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Extended Heine-Stieltjes polynomials related to the isovector pairing model

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Abstract

New polynomials related to the mean-field plus isovector pairing model are constructed based on the Stieltjes correspondence. It is shown that there is an one-to-one correspondence between zeros of the two related extended Heine-Stieltjes polynomials satisfying coupled differential equations and the solutions of the Bethe ansatz equations for the model. Similar to the standard pairing among like valence nucleons, an electrostatic interpretation of the location of zeros of the two polynomials is provided. As examples of the solution, the two polynomials related to the solution for three pairs over \(j=1/2,\,3/2,\,5/2\) orbits within the O(5) seniority-zero subspace are provided explicitly, which shows that the number of possible configurations of equilibrium positions of the charges in the two separate systems equals exactly to the number of energy levels in the mean-field plus isovector pairing model.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The associated data have been included in the article. A Mathematica code used is available upon request.]

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Acknowledgements

One of the authors (F. P.) is grateful to Prof. Jorge Dukelsky for the lectures on the problem and his suggestion on carrying out this work through many helpful exchanges. Support from the National Natural Science Foundation of China (11675071), the Liaoning Provincial Universities Overseas Training Program (2019GJWYB024), the U.S. National Science Foundation (OIA-1738287 and PHY-1913728), and the LSU-LNNU joint research program with modest but important collaboration-maintaining support from the Southeastern Universities Research Association.

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Correspondence to Feng Pan.

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Communicated by Mark Caprio.

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Pan, F., He, Y., Li, A. et al. Extended Heine-Stieltjes polynomials related to the isovector pairing model. Eur. Phys. J. A 57, 218 (2021). https://doi.org/10.1140/epja/s10050-021-00535-3

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  • DOI: https://doi.org/10.1140/epja/s10050-021-00535-3

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