Z(4): gamma-rigid solution of the Bohr Hamiltonian for gamma=30 degrees compared to the E(5) critical point symmetry

Abstract

A gamma-rigid solution of the Bohr Hamiltonian for gamma = 30 degrees is derived, its beta-part being related to the second order Casimir operator of the Euclidean algebra E(4). The solution is called Z(4), since it corresponds to the Z(5) model with the gamma variable "frozen". Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are in close agreement to the E(5) critical point symmetry, as well as to experimental data in the Xe region around A = 130.