The exact solutions of either spherical or deformed mean-field plus various types of pairing models are briefly reviewed. It is shown that, besides the standard pairing model, there are several special types of pairing interaction that can be solved exactly. In comparison to the standard pairing, the results of several pairing-driven quantities, such as pairing excitation energies, even–odd mass differences, the moment of inertia, etc., show that these types of pairing interaction can indeed be used to describe pairing correlations in nuclei either more accurately or efficiently. Moreover, the shape phase transitional behaviors of nuclei described by the consistent-Q formalism of the interacting boson model are summarized.

简要回顾了球形或变形平均场以及各种类型的配对模型的精确解。结果表明，除了标准的配对模型外，还有几种特殊类型的配对交互可以精确解决。与标准配对相比，几种配对驱动量的结果，例如配对激发能，奇偶质量差，惯性矩等，表明这些配对相互作用的类型确实可以用来描述配对核中的相关性更精确或更有效。此外，总结了相互作用玻色子模型的一致Q形式描述的原子核的形状相转变行为。