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.

基于用于标准配对模型的 Bethe-Richardson-Gaudin ansatz，提出了针对具有三个非退化j轨道的球面平均场加可分离配对模型的特征向量的扩展 Bethe-Richardson-Gaudin ansatzes 。结果表明，对于给定的对数N ，出现在一般扩展 ansatz 特征向量中的变量数为$ñ(ñ+1)/2$. 更重要的是，当j轨道之一为 1/2 时，替代扩展 ansatz 特征向量中仅涉及 2 N个变量，与标准配对模型一样，可以有效求解。给出了在ds -shell中应用模型直至其半填充的数值结果，用于验证过程并说明其呈现的解决方案的完整性。