Reduction of two two-body operators in the effective hyperfine hamiltonian to one-body operators

The two two-body operators representing the effect of far configurations on the contact hyperfine interaction in annl ^N n′s configuration are shown to reduce to one-body operators. In such a configuration the operator for the contact hyperfine field is (a _nlS_nl +a_n,ss_n′s), where a_nl and a_n′s take the same values in all terms of the configuration. A discrepancy between expectation values of these two-body operators deduced from experiment and calculated values is explained.