  We consider superconductivity in boron (B) doped diamond using a simplified
model for the valence band of diamond. We treat the effects of substitutional
disorder of B ions by the coherent potential approximation (CPA) and those of
the attractive force between holes by the ladder approximation under the
assumption of instantaneous interaction with the Debye cutoff. We thereby
calculate the quasiparticle life time, the evolution of the single-particle
spectra due to doping, and the effect of disorder on the superconducting
critical temperature $T_c$. We in particular compare our results with those for
supercell calculations to see the role of disorder, which turns out to be of
crucial importance to $T_c$.
