A Refined Grodzins Based Signature for Shape Phase Transitions in Rare Earth Nuclei Using the Interacting Boson Approximation

This study investigates a refined empirical signature, the Grodzins systematics expressed as dE4/2 ×B(E2; 0+→2+) within the framework of the Interacting Boson Approximation (IBA), focusing on its correlation to the control parameter (ζ) and its role in nuclear shape transitions. By analyzing even-even nuclei with Z < 76, N = 86–102, a critical transition point is identified near ζ ≈ 0.6, corresponding to the boundary between spherical U(5) and deformed SU(3)/γ-soft O(6) regimes, where rapid changes in collectivity and excitation systematics occur. This critical value corresponds to the point where quadrupole–quadrupole correlations begin to dominate over single-boson dynamics, leading to abrupt changes in excitation energy ratios and electromagnetic collectivity, as supported by abrupt shifts in R6/0 energy ratios and B(E2; 0+→2+) transition probabilities. Notable anomalies around N ~ 90-100, suggest the onset of shape coexistence. This approach offers a sensitive diagnostic for nuclear collectivity and shape transitions without invoking model dependent assumptions.