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.

基于 Stieltjes 对应关系构建了与平均场加等向量配对模型相关的新多项式。结果表明，满足耦合微分方程的两个相关扩展Heine-Stieltjes多项式的零点与模型的Bethe ansatz方程的解之间存在一一对应关系。类似于价核子之间的标准配对，提供了两个多项式零点位置的静电解释。作为解的例子，与\(j=1/2,\,3/2,\,5/2\) 上三对的解相关的两个多项式 明确提供了 O(5) 资历零子空间内的轨道，这表明两个独立系统中电荷平衡位置的可能配置数恰好等于平均场中的能级数加上等向量对模型。