  The co-existence of band Jahn-Teller (BJT) effect with superconductivity (SC)
is studied for correlated systems, with orbitally degenerate bands using a
simple model. The Hubbard model for a doubly degenerate orbital with the
on-site intraorbital Coulomb repulsion treated in the slave boson formalism and
the interorbital Coulomb repulsion treated in the Hartree-Fock mean field
approximation, describes the correlated system. The model further incorporates
the BJT interaction and a pairing term to account for the lattice distortion
and superconductivity respectively. It is found that structural distortion
tends to suppress superconductivity and when SC sets in at low temperatures,
the growth of the lattice distortion is arrested. The phase diagram comprising
of the SC and structural transition temperatures $T_c$ and $T_s$ versus the
dopant concentration $\delta $ reveals that the highest obtainable $T_c$ for an
optimum doping is limited by structural transition. The dependence of the
occupation probabilities of the different bands as well as the density of
states (DOS) in the distorted-superconducting phase, on electron correlation
has been discussed.
