Unification of the nuclear collective and single particle models

The unification of the nuclear collective and single particle models with the help of a transformation, first published by the author, is presented. The Schrödinger equation with the new coordinates exhibits all relevant features of the so-called unified nuclear model, but it is no longer an artificial combination of the continuum, used in the collective model, and the conventional shell model. As a first application a sum rule for the quadrupole moments of mirror nuclei is derived. Estimates are given for the deformations of the charge and mass distributions of ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$. The approximation of strong coupling of the nucleon motions to a symmetry axis gives good results, while the weak coupling approximation does not work at all.