H-, He-like recombination spectra - II. l-changing collisions for He Rydberg states

Cosmological models can be constrained by determining primordial abundances. Accurate predictions of the He I spectrum are needed to determine the primordial helium abundance to a precision of <1 per cent in order to constrain big bang nucleosynthesis models. Theoretical line emissivities at least this accurate are needed if this precision is to be achieved. In the first paper of this series, which focused on H _I, we showed that differences in l-changing collisional rate coefficients predicted by three different theories can translate into 10 per cent changes in predictions for H _I spectra. Here, we consider the more complicated case of He atoms, where low-l subshells are not energy degenerate. A criterion for deciding when the energy separation between l subshells is small enough to apply energy-degenerate collisional theories is given. Moreover, for certain conditions, the Bethe approximation originally proposed by Pengelly & Seaton is not sufficiently accurate. We introduce a simple modification of this theory which leads to rate coefficients which agree well with those obtained from pure quantal calculations using the approach of Vrinceanu et al. We show that the l-changing rate coefficients from the different theoretical approaches lead to differences of ~10 per cent in He I emissivities in simulations of H _II regions using spectral code CLOUDY.