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arXiv:nucl-th/0406001

Generalized Richardson-Gaudin Nuclear Models

J. Dukelsky, V. G. Gueorguiev, P. Van Isacker

Published Jun 1, 2004• 1 citation
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Abstract

The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the $su(2)$-based fermion pairing, to any simple Lie algebra. As an example, the $so(5)\sim sp(4)$ model of T=1 pairing is discussed and illustrated for the case of $^{64}$Ge with non-degenerate single-particle energies.

DOI
10.48550/arxiv.nucl-th/0406001

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The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the su(2)su(2)su(2)-based fermion pairing, to any simple Lie algebra. As an example, the so(5)∼sp(4)so(5)\sim sp(4)so(5)∼sp(4) model of T=1 pairing is discussed and illustrated for the case of 64^{64}64Ge with non-degenerate single-particle energies.
The exact solution of the SU(2) pairing Hamiltonian with non-degenerate single particle orbits was introduced by Richardson in the early sixties. Since then it has been extended to several families of integrable models, called the Richardson-Gaudin (RG) models. In particular, the rational family of integrable RG models has been widely applied to mesoscopic systems like small grains, quantum dots and nuclear systems where finite size effects play an important role. We introduce these families of integrable models and then we describe a new separable pairing Hamiltonian derived from the hyperbolic family that provides an excellent reproduction of Gogny self-consistent mean-field calculations for heavy nuclei.
The exact solution of the SU(2) pairing Hamiltonian with non-degenerate single particle orbits was introduced by Richardson in the early sixties. The exact solution passed almost unnoticed till was recovered in the last decade in an effort to describe the disappearance of superconductivity in ultrasmall superconducting grains. Since then it has been extended to several families integrable models, called the Richardson-Gaudin (RG) models. In particular, the rational family of integrable RG models has been widely applied to mesoscopic systems like small grains, quantum dots and nuclear systems where finite size effects play an important role. We will first introduce these families of integrable models and then we will describe the first applications of the hyperbolic family to spinless cold fermionic atonies in two dimensional lattices and to heavy nuclei.