Abstract
The exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits, which is an extension of the widely used standard (two-body) pairing model, is derived based on the Bethe–Richardson–Gaudin approach. The Bethe–Richardson–Gaudin equations in determining eigenstates and the corresponding eigen-energies of the model are provided and exemplified with up to three-pair interactions. With a suitable parameterization of the overall multi-pair interaction strengths, the model with one adjustable parameter and valence nucleons confined in the \(1d_{5/2}\) and \(0g_{7/2}\) orbits is applied to fit binding energies of \(^{102{\text {--}}112}\)Sn. It is shown that the ground-state occupation probabilities of nucleon pairs calculated from this model and those from the standard pairing model are almost the same with perfect ground-state overlap of the two models. A noticeable feature of the multi-pair interactions is that the even–odd staggering of pairing interaction strength appearing in the standard pairing model due to the Pauli-blocking is suppressed. As the result, the pairing interaction strength of the model only depends on the number of valence nucleon pairs in the system.
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Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Theoretical data have already been provided in this paper, while all experimental data have been taken from the website https://www-nds.iaea.org.]
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Acknowledgements
Support from the National Natural Science Foundation of China (11675071), the Liaoning Provincial Universities Overseas Training Program (2019-46), the U. S. National Science Foundation (OIA-1738287 and ACI-1713690), U. S. Department of Energy (DE-SC0005248), the Southeastern Universities Research Association, and the LSU-LNNU joint research program (9961) is acknowledged.
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Pan, F., Li, D., Cui, S. et al. Exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits. Eur. Phys. J. A 56, 78 (2020). https://doi.org/10.1140/epja/s10050-020-00084-1
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DOI: https://doi.org/10.1140/epja/s10050-020-00084-1