Relativistic and retardation effects in the Thomas-Reiche-Kuhn sum rule for a bound particle

Abstract

Relativistic and retardation corrections of lowest order are evaluated for the photoabsorption Thomas-Reiche-Kuhn (TRK) sum rule of a particle bound in a potential. It is found that the retardation corrections partially cancel and the remainder is canceled by part of the relativistic corrections. The latter corrections depend on the Lorentz-transformation properties of the potential. The complete integrated photoabsorption cross section including first-order relativistic corrections, is found to be equal to the high-energy limit of the Compton amplitude calculated by Goldberger and Low, a result which is the dispersion-relation form of the TRK sum rule. A heuristic derivation of the latter results is presented.