Effect of Radiative Feedbacks for Resonant Transitions during Cosmological Recombination

The inhibition of the total HI $n\leftrightarrow 1$ transition rate by delayed resonant reabsorption of HI $(n+1)\to 1$ photons by HI $n\to 1$ line which is possible due to cosmological redshift is considered semi-analytically. The method taking into account this effect in the frame of simple three-level approximation model of recombination is suggested. It is confirmed that the resonant feedbacks affect ionization fraction at the level about 0.2% for the epoch of last scattering. Similar consideration of HeI $2^1P\leftrightarrow 1^1S$ $\Rightarrow$ HeI $2^3P\leftrightarrow 1^1S$ feedback for helium is provided. It is confirmed that allowance of this feedback leads to increase of predicted free electron fraction by 0.12% at $z\simeq 2300$. It is shown that taking into account absorption and thermalization of HeI $2^1P\leftrightarrow 1^1S$ resonant superequilibrium photons (during their redshifting to the HeI $2^3P\leftrightarrow 1^1S$ frequency) by small amount of neutral hydrogen ($10^{\rm -7} - 10^{\rm -4}$ of total number of hydrogen atoms and ions) existing in helium recombination epoch is important for correct consideration of this helium feedback.