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We present a theoretical study of a possibility of superconductivity in athree dimensional molecular conductor in which the interaction betweenelectrons in doubly degenerate molecular orbitals and an {\em intra}molecularvibration mode is large enough to lead to the formation of $E\otimes \beta$Jahn-Teller small polarons. We argue that the effective polaron-polaroninteraction can be attractive for material parameters realizable in molecularconductors. This interaction is the source of superconductivity in our model.On analyzing superconducting instability in the weak and strong couplingregimes of this attractive interaction, we find that superconducting transitiontemperatures up to 100 K are achievable in molecular conductors within thismechanism. We also find, for two particles per molecular site, a novel Mottinsulating state in which a polaron singlet occupies one of the doublydegenerate orbitals on each site. Relevance of this study in the search for newmolecular superconductors is pointed out.Comment: Submitted to Phys. Rev.

Jahn-Teller polarons and their superconductivity in a molecular conductor