### 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.

Original language | English |
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Article number | 022505 |

Journal | Physical Review A |

Volume | 80 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 13 2009 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Relativistic (Zα) 2 corrections and leading quantum electrodynamic corrections to the two-photon decay rate of ionic states.** / Wundt, Benedikt J.; Jentschura, U.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Relativistic (Zα) 2 corrections and leading quantum electrodynamic corrections to the two-photon decay rate of ionic states

AU - Wundt, Benedikt J.

AU - Jentschura, U.

PY - 2009/8/13

Y1 - 2009/8/13

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.80.022505

DO - 10.1103/PhysRevA.80.022505

M3 - Article

AN - SCOPUS:68949119478

VL - 80

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022505

ER -