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 Ru112, Os188, Nd150, Sm150, Er168, and U238, 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 Ru112 and Os188 showing an increasing entanglement entropy, the axial γ-soft nuclei Nd150 and Sm150 displaying a uniform staggering pattern, and the axial γ-rigid nuclei Er168 and U238 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).