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

A gamma-rigid solution of the Bohr Hamiltonian for gamma=30 degrees is derived. Bohr Hamiltonians beta-part being related to the second order Casimir operator of the Euclidean algebra E(4). The solution is called Z(4) since it is 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 the experimental data in the Xe region around A=130