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 (nlnl′ = 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.

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Published in Monthly Notices of the Royal Astronomical Society, v. 459, issue 4, p. 3498-3504.

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. Published by Oxford University Press on behalf of The Royal Astronomical Society 2015. This work is written by (a) US Government employee(s) and is in the public domain in the US.

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This work has been supported by the NSF (1108928, 1109061, and 1412155), NASA (10-ATP10-0053, 10-ADAP10-0073, NNX12AH73G, and ATP13-0153), and STScI (HST-AR- 13245, GO-12560, HST-GO-12309, GO-13310.002-A, and HST-AR-13914). MC has been supported by STScI (HST-AR-14286.001-A).