Quantum Phase Transitions Of Rare-earth Well-deformed Nuclei In The Nilsson Mean-field Plus Pairing Models

In this thesis,algebraic approaches to the deformed mean-field plus pairing models are studied in detail.Basic properties of well-deformed nuclei in rare earth region are described by the two models in calculating ground state energies of^146-157Sm and^148-159Gd isotopes.The advantage of the standard pairing model and the extended pairing model is that these models can be solved exactly.The pairing interaction strength of both models is determined by the first pairing excitation energy of^146-157Sm and^148-159Gd in the proton-pair and neutron-pair excitation frozen limit.The odd-even mass differences,the odd-even differences of two-neutron separation energy,the odd-even differences of?-decay energy and the odd-even differences of double?-decay energy are then calculated.The theoretical value of the both models fits the corresponding experimental value rather well,but the extended pairing model seems more advantageous in calculation efficiency and saving CPU time.It can be observed that the odd-even effects of these nuclei can be elucidated by the pairing interactions of the model,and the critical phenomena in^148-159Gd nuclei are obvious in the odd-even differences related to the ground state energy described by the two pairing models.Based on the results of the odd-even differences,information entropy and its derivative to the pairing interaction strength for^148-159Gd are calculated.It can be seen that there are noticeable peaks in the derivative of information entropy,and the peak becomes the sharpest at the critical point near N=90,which is just the critical point of the quantum phase transitions in this region.