GENERAL FORMULATION OF THE SEMIRELATIVISTIC APPROACH TO ATOMIC SUM-RULES

A general scheme is presented for obtaining systematic relativistic co rrections to quantum-mechanical sum rules for various calculations in atomic physics. The single-particle picture and the Foldy-Wouthuysen t ransformation [Phys. Rev. 78, 29 (1950)] are adopted to derive such co rrections. Results are obtained for the ''generalized Bethe sums,'' wh ich include all higher moments of the energy transfer, and explicit re sults are given to the lowest order of relativistic corrections.