Shape Polarization and Quasiparticle Alignment in the [523]5/2 and [642]5/2 bands of $^{169}$Hf

Abstract

Rotational properties of [523]5/2 (h11/2) and [642]5/2 (i13/2) signature partner bands in 169Hf are investigated using the Total Routhian Surface (TRS) method. Experimental data show a distinct signature inversion in the [523]5/2 band at high spin, while the [642]5/2 band exhibits conventional signature splitting. Our analysis identifies a proton subshell gap at Z=72 (beta2 ~ 0.35) that 'locks' the proton core, allowing neutron-driven dynamics to dominate signature staggering. A critical shape bifurcation is identified in the [523]5/2 configuration: the alpha = -1/2 branch remains rigid at high deformation (beta2 ~ 0.32, gamma ~ -10 deg), whereas the alpha = +1/2 branch transitions toward reduced beta2 ~ 0.20 and enhanced hexadecapole deformation. This shift facilitates prompt i13/2 neutron alignment at h-bar omega ~ 0.3 MeV for the alpha = +1/2 branch. Furthermore, the alpha = -1/2 signature enters a gamma-soft regime at high spin (gamma fluctuating between -10 and +10 deg), favoring the unfavored signature and reinforcing the Routhian crossing. In contrast, the [642]5/2 band maintains a stable triaxial shape (gamma ~ -18 deg), preventing inversion. At h-bar omega ~ 0.5 MeV, a "shape-jump" to beta2 ~ 0.38 is predicted for the i13/2 band, signaling the breakthrough of the Z=72 gap and the onset of a highly deformed proton-aligned regime.