Geometrical Interpretation of the Hydrogen Atom Hyperfine Structure

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Abstract

A phenomenological geometrical model is presented for the hyperfine structure of hydrogenic systems. The approach extends a previously published fine-structure analysis to hyperfine splittings by introducing a compact set of empirically constrained geometric corrections. Unlike conventional quantum electrodynamic treatments which reference the Lamb shift to the hyperfine centroid, the present framework targets the hyperfine mid-point, corresponding to a substantially larger reference interval. Despite this difference in reference scale, agreement with experimental hyperfine and Lamb-shift-related data at the 0.01 MHz level is obtained across multiple hydrogen states. The model is further extended to deuterium, tritium, 3He+, and 7Li2+, revealing systematic cross-nuclear behaviour and a universal scaling relation involving nuclear mass number and charge. The calculations employ a simplified geometric scheme that does not rely on perturbative quantum electrodynamics but is intended as a complementary phenomenological description. Possible physical interpretations in terms of structured internal dynamics are discussed, together with limitations and directions for further development.

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