Extended Bethe-Richardson-Gaudin ansatzes for the solution of a mean-field plus separable pairing model with three non-degenerate j-orbits

Based on the Bethe-Richardson-Gaudin ansatz for the standard pairing model, extended Bethe- Richardson-Gaudin ansatzes for eigenvectors of a spherical mean-field plus separable pairing model with three non-degenerate j-orbits are proffered. It is shown that the number of variables appearing in the g...

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Bibliographic Details
Published in:Physics letters. B 2022-10, Vol.833, p.137362, Article 137362
Main Authors: Pan, Feng, Wu, Yingxin, Guan, Shengze, Qu, Zhibo, Dai, Lianrong, Draayer, J.P.
Format: Article
Language:English
Subjects:
Bethe ansatz
Exactly solvable models
Separable pairing
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Summary:Based on the Bethe-Richardson-Gaudin ansatz for the standard pairing model, extended Bethe- Richardson-Gaudin ansatzes for eigenvectors of a spherical mean-field plus separable pairing model with three non-degenerate j-orbits are proffered. It is shown that the number of variables appearing in the general extended ansatz eigenvectors for given number of pairs N is N(N+1)/2. More importantly, when one of the j orbits is 1/2, there are only 2N variables involved in the alternative extended ansatz eigenvectors, which, like the standard pairing model, can be solved efficiently. Numerical results for an application of the model in the ds-shell up to its half-filling are presented, which serves to validate the procedure and illustrates the completeness of the solutions it renders.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2022.137362