Primordial helium recombination. III. Thomson scattering, isotope shifts, and cumulative results

Upcoming precision measurements of the temperature anisotropy of the cosmic microwave background at high multipoles will need to be complemented by a more complete understanding of recombination, which determines the damping of anisotropies on these scales. This is the third in a series of papers describing an accurate theory of He I and He II recombination. Here we describe the effect of Thomson scattering, the He-3 isotope shift, the contribution of rare decays, collisional processes, and peculiar motion. These effects are found to be negligible: Thomson and He-3 scattering modify the free electron fraction x(e) at the level of several x 10(-4). The uncertainty in the 2(3)P(o)-1(1)S rate is significant, and for conservative estimates, gives uncertainties in x(e) of order 10(-3). We describe several convergence tests for the atomic level code and its inputs, derive an overall C-l error budget, and relate shifts in x(e)(z) to the changes in C-l, which are at the level of 0.5% at l = 3000. Finally, we summarize the main corrections developed thus far. The remaining uncertainty from known effects is similar to 0.3% in x(e).