The quantum shape phase transitions in odd-even nuclei are investigated within the intrinsic frame approach to the interacting boson-fermion model. In this work, the case of a single-j fermion coupled to a bosonic core that performs a transition from prolate to oblate shapes is considered. The focus is on the effect of the coupled fermion on the whole system along the transitional path from prolate to oblate shapes, passing through the \({\gamma }\)-unstable shape. One could expect that all the magnetic substates of the coupled single-fermion with \(j=9/2\) would be driven by the shape of the bosonic core. However, the present work shows that the odd-fermion follows some unexpected and unique paths. The five-components of the \(j=9/2\) orbital do show quite interesting and diverse behaviour. Two of them move slowly from the prolate to the oblate shape by venturing into the triaxial region and also show \(\gamma \)-softness around their slow shape-changing region. The other three odd-states show sudden jumps from prolate side to oblate side and shape coexistence appears, although one of them is fairly close to \(\gamma \)-instability. These unexpected situations make this shape phase transition worth of investigation and discussion.

在相互作用的玻色子-费米子模型的本征框架方法内，研究了奇偶核中的量子形状相变。在这项工作中，考虑了单j费米子耦合到执行从长形到扁形形状的转变的玻色子核的情况。重点是耦合费米子沿着从扁长形状到扁圆形状的过渡路径（通过\（{\ gamma} \）-不稳定形状）对整个系统的影响。可以预料到，具有\（j = 9/2 \）的耦合单费米子的所有磁子状态都将由玻色子磁芯的形状驱动。然而，目前的工作表明奇数费米子遵循了一些意想不到的独特路径。\（j = 9/2 \）的五个组成部分轨道确实显示出非常有趣和多样化的行为。他们中的两个通过冒险进入三轴区域而从扁长形状逐渐变为扁圆形，并且在它们缓慢的形状变化区域周围也显示出\（\γ\）-柔软度。其他三个奇数状态显示从扁长的一侧突然过渡到扁圆的一侧，并且出现了形状共存，尽管其中之一非常接近\（\ gamma \）-不稳定性。这些意外情况使这种形状相变值得研究和讨论。