Analytic expressions for energy centroids and widths in the microscopic collective model

G. Rosensteel, Tulane University
J. P. Draayer, Louisiana State University


Analytic formulae are given for the U(3) centroids of the collective Bohr-Mottelson potential in the microscopic collective model. In particular, formulae are reported for the centroids of the quadratic [Q · Q ∼ β2] and cubic [Q · (Q × Q ∼ β3cos 3γ] rotational scalars in the microscopic quadrupole operator. Favorable comparisons for ground-state intensities are achieved between shell-model diagonalizations and statistical predictions based upon the gaussian approximation to the energy density. These results suggest that statistical measures can be used reliably for truncation of the infinite-dimensional representation spaces of the microscopic symplectic collective theory. © 1985.