Exactly solvable pairing Hamiltonian for heavy nuclei

Physical Review C (Impact Factor: 3.88). 09/2011; 84. DOI: 10.1103/PhysRevC.84.061301
Source: arXiv

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

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    ABSTRACT: 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.

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