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Journal articles on the topic 'Proton radius'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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1

L. Khokhlov, D. "Gravitation near the Schwarzschild radius." International Journal of Advanced Astronomy 9, no. 1 (2021): 28. http://dx.doi.org/10.14419/ijaa.v9i1.31444.

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The problem of gravitation near the Schwarzschild radius is addressed. The pressure due to free fall velocity is introduced. At the Schwarz-schild radius, this pressure produces the force balancing the gravity thus stopping the collapse of the matter. The minimum radius of the source of gravity is defined as a radius at which the proton reaches the Planck energy. The compact object as a thin shell at the minimum radius is considered. The proton is assumed to decay at the Planck scale into positron and hypothetical Planck neutrinos. Under accretion onto the compact object, half the protons decay, and the other protons retain at the minimum radius.

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2

Bonesini, Maurizio. "The proton radius puzzle." EPJ Web of Conferences 164 (2017): 07048. http://dx.doi.org/10.1051/epjconf/201716407048.

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3

Downie, E. J. "The Proton Radius Puzzle." EPJ Web of Conferences 113 (2016): 05021. http://dx.doi.org/10.1051/epjconf/201611305021.

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4

Antognini, A., F. D. Amaro, F. Biraben, et al. "The proton radius puzzle." Journal of Physics: Conference Series 312, no. 3 (2011): 032002. http://dx.doi.org/10.1088/1742-6596/312/3/032002.

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5

Carlson, Carl E. "The proton radius puzzle." Progress in Particle and Nuclear Physics 82 (May 2015): 59–77. http://dx.doi.org/10.1016/j.ppnp.2015.01.002.

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6

Bernauer, Jan C., and Randolf Pohl. "The Proton Radius Problem." Scientific American 310, no. 2 (2014): 32–39. http://dx.doi.org/10.1038/scientificamerican0214-32.

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7

Huber, G. M. "The Proton Radius Puzzle." Physics International 6, no. 1 (2015): 1–2. http://dx.doi.org/10.3844/pisp.2015.1.2.

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8

Vassen, Wim. "The proton radius revisited." Science 358, no. 6359 (2017): 39–40. http://dx.doi.org/10.1126/science.aao3969.

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9

Cui, Zhu-Fang, Daniele Binosi, Craig D. Roberts, and Sebastian M. Schmidt. "Pauli Radius of the Proton." Chinese Physics Letters 38, no. 12 (2021): 121401. http://dx.doi.org/10.1088/0256-307x/38/12/121401.

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Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyze proton magnetic form factor data obtained via electron+proton scattering on Q 2 ∈ [0.027, 0.55] GeV2 with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto Q 2 ≃ 0 for extraction of the form factor slope. In this way, we find r M = 0.817(27) fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, F 1,2(Q 2), are not truly independent observables; to wit, the difference F ′ 1 ( 0 ) − F ′ 2 ( 0 ) / κ p = [ 1 + κ p ] / [ 4 m p 2 ] , viz., the proton Foldy term.

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10

Robson, D. "Solution to the proton radius puzzle." International Journal of Modern Physics E 23, no. 12 (2014): 1450090. http://dx.doi.org/10.1142/s0218301314500906.

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The relationship between the static electric form factor for the proton in the rest frame and the Sachs electric form factor in the Breit momentum frame is used to provide a value for the difference in the mean squared charge radius of the proton evaluated in the two frames. Associating the muonic–hydrogen data analysis for the proton charge radius of 0.84087 fm with the rest frame and associating the electron scattering data with the Breit frame yields a prediction of 0.87944 fm for the proton radius in the relativistic frame. The most recent value deduced via electron scattering from the proton is 0.877(6) fm so that the frame dependence used here yields a plausible solution to the proton radius puzzle.

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11

Paz, Gil. "Model-independent extraction of the proton charge radius from PRad data." Modern Physics Letters A 36, no. 20 (2021): 2150143. http://dx.doi.org/10.1142/s0217732321501431.

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The proton radius puzzle has motivated several new experiments that aim to extract the proton charge radius and resolve the puzzle. Recently, PRad, a new electron–proton scattering experiment at Jefferson Lab, reported a proton charge radius of [Formula: see text]. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using [Formula: see text]-expansion of the proton charge radius from PRad data. We find that the model-independent statistical error is more than 50% larger compared to the statistical error reported by PRad.

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12

Jentschura, Ulrich D. "Proton Radius: A Puzzle or a Solution!?" Journal of Physics: Conference Series 2391, no. 1 (2022): 012017. http://dx.doi.org/10.1088/1742-6596/2391/1/012017.

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Abstract The proton radius puzzle is known as the discrepancy of the proton radius, obtained from muonic hydrogen spectroscopy (obtained as being roughly equal to 0.84 fm), and the proton radius obtained from (ordinary) hydrogen spectroscopy where a number of measurements involving highly excited states have traditionally favored a value of about 0.88 fm. Recently, a number of measurements of hydrogen transitions by the Munich (Garching) groups (notably, several hyperfine-resolved sublevels of the 2S–4P) and by the group at the University of Toronto (2S–2P 1/2) have led to transition frequency data consistent with the smaller proton radius of about 0.84 fm. A recent measurement of the 2S–8D transition by a group at Colorado State University leads to a proton radius of about 0.86 fm, in between the two aforementioned results. The current situation points to a possible, purely experimental, resolution of the proton radius puzzle. However, a closer look at the situation reveals that the situation may be somewhat less clear, raising the question of whether or not the proton radius puzzle has been conclusively solved, and opening up interesting experimental possiblities at TRIUMF/ARIEL.

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13

Oks, Eugene. "A Possible Explanation of the Proton Radius Puzzle Based on the Second Flavor of Muonic Hydrogen Atoms." Foundations 2, no. 4 (2022): 912–17. http://dx.doi.org/10.3390/foundations2040062.

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The proton radius puzzle is one of the most fundamental challenges of modern physics. Before the year 2010, the proton charge radius rp was determined by the spectroscopic method, relying on the electron energy levels in hydrogen atoms, and by the elastic scattering of electrons on protons. In 2010, and then in 2013, two research teams determined rp from the experiment on muonic hydrogen atoms and they claimed rp to be by about 4% smaller than it was found from the experiments with electronic hydrogen atoms. Since then, several research groups performed corresponding experiments with electronic hydrogen atoms and obtained contradictory results: some of them claimed that they found the same value of rp as from the muonic hydrogen experiments, while others reconfirmed the larger value of rp. The conclusion of the latest papers (including reviews) is that the puzzle is not resolved yet. In the present paper, we bring to the attention of the research community, dealing with the proton radius puzzle, the contributing factor never taken into account in any previous calculations. This factor has to do with the hydrogen atoms of the second flavor, whose existence is confirmed in four different types of atomic experiments. We present a relatively simple model illustrating the role of this factor. We showed that disregarding the effect of even a relatively small admixture of the second flavor of muonic hydrogen atoms to the experimental gas of muonic hydrogen atoms could produce the erroneous result that the proton charge radius is by about 4% smaller than its actual value, so that the larger out of the two disputed values of the proton charge radius could be, in fact, correct.

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14

Meyl, Konstantin. "Calculation of the proton radius." Physics Essays 28, no. 4 (2015): 603–4. http://dx.doi.org/10.4006/0836-1398-28.4.603.

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15

Horowitz, C. J. "Weak radius of the proton." Physics Letters B 789 (February 2019): 675–78. http://dx.doi.org/10.1016/j.physletb.2018.12.029.

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16

Trinhammer, Ole L., and Henrik G. Bohr. "On proton charge radius definition." EPL (Europhysics Letters) 128, no. 2 (2019): 21001. http://dx.doi.org/10.1209/0295-5075/128/21001.

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17

Kanwal, Mehak, Sarwat Zahra, and Samreen Zahra. "Proton electromagnetic form factor and radius extracted from elastic pp scattering at √s ≈ 7, 8, and 13 TeV using the Chou-Yang model." Nuclear Physics and Atomic Energy 26, no. 1 (2025): 55–59. https://doi.org/10.15407/jnpae2025.01.055.

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Chou-Yang model has been used to obtain the electromagnetic form factor and the root mean square (rms) radius of the proton, using experimental data for proton-proton elastic scattering at √s ≈ 7, 8, and 13 TeV. The differential cross-section data at low squared four-momentum transfer ∣t∣ is fitted to a single exponential function to extract the form factor at the aforementioned center of mass energies. Extracted electromagnetic form factors are used for the prediction of rms radius of the proton. A comparison of electromagnetic form factor and rms charge radius at the different centers of mass energies truly reflects the fact that our results agree well with the experiment and theory. Predicted values of rms radius of the proton confirm its energy-independent nature.

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18

Meißner, Ulf-G. "The proton radius and its relatives - much ado about nothing?" Journal of Physics: Conference Series 2586, no. 1 (2023): 012006. http://dx.doi.org/10.1088/1742-6596/2586/1/012006.

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Abstract I summarize the dispersion-theoretical analysis of the nucleon electromagnetic form factors. Special emphasis is given on the extraction of the proton charge radius and its relatives, the proton magnetic radius as well as the neutron magnetic radius. Some recent work on the hyperfine splitting in leptonic hydrogen and on radiative corrections to muon-proton scattering is also discussed. Some views on future studies are given.

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19

Bezginov, N., T. Valdez, M. Horbatsch, A. Marsman, A. C. Vutha, and E. A. Hessels. "A measurement of the atomic hydrogen Lamb shift and the proton charge radius." Science 365, no. 6457 (2019): 1007–12. http://dx.doi.org/10.1126/science.aau7807.

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The surprising discrepancy between results from different methods for measuring the proton charge radius is referred to as the proton radius puzzle. In particular, measurements using electrons seem to lead to a different radius compared with those using muons. Here, a direct measurement of the n = 2 Lamb shift of atomic hydrogen is presented. Our measurement determines the proton radius to be rp = 0.833 femtometers, with an uncertainty of ±0.010 femtometers. This electron-based measurement of rp agrees with that obtained from the analogous muon-based Lamb shift measurement but is not consistent with the larger radius that was obtained from the averaging of previous electron-based measurements.

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20

Jamil, KOOLI. "The proton radius puzzle: an absolute expression emerges for the muonic proton - neutron radius ratio." International Journal of Digital Signals and Smart Systems 1, no. 1 (2021): 1. http://dx.doi.org/10.1504/ijdsss.2021.10044738.

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21

Gakh, G. I., A. Dbeyssi, E. Tomasi-Gustafsson, D. Marchand, and V. V. Bytev. "Proton-electron elastic scattering and the proton charge radius." Physics of Particles and Nuclei Letters 10, no. 5 (2013): 393–97. http://dx.doi.org/10.1134/s1547477113050099.

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22

Stojanov, Nace, Srdjan Petrovic, and Nebojsa Neskovic. "Energy loss distributions of 7 TeV protons channeled in a bent silicon crystals." Nuclear Technology and Radiation Protection 28, no. 1 (2013): 31–35. http://dx.doi.org/10.2298/ntrp1301031s.

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The energy loss distributions of relativistic protons axially channeled through the bent <100> Si crystals, with the constant curvature radius, R = 50 m, are studied here. The proton energy is 7 TeV and the thickness of the crystal is varied from 1 mm to 5 mm, which corresponds to the reduced crystal thickness, L, from 2.1 to 10.6, respectively. The proton energy was chosen in accordance with the large hadron collider project, at the European Organization for Nuclear Research, in Geneva, Switzerland. The energy loss distributions of the channeled protons were generated by the computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. Dispersion of the proton scattering angle caused by its collisions with the crystal?s electrons was taken into account.

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23

Sick, Ingo. "Proton Charge Radius from Electron Scattering." Atoms 6, no. 1 (2017): 2. http://dx.doi.org/10.3390/atoms6010002.

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24

Mihovilovič, Miha, Harald Merkel, and Adrian Weber. "Puzzling out the proton radius puzzle." EPJ Web of Conferences 81 (2014): 01009. http://dx.doi.org/10.1051/epjconf/20148101009.

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25

Karr, Jean-Philippe, and Dominique Marchand. "Progress on the proton-radius puzzle." Nature 575, no. 7781 (2019): 61–62. http://dx.doi.org/10.1038/d41586-019-03364-z.

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26

Głazek, Stanisław D. "Proton Radius Puzzle in Hamiltonian Dynamics." Few-Body Systems 56, no. 6-9 (2014): 311–17. http://dx.doi.org/10.1007/s00601-014-0919-y.

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27

Sick, Ingo. "Troubles with the Proton rms-Radius." Few-Body Systems 50, no. 1-4 (2011): 367–69. http://dx.doi.org/10.1007/s00601-010-0200-y.

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28

WANG, LI-BANG, and WEI-TOU NI. "PROTON RADIUS PUZZLE AND LARGE EXTRA DIMENSIONS." Modern Physics Letters A 28, no. 20 (2013): 1350094. http://dx.doi.org/10.1142/s0217732313500946.

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We propose a theoretical scenario to solve the proton radius puzzle which recently arises from the muonic hydrogen experiment. In this framework, (4+n)-dimensional theory is incorporated with modified gravity. The extra gravitational interaction between the proton and muon at very short range provides an energy shift which accounts for the discrepancy between spectroscopic results from muonic and electronic hydrogen experiments. Assuming the modified gravity is a small perturbation to the existing electromagnetic interaction, we find the puzzle can be solved with stringent constraint on the range of the new force. Our result not only provides a possible solution to the proton radius puzzle but also suggests a direction to test new physics at very small length scale.

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29

Arrington, John, and Ingo Sick. "Evaluation of the Proton Charge Radius from Electron–Proton Scattering." Journal of Physical and Chemical Reference Data 44, no. 3 (2015): 031204. http://dx.doi.org/10.1063/1.4921430.

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30

Conceição, R., J. Dias de Deus, and M. Pimenta. "Proton–proton cross-sections: The interplay between density and radius." Nuclear Physics A 888 (August 2012): 58–66. http://dx.doi.org/10.1016/j.nuclphysa.2012.02.019.

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31

Bernauer, Jan C. "The proton radius puzzle – 9 years later." EPJ Web of Conferences 234 (2020): 01001. http://dx.doi.org/10.1051/epjconf/202023401001.

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High-precision measurements of the proton radius via scattering, electric hydrogen spectroscopy and muonic hydrogen spectroscopy do not agree on the level of more than 5 σ. This proton radius puzzle persists now for almost a decade. This paper gives a short summary over the progress in the solution of the puzzle as well as an overview over the planned experiments to finally solve this puzzle at the interface of atomic and nuclear physics.

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32

Karshenboim, S. G. "What do we actually know about the proton radius?" Canadian Journal of Physics 77, no. 4 (1999): 241–66. http://dx.doi.org/10.1139/p98-063.

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This paper considers the different determinations of the proton charge radius. It demonstrates that the results from the elastic electron-proton scattering have to be assigned a higher uncertainty. A review of the hydrogen Lamb-shift measurements and the radius determination from them is also presented.PACS No.: 27.10 and 35.10B

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33

Fedosin, Sergey G. "The radius of the proton in the self-consistent model." Hadronic Journal 35, no. 4 (2012): 349–63. https://doi.org/10.5281/zenodo.889451.

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<em>Based on the notion of strong gravitation, acting at the level of elementary particles, and on the equality of the magnetic moment of the proton and the limiting magnetic moment of the rotating non-uniformly charged ball, the radius of the proton is found, which conforms to the experimental data. At the same time the dependence is derived of distribution of the mass and charge density inside the proton. The ratio of the density in the center of the proton to the average density is found, which equals 1.57</em>.

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34

Fedosin, Sergey G., and Anatolii S. Kim. "The Moment of Momentum and the Proton Radius." Russian Physics Journal 45, no. 5 (2002): 534–38. https://doi.org/10.1023/A:1021001025666.

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<em>The theory of nuclear gravitation is used to calculate the moment of momentum of the gravitational field of a </em><em>proton, which is compared to the corresponding moment of momentum of the electromagnetic field. As a result, the </em><em>proton radius is estimated and a relation for the moment of momentum of the field is established, which coincides </em><em>in form with the expression of the virial theorem for energy.</em>

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35

Putilov, Lev, and Vladislav Tsidilkovski. "Proton Conduction in Acceptor-Doped BaSnO3: The Impact of the Interaction between Ionic Defects and Acceptor Impurities." Materials 15, no. 14 (2022): 4795. http://dx.doi.org/10.3390/ma15144795.

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Barium stannate is known as a promising proton-conducting material for clean energy applications. In this work, we elucidate the effect of the interaction of protons and oxygen vacancies with acceptor impurities on proton conduction in acceptor-doped BaSnO3. The analysis relies on our theoretical developments in hydration and proton hopping in proton-conducting perovskites. The transport theory, based on the master equation and effective medium approximation, provides the analytical description of hopping conduction considering the effects of disorder and changes in the potential energy landscape for protons caused by acceptor impurities. Using the proposed approach, we establish the dependence of the proton mobility and conductivity on the energies of the acceptor-bound states of ionic defects and external conditions. It is shown that the considered interactions can substantially affect the effective activation energies and prefactors of these transport coefficients. We also demonstrate that the correlation between the ionic radius rA of an acceptor impurity and the energies of its interaction with ionic defects leads to a non-monotonic dependence of the proton conductivity on rA. The obtained results are in reasonable agreement with the experimental data on the bulk conductivity of BaSnO3 doped with different acceptors.

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36

Xiong, Weizhi, and Chao Peng. "Proton Electric Charge Radius from Lepton Scattering." Universe 9, no. 4 (2023): 182. http://dx.doi.org/10.3390/universe9040182.

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A proton is a bound state of a strong interaction, governed by Quantum Chromodynamics (QCD). The electric charge radius of a proton, denoted by rEp, characterizes the spatial distribution of its electric charge carried by the quarks. It is an important input for bound-state Quantum Electrodynamic (QED) calculations of the hydrogen atomic energy levels. However, physicists have been puzzled by the large discrepancy between rEp measurements from muonic hydrogen spectroscopy and those from ep elastic scattering and ordinary hydrogen spectroscopy for over a decade. Tremendous efforts, both theoretical and experimental, have been dedicated to providing various insights into this puzzle, but certain issues still remain unresolved, particularly in the field of lepton scatterings. This review will focus on lepton-scattering measurements of rEp, recent theoretical and experimental developments in this field, as well as future experiments using this technique.

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37

Xiong, W., A. Gasparian, H. Gao, et al. "A small proton charge radius from an electron–proton scattering experiment." Nature 575, no. 7781 (2019): 147–50. http://dx.doi.org/10.1038/s41586-019-1721-2.

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38

Borisyuk, Dmitry, and Alexander Kobushkin. "Reanalysis of low-energy electron-proton scattering data and proton radius." Nuclear Physics A 1002 (October 2020): 121998. http://dx.doi.org/10.1016/j.nuclphysa.2020.121998.

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39

Vorobyev, A. A. "Precision Measurement of the Proton Charge Radius in Electron Proton Scattering." Physics of Particles and Nuclei Letters 16, no. 5 (2019): 524–29. http://dx.doi.org/10.1134/s1547477119050303.

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40

Napolitano, J. "Measuring the strangeness radius of the proton." Physical Review C 43, no. 3 (1991): 1473–75. http://dx.doi.org/10.1103/physrevc.43.1473.

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41

Pohl, Randolf, Ronald Gilman, Gerald A. Miller, and Krzysztof Pachucki. "Muonic Hydrogen and the Proton Radius Puzzle." Annual Review of Nuclear and Particle Science 63, no. 1 (2013): 175–204. http://dx.doi.org/10.1146/annurev-nucl-102212-170627.

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42

Bawin, M., and S. A. Coon. "Darwin–Foldy term and proton charge radius." Nuclear Physics A 689, no. 1-2 (2001): 475–77. http://dx.doi.org/10.1016/s0375-9474(01)00885-5.

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43

De Rújula, A. "QED confronts the radius of the proton." Physics Letters B 697, no. 1 (2011): 26–31. http://dx.doi.org/10.1016/j.physletb.2011.01.025.

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44

Sick, Ingo. "On the rms-radius of the proton." Physics Letters B 576, no. 1-2 (2003): 62–67. http://dx.doi.org/10.1016/j.physletb.2003.09.092.

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45

Rohollahpour, Elham, and Hadi Taleshi Ahangari. "Feasibility of Proton Range Estimation with Prompt Gamma Imaging in Proton Therapy of Lung Cancer: Monte Carlo Study." Journal of Medical Physics 49, no. 4 (2024): 531–38. https://doi.org/10.4103/jmp.jmp_74_24.

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Context: Using prompt gamma (PG) ray is proposed as a promising solution for in vivo monitoring in proton therapy. Despite significant and diverse approaches explored over the past two decades, challenges still persist for more effective utilization. Aims: The feasibility of estimating proton range with PG imaging (PGI) as an online imaging guide in an anthropomorphic phantom with lung cancer was investigated through GATE/GEANT4 Monte Carlo simulation. Setting and Design: Once the GATE code was validated for use as a simulation tool, the gamma energy spectra of NURBS-based cardiac-torso (NCAT) and polymethyl methacrylate phantoms, representing heterogeneous and homogeneous phantoms respectively, were compared with the gamma emission lines known in nuclear interactions with tissue elements. A 5-mm radius spherical tumor in the lung region of an NCAT phantom, without any physiological or morphological changes, was simulated. Subjects and Methods: The proton pencil beam source was defined as a function of the tumor size to encompass the tumor volume. The longitudinal spatial correlation between the proton dose deposition and the distribution of detected PG rays by the multi-slit camera was assessed for proton range estimation. The simulations were conducted for both 108 and 109 protons. Results: The deviation between the proton range and the range estimated by PGI following proton beam irradiation to the center of the lung tumor was determined by evaluating the longitudinal profiles at the 80% fall-off point, measuring 1.9 mm for 109 protons and 4.5 mm for 108 protons. Conclusions: The accuracy of proton range estimation through PGI is greatly influenced by the number of incident protons and tissue characteristics. With 109 protons, it is feasible to utilize PGI as a real-time monitoring technique during proton therapy for lung cancer.

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46

Grinin, Alexey, Arthur Matveev, Dylan C. Yost, et al. "Two-photon frequency comb spectroscopy of atomic hydrogen." Science 370, no. 6520 (2020): 1061–66. http://dx.doi.org/10.1126/science.abc7776.

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We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [f1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [R∞ = 10,973,731.568226(38) per meter] and the proton charge radius [rp = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment.

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47

Arbuzov, Andrej, and Tatiana Kopylova. "Radiative corrections to elastic-electron proton scattering and uncertainty in proton charge radius." EPJ Web of Conferences 218 (2019): 04004. http://dx.doi.org/10.1051/epjconf/201921804004.

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Higher-order QED radiative corrections to elastic electron-proton scattering are discussed. It is shown that they are relevant for high-precision experiments on proton form factor measurements. Analytic result are obtained for next-to-leading second order corrections to the electron line. Light pair corrections are taken into account. The role of the hadronic contribution to vacuum polarization is discussed. Numerical results are given for the conditions of the experiment on proton form factors performed by A1 Collaboration. Preliminary results are also shown for the set-up with reconstruction of momentum transfer from the recoil proton momentum.

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48

Zahra, S., and B. Shafaq. "Prediction of rms charge radius of proton using proton-proton elastic scattering data at TeV." Revista Mexicana de Física 67, no. 3 May-Jun (2021): 491. http://dx.doi.org/10.31349/revmexfis.67.491.

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Using proton–proton elastic scattering data at TeV and squared four-momentum transfer 0.36 < -t < 0.76 (GeV/c)2 for 13 σBeam distance and 0.07 < -t < 0.46 (GeV/c)2 for 4.3 σBeam distance, form factor of proton is predicted. Simplest version of Chou–Yang model is employed to extract the form factor by fitting experimental data of differential cross section from TOTEM experiment (for 13σBeamand 4.3 σBeam distance) to a single Gaussian. Root mean square (rms) charge radius of proton is calculated using this form factor. It is found to be equal to 0.91 fm and 0.90 fm respectively. Which is in good agreement with experimental data and theoretically predicted values.

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49

Rosenfelder, R. "Coulomb corrections to elastic electron–proton scattering and the proton charge radius." Physics Letters B 479, no. 4 (2000): 381–86. http://dx.doi.org/10.1016/s0370-2693(00)00316-6.

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Buchmann, A. J. "Non-spherical proton shape and hydrogen hyperfine splittingThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008." Canadian Journal of Physics 87, no. 7 (2009): 773–83. http://dx.doi.org/10.1139/p09-059.

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Abstract:

We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.

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