1999ApJ...514..307B

We have combined the detailed He I recombination model of Smits with the collisional transitions of Sawey & Berrington in order to produce new accurate helium emissivities that include the effects of collisional excitation from both the 2³S and 2¹S levels. We present a grid of emissivities for a range of temperature and densities along with analytical fits and error estimates. These grids eliminate the necessity of making corrections for collisional enhancements as in the work of Clegg or Kingdon & Ferland for lines with upper levels below n=5. For densities greater than n_e~10⁶ cm^–3, inclusion of collisional excitation from the 2¹S level is also necessary if accuracies of greater than a few percent are required. Atomic data for a model atom with 29 levels (n_max=5) are presented that match the recombination model of Smits to within 5% over the temperature range T=5000-20,000 K. Collisional effects are calculated self-consistently using the algorithm of Almog & Netzer. This model atom will be useful in models of radiative transfer. A notable feature of this technique is an algorithm that calculates the ``indirect'' recombination rates, the recombination to individual levels that go through n>n_max first. Fits accurate to within 1% are given for the emissivities of the brightest lines over a restricted range for estimates of primordial helium abundance. We characterize the analysis uncertainties associated with uncertainties in temperature, density, fitting functions, and input atomic data. We estimate that atomic data uncertainties alone may limit abundance estimates to an accuracy of ∼1.5%; systematic errors may be greater than this. This analysis uncertainty must be incorporated when attempting to make high-accuracy estimates of the helium abundance. For example, in recent determinations of the primordial helium abundance, uncertainties in the input atomic data have been neglected. Finally, we compare our theoretical calculations to the measured strengths of a few dozen helium emission lines in three nebulae, Orion (NGC 1976) and the planetary nebulae NGC 6572 and IC 4997. Incorporation of collisional effects yields noticeable improvements for some lines, but some notable discrepancies remain.