Reconstructed proton mass/energy structure: Insights from Patterson function analysis

Abstract

This study employs the gravitational form factor Ai of the proton to reconstruct its internal mass/energy distribution using Patterson function analysis combined with a scaling procedure. The reconstruction reveals a sharply localized central peak, reaching 47 400 fm⁻³, with a half‑maximum radius of 0.0526 fm, underscoring the compact nature of the distribution. Grid integration confirms a strictly non‑negative density that yields a net mass/energy of 53 in normalized units. These findings demonstrate that Patterson analysis, when paired with scaling, provides a reproducible, model‑independent framework for visualizing the internal charge, magnetic, and mass/energy structures of nucleons, light nuclei, and elementary particles. The present work highlights the methodological strength of Patterson reconstruction while pointing to the need for empirical gravitational form factors to advance future studies.