  Interpretation of precision measurements of the cosmic microwave background
(CMB) will require a detailed understanding of the recombination era, which
determines such quantities as the acoustic oscillation scale and the Silk
damping scale. This paper is the second in a series devoted to the subject of
helium recombination, with a focus on two-photon processes in He I. The
standard treatment of these processes includes only the spontaneous two-photon
decay from the 2^1S level. We extend this treatment by including five
additional effects, some of which have been suggested in recent papers but
whose impact on He I recombination has not been fully quantified. These are:
(i) stimulated two-photon decays; (ii) two-photon absorption of redshifted HeI
line radiation; (iii) two-photon decays from highly excited levels in HeI (n^1S
and n^1D, with n>=3); (iv) Raman scattering; and (v) the finite width of the
2^1P^o resonance. We find that effect (iii) is highly suppressed when one takes
into account destructive interference between different intermediate states
contributing to the two-photon decay amplitude. Overall, these effects are
found to be insignificant: they modify the recombination history at the level
of several parts in 10^4.
