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

TL;DR

This study uses the Total Routhian Surface method to analyze shape polarization and quasiparticle alignment in specific bands of 169Hf, revealing shape bifurcations, signature inversion mechanisms, and the role of proton subshell gaps in high-spin nuclear behavior.

Contribution

It provides a detailed theoretical analysis of shape and quasiparticle dynamics in 169Hf, highlighting the impact of shape bifurcations and subshell gaps on signature inversion and neutron alignment.

Findings

Signature inversion in the [523]5/2 band at high spin

Identification of a proton subshell gap at Z=72

Prediction of a shape jump at high rotational frequency

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.