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Hydrogen and helium emission lines in nebulae form by radiativerecombination. This is a simple process which, in principle, can be describedto very high precision. Ratios of He I and H I emission lines can be used tomeasure the He$^+$/H$^+$ abundance ratio to the same precision as therecombination rate coefficients. This paper investigates the controversy overthe correct theory to describe dipole $l$-changing collisions ($nl\rightarrownl'=l\pm 1$) between energy-degenerate states within an $n$-shell. The work ofPengelly & Seaton (1964) has, for half-a-century, been considered thedefinitive study which "solved" the problem. Recent work by Vrinceanu etal.(2012) recommended the use of rate coefficients from a semi-classicalapproximation which are nearly an order of magnitude smaller than those ofPengelly & Seaton (1964), with the result that significantly higher densitiesare needed for the $nl$ populations to come into local thermodynamicequilibrium.  Here, we compare predicted H~I emissivities from the two works and findwidespread differences, of up to $\approx 10$%. This far exceeds the 1%precision required to obtain the primordial He/H abundance ratio fromobservations so as to constrain Big Bang cosmologies. We recommend using therate coefficients of Pengelly & Seaton (1964) for $l$-changing collisions, todescribe the H recombination spectrum, based-on their quantum mechanicalrepresentation of the long-range dipole interaction.

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