Employing the five-dimensional collective Hamiltonian based on relativistic density functional theory, we investigate how the entanglement between collective shape and rotational degrees of freedom evolves along the even-even hafnium chain ${}^{154–198}\mathrm{Hf}$. Potential-energy surfaces, deformation parameters, and low-lying spectra delineate a coherent shape transition with distinct deformation characteristics. The entanglement entropy decreases monotonically as the nucleus departs from sphericity and locks into a stable prolate minimum, remains flat at maximal axial symmetry, then ascends anew with the resurgence of $\gamma$ softness and shape transition. A connection is established between the calculated entanglement entropy and the experimentally accessible $B\left(E2\right)$ ratio $R_B=B(E2,2_2^{+}\to 2_1^{+})/B(E2,2_1^{+}\to 0_1^{+})$, demonstrating the effectiveness of $R_B$ as a sensitive probe of the structural information encoded in the entanglement entropy.

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• Collective levels
• Entanglement entropy
• Nucleon distribution
• 150 ≤ A ≤ 189
• 190 ≤ A ≤ 219
• Collective models
• Nuclear density functional theory