Relativistic (Z\alpha)^2 corrections and leading quantum electrodynamic corrections to the two-photon decay rate of ionic states

Benedikt J. Wundt and Ulrich D. Jentschura

Accepted Tuesday Jun 23, 2009

We calculate the relativistic corrections of relative order (Za)2 to the two-photon decay rate of higher excited S and D states in ionic atomic systems, and we also evaluate the leading radiative corrections of relative order a(Za)2  ln[(Za)-2]. We thus complete the theory of the two-photon decay rates up to relative order a3  ln(a). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Za)2 to the two-photon decay are given by the zitterbewegung, the spin-orbit coupling and by relativistic corrections to the electron mass, and by quadrupole interactions. We show that all corrections are separately gauge-invariant with respect to a "hybrid" transformation from velocity to length gauge, where the gauge transformation of the wave function is neglected. The corrections are evaluated for the two-photon decay from 2S, 3S, 3D, and 4S states in one-electron (hydrogenlike) systems, with 1S and 2S final states.