Regular Article - Theoretical Physics
Extended Heine-Stieltjes polynomials related to the isovector pairing model
Department of Physics, Liaoning Normal University, 116029, Dalian, People’s Republic of China
2 Department of Physics and Astronomy, Louisiana State University, 70803-4001, Baton Rouge, LA, USA
Accepted: 20 June 2021
Published online: 3 July 2021
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 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021