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 $< 1$% 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% 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 (1964) 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. (2012). We show that the $l$-changing rate
coefficients from the different theoretical approaches lead to differences of
$\sim 10$% in He I emissivities in simulations of H II regions using spectral
code Cloudy.
