Thresholded Zipf Scaling Across 14 Highly-Charged-Ion Isoelectronic Sequences: Identification of an nd65D0 jj-Coupling Pair

Earlier work by some of the present authors identified power-law statistical regularities across the periodic table: a near-Zipf relationship W∝Z1.09 between atomic weight and atomic number in neutral atoms, and a fine-structure splitting scaling ΔE∝Z1.78 in the 3d2+ (Cr-like) isoelectronic sequence of highly charged ions (HCIs). The apparent tension between this superlinear empirical exponent and the linear-in-Z scaling derived analytically by Lyu, Keitel, and Harman for relativistic clock-state transitions in nd6 ions is resolved by writing the scaling law in the form ΔE=A(Z−Z∗)γ, which gives γ=1.03 and Z∗=25.83 for the 3d2+ data and restores a near-Zipf interpretation. We extend the thresholded model from the single 3d2+ sequence to fourteen isoelectronic sequences spanning C-like (Z≥6) through Mo-like (Z≥42), drawing on the NIST Atomic Spectra Database, evaluated compilations of strontium, copper, and tungsten ion data, and digitization of GRASP MCDHF Mo-like results. Comparing the fitted threshold Z∗ against the classical Slater shielding σSlater of the valence shell reveals three regimes: (i) Coulomb-LS sequences (C/N/O/Ne-like) with Z∗ fixed at zero by construction; (ii) a mainstream cluster of nine sequences (a mix of spin–orbit fine-structure and, for the d2 Ca-/Sr-like members, Coulomb term separations) for which Z∗ tracks σSlater within ±1.5 units; (iii) a pair of nd6D05 sequences (Cr-like 3d6 and Mo-like 4d6) with Z∗−σSlater=+7.20 and +10.36, scaling linearly with Z in the jj regime (after resolving a low-Z LS–jj crossover for the Mo-like member). The slope ratio AMo/ACr≈0.48 is of the order of the hydrogenoid radial-extent ratio ⟨r2⟩(3d)/⟨r2⟩(4d)≈0.32, exceeding it by ∼50% as expected from relativistic 4d contraction. A falsifiable extrapolation for the W-like 5d6D05 sequence is offered: Δ∈[+7,+11], AW∈[0.12,0.18] eV/Z, with explicit failure modes specified for an independent GRASP MCDHF test.