  Diffusive nuclear burning of H by an underlying material capable of capturing
protons can readily consume H from the surface of neutron stars (NSs) during
their early cooling history. In the absence of subsequent accretion, it will be
depleted from the photosphere. We now extend diffusive nuclear burning to He,
motivated by the recent observation by Ho \& Heinke of a carbon atmosphere on
the NS in the Cassiopeia A supernova remnant. We calculate the equilibrium
structure of He on an underlying $\alpha$ capturing material, accounting for
thermal, mass defect, and Coulomb corrections on the stratification of material
with the same zeroth order $\mu_e = A/Z$. We show that Coulomb corrections
dominate over thermal and mass defect corrections in the highly degenerate part
of the envelope. We also show that the bulk of the He sits deep in the envelope
rather than near the surface. Thus, even if the photospheric He abundance is
low, the total He column could be substantially larger than the photospheric
column, which may have implications for rapid surface evolution ($\approx 1$ yr
timescales) of neutron stars. When nuclear reactions are taken into account, we
find that for base temperatures $\gtrsim 1.6 \times 10^8$ K, He is readily
captured onto C. As these high temperatures are present during the early stages
of NS evolution, we expect that the primordial He is completely depleted from
the NS surface like the case for primordial H. We also find that magnetic
fields $\lesssim 10^{12}$ G do not affect our conclusions. Armed with the
results of this work and our prior efforts, we expect that primordial H and He
are depleted, and so any observed H or He on the surfaces of these NS must be
due to subsequent accretion (with or without spallation). If this subsequent
accretion can be prevented, the underlying mid-Z material would be exposed.
