Proton mechanical forces structure revisited: Insights from Patterson function analysis

This study applies Patterson function analysis to gravitational form factors to reconstruct the proton’s mechanical force distribution. The resulting density profile is strictly positive and sharply localized, with a half‑maximum radius of 0.109 fm that defines the proton’s compact spatial extent. Taken literally, such a profile would suggest that the proton experiences only outward pressure—an unphysical scenario implying instability. Nevertheless, the reconstruction reveals a pronounced central peak and provides a stringent measure of spatial compactness. Comparative evaluations across nucleons, mesons, and light nuclei show that the proton’s mechanical forces distribution occupies an intermediate position between neutron and proton charge profiles. These findings highlight the versatility of Patterson imaging as a transparent and reproducible tool for probing the internal organization of matter, extending its reach beyond charge and mass/energy densities to mechanical forces.