SOME ASPECTS OF SHAPE PHASE TRANSITION IN EVEN-EVEN NUCLEI
Abstract
We have reviewed the study on the signatures of shape phase transition in even-even nuclei and investigated the statistical properties of the E(5) and X(5) symmetries and their location in the Casten's triangle and the effect of some modes of nucleon-nucleon interaction on the nuclear shape phases and their transitions. We show that the ratios of the E2 transition rates and the ratio of the energies of 
state and the 
state can serve as the effective order parameters not only identifying the nucleon number driven phase transition but also distinguishing the first order one form the second order one. Our calculations show that the states in E(5) and X(5) symmetries are almost regular ones and the X(5) symmetry may actually locate at the middle of the "AW arc" inside the Casten's triangle and the E(5) symmetry at the U(5)-O(6) chain. Our study also indicates that strong or weak monopole-pair interaction leads to a vibration or an axially oblate deformation. While quadrupole-pair and QQ interactions induce deformations. Then a complete shape phase structure of nucleus is given in a study at nucleon level.
This work is supported by the National Natural Science Foundation of China under the contract Nos. 10425521 and 10675007, the Major State Basic Research Development Program under contract No. G2007CB815000, the Key Grant Project of Chinese Ministry of Education (CMOE) under contact No. 305001.
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