Empirical Correlation of Nuclear Magnetic Moments

Abstract

A simple generalization of the extreme shell model, based upon the kinematics of the collective model, is proposed for the correlation of nuclear magnetic moments. It is shown that, if the concept of a rotating core is adjoined to that of the single-particle model, largely in disregard of dynamical considerations, then by the aid of three simple empirical rules ground-state wave functions may be easily constructed which correctly express the parities, spins, and magnetic moments of all nuclei for which A>~7, with the exception of W183. ** The choice of a particular set of empirical rules was dictated primarily by the twofold desire to keep their number to a minimum and at the same time restrict the consequent wave function to but two components; hence, considerable oversimplification of the true state of affairs is inevitable. However, the internal consistency of the results does point up strikingly the previously observed, but not explicitly investigated, possibility that the nature of the variable degrees of freedom required for generalization of the single-particle model may differ fundamentally for j=l+1/2 in contrast to j=l-1/2 single-particle configurationsÑbeing predominantly those of the core in the former instance and those of the single particle in the latter.