Entanglement between shape and rotation in the low-lying states

The entanglement between shape and rotation in the low-lying states is investigated for six even-even nuclei $^{112}\mathrm{Ru}, ^{188}\mathrm{Os}, ^{150}\mathrm{Nd}, ^{150}\mathrm{Sm}, ^{168}\mathrm{Er}$, and $^{238}\mathrm{U}$, using the five-dimensional collective Hamiltonian based on relativistic density functional theory. Analyses of potential energy surfaces, rotational frequencies, and staggering parameters reveal distinct deformation characteristics. The entanglement entropy exhibits divergent trends across the nuclei, with the triaxial nuclei $^{112}\mathrm{Ru}$ and $^{188}\mathrm{Os}$ showing an increasing entanglement entropy, the axial $\ensuremath{\gamma}$-soft nuclei $^{150}\mathrm{Nd}$ and $^{150}\mathrm{Sm}$ displaying a uniform staggering pattern, and the axial $\ensuremath{\gamma}$-rigid nuclei $^{168}\mathrm{Er}$ and $^{238}\mathrm{U}$ maintaining relatively low entanglement entropy values. The relationship between nuclear deformation and entanglement entropy is further elucidated by examining the corresponding probability distributions on the principal axes ($K$ distributions).