Additive nature of correlation and relativistic effects in atomic hyperfine structure

In the calculation of atomic hyperfine structure, it is generally assumed that core polarization effects and relativistic effects can be calculated separately. We examine in detail the validity of this assumption and obtain the lowest-order corrections to such an approach. This correction is described by new operators to be added to the hyperfine Hamilionian, as well as second-order perturbation terms. The systematic effects of the second-order terms are investigated using the effective-operator approach.