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 nonzero optical depth in He I lines arising from transitions to the metastable $2{}^3\mathrm{S}$ state. The model reveals substantial deviations in the emissivities of the $\lambda 3889$ and $\lambda 7065$ lines in case of a nonzero optical depth, with previous models systematically underestimating and overestimating them by 5% to 20%, 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 which are typical for H II regions and planetary nebulae ($1\le n_e\le {10}^4{\mathrm{cm}}^{-3}$, $8000\le T_e\le 22000\mathrm{K}$). In addition, we present new fitting formulas for radiative transfer corrections for several He I lines relevant to optical and near-IR observations, covering $0\le {\tau }_{3889}\le 10$ within the same density and temperature ranges. The accuracy of the obtained approximations is $\lesssim 0.1\%$ within the specified parameter range. These results can be readily implemented in modern codes for determining the primordial ${}^4\mathrm{He}$ abundance and are also applicable to a broader range of spectroscopic analyses of He I emission lines.

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• Atomic & molecular collisions
• Atomic spectra
• Electronic excitation & ionization
• Spontaneous emission