Relativistic (Z alpha)^2-Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States

TL;DR

This paper calculates relativistic and quantum electrodynamic corrections to the two-photon decay rates of excited ionic states, completing the theoretical framework up to order alpha^3 ln(alpha) with detailed gauge-invariant analysis.

Contribution

It provides the first comprehensive calculation of (Z alpha)^2 and leading radiative corrections to two-photon decay rates using a nonrelativistic QED approach, including gauge invariance considerations.

Findings

Corrections include zitterbewegung, spin-orbit coupling, relativistic mass corrections, and quadrupole interactions.

All corrections are gauge-invariant under a specific hybrid transformation.

Results are applied to hydrogenlike ions for various excited states.

Abstract

We calculate the relativistic corrections of relative order (Z alpha)^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 alpha (Z alpha)^2 ln[(Z alpha)^(-2)]. We thus complete the theory of the two-photon decay rates up to relative order alpha^3 ln(alpha). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Z alpha)^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.