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

#### Abstract

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.

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