Three-Particle Operators for Equivalent Electrons

Interaction between the electronic configurations ${\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}^N$ and ${\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}^{N\pm 1}{\left(n^{\prime }{l}^{\prime }\right)}^{\mp 1}$ can be represented for ${\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}^N$ by the addition of effective three-particle operators to the Hamiltonian, the effective two-particle parts being absorbed by operators already present in the elementary linear theory of configuration interaction. For $f$ electrons, the three-particle operators are decomposed into nine operators $t_i$ that are labeled by irreducible representations of $R_7$ and $G_2$. The effects of three of them can be reproduced by two-particle operators; hence, only six additional parameters are required to describe the interaction. Tables of matrix elements are given, and the properties of the operators $t_i$ with respect to symplectic symmetry and quasispin are examined.