Integrated photoabsorption strength and sum rules for a bound Dirac particle

Abstract

Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a few percent. Whereas the total M1-strength is strongly underestimated by the lowest order M1-sum rule, the total E2-strength is reasonably well reproduced up to about 10% by the lowest order E2-sum rule.