  We study a multiorbital Hubbard model coupled to local Jahn-Teller phonons to
investigate the superconducting state realized in fullerides. A weak-coupling
approach is employed in combination with a local self-energy approximation. In
addition to the normal and anomalous self-energies of the electrons, we
consider the phonon self-energy, which allows a self-consistent treatment of
the energetics. The frequency dependence of the self-energies and their
characteristic coefficients, such as renormalization factors and dampings, are
investigated in detail using numerical calculations. It is clarified that the
anisotropic phonons play an important role in the stabilization of the
superconducting state. By comparing the full results to those without phonon
self-energies, we show that the superconductivity is stabilized by the
softening of the phonon frequency. The effects of electronic fluctuations are
also considered, which leads to the coupling to orbitons, an analog of plasmons
in the electron gas. This additional contribution further stabilizes the
superconducting state.
