We discuss a many-electron Hamiltonian with Hubbard-like repulsive
interaction and linear coupling to the phonon branches, having the Cu-O plane
of the superconducting cuprates as a paradigm. A canonical transformation
extracts an effective two-body problem from the many-body theory. As a
prototype system we study the \cu cluster, which yields electronic pairing in
the Hubbard model; moreover, a standard treatment of the Jahn-Teller effect
predicts distortions that destroy electronic pairing. Remarkably, calculations
that keep all the electronic spectrum into account show that vibrations are
likely to be synergic with electronic pairing, if the coupling to
half-breathing modes predominates, as experiments suggest.Comment: 4 pages, 3 figures, accepted by Phys. Rev.
