Symmetry and Supersymmetry in Nuclear Pairing: Exact Solutions

TL;DR

This paper reviews exact solutions of nuclear pairing models, highlighting the role of symmetry and supersymmetry, and discusses challenges in extending these solutions to more complex systems.

Contribution

It summarizes recent exact solutions of nuclear pairing Hamiltonians, emphasizing supersymmetry and exploring potential generalizations beyond simple models.

Findings

Exact solutions for degenerate single particle states with different pairing strengths.

Identification of supersymmetry in the strong coupling limit.

Discussion of challenges in extending solutions to multiple states and d-wave pairing.

Abstract

Pairing plays a crucial role in nuclear spectra and attempts to describe it has a long history in nuclear physics. The limiting case in which all single particle states are degenerate, but with different s-wave pairing strengths was only recently solved. In this strong coupling limit the nuclear pairing Hamiltonian also exhibits a supersymmetry. Another solution away from those limits, namely two non-degenerate single particle states with different pairing strengths, was also given. In this contribution these developments are summarized and difficulties with possible generalizations to more single particle states and d-wave pairing are discussed.