The quadrupole collectivity and possible existence of macroscopic SU(3) symmetry in some collective shell model states

Abstract

The shell model eigenfunctions for low-lying states of 56Fe and 54Cr are analyzed to illustrate that the “collective” states of these nuclei can be described as the coupling of a small number of low-lying collective states of the proton and neutron groups. A truncation scheme for doing shell model calculations which would take advantage of the multipole collectivity of the low-lying states of the proton and neutron states is discussed. Finally, it is suggested that the rotational features observed even in the heavy deformed nuclei could be a consequence of the existence of what might be called an approximate “macroscopic” SU(3) symmetry.