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

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.

Figure 1

Emission line profiles Eq. (14) for the transitions $\overline{2p}\to 1s+\gamma \left(\mathrm{E}1\right)$ (yellow dashed line) and $\overline{2s}\to 1s+\gamma \left(\mathrm{E}1\right)$ (blue solid line) at the BBR temperature $T=3000$ K. The magnitudes of emission line profiles and frequency interval are normalized to unity. The ${\mathrm{Ly}}_{\alpha }$ frequency corresponds to $\omega =0.5$. The corresponding values of transition rates and level widths are presented in Table 1.

Figure 2

Ionization fraction $x_e$ as a function of redshift $z$. The dotted green line corresponds to the LTE case (Saha equation), the dashed yellow line is given by the evaluation of the “ordinary” rate equation, and the solid blue line represents the ionization fraction accounting for BBR-induced level mixing.

Figure 3

Relative difference $\mathrm{\Delta }{x}_e/x_e$ as a function of redshift $z$.