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 tᵢ 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 tᵢ with respect to symplectic symmetry and quasispin are examined.