Three-Particle Operators for Equivalent Electrons

Interaction between the electronic configurations (nl)^N and (nl)^N±1(n^′l^′)^∓1 can be represented for (nl)^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 R₇ and G₂. 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.