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.
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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).
Guzmán, Francisco; Badnell, N. R.; Williams, R. J. R.; van Hoof, P. A. M.; Chatzikos, Marios; and Ferland, Gary J., "H, He-Like Recombination Spectra – I. l-Changing Collisions for Hydrogen" (2016). Physics and Astronomy Faculty Publications. 464.