Improved radiative transfer corrections in helium emission lines

We present a new detailed model of the He I collisional-recombination spectrum based on the most up-to-date atomic data. The model accounts for radiative transfer effects and the influence of a non-zero optical depth in He I lines arising from transitions to the metastable 2^3S state. The model reveals substantial deviations in the emissivities of the lambda3889 and lambda7065 lines in the case of a non-zero optical depth, with previous models systematically underestimating and overestimating them by 5 to 20 percent, respectively. In the optically thin case, however, our results show good agreement with previous studies. Using the new model, we compute optically thin emissivities for a wide set of UV, optical, and IR He I recombination lines over a fine grid of electron densities and temperatures typical for H II regions and planetary nebulae (1 <= ne <= 10^4 cm^-3, 8000 <= Te <= 22000 K). In addition, we present new fitting formulae for radiative transfer corrections for several He I lines relevant to optical and near-infrared observations, covering 0 <= tau_3889 <= 10 within the same density and temperature ranges. The accuracy of the obtained approximations is <= 0.1 percent within the specified parameter range. These results can be readily implemented in modern codes for determining the primordial 4He abundance and are also applicable to a broader range of spectroscopic analyses of He I emission lines.