Strong-coupling Critical Point Symmetries for Axially-symmetric Odd-A Nuclei

In view of the successful application of the methods based on critical point symmetries (CPSs) in nuclear shape phase transitions, the new CPSs named SX(n) are established in this work for axially-symmetric odd-A nuclei through extending the original X(n) CPSs with n=3,4,5, which were used to describe the spherical to prolate shape phase transitions in even-even nuclei, in the strong-coupling scheme. By comparing the spectral structures in between the X(n) and the SX(n) CPSs, it is revealed that the dynamical structures of SX(n) are closer to the rigid rotor and less changed with the model dimension in comparison with X(n). Moreover, these features of SX(n) are preliminarily verified by checking the rotational structures of ^{150,151,152,153}Sm and ^{172,173,174,175}Os nuclei.