Empirical Quadratic Scaling of Static Dipole Polarizability in Noble Gas Atoms

This work presents an empirical analysis of static dipole polarizability scaling in noble gas atoms from helium to radon. Using experimental reference data, a phenomenological relationship of the form α ∝ n² is identified, where n represents the principal quantum number of the outer electronic shell. The observed scaling provides a strong empirical fit across the noble gas series and differs substantially from simple hydrogenic scaling expectations. Statistical analysis yields an optimal exponent close to p ≈ 2, suggesting the presence of effective screening and closed-shell correlation effects that may suppress higher-order scaling behavior. The study is intended as an exploratory phenomenological observation rather than a derivation from first principles. Possible implications for atomic response theory, electron correlation, and closed-shell electronic structure are briefly discussed.