Proton mass/energy structure revisited: Insights from Patterson function analysis

This study employs Patterson function analysis to reconstruct the spatial distribution of the proton’s mass and energy directly from gravitational form factors. By bypassing model assumptions, the method yields a density profile that is entirely positive and sharply localized. The reconstruction reveals a compact central peak with a half‑maximum radius of 0.0592 fm, establishing a stringent measure of the proton’s spatial extent. Comparative evaluations with nucleons, light nuclei, and mesons show that the proton’s mass/energy distribution occupies an intermediate position between neutron and proton charge profiles. These results demonstrate that Patterson imaging provides a transparent, reproducible framework for probing the internal structure of hadrons and light nuclei, offering new perspectives on the fundamental organization of charge and mass/energy in matter.