We update our prior work on the case B collisional-recombination spectrum of He I to incorporate textit{ab initio} photoionisation cross-sections. This large set of accurate, self-consistent cross-sections represents a significant improvement in He I
emissivity calculations because it largely obviates the piecemeal nature that has marked all modern works. A second, more recent set of textit{ab initio} cross-sections is also available, but we show that those are less consistent with bound-bound transition probabilities than our adopted set. We compare our new effective recombination coefficients with our prior work and our new emissivities with those by other researchers, and we conclude with brief remarks on the effects of the present work on the He I error budget. Our calculations cover temperatures $5000 le T_e le 25000$ K and densities $10^1 le n_e le 10^{14}$ cm$^{-3}$. Full results are available online.
