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Why is it important?
New experiments in connection with attempts to unravel the puzzle of the proton charge radius have been carried out up to the present time and, apparently, will continue in the future, although at the moment (end of 2022) many researchers began to believe that this riddle has already been largely solved since it was possible to almost reconcile the results of many experiments, and the transition to "new physics" will not be required. Incomplete agreement of experimental data concerns the results of spectroscopic studies using the 1S state of the "electronic" hydrogen atom. In our article, we tried to explain the reason for this by the fact that the formula for the energy of an electron in a hydrogen atom in the 1S state is incorrectly used in data analysis. We managed to numerically solve the Dirac equation for the potential energy of the interaction of an electron with a proton, based on the exponential charge distribution in the proton. By setting three different values of the proton radii 0.8751, 0.8414 and 0.8335 fm as “seed” parameters and using two variants of the CODATA 2014 and 2019 constants, we found that it is not only important to take into account the relativistic correction itself, which is proportional to α4, but also that a proton is not a ball. For example, for the CODATA 2019 constants, the correction expressed in hertz proportional to α4 is -1.17 MHz, the Darwin-Foldy correction for the proton radius of 0.8751 fm is 1.198 MHz, and for the proton radius of 0.8414 fm it is 1.107 MHz. These corrections, as can be seen, are approximately the same in magnitude, but moreover, even less than the "correction for the fact that the proton is not a ball", which turned out to be -1.607 MHz, and the same for both values of 0.8751, 0.8414 fm of the proton radius. This study allows us to conclude that the puzzle of the proton radius can be solved, particular, by more correct calculations of the energy levels of the electron in atom and, possibly, a muon in a mesoatom, taking into account the charge distribution in the proton.
Perspectives
I hope that this article will arouse interest in the sense that sometimes, in order to clarify some very puzzling questions, it is worth looking at the origins of the creation of new theories and applying these origins to a new situation. In this case, the analysis shows that when describing very subtle physical phenomena at the fundamental level, not only the most “advanced” ideas and methods of QED, but also the theory on which QED is based - relativistic quantum mechanics, can play a certain role. In particular, as shown in our article, an important role in solving the puzzle of the proton charge radius is played by the Dirac equation and its solution, in this case numerical, for describing the 1S state of the electron in a hydrogen atom, taking into account the exponential charge distribution in the proton.
Alexandr Davydov
Nosov Magnitogorsk State Technical University
Read the Original
This page is a summary of: The problem of the proton radius in the framework of numerical solution of Dirac equation for electron in 1S state with the exponential proton charge distribution, January 2022, American Institute of Physics,
DOI: 10.1063/5.0104425.
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