H, He-like recombination spectra I: l-changing collisions for hydrogen

Hydrogen and helium emission lines in nebulae form by radiative recombination. This is a simple process which, in principle, can be described to very high precision. Ratios of He I and H I emission lines can be used to measure the He+/H+ abundance ratio to the same precision as the recombination rate coefficients. This paper investigates the controversy over the correct theory to describe dipole l-changing collisions (nl → nl0 = l ±1) between energy-degenerate states within an n-shell. The work of Pengelly & Seaton (1964) has, for half-a-century, been considered the definitive study which “solved” the problem. Recent work by Vrinceanu et al. (2012) recommended the use of rate coefficients from a semi-classical approximation which are nearly an order of magnitude smaller than those of Pengelly & Seaton (1964), with the result that significantly higher densities are needed for the nl populations to come into local thermodynamic equilibrium. Here, we compare predicted H I emissivities from the two works and find widespread differences, of up to ≈ 10%. This far exceeds the 1% precision required to obtain the primordial He/H abundance ratio from observations so as to constrain Big Bang cosmologies. We recommend using the rate coefficients of Pengelly & Seaton (1964) for l-changing collisions, to describe the H recombination spectrum, based-on their quantum mechanical representation of the long-range dipole interaction.