Quantum phase transitions and spectral statistical properties in nuclei near N∼90

The phase transitions and spectral statistical properties in Nd, Sm, Gd, and Dy isotopes are investigated by spherical mean-field plus standard pairing model. The results of the model calculations successfully reproduce the critical phenomena observed experimentally in the two-neutron separation energy, odd–even mass differences, α-decay, double β${}^{-}$-decay energy and the first pairing excitation states of these isotopes with the critical point at the neutron number N∼90. As the only parameter in the model, the pairing interaction strength G is determined by fitting the binding energies, the odd–even mass differences and the energies of the first and second pairing excitation states for the ${}^{144-157}$Nd, ${}^{146-159}$Sm, ${}^{148-161}$Gd, and ${}^{150-163}$Dy isotopes. The spectral statistical properties of the excited levels of Sm isotopes show that the quantum chaos exists in ${}^{151-153}$Sm which corresponds to the critical point at N∼90. It is inferred that the transitional region is the most sensitive region to perturbation, leading generically to the typical signature of quantum chaos. Moreover, the results indicate that this critical behavior is related not only to the ground-state but also to the excited-state under the present model. It may provide us a microscopic picture that the ground-state phase transition and the quantum chaos behaviors may drive by the competition between the spherical mean-field and the pairing interaction based on the present model for Nd, Sm, Gd, and Dy isotopes.