Spin‑Dependent Contact Interaction in Polarised Hydrogen and Deuterium Lyman‑α Spectroscopy: Projected Sensitivity

We propose a phenomenological contact interaction Ĥ_comp = β Î_z δ³(r) as a possible low‑energy manifestation of the Cosmic Energy Compression framework. The interaction couples nuclear spin to the electron density at the nucleus, shifting only s‑states. Using high‑precision NIST energy levels for the Lyman‑α transition (2p → 1s) in hydrogen (H I) and deuterium (D I), we show that existing zero‑field, unpolarised data cannot constrain β because the expectation value of Î_z averages to zero and the shift cancels for p‑states. However, the achieved precision (σ = 2×10⁻⁶ cm⁻¹) demonstrates that a future polarised experiment would be sensitive to a coupling constant |β| ≲ 2×10⁻³⁰ eV·cm³ (1σ; dimensions: energy × volume). This provides a concrete, falsifiable experimental proposal distinct from standard hyperfine and Zeeman effects. We do not claim to have proven a quantum theory of gravity; rather, we present a testable phenomenological model inspired by the Cosmic Energy Compression framework. The result does not invalidate the broader framework but refines its quantum‑scale phenomenology and sets a target for precision spectroscopy on polarised hydrogenic targets. A brief comparison with existing exotic spin‑force constraints shows that our proposed coupling is complementary and not yet ruled out. Keywords: spin‑dependent contact interaction, polarised spectroscopy, Lyman‑α, hydrogen, deuterium, projected sensitivity, Cosmic Energy Compression framework, phenomenological model, version 3 Version 3 : Zenodo DOI:10.5281/zenodo.20261122