Unification of the nuclear collective and single particle models

Abstract

The unification of the nuclear collective and single particle models with the help of a transformation, first published by the author, is presented. The Schr\"odinger 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.NUCLEAR STRUCTURE Genuine definition of single particle and collective states from $A$ nucleon Schr\"odinger equation. Sum rule for $q$ of mirror nuclei.