Partial support from the Faculty Development Committee of Portland State University is acknowledged.
Physical Review A
Molecular structure, Electromagnetic fields, Sum rules (Physics)
A general scheme is presented for obtaining systematic relativistic corrections to quantum-mechanical sum rules for various calculations in atomic physics. The single-particle picture and the Foldy-Wouthuysen transformation [Phys. Rev. 78, 29 (1950)] are adopted to derive such corrections. Results are obtained for the ldquogeneralized Bethe sums,rdquo which include all higher moments of the energy transfer, and explicit results are given to the lowest order of relativistic corrections.
Cohen, S. M., & Leung, P. T. (1998). General formulation of the semirelativistic approach to atomic sum rules. Physical Review A (Atomic, Molecular, And Optical Physics), 57(6), 4994-4997.