Quasi-exactly solvable decatic model description of nuclei near the X(5) critical point

The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied. It is shown that the decatic model can well reproduce the X(5) model results as far as the energy ratios in the ground and beta band and related B(E2) values are concerned. Fitting results to the low-lying energy ratios and relevant B(E2) values of even–even X(5) candidates ¹⁵⁰Nd, ¹⁵⁶Dy, ¹⁶⁴Yb, ¹⁶⁸Hf, ¹⁷⁴Yb, ^176,178,180Os, and ^188,190Os show that the decatic model provides the best fitting results for the energy ratios, while the X(5) model is the best at reproducing the B(E2) values of these nuclei, in which the beta-bandhead energy is lower than that of the gamma band. While for even–even nuclei, such as ^154,156,158Gd, with bandhead energies of the beta and gamma bands more or less equal within the X(5) critical point to the axially deformed region, our numerical analysis indicates that the decatic model is better than the X(5) model in describing both the low-lying level energies and related B(E2) values.