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arXiv:2006.03928 · Physical Review A

Two-photon atomic level widths at finite temperatures

Timur A. Zalialiutdinov, A. Anikin, Dmitry A. Solovyev

Published Sep 2, 2020• 9 citations
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Abstract

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 $2s$ 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.

DOI
10.1103/physreva.102.032204

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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.
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 effect of a thermal field on Rydberg states of the nS-, nP- and nD-series in beryllium ions Be+ is investigated. The blackbody radiation-induced depopulation rates caused by transitions to upper (excitations) and lower (decays) bound levels and to the continuum (ionization) are calculated in wide ranges of the principal quantum numbers n and ambient temperatures. Simple and reliable approximations for natural lifetimes and stimulated by thermal radiation depopulation rate components are proposed. The blackbody-radiation-induced shifts of Rydberg levels are also calculated and their qualitative and quantitative properties are analysed.
Photon emission by an atom in the metastable 2S2S2S state in a weak static electric field is examined within the context of bound-state quantum electrodynamics. Low's method is applied to obtain the expansion in terms of Coulomb wave functions of the propagation function for an electron interacting with the nuclear Coulomb field, the applied electric field, and the quantized radiation field. For a weak applied field, and to lowest relative order in $\frac{\ensuremath{\alpha}}{\ensuremath{\pi}}$, the 2S2S2S-state resonant contribution to the propagation function can be factorized to provide the basis for a calculation of the angular distribution of single-photon radiation and lifetime of the excited state. A numerical evaluation is given, which takes into account effects of electric dipole, magnetic dipole, and magnetic quadrupole emission, relativistic corrections, and finite level widths.
Two-photon decay of hydrogenlike ions is studied within the framework of second-order perturbation theory, based on the relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative-energy (intermediate virtual) states that occur in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ and $2{p}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ transitions in neutral hydrogen H as well as for hydrogenlike xenon Xe53+{\text{Xe}}^{53+}Xe53+ and uranium U91+{\text{U}}^{91+}U91+ ions. We found that for a correct evaluation of the total and energy-differential decay rates, summation over the negative-energy part of Dirac's spectrum should be properly taken into account both for high-ZZZ and low-ZZZ atomic systems.
New features of the blackbody-induced radiation processes on Rydberg atoms were discovered on the basis of numerical data for the blackbody-induced decay P d nl ( T ), excitation P e nl ( T ) and ionization P ion nl ( T ) rates of n S, n P and n D Rydberg states calculated together with the spontaneous decay rates P sp nl in neutral hydrogen, and singlet and triplet helium atoms for some values of the principal quantum number n from 10 to 500 at temperatures from T = 100 K to 2000 K. The fractional rates R d ( e , ion) nl ( T ) = P nl d ( e , ion) ( T )/ P sp nl equal to the ratio of the induced decay (excitation, ionization) rates to the rate of spontaneous decay were determined as functions of T and n in every series of states with a given angular momentum l = 0, 1, 2. The calculated data reveal an essential difference between the asymptotic dependence of the ionization rate P ion nl ( T ) and the rates of decay and excitation P d ( e ) nl ( T )∝ T / n 2 . The departures appear in each Rydberg series for n > 100 and introduce appreciable corrections to the formula of Cooke and Gallagher. Two different approximation formulae are proposed on the basis of the numerical data, one for R d ( e ) nl ( T ) and another one for R ion nl ( T ), which reproduce the calculated values in wide ranges of principal quantum number from n = 10 to 1000 and temperatures between T = 100 K and T = 2000 K with an accuracy of 2% or better. Modified Fues' model potential approach was used for calculating matrix elements of bound–bound and bound–free radiation transitions in helium.
Two different effects of the blackbody-radiation-induced atomic line broadening are compared. The first one (stimulated Raman scattering) has been discussed by many authors; the second one (quadratic level mixing) was discussed in our previous work. It is shown that the mixing effect gives the most significant contribution to the line broadening and it is indicated how to distinguish these two effects in laboratory experiments. The influence of the level mixing on the recombination history of primordial plasma is also discussed.