  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 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
estimates.
  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.
