We analyze systematically the effective order parameters in nuclear shape phase transition both in experiments and in the interacting boson model. We find that energy ratios and B(E2) ratios can distinguish the first from the second-order phase transition in theory above a certain boson number N (about 50), but in experiments, only those quantities, such as E(L1+)/E(02+) and B(E2; (L+2)1 → L1)/B(E2; 21 → 01), etc., of which the monotonous transitional behavior in the second-order phase transition is broken in the first order phase transition independent of N, are qualified as the effective order parameters. By implementing the originally proposed effective order parameters and the new ones, we find that the isotones with neutron number Nn = 62 are a trajectory of the second order phase transition. In addition, we predict that the transitional behavior of isomer shifts of Xe, Ba isotopes and Nn = 62 isotones is approximately monotonous due to the finiteness of nuclear system.
ZHANG Yu1,2, HOU ZhanFeng2 & LIU YuXin2,3 1Department of Physics, Liaoning Normal University, Dalian 116029, China
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.
In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.
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.
