  We theoretically analyze the cooling dynamics of an atom which is tightly
trapped inside a high-finesse optical resonator. Cooling is achieved by
suitably tailored scattering processes, in which the atomic dipole transition
either scatters a cavity photon into the electromagnetic field external to the
resonator, or performs a stimulated emission into the cavity mode, which then
dissipates via the cavity mirrors. We identify the parameter regimes in which
the atom center-of-mass motion can be cooled into the ground state of the
external trap. We predict, in particular, that for high cooperativities
interference effects mediated by the atomic transition may lead to higher
efficiencies. The dynamics is compared with the cooling dynamics of a trapped
atom inside a resonator studied in [Phys. Rev. Lett. 95, 143001, (2005)] where
the atom, instead of the cavity, is driven by a laser field.
