Note on the oblate and prolate deformations in nuclear matter from the viewpoint of the quantum-mechanical off-center effect

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.