Nonidentical protons

Abstract

We have calculated the proton charge radius by assuming that the real proton radius is not unique and the radii are randomly distributed in a certain range. This is performed by averaging the elastic electron-proton differential cross section over the form factor cut-off. By using a dipole form factor and fitting the middle value of the cut-off to the low $Q^2$ Mainz data, we found the lowest ${\chi }^2/N$ for a cut-off $\Lambda =0.8203\pm 0.0003$ GeV, which corresponds to a proton charge radius $r_E=0.8333\pm 0.0004$ fm. The result is compatible with the recent precision measurement of the Lamb shift in muonic hydrogen as well as recent calculations using more sophisticated techniques. Our result indicates that the relative variation of the form factor cut-off should be around 21.5%. Based on this result we have investigated effects of the nucleon radius variation on the symmetric nuclear matter (SNM) and the neutron star matter (NSM) by considering the excluded volume effect in our calculation. The mass-radius relation of neutron star is found to be sensitive to this variation. The nucleon effective mass in the SNM as well as the equation of state of both the SNM and the NSM exhibit a similar sensitivity.

23 pages, 12 figures

References in corpus (19)

• Shapiro delay measurement of a two solar mass neutron star
• The Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter
• High-precision determination of the electric and magnetic form factors of the proton
• Relativistic effective interaction for nuclei, giant resonances, and neutron stars
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• The size of the proton - closing in on the radius puzzle
• Muonic hydrogen and MeV forces
• The RMS Charge Radius of the Proton and Zemach Moments
• New Parity-Violating Muonic Forces
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Proton size anomaly
• Spectroscopy as a test of Coulomb's law - A probe of the hidden sector
• Atomic Precision Tests and Light Scalar Couplings
• QED is not endangered by the proton's size
• Third Zemach Moment of the Proton
• Shapes of the Nucleon
• Nuclear Quasi-Elastic Electron Scattering Limits Nucleon Off-Mass Shell Properties
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• Landau parameters for isospin asymmetric nuclear matter based on a relativistic model of composite and finite extension nucleons

Cited by in corpus (7)

• Model independent extraction of the proton magnetic radius from electron scattering
• Polynomial fits and the proton radius puzzle
• Boson star at finite temperature
• Quark mean-field model for nuclear matter with or without bag
• Nucleon radius effects on neutron stars in quark mean field model
• Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$
• Note on the electromagnetic radius of proton