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Physical Review A

Two-photon transitions with cascades: Two-photon transition rates and two-photon level widths

Timur A. Zalialiutdinov, Dmitry A. Solovyev, Leonti N Labzowsky, G. Plunien

Published May 1, 2014• 13 citations
Publisher

Abstract

An ambiguity of the separation of cascades from ``pure'' two-photon decay is confirmed with accurate numerical calculations in a gauge-invariant way. A direct evaluation of the two-photon decay width of excited states in H-like ions via the imaginary part of two-loop self-energy is presented. We demonstrate that there is a fundamental difference between the level width and the transition probability in the presence of cascades. The two-photon widths are shown to be different from the two-photon decay rates for the transitions including cascades.

DOI
10.1103/physreva.89.052502

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An ambiguity of the separation of cascades from ``pure'' two-photon decay is confirmed with accurate numerical calculations in a gauge-invariant way. A direct evaluation of the two-photon decay width of excited states in H-like ions via the imaginary part of two-loop self-energy is presented. We demonstrate that there is a fundamental difference between the level width and the transition probability in the presence of cascades. The two-photon widths are shown to be different from the two-photon decay rates for the transitions including cascades.
The problem of the evaluation of the two-photon decay width of excited states in hydrogen is considered. Two different approaches to the evaluation of the width including cascades channels are employed: the summation of the transition probabilities for various decay channels and the evaluation of the imaginary part of the Lamb shift. As application, the two-photon decay channels for the 3s3s3s level of the hydrogen atom are evaluated, including the cascade transition probability $3s\text{\ensuremath{-}}2p\text{\ensuremath{-}}1s$. An important role is assigned to the two-photon decays in astrophysics context, since processes of this kind provide a possibility for the decoupling of radiation and matter in the early universe. We demonstrate the ambiguity of separation of the ``pure'' two-photon contribution and criticize the existing methods for such a separation.
We consider the general scenario of an excited level $|i\ensuremath{\rangle}$ of a quantum system that can decay via two channels: (i) via a single-quantum jump to an intermediate, resonant level $|\overline{m}\ensuremath{\rangle}$, followed by a second single-quantum jump to a final level $|f\ensuremath{\rangle}$, and (ii) via a two-quantum transition to a final level $|f\ensuremath{\rangle}$. Cascade processes $|i\ensuremath{\rangle}\ensuremath{\rightarrow}|\overline{m}\ensuremath{\rangle}\ensuremath{\rightarrow}|f\ensuremath{\rangle}$ and two-quantum transitions $|i\ensuremath{\rangle}\ensuremath{\rightarrow}|m\ensuremath{\rangle}\ensuremath{\rightarrow}|f\ensuremath{\rangle}$ compete (in the latter case, $|m\ensuremath{\rangle}$ can be both a nonresonant as well as a resonant level). General expressions are derived within second-order time-dependent perturbation theory, and the cascade contribution is identified. When the one-quantum decay rates of the virtual states are included into the complex resonance energies that enter the propagator denominator, it is found that the second-order decay rate contains the one-quantum decay rate of the initial state as a lower-order term. For atomic transitions, this implies that the differential-in-energy two-photon transition rate with complex resonance energies in the propagator denominators can be used to good accuracy even in the vicinity of resonance poles.
The thermal two-photon level broadening of the excited energy levels in the hydrogen and H-like helium is evaluated via the imaginary part of thermal two-loop self-energy correction for bound electrons. All the derivations are presented in the framework of rigorous quantum electrodynamic theory at finite temperatures and are applicable for the H-like ions. On this basis, we found a contribution to the level broadening induced by the blackbody radiation which is fundamentally different from the usual line broadening caused by the stimulated two-photon decay and the Raman scattering of thermal photons. Numerical calculations of the two-loop thermal correction to the two-photon width for the 2s2s2s state in hydrogen and singly ionized helium atoms show that the effect could significantly exceed the higher-order relativistic and radiative QED corrections commonly included in the calculations. In addition, the thermal two-loop self-energy correction significantly exceeds the ``ordinary'' stimulated one-photon depopulation rate at the relevant laboratory temperatures. In this work, detailed analysis and the corresponding comparison of the effect with the existing laboratory measurements in H-like ions are carried out.
The 4 s -1 s two-quantum decay in the hydrogen atom is calculated in the framework of quantum electrodynamics with allowance for cascades. It is shown that the pure two-photon contribution cannot be separated from the contribution of cascade processes. Interference between the transitions of these two types is comparable in magnitude with the pure two-photon contribution. The separation of pure two-photon contributions is discussed recently in connection with the role of two-photon decays in the separation of radiation from matter in the early Universe.
Abstract The quantum electrodynamical theory of three-photon transitions in hydrogen-like ions is presented. Emission probabilities of various three-photon decay channels for , and states are calculated for Z, the nuclear charge value, The results are given in two different gauges. The fully relativistic three-photon decay rates of hydrogen-like ions with half-integer nuclear spin are given for transitions between fine structure components. The results can be applied to the Bose–Einstein statistics tests for multiphoton systems.
One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability is also evaluated and possible applications of the results are discussed.