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

• Published in: Monthly notices of the Royal Astronomical Society 2016-07, Vol.459 (4), p.3498-3504
• Main Authors: Guzmán, F., Badnell, N. R., Williams, R. J. R., van Hoof, P. A. M., Chatzikos, M., Ferland, G. J.
• Format: Article
• Language: English
• Subjects: Abundance; Collisions; Cosmology; Emission; Helium; Hydrogen; Local thermodynamic equilibrium; Nebulae; Populations; Radiative recombination; Star & galaxy formation; Symbols; Thermodynamics
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stw893

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 → nl′ = l ± 1) between energy-degenerate states within an n-shell. The work of Pengelly & Seaton has, for half-a-century, been considered the definitive study which ‘solved’ the problem. Recent work by Vrinceanu et al. recommended the use of rate coefficients from a semiclassical approximation which are nearly an order of magnitude smaller than those of Pengelly & Seaton, 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 per cent. This far exceeds the 1 per cent 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 for l-changing collisions, to describe the H recombination spectrum, based-on their quantum mechanical representation of the long-range dipole interaction.