Unitarity, the pole approximation, and interference between radiative emission and autoionization

In model problems involving the "decay" of discrete states into electron and photon continua there is frequently a final-state coupling between the two continua which must be considered. Armstrong, Theodosiou, and Wall have shown that this coupling can change the relative decay probabilities into the two channels. We examine and interpret this continuum-continuum coupling further, paying particular attention to questions of unitarity violation and the validity of the pole or Markov approximation for the continuum-continuum coupling. We also examine unitarity violation and the pole approximation in a more general context, and discuss criteria under which the approximation can be made in sequential diagonalizations. Finally, we interpret the square of the Fano $q$ value as the ratio of two rates in the pole approximation.