  We consider the possibility that a quantum-mechanical off-center effect may
be behind the deformed oblate and prolate shapes of nuclei in nuclear physics.
In solid state physics, finite off-center displacements result from the mixing
of electronic states through their coupling to vibrational (phonon) modes of
appropriate symmetries. This is an example of fermion-boson interaction which
may materialize in nuclear physics as well in the form of a coupling of
nucleons to the pi-meson field. We carry out calculations to substantiate the
proposal.
