Center-of-Gravity Theorem in Nuclear Spectroscopy

The $j\ensuremath{-}j$ coupling shell model implies the existence of certain geometrical relations among the spectra of neighboring nuclei. We have considered one such relationship between states of a nucleus that is one proton or neutron away from a closed shell with states of the corresponding closed-shell nucleus. Use of this relationship has enabled us to predict excited-state spins for several nuclei, most of which are in the vicinity of mass number 60. In two cases we predict the existence of states that have not been observed.