Some binding energy related quantities serving as effective order parameters have been used to analyze the shape phase transition in the odd Sm nuclei. It is found that the signals of phase transition in the odd Sm nuclei are greatly enhanced in contrast to the even Sm nuclei. A further analysis shows that the transitional behaviors related to pairing in the Sm nuclei can be well described by the mean field plus pairing interaction model, with a monotonic decrease in the pairing strength G.
The triaxial dynamics of the quadrupole-deformed rotor model of both the rigid and the irrotational type are investigated in detail. The results indicate that level patterns of the two types of model can be matched with each other to the leading order of the deformation parameter β. In particular, it is found that the dynamical structure of the irrotational type with most triaxial deformation （γ = 30°） is equivalent to that of the rigid type with oblate deformation （7=60°）, and the associated spectrum can be classified into the standard rotational bands obeying the rotational L（L＋1）-law or regrouped into a new ground- and γ-band with odd-even staggering in the new γ-band, commonly recognized as a signature of the triaxiality. The differences between the two types of the model in this case are emphasized, especially in the E2 transitional characteristics.
A classical analysis of shape phase transitions and phase coexistence in odd-even nuclei has been performed in the framework of the interacting boson-fermion model. The results indicate that the effects of a single particle may influence different types of transitions in different ways. Especially, it is revealed that phase coexistence can clearly emerge in the critical region and thus be taken as a indicator of the shape phase transitions in odd-even nuclei.
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂Landau＂ potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.
