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.
The O( N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions.The problem is directly related to that of a quantum double well anharmonic oscillator in an external field.A finite dimensional matrix equation for the problem is constructed explicitly,along with analytical expressions for some excited states in the system.The corresponding Niven equations for determining the polynomial solutions for the problem are given.
