Relativistic sum rules and integral properties of the Dirac equation

S. P. Goldman
Gordon W. F. Drake, University of Windsor

copyright American Physical Society


Relativistic generalizations are derived for the well-known nonrelativistic electric-dipole oscillator-strength sum rules. The relativistic sum rules include both positive- and negative-energy states. The derivations are valid for a Dirac electron in an arbitrary local potential. We also present a number of simple integral properties related to the relativistic virial theorem which are useful in the calculation of matrix elements. © 1982 The American Physical Society.