Abstract
We determine the proton and electron radii by analyzing constructive resonances at minimum entropy for elements with atomic number Z ≥ 11.We note that those radii can be derived from entropy principles and published photoelectric cross sections data from the National Institute of Standards and Technology (NIST). A resonance region with optimal constructive interference is given by a principal wavelength λ of the order of Bohr atom radius. Our study shows that the proton radius deviations can be measured. Moreover, in the case of the electron, its radius converges to electron classical radius with a value of 2.817 fm. Resonance waves afforded us the possibility to measure the proton and electron radii through an interference term. This term, was a necessary condition in order to have an effective cross section maximum at the threshold. The minimum entropy means minimum proton shape deformation and it was found to be (0.830 ± 0.015) fm and the average proton radius was found to be (0.825 − 0.0341; 0.888 + 0.0405) fm.
Highlights
The so-called proton radius puzzle was born when electron scattering experiments or atomic spectroscopy gave different value for the radius of the proton when compared to a muonic experiment [1,2,3,4]
At low energy, it is well known that the photoelectric effect is more important than other effects for most elements on the periodic table [8], Figures 1–4
Using the minimum entropy theory, we can calculate the optimal dimension of the proton radius and the conditions for the photon to be trapped in the resonance region corresponding to the K-shell
Summary
The so-called proton radius puzzle was born when electron scattering experiments or atomic spectroscopy gave different value for the radius of the proton when compared to a muonic experiment [1,2,3,4]. It was found in the former that the deuteron radius is smaller when measured in muonic deuterium, as compared to the average value using electronic deuterium [5,6,7]. At low energy (up to 0.116 MeV), it is well known that the photoelectric effect is more important than other effects for most elements on the periodic table [8], Figures 1–4. The data base at the National Institute of Standards and Technology (NIST) [9] contains the tabulated photoelectric peak cross sections for every element on the periodic table. Resonance is discoverable when the energy in a system changes
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