Improving predictions for helium emission lines

We have combined the detailed He I recombination model of Smits with the co llisional transitions of Sawey & Berrington in order to produce new accurat e helium emissivities that include the effects of collisional excitation fr om both the 2(3)S and 2(1)S levels. We present a grid of emissivities for a range of temperature and densities along with analytical fits and error es timates. These grids eliminate the necessity of making corrections for coll isional enhancements as in the work of Clegg or Kingdon & Ferland for lines with upper levels below n = 5. For densities greater than n(e) approximate to 10(6) cm(-3), inclusion of collisional excitation from the 21S level is also necessary if accuracies of greater than a few percent are required. A tomic 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 ra nge T = 5000-20,000 K. Collisional effects are calculated self-consistently using the algorithm of Almog & Netzer. This model atom will be useful in m odels of radiative transfer. A notable feature of this technique is an algo rithm that calculates the "indirect" recombination rates, the recombination to individual levels that go through n > n(max) first. Fits accurate to wi thin 1% are given for the emissivities of the brightest lines over a restri cted range for estimates of primordial helium abundance. We characterize th e analysis uncertainties associated with uncertainties in temperature, dens ity, fitting functions, and input atomic data. We estimate that atomic data uncertainties alone may limit abundance estimates to an accuracy of simila r to 1.5%; systematic errors may be greater than this. This analysis uncert ainty must be incorporated when attempting to make high-accuracy estimates of the helium abundance. For example, in recent determinations of the primo rdial helium abundance, uncertainties in the input atomic data have been ne glected. Finally, we compare our theoretical calculations to the measured s trengths of a few dozen helium emission lines in three nebulae, Orion (NGC 1976) and the planetary nebulae NGC 6572 and IC 4997. Incorporation of coll isional effects yields noticeable improvements for some lines, but some not able discrepancies remain.