#### Abstract

We calculate the relativistic corrections of relative order (Zα) 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 α (Zα) 2 ln [(Zα) -2]. We thus complete the theory of the two-photon decay rates up to relative order α3 ln (α). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Zα) 2 to the two-photon decay are given by the Zitterbewegung, by 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.

#### Recommended Citation

B.
J.
Wundt
and
U.
D.
Jentschura,
"Relativistic (Zα)2 Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States," *Physical Review a - Atomic Molecular, and Optical Physics*, American Physical Society (APS), Aug 2009.

The definitive version is available at https://doi.org/10.1103/PhysRevA.80.022505

#### Department(s)

Physics

#### Keywords and Phrases

Decay (Organic); Electrodynamics; Gages; Photons; Quantum electronics; Wave functions

#### Document Type

Article - Journal

#### Document Version

Final Version

#### File Type

text

#### Language(s)

English

#### Rights

© 2009 American Physical Society (APS), All rights reserved.

#### Publication Date

01 Aug 2009