  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.
