Centroids and widths in the symplectic collective model

Methods of statistical spectroscopy are applied to the symplectic collective shell model. Analytic expression are given for determining the distribution of U(3) centroids within an irreducible representation of Sp(3, R) for the Bohr-Mottelson collective V(#betta#, #betta#) potential. For 20Ne, a comparison is made between statistical predictions and shell-model results for the U(3) content of states in the ground state domain. The results suggest that statistical measures can be used reliably to truncate symplectic model spaces so that microscopic calculations become feasible. (orig.)