Accurate spectroscopic measurements of calculable systems provide a powerful method for testing the Standard Model and extracting fundamental constants. Recently, spectroscopic measurements of finite nuclear size effects in normal and muonic hydrogen resulted in unexpectedly large adjustments of the proton charge radius and the Rydberg constant. We measured the $2^3\mathrm{S}\rightarrow2^1\mathrm{S}$ transition frequency in a Fermi gas of $^3$He with an order of magnitude higher accuracy than before. Together with a previous measurement in a $^4$He Bose-Einstein condensate, a squared charge radius difference $r^2_h - r^2_{\alpha} = 1.0757(15)\ \mathrm{fm^2}$ is determined between the helion and alpha particle. This measurement provides a benchmark with unprecedented accuracy for nuclear structure calculations. A deviation of 3.6$\sigma$ is found with a determination (arXiv:2305.11679) based on spectroscopy of muonic helium ions.

The proton charge distribution radius is a nuclear physics related observable. QED calculations involve its value. It depends on the Lamb shift and hyperfine splitting which experimentally measured, are considered tests of QED, involving the Rydberg and the fine structure constant. The CREMA collaboration measured the proton radius by using muonic hydrogen spectroscopy. Muon, which is 200 times heavier than the electron, orbits close to the nucleus offering a unique probe for the proton structure. They obtained a precise measurement of the proton radius but 5% smaller than the one from hydrogen spectroscopy and electron-proton scattering. This discrepancy, called "the proton radius puzzle" and it is still an unanswered problem. There is another proton observable, related to both the charge and magnetic distribution, called the Zemach radius. This is dependent on QED and is strictly related to the hyperfine splitting. Different methods for measuring the Zemach radius are not in agreement and so far, a precise estimation of this observable for muonic hydrogen doesn't exist. In this context, FAMU, aims to measure the hyperfine splitting of the muonic hydrogen in the ground state which allows a level of uncertainty better than 1%. This will result in the first precise measurement of the Zemach radius with muonic hydrogen spectroscopy. Adding an independent precise measurement of the Zemach radius in the current panorama should give a hint to the proton radius puzzle solution. Mor

The hydrogen Lamb shift and the proton radius The Lamb shift measurement and theory are now both a dynamically developing field and we give a review of the current data. Critical comparison of theory and experiment can be done using a value of the proton charge radius and we pay attention to several results of its determination. Published as: Proceedings of the International Workshop `Hadronic Atoms and Positronium in the Standard Model'. Ed. By M. A. Ivanov et al., Dubna (1998) 224-231 arXiv categories: hep-ph physics.atom-ph

The core of the “proton radius puzzle” is the discrepancy of four standard deviations between the proton root mean square charge radii (rp) determined from regular hydrogen (H), and the muonic hydrogen atom (μp). We have measured the 2S-4P transition frequency in H, utilizing a cryogenic beam of H and directly demonstrate that quantum interference of neighboring atomic resonances can lead to line shifts much larger than the proton radius discrepancy. Using an asymmetric fit function we obtain rp = 0.8335(95) fm and the Rydberg constant R∞ = 10 973 731.568 076 (96) m−1. The new value for rp is 3.3 combined standard deviations smaller than the latest CODATA value, but in good agreement with the value from μp.

This paper addresses the proton radius puzzle by re-examining how the proton charge radius is operationally extracted from atomic spectroscopy. Rather than treating the radius as a system-independent property of the proton, the analysis shows that finite-size effects necessarily probe a reduced-mass–dependent short-range interaction region. Using only experimentally measured differences and dimensional scaling arguments, the work demonstrates that a single interface length resolves the discrepancy between electronic and muonic hydrogen without introducing new parameters or modifying quantum electrodynamics. Transfer tests to deuterium, muonic deuterium, and helium-3 are discussed. The results suggest that the proton radius puzzle may serve as a sensitive probe of underlying interface or geometric descriptions of short-range atomic physics.

The proton charge radius is a fundamental property of the proton, sensitive to its charge distribution. The proton radius puzzle is the discrepancy between the muonic hydrogen spectroscopy measurement of 0.84 fm and the consensus of 0.88 fm from two traditional methods, electron-proton scattering and electronic hydrogen spectroscopy. A recent electron-proton scattering experiment, PRad, measured a smaller radius but also large electric form factor values within 0.02 ≤ Q² ≤ 0.06 (GeV/c)² conflicting with previous experiments. Motivated by those issues, we developed an innovative background-free target system, including a windowless gas jet target, a beam halo collimator and an active beam halo veto, to measure the proton electric form factor at momentum transfers of 0.01 ≤ Q² ≤ 0.065 (GeV/c)². The experiment was conducted in early 2020 at the three-spectrometer facility of the A1-collaboration at the Mainz Microtron in Mainz, Germany. Due to the COVID-19 lockdown, we measured the cross section only up to Q² = 0.043 (GeV/c)² with limited statistics. Although our form factor data cannot give a definitive answer to the form factor discrepancy and the proton radius puzzle yet, our work demonstrated the feasibility of such a background-free target design and we believe that further data taking with this technique can help to resolve the radius puzzle. In this work, we also study the extraction of the proton charge radius using non-parametric models. We demonstrate that the kernel r

Elastic electron–proton scattering (e–p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, r$_{p}$. In 2010, a new method using muonic hydrogen atoms 1 found a substantial discrepancy compared with previous results 2 , which became known as the ‘proton radius puzzle’. Despite experimental and theoretical efforts, the puzzle remains unresolved. In fact, there is a discrepancy between the two most recent spectroscopic measurements conducted on ordinary hydrogen 3$^{,}$4 . Here we report on the proton charge radius experiment at Jefferson Laboratory (PRad), a high-precision e–p experiment that was established after the discrepancy was identified. We used a magnetic-spectrometer-free method along with a windowless hydrogen gas target, which overcame several limitations of previous e–p experiments and enabled measurements at very small forward-scattering angles. Our result, r$_{p}$ = 0.831 ± 0.007$_{stat}$ ± 0.012$_{syst}$ femtometres, is smaller than the most recent high-precision e–p measurement 5 and 2.7 standard deviations smaller than the average of all e–p experimental results 6 . The smaller r$_{p}$ we have now measured supports the value found by two previous muonic hydrogen experiments 1$^{,}$7 . In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant 8 —one of the most accurately evaluated fundamental constants in physics.

Proton is not a point-like particle; it has a finite size and an internal structure. The proton charge radius is usually measured through two different methods: using spectroscopy of hydrogen atoms, or through electron-proton (e − p) elastic scattering at low momentum transfer. In 2010, Phol et al [1] published a new measurement for proton charge radius obtained using the spectroscopy method from muonic hydrogen atoms. An ordinary hydrogen (H) atom is a bound state of an electron orbiting a proton. Likewise, a muonic hydrogen atom has a muon orbiting a proton. Since a muon has 200 times more mass than an electron, resulting in a much smaller orbiting radius, its orbit is much more sensitive to the proton charge distribution in space than the electron’s of an ordinary H-atom. Thus, the measurement from muonic hydrogen provides a 10 times more precise result than the previous methods. The radius from the muonic hydrogen measurement reported in [1] was significantly smaller than all the previous measurements combined. The difference between the two values is more than 5σ away. This large discrepancy triggered the so-called Proton Charge Radius Crisis. In order to investigate the proton charge radius, the PRad experiment was performed in experimental hall B at Jefferson Lab in June, 2016. PRad experiment used a novel e − p elastic scattering method. Considering the limitations introduced by magnetic spectrometers in all previous e − p elastic scattering experiments, PRad adopted

We briefly review the progress of our investigation on the electric (charge) radius of the proton. In order to explain the recently measured proton radius, which is significantly smaller than the standard CODATA value, we assume that the real protons radii are not identical, they are randomly distributed in a certain range. To obtain the measured radius we average the radii and fit both the mean radius and the range. By using an averaged dipole form factor we obtain the charge radius rE = 0.8333 fm, in accordance with the recent measurement of the Lamb shift in muonic hydrogen.

The radius of the proton measured by electron–proton scattering differs from the value measured via the Lamb shift in muonic hydrogen (an exotic atom A proton is a stable subatomic particle, symbol p, H+, or 1H+ with a positive electric charge of +1 e (elementary charge). Its mass is slightly less than the mass of a neutron and approximately 1836 times the mass of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of approximately one dalton, are jointly referred to as nucleons (particles present in atomic n The CODATA recommended value of a proton's charge radius is 8.4075(64)×10−16 m. The radius of the proton measured by electron–proton scattering differs from the value measured via the Lamb shift in muonic hydrogen (an exotic atom made of a proton and a negatively charged muon). As a muon is 200 times heavier than an electron, resulting in a smaller atomic orbital, it is much more sensitive to the proton's charge radius and thus allows a more precise measurement. Subsequent improved scattering and electron-spectroscopy measurements agree with the new small radius. Work continues to refine and check this new value. A third kind of high precision measurement agrees most closely with the value given by the muonic hydrogen spectroscopy but unexplained differences remain. The exact nature of what these measurement mean has also been questioned.

The static properties of hadrons, such as their radii and other moments of the electric and magnetic distributions, can only be extracted using theoretical methods and cannot be directly measured from experiments. As a result, discrepancies between the extracted values from different precision measurements can exist. The proton charge radius, rp, which is extracted either from electron-proton (e-p) elastic scattering data or from hydrogen atom spectroscopy, seems to be no exception. The value rp = 0.84087(39) fm extracted from muonic hydrogen spectroscopy is about 4% smaller than that obtained from e-p scattering or standard hydrogen spectroscopy. The resolution of this so-called proton radius puzzle has been attempted in many different ways over the past six years. The present article reviews these attempts with a focus on the methods of extracting the radius.

Atoms are the basic particles of the chemical elements and the fundamental building blocks of matter. An atom consists of a nucleus of protons and generally Atoms are the basic particles of the chemical elements and the fundamental building blocks of matter. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and an Though the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton, and the neutron. The electron is the least massive of these particles by four orders of magnitude at 9.11×10−31 kg, with a negative electrical charge and a size that is too small to be measured using available techniques. It was the lightest particle with a positive rest mass measured, until the discovery of neutrino mass. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details. Protons have a positive charge and a mass of 1.6726×10−27 kg. The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920, he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton. Neutrons have no electrical charge and have a mass of 1.6749×10−27 kg. Neutrons are the heaviest of the three constituent particles, but their mass can…

rotating about the proton, the hydrogen atom reacts in a similar manner. The individual hydrogen atom can therefore … the radius of the hydrogen atom that correlated with the spectrum of radiation of hydrogen. The radiation … opposed to the behavior of a single atom. The proton of the hydrogen atom is in the nucleus, and it holds