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

TL;DR

This paper compares two theories of $l$-changing collisions affecting hydrogen emission lines, finding significant differences that impact primordial abundance measurements, and recommends using the older quantum mechanical model for accurate cosmological inferences.

Contribution

It evaluates and compares the predictions of two different $l$-changing collision theories for hydrogen, recommending the more accurate quantum mechanical model for precise abundance measurements.

Findings

Differences up to 10% in predicted H I emissivities between the two models.

The semi-classical approximation underestimates rate coefficients, affecting density estimates.

Using the older model improves the accuracy of primordial abundance determinations.

Abstract

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 ($nl\rightarrow nl'=l\pm 1$) 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 $\approx 10$%. 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.