Polaron in the Jahn-Teller system and its superconductivity

We approach superconductivity in a crystal composed of the E circle times e Jahn-Teller centers from the weak-coupling region. We find that the vertex correction is less important in this system than in the usual electron-phonon coupled systems due to the presence of rotational symmetry in the pseudospin space representing twofold degeneracy. This ineffectiveness of the vertex correction results in the expansion of the applicable range of the conventional Migdal-Eliashberg theory. (C) 2001 Elsevier Science B.V. All rights reserved.