The Coulomb Green Functions with Applications to Two Photon Transitions.

A comprehensive examination of the properties of the Schrodinger- and Dirac-Coulomb Green function as applied to bound state problems is presented. A method of treating the Dirac-Coulomb radial equations is described which allows both the Dirac wavefunctions and Green functions to be treated quite analogously to the corresponding Schrodinger functions. Matrix elements in the form of double Laplace transforms of the Green functions are calculated and presented in a variety of useful forms. The results are applied specifically to two photon transitions in hydrogenic ions, with a calculation of the decay of the 2s_ {1/2} state.