouped into T=0 quartets, emphasizing the pairing force's role in nuclear quarteting.

Contribution

It provides the first analytic expression of these eigenstates, demonstrating the formation of T=0 quartets from T=1 pairs in the isovector pairing model.

Findings

Eigenstates are superpositions of T=1 pairs forming T=0 quartets.

Ground state is a linear combination of proton-neutron quartets.

Highlights the importance of isovector pairing in nuclear structure.

Abstract

We derive the exact $T=0$ seniority-zero eigenstates of the isovector pairing Hamiltonian for an even number of protons and neutrons. Nucleons are supposed to be distributed over a set of non-degenerate levels and to interact through a pairing force with constant strength. We show that these eigenstates (and among them, in particular, the ground state) are linear superpositions of products of $T=1$ collective pairs arranged into $T=0$ quartets. This grouping of protons and neutrons first into $T=1$ collective pairs and then into $T=0$ quartets represents the distinctive feature of these eigenstates. This work highlights, for the first time on the grounds of the analytic expression of its eigenstates, the key role played by the isovector pairing force in the phenomenon of nuclear quarteting.