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