High-order Anharmonic Vibration In Transitional Nuclei

It is well known that the shell model,the collective model,and the interacting boson model have been playing important roles in nuclear structure theory,among which the shell model emphasizes independent particle motion,while the collective model and the interacting boson model focus on the many-body correlation effects of nucleons with the shell model as the common microscopic foundation.Within the collective model,Iachello proposed the E(5)critical point symmetry model with a β-part infinite square well potential to describe nuclei in the critical point of the vibration to γ-unstable transitional region.Then,Levai and Arias replaced the infinite square well potential by the quasi-exactly solvable sextic potential in improving the description for nuclei near the critical point of the vibration to γ-unstable shape phase transition.Motivated by these developments,further correction in description of nuclei near the critical point of the vibration to γ-unstable shape phase transition is made in using a quasi-exactly solvable decatic potential with a centrifugal barrier in the Bohr Hamiltonian of the collective model,which is used with the help of its quasi-exact solution to describe low-lying spectra and E2 transitions of transitional nuclei.Some low-lying level energy ratios and related B(E2)ratios of the E(5)model are fitted by this theory and compared with the results obtained from the quasi-exactly solvable sextic potential.It is clearly shown that the present model can reproduce the E(5)model results better then the sextic model.As a further analysis and the model application,some low-lying level energy ratios and related B(E2)ratios of typical E(5)critical point nuclei,102Pd,104Ru,108Pd,114Cd,116Cd,134Ba are fitted and compared with those obtained from the E(5)and the sextic model.In combining the fitting quality of both the energy ratios and B(E2)ratios,it is observed that the E(5)model is the best in describing these critical point nuclei,while this theory is better than the sextic model.In order to examine the validity of this theory in description of nuclei near the critical point,some low-lying level energy ratios and related B(E2)ratios of even-even 118-128Xe are fitted and also compared to the results of the E(5)model and those of the sextic model.Though further check on the fitting quality to the B(E2)values is needed,the fitting results for even-even 118-128Xe show that the decatic model seems the best in fitting the energy ratios,while the fitting qualities of both the decatic model and the E(5)model to the B(E2)ratios are quite the same,which are always better than the sextic model.Thus,it can be concluded that high-order anharmonic vibration is likely to occur in nuclei near to the critical point.