Projected shell model study of low-lying three-quasiparticle high-$K$ configurations in neutron-rich odd-mass $^{153-171}$Pm

摘要: High-$K$ structures in neutron-rich rare-earth nuclei are sensitive probes of multi-quasiparticle excitations and deformed shell structure. The projected shell model (PSM) is applied to neutron-rich odd-mass $^{153-171}$Pm isotopes with neutron numbers $N=92$--110 to investigate rotational properties and low-lying three-quasiparticle high-$K$ configurations. Modified Nilsson parameters are adopted for the neutron $N_{\rm osc}=6$ shell, providing a reasonable description of the band structures associated with the experimentally identified high-$K$ isomeric states in $^{159}$Pm and $^{161}$Pm. A systematic evolution of low-lying three-quasiparticle high-$K$ configurations is predicted along the Pm isotopic chain. The dominant proton component is associated with the $\pi5/2^-[532]$ Nilsson orbital originating from the spherical $h_{11/2}$ shell, corresponding to the one-quasiparticle ground-state configuration. With increasing neutron number, the neutron components evolve from configurations mainly involving the $\nu11/2^-[505]$ orbital in $^{153,155}$Pm to those dominated by neutron $N_{\rm osc}=6$ orbitals in heavier isotopes. Configurations involving neutron $i_{13/2}$ orbitals become competitive in $^{157,159}$Pm and enter the lowest three-quasiparticle high-$K$ configurations from $^{161}$Pm onward. These results highlight the role of neutron $i_{13/2}$ orbitals in the evolution of low-lying high-$K$ structures and provide guidance for future spectroscopic studies and searches for possible isomeric states in neutron-rich Pm isotopes.