Hydrogen Recombination with Multilevel atoms
  Hydrogen recombination is one of the most important atomic processes
  in many astrophysical objects such as Type II supernova (SN~II)
  atmospheres, the high redshift universe during the cosmological recombination
  era, and H II regions in the interstellar medium. Accurate predictions of
  the ionization fraction can be quite different from those given by a
  simple solution
  if one takes into account many angular momentum sub-states,
  non-resonant processes, and calculates the rates of all atomic
  processes from the solution of the radiative transfer equation
  instead of using a Planck function under the assumption of thermal
equilibrium. We use the general
  purpose model atmosphere code PHOENIX 1D to
  compare how the fundamental probabilities such as the photo-ionization
  probability, the escape probability, and the collisional de-excitation
  probability are affected by the presence of other metals in the
  environment, multiple angular momentum sub-states, and
  non-resonant processes. Our comparisons are based on a model of SN
  1999em, a SNe Type II, 20 days after its explosion.
