Theory of Umklapp-assisted recombination of bound excitons in Si:P
  We present the calculations for the oscillator strength of the recombination of excitons bound to phosphorous donors in silicon. We show that the direct recombination of the bound exciton cannot account for the experimentally measured oscillator strength of the no-phonon line. Instead, the recombination process is assisted by an umklapp process of the donor electron state. We make use of the empirical pseudopotential method to evaluate the Umklapp-assisted recombination matrix element in second-order perturbation theory. Our result is in excellent agreement with the experiment. We also present two methods to improve the optical resolution of the optical detection of the spin state of a single nucleus in silicon. 
Michael N. Leuenberger, L. J. Sham