Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations

Abstract To understand how collective motion can develop in the shell-model framework it is necessary to study configuration interaction. With this in mind, group-theoretical methods are used to investigate the possible classification schemes for a number of nucleons in m xed configurations. One particular coupling scheme, which is associated with the degeneracy of a harmonic oscillator potential and which, in a following paper, will be shown to have collective properties is described in detail. The wave functions in this scheme are seen to be very similar to those resulting from an actual shell-model calculation with configurational mixing.