Level-mixing effect induced by blackbody radiation and its influence on the cosmological hydrogen recombination problem

Abstract

Two different effects of the blackbody radiation (BBR)-induced atomic line broadening are compared. The first one (stimulated Raman scattering) was discussed by many authors, the second one (quadratic level mixing) was predicted earlier in our publication. 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.The influence of external fields on atomic characteristics is still one of the interesting subjects for investigations in modern atomic physics. In particular a question about the blackbody radiation (BBR) influence on atoms is widely discussed. First the BBR induced effects were observed experimentally and then the theoretical description was given in [1,2] within the frameworks of quantum mechanical (QM) approach. In particular, it was shown that the blackbody radiation induces the ac-Stark shift of energy levels and an additional line broadening in atoms. Theoretical calculations of the dynamic Stark shifts and depopulation rates of Rydberg energy levels caused by the BBR and the corresponding experimental measurements were widely discussed in literature [3]- [8]. The most important consequence of these investigations corresponds to the improvement of atomic clocks and the development of optical standards of frequency measurements [9].Finally, in [10] the effect of level mixing induced by the blackbody radiation was firstly described theoretically within the rigorous quantum electrodynamic (QED) theory. The mixing effect for the states of opposite parity arising in the presence of an external electric field leads to a significant changes of the decay rates, see, for example, [11,12]. We should note that all effects in the presence of the BBR are similar to the phenomena which take place in an external electric field. Similar to the Stark (static or dynamic) effect in the presence of 'ordinary' external electric field the energy shift of atomic levels induced by the BBR can be estimated with the use of rootmean square value of the field strength of thermal radiation (in a.u.):where E 2 (ω) is rms electric field strength, ω is the radiation frequency. The Planck's distribution function is presented by n β (ω) with β = 1/k B T , k B is the Boltzman's constant, T is the temperature in Kelvin and α is the fine structure constant. Then the integral rms value of electric field isIn conjunction with the expression (2) the level mixing effect induced by the thermal radiation can be introduced. The level mixing effect in an external electric field was considered in connection with the Lamb shift measurements in hydrogen and hydrogen-like ions [13,14] and the corresponding theoretical analysis of the electric field influence on atomic levels can be found in [15,16]. An accurate description of level mixing effect in hydrogen atom was given in [17]. In particular, the authors of [17] have sh...

BBR-induced Stark shifts and level broadening in a helium atom

“…As it was found in [5] the effect of BBR-induced level mixing influences significantly on the processes of radiation escape from the matter in cosmological recombination epoch of the early universe. The ionization fraction undergoes modification upto the level of 20% for the 2s state in hydrogen atom with the account for mixing effect.…”

“…partial width Γ mix 2 1(3) S,2 1(3) P →1 1 S . The latter represents the one-photon decay of the mixed 2 1(3) S state [3,5]. It is important to note that the frequencies of photons emitted in transitions 2 1 S → 1 1 S + 2γ(E1) and…”

“…Moreover, in that case the decay of the 2s state occurs with the emission of E1 photon. Although this effect is negligible for low temperatures T ≈ 3 K it could be important [5] for the ionization history of primordial plasma where 2s state in hydrogen atom plays the crucial role for formation processes of the Cosmic Microwave Background (CMB) [6,7]. With the same reasons BBR-induced level mixing effect and corresponding line broadening should be significant for helium atom since its recombination occurs earlier than the hydrogen one and takes place at temperatures 4 × 10 3 < T < 10 4 K [8,9].Another reason for the further investigation of BBR influence on atoms is the recent accurate measurements of light atoms by the spectroscopic methods.…”

Radiative QED corrections to one-photon transition rates in hydrogen atom at finite temperatures

“…The quantum mechanical (QM) theory of energy shift and transition rates induced by the BBR was given in [36]. Theoretical calculations within the framework of rigorous quantum electrodynamics (QED) of the thermal Stark shift, level broadening and BBR-induced bound-free transitions have been carried out in [37], and later in [38][39][40]. The advantage of QED theory application to investigations of this kind is the accurate accounting for finite life times of atomic levels.…”

“…The advantage of QED theory application to investigations of this kind is the accurate accounting for finite life times of atomic levels. Although such effects are outside the scope of this work, the formalism developed in [37][38][39][40], see also [41], can reveal new (unknown) thermal corrections to transition rates between bound states and to analyze their significance at astrophysical and laboratory conditions.…”