Statistical Properties of E(5) and X(5) Symmetries
We investigate the statistical properties of the E(5) and X(5) symmetries, which describe states at the critical points of nuclear shape phase transitions in the geometric model, and analyze the fluctuations in both the energy spectrum and the E2 transition intensities using different angular momenta and Hamiltonian parameters. The results indicate that the spectrum of the E(5) symmetry exhibits highly regular statistical behavior and that the X(5) symmetric states are also nearly regular, with little deviation for different angular momenta and Hamiltonian parameters.