Exactly solvable pairing Hamiltonian for heavy nuclei

TL;DR

This paper introduces a new exactly solvable pairing Hamiltonian for heavy nuclei, derived from Richardson-Gaudin models, with adjustable parameters that accurately reproduce Gogny mean-field calculations.

Contribution

It develops a novel solvable Hamiltonian with adjustable parameters, bridging exact solutions and realistic nuclear models.

Findings

Accurately reproduces Gogny mean-field results

Introduces a Hamiltonian with two tunable parameters

Provides an exact solution for pairing in heavy nuclei

Abstract

We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one related to an interaction cutoff and the other to the pairing strength. These two parameters can be adjusted to give an excellent reproduction of Gogny self-consistent mean-field calculations in the canonical basis.