Proton Radius Research Articles

Classical excluded volume of loosely bound light (anti) nuclei and their chemical freeze-out in heavy ion collisions

From the analysis of light (anti)nuclei multiplicities that were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy [Formula: see text][Formula: see text]TeV, there arose a highly nontrivial question about the excluded volume of composite particles. Surprisingly, the hadron resonance gas model (HRGM) is able to perfectly describe the light (anti) nuclei multiplicities under various assumptions. Thus, one can consider the (anti)nuclei with a vanishing hard-core radius (as the point-like particles) or with the hard-core radius of proton, but the fit quality is the same for these assumptions. It is clear, however, that such assumptions are unphysical. Hence we obtain a formula for the classical excluded volume of loosely bound light nuclei consisting of A baryons. To implement a new formula into the HRGM, we have to modify the induced surface tension concept to treat the hadrons and (anti)nuclei on the same footing. We perform a thorough analysis of hadronic and (anti)nuclei multiplicities measured by the ALICE collaboration. The HRGM with the induced surface tension allows us to verify different assumptions on the values of hard-core radii and different scenarios of chemical freeze-out of (anti)nuclei. It is shown that the unprecedentedly high quality of fit [Formula: see text] is achieved, if the chemical freeze-out temperature of hadrons is about [Formula: see text][Formula: see text]MeV, while the one for all (anti)nuclei is [Formula: see text][Formula: see text]MeV.

The proton size

The proton charge radius has been measured since the 1950s using elastic electron–proton scattering and ordinary hydrogen atomic spectroscopy. In 2010, a highly precise measurement of the proton charge radius using, for the first time, muonic hydrogen spectroscopy unexpectedly led to controversy, as the value disagreed with the previously accepted one. Since then, atomic and nuclear physicists have been trying to understand this discrepancy by checking theories, questioning experimental methods and performing new experiments. Recently, two measurements from electron scattering and ordinary hydrogen spectroscopy were found to agree with the results from muonic atom spectroscopy. Is the ‘proton-radius puzzle’ now resolved? In this Review, we scrutinize the experimental studies of the proton radius to gain insight on this issue. We provide a brief history of the proton before describing the techniques used to measure its radius and the current status of the field. We assess the precision and reliability of available experimental data, with particular focus on the most recent results. Finally, we discuss the forthcoming new generation of refined experiments and theoretical calculations that aim to definitely end the debate on the proton size. The charge radius of the proton is controversial because measurements by different methods disagree. Recent results indicate that these measurements might be reconciled. In this Review, we discuss the experimental techniques used to measure the proton radius and describe the current status of the field as well as forthcoming experiments.

Form Factor of Proton Predicted Using the Data of ppbar Elastic Scattering at $$\boldsymbol{\sqrt{s}=1.96}$$ eV

Based on the behavior of elastic scattering of proton and anti-proton at $$\sqrt{s}=1.96$$ TeV for squared four-momentum transfer $$0.26<{-}t<1.2($$ GeV $$/c)^{2}$$ , form factor of proton is predicted. Simplest version of Chou–Yang model is employed for extracting this form factor by fitting experimental data of differential cross section from D0 experiment to a single Gaussian. Root mean square (rms) matter radius of proton is calculated using this form factor. It is found to be equal to 0.89 fm. Which is in good agreement with experimental data and theoretically predicted values from other models.

Precision spectroscopy of atomic helium.

Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the ‘proton radius puzzle’. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

Reanalysis of low-energy electron-proton scattering data and proton radius

We reanalyze electron-proton scattering data in the momentum transfer region Q2<1GeV2, which were used to determine proton electric radius, with main focus on the Mainz experiment (Bernauer et al. 2010). We examine dependence of fit results and χ2 on the cut-off in Q2 and degree of fitting polynomial, using pseudo-data and compare it with the case of real experimental data. We find that under some assumptions, the data could be consistent with the radius, obtained from muonic hydrogen.

Connecting spatial moments and momentum densities

The precision of experimental data and analysis techniques is a key feature of any discovery attempt. A striking example is the proton radius puzzle where the accuracy of the spectroscopy of muonic atoms challenges traditional electron scattering measurements. The present work proposes a novel method for the determination of spatial moments from densities expressed in the momentum space. This method provides a direct access to even, odd, and more generally any real, negative and positive moment with order larger than −3. As an illustration, the application of this method to the electric form factor of the proton is discussed in detail.

Generalized Uncertainty Principle in Astrophysics from Fermi Statistical Physics Arguments

The Heisenberg’s uncertainty principle is one of the most important concepts in quantum mechanics. One of its important outcomes is that enormously high momentum is required to look at extremely small length-scales. Nevertheless, quantum gravity and Grand Unified models taught us that a minimal observable length cutoff which is of the order of the Planck length is required. Such an important feature suggests that the conventional uncertainty principle must be generalized and accordingly the Heisenberg’s uncertainty principle is replaced by a generalized uncertainty relation. Although the effects of the generalized uncertainty relation can only be found in the context of extremely high energies/short distances and not at any scale currently probed in the laboratory, we discuss in this study its impacts on white dwarfs using the quantum mechanical statistical properties of a degenerate Fermi gas in D-spatial dimensions. Both the non-relativistic and extreme relativistic cases were discussed. It was observed that the effect of the generalized uncertainty relation is to shrink the radius of proton, a phenomenon which was observed recently using high precision laser spectroscopy of atomic hydrogen. Several points were discussed and a number of quantum statistical properties were derived.

Laboratory tests for MIR light detection and transport with specialty optical fibres

The FAMU (Fisica degli Atomi Muonici) experiment at the RIKEN RAL pulsed muon facility will measure the proton Zemach radius with high precision, thus contributing to the solution of the so-called “proton radius puzzle”. The situation is now confused and new measurements will help reduce the discrepancy as measured with electrons or muons. To this aim, FAMU will make use of a high-intensity pulsed muon beam at RIKEN-RAL impinging on a cryogenic hydrogen target and a tunable Mid-infrared (MIR) laser emitting at about 6.78 μm, to measure the hyperfine (HFS) splitting of the 1S state of muonic hydrogen. The injection of light into the cryogenic target and its monitoring via dedicated MIR sensors is an asset for the experiment. A possible solution is via specialty MIR fibres based on hollow core waveguides or polycrystalline fibres. Two dedicated setups based on pulsed QCL lasers, from Alpes Laser, emitting around 6.78 μm have been used to study the fibre attenuation while the high energy laser specifically developed for the FAMU project has been used to study the damage threshold at high energies. The alignment of MIR laser radiation into an optical cavity presents criticalities due to geometrical constraints. Its control requires the use of small and sensitive detectors. The results obtained with a quantum IR sensor with an integrated circuit for signal processing are reported.

Evaluation of low-Q2 fits to ep and ed elastic scattering data

We examined several low-Q2 elastic ep and ed scattering data sets using various models to extract the proton and deuteron rms radii and developed a comprehensive algorithm for estimating the systematic bias of each extracted radius. In each case, we chose the model and upper bound for Q2 that minimized the combination of statistical uncertainty and bias. We attribute the discrepancy between small (≈0.84 fm) and large (≈0.88 fm) proton radius extractions to the absence of data that can accurately isolate the linear and quadratic contributions to the form factor at low-Q2. In light of this ambiguity, we estimated the model-dependence of each extracted radius by studying the distribution of many possible fits. The resulting radii are 0.842(4) fm for the proton and 2.092(19) fm for the deuteron. These results indicate radii consistent with those determined from muonic hydrogen and deuterium measurements.

Thermal QED theory for bound states

This paper presents the Quantum Electrodynamics theory for bound states at finite temperatures. To describe the thermal effects arising in a heat bath, the Hadamard form of a thermal photon propagator is employed. As the form allows a simple introduction of thermal gauges in a way similar to the ‘ordinary’ Feynman propagator, the gauge invariance can be proved for all of the considered effects. Moreover, unlike the ‘standard’ form of the thermal photon propagator, the Hadamard expression offers well-defined analytical properties, yet contains a divergent contribution, which requires the introduction of a regularization procedure within the framework of the constructed theory. The method and physical interpretation of regularization are given in the paper. Correctness of the procedure is confirmed also by the gauge invariance of final results and the coincidence of the results (as exemplified by the self-energy correction) for two different forms of photon propagators. The constructed theory is used to find the thermal Coulomb potential and its asymptotic at large distances. Finally, the thermal effects of the lowest order in the fine structure constant and temperature are discussed in detail. Such effects are represented by the thermal one-photon exchange between a bound electron and the nucleus, thermal one-loop self-energy, thermal vacuum polarization, and recoil corrections and that of the finite size of the nucleus. Introduction of regularization allows one to avoid applying the renormalization procedure. To confirm this, the thermal vertex (with one, two, and three vertices) corrections are also described within the adiabatic S-matrix formalism. Finally, the paper discusses the influence of thermal effects on the finding of the proton radius and Rydberg constant.

Sensitivity of the elastic electron–proton cross section to the proton radius

The precise determination of the proton radius from recent elastic scattering electron–proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that its uncertainty is two orders of magnitude larger that the error on the cross section, that is the measured observable. Different fits of the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be also orders of magnitude larger than commonly assumed.

Reinterpretation of Classic Proton Charge Form Factor Measurements

In 1963, a proton radius of $0.805(11)~\mathrm{fm}$ was extracted from electron scattering data and this classic value has been used in the standard dipole parameterization of the form factor. In trying to reproduce this classic result, we discovered that there was a sign error in the original analysis and that the authors should have found a value of $0.851(19)~\mathrm{fm}$. We additionally made use of modern computing power to find a robust function for extracting the radius using this 1963 data's spacing and uncertainty. This optimal function, the Pad\'{e} $(0,1)$ approximant, also gives a result which is consistent with the modern high precision proton radius extractions.

Muonic Lithium atoms: nuclear structure corrections to the Lamb shift

In view of the future plans to measure the Lamb shift in muonic Lithium atoms we address the microscopic theory of the \mu\,μ-^66Li^{2+}2+ and \mu\,μ-^77Li^{2+}2+ systems. The goal of the CREMA collaboration is to measure the Lamb shift to extract the charge radius with high precision and compare it to electron scattering data or atomic spectroscopy to see if interesting puzzles, such as the proton and deuteron radius puzzles, arise. For this experiment to be successful, theoretical information on the nuclear structure corrections to the Lamb shift is needed. For \muμ-^66Li^{2+}2+ and \mu\,μ-^77Li^{2+}2+ there exist only estimates of nuclear structure corrections based on experimental data that suffer from very large uncertainties. We present the first steps towards an ab initio computation of these quantities using few-body techniques.

The proton radius puzzle – 9 years later

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.

First principles electromagnetic responses in medium-mass nuclei

We review the recent progress made in the computation of electromagnetic response functions in light and medium-mass nuclei using coupled-cluster theory. We show how a many-body formulation of the Lorentz integral transform method allows to calculate the photoabsorption cross sections of 16, 22O and 40Ca. Then, we discuss electromagnetic sum rules, with particular emphasis on the electric dipole polarizability, $ \alpha_D$. By including triples corrections in coupled-cluster theory, we revisit 48Ca, for which, beside the electric dipole polarizability, we had previously investigated the neutron and proton radii, as well as the size of the neutron-skin thickness (G. Hagen et al. Nat. Phys. 12, 186 (2016)). We show that correlations among these observables still hold, albeit a better agreement with experiment is obtained for $ \alpha_D$ and the prediction of a small neutron-skin thickness is further corroborated.

A small proton charge radius from anelectron-proton scattering experiment.

Elastic electron-proton scattering (e-p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, rp. In 2010, a new method using muonic hydrogen atoms1 found a substantial discrepancy compared with previous results2, 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 hydrogen3,4. 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, rp=0.831±0.007stat± 0.012systfemtometres, is smaller than the most recent high-precision e-p measurement5 and 2.7 standard deviations smaller than the average of all e-p experimental results6. The smaller rp we have now measured supports the value found by two previous muonic hydrogen experiments1,7. In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant8-one of the most accurately evaluated fundamental constants in physics.

Proton radius puzzle may be solved

Proton radius puzzle may be solved

Search for exotic features in the ground state light nuclei with 10 ≤Z ≤ 18 from stable valley to drip lines

We present a systematic description of the exotic features in the ground states of light nuclei from the stable valley to the drip lines. A study with the even and odd isotopes of Ne, Mg, Si, S and Ar has been performed using theoretical formalisms (i) Relativistic mean-field plus state-dependent BCS approach and (ii) Macroscopic–Microscopic (MM) approach using the triaxially deformed Nilsson–Strutinsky Method. The computed binding energies and one- and two-neutron separation energies using both the theories show magic character of [Formula: see text] and 40. The neutron and proton radii and the neutron densities show a well-developed neutron skin in the neutron-rich isotopes. The exotic phenomena such as weakly bound structures and the central density depletion characterized as bubble effect are explored. Our calculations for the single particle levels, density profiles and the charge form factors indicate bubble-like structures. Few new candidates of bubble nuclei are identified. Most of the nuclei in this region are found deformed with mostly prolate shape and few triaxial shapes while many nuclei exhibit the phenomenon of shape coexistence. Our results display a reasonable agreement between both the theories and the available experimental data.

On separate chemical freeze-outs of hadrons and light (anti)nuclei in high energy nuclear collisions

The multiplicities of light (anti)nuclei were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy . Surprisingly, the hadron resonance gas model is able to perfectly describe their multiplicities under various assumptions. For instance, one can consider the (anti)nuclei with a vanishing hard-core radius (as the point-like particles) or with the hard-core radius of proton, but the fit quality is the same for these assumptions. In this paper we assume the hard-core radius of nuclei consisting of A baryons or antibaryons to follow the simple law , where Rb is the hard-core radius of nucleon. To implement such a relation into the hadron resonance gas model we employ the induced surface tension concept and analyze the hadronic and (anti)nuclei multiplicities measured by the ALICE collaboration. The hadron resonance gas model with the induced surface tension allows us to verify different scenarios of chemical freeze-out of (anti)nuclei. It is shown that the most successful description of hadrons can be achieved at the chemical freeze-out temperature Th = 150 MeV, while the one for all (anti)nuclei is TA = 168.5 MeV. Possible explanations of this high temperature of (anti)nuclei chemical freeze-out are discussed.

Collimation of target induced halo following MAGIX at MESA

The Mainz Energy-recovering Superconducting Accelerator (MESA) will be an electron accelerator allowing operation in energy-recovery linac (ERL) mode. It provides the opportunity to operate scattering experiments at energies of ~ 100 MeV with thin gas-targets. The MESA Internal Gas Target Experiment (MAGIX) aims to operate windowless jet targets and different gases up to Xenon to search for possible dark photon interactions, to precisely measure the magnetic proton radius and astrophysical S-factors. Investigations on the impact of the target on beam dynamics and beam losses are required for machine safety and to examine limits to ERL operation. The goal of this work is to understand target induced halo in the different experimental setups, track halo particles through downstream sections to examine beam losses and include a suitable collimation system and shielding into the accelerator layout to protect the machine from direct and indirect damage through beam losses and radiation. The present status of the investigations is presented.