A scheme that elucidates the nature of critical point symmetries in deformed odd-A nuclei by linking them to critical point symmetries of neighboring even-even nuclei is introduced. Specifically, a new symmetry, called SX(3), is advanced that shows primary characteristics of an assumed strong-coupling limit for odd-A systems. It is found that the SX(3) symmetry can be used to identify the soft collective structures in odd-A system. A preliminary application of the new scheme to describe the lowest positive parity bands of ${}^{193}$Ir is also shown.

• Received 28 June 2011

DOI:https://doi.org/10.1103/PhysRevC.84.054319