Hartree-Fock distortion energy of the nucleus

The Hartree-Fock energy of a nucleus in an external field is expressed in terms of two auxiliary density matrices. One of them is a smoothed distribution $\text{?}$ which generates the non-selfconsistent deformed shell-model potential and is directly related to the nuclear shape. The other represents the volume polarization effect by the external field. The final expression suggests a possibility of a two-mode model for the nuclear vibrations. Renormalisation of smoothed quantities by means of phenomenological models is indicated.