  Superconductivity of boron-doped diamond, reported recently at T_c=4 K, is
investigated exploiting its electronic and vibrational analogies to MgB2. The
deformation potential of the hole states arising from the C-C bond stretch mode
is 60% larger than the corresponding quantity in MgB2 that drives its high Tc,
leading to very large electron-phonon matrix elements. The calculated coupling
strength \lambda ~ 0.5 leads to T_c in the 5-10 K range and makes phonon
coupling the likely mechanism. Higher doping should increase T_c somewhat, but
effects of three dimensionality primarily on the density of states keep doped
diamond from having a T_c closer to that of MgB2.
