  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.
