Measurements of minimum entropy at K-shell photoelectric effect provides the radius and shape of the proton

Abstract

Constructive resonances with minimum entropy are derived from measurements of photoelectric effect cross sections at atomic K-shell thresholds. A resonance region with optimal constructive interference is given by a principal wave length {\lambda} of the order of Bohr atom radius. Our study shows that the proton shape is not a sphere but it has an elliptical volumetric shape with two equal axes and the other different. Resonance waves allowed us the possibility to measure both proton radius and shape through an interference term. This last, was a necessary condition in order to have an effective cross section maximum at threshold. The minimum entropy means minimum shape deformation and it was found to be (0.830 +/- 0.015) fm and the average proton radius was found to be (0.851 +/- 0.201) fm.