An Accelerated Lambda Iteration Method for Multilevel Radiative Transfer   III. Noncoherent Electron Scattering
  Since the mass of the electron is very small relative to atomic masses, Thomson scattering of low-energy photons ($h\nu \ll m_ec^2$) produces thermal Doppler frequency shifts that are much larger than atomic Doppler widths. A method is developed here to evaluate the electron scattering emissivity from a given radiation field which is considerably faster than previous methods based on straightforward evaluation of the scattering integral. This procedure is implemented in our multilevel radiative code (MALI), which now takes full account of the effects of noncoherent electron scattering on level populations, as well as on the emergent spectrum. Calculations using model atmospheres of hot, low-gravity stars display not only the expected broad wings of strong emission lines but also effects arising from the scattering of photons across continuum edges. In extreme cases this leads to significant shifts of the ionization equilibrium of helium. 
G.B. Rybicki and D.G. Hummer