Proton Radius Research Articles

2nd-order optical model of the isotopic dependence of heavy ion absorption cross sections for radiation transport studies

Abstract Heavy ion absorption cross sections play an important role in radiation transport codes used in risk assessment and for shielding studies of galactic cosmic ray (GCR) exposures. Due to the GCR primary nuclei composition and nuclear fragmentation leading to secondary nuclei heavy ions of charge number, Z with 3 ≤ Z ≥ 28 and mass numbers, A with 6 ≤ A ≥ 60 representing about 190 isotopes occur in GCR transport calculations. In this report we describe methods for developing a data-base of isotopic dependent heavy ion absorption cross sections for interactions. Calculations of a 2nd-order optical model solution to coupled-channel solutions to the Eikonal form of the nucleus-nucleus scattering amplitude are compared to 1st-order optical model solutions. The 2nd-order model takes into account two-body correlations in the projectile and target ground-states, which are ignored in the 1st-order optical model. Parameter free predictions are described using one-body and two-body ground state form factors for the isotopes considered and the free nucleon-nucleon scattering amplitude. Root mean square (RMS) matter radii for protons and neutrons are taken from electron and muon scattering data and nuclear structure models. We report on extensive comparisons to experimental data for energy-dependent absorption cross sections for over 100 isotopes of elements from Li to Fe interacting with carbon and aluminum targets. Agreement between model and experiments are generally within 10% for the 1st-order optical model and improved to less than 5% in the 2nd-order optical model in the majority of comparisons. Overall the 2nd-order optical model leads to a reduction in absorption compared to the 1st-order optical model for heavy ion interactions, which influences estimates of nuclear matter radii.

Measuring the Rydberg constant using circular Rydberg atoms in an intensity-modulated optical lattice

A method for performing a precision measurement of the Rydberg constant, $R_{\infty}$, using cold circular Rydberg atoms is proposed. These states have long lifetimes, as well as negligible quantum-electrodynamics (QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle" [Bernauer, Pohl, Sci. Am. 310, 32 (2014)]. The atoms are trapped using a Rydberg-atom optical lattice, and transitions are driven using a recently-demonstrated lattice-modulation technique to perform Doppler-free spectroscopy. The circular-state transition frequency yields $R_{\infty}$. Laser wavelengths and beam geometries are selected such that the lattice-induced transition shift is minimized. The selected transitions have no first-order Zeeman and Stark corrections, leaving only manageable second-order Zeeman and Stark shifts. For Rb, the projected relative uncertainty of $R_{\infty}$ in a measurement under the presence of the Earth's gravity is $10^{-11}$, with the main contribution coming from the residual lattice shift. This could be reduced in a future micro-gravity implementation. The next-important systematic arises from the Rb$^+$ polarizability (relative-uncertainty contribution of $\approx 3 \times10^{-12}$).

Extraction of the Proton and Electron Radii from Characteristic Atomic Lines and Entropy Principles

We determine the proton and electron radii by analyzing constructive resonances at minimum entropy for elements with atomic number Z ≥ 11.We note that those radii can be derived from entropy principles and published photoelectric cross sections data from the National Institute of Standards and Technology (NIST). A resonance region with optimal constructive interference is given by a principal wavelength λ of the order of Bohr atom radius. Our study shows that the proton radius deviations can be measured. Moreover, in the case of the electron, its radius converges to electron classical radius with a value of 2.817 fm. Resonance waves afforded us the possibility to measure the proton and electron radii through an interference term. This term, was a necessary condition in order to have an effective cross section maximum at the threshold. The minimum entropy means minimum proton shape deformation and it was found to be (0.830 ± 0.015) fm and the average proton radius was found to be (0.825 − 0.0341; 0.888 + 0.0405) fm.

Nucleon spin-averaged forward virtual Compton tensor at large Q2

The nucleon spin-averaged forward virtual Compton tensor determines important physical quantities such as electromagnetically-induced mass differences of nucleons, and two-photon exchange contributions in hydrogen spectroscopy. It depends on two kinematic variables: $\nu$, the virtual photon energy in the proton rest frame, and $Q^2$, the photon's invariant four-momentum squared. Using the operator product expansion, we calculate the tensor's large-$Q^2$ behavior for $\nu=0$, including for the first time the full spin-2 contribution and correcting a previous result in the literature for the spin-0 contribution. Implications for the proton radius puzzle are discussed.

Surprisingly large uncertainties in temperature extraction from thermal fits to hadron yield data at LHC

The conventional hadron-resonance gas (HRG) model with the Particle Data Group hadron input, full chemical equilibrium, and the hadron-type dependent eigenvolume interactions, is employed to fit the hadron midrapidity yield data of the ALICE collaboration for the most central Pb+Pb collisions. For the case of point-like hadrons, the well-known fit result is reproduced. However, the situation changes if the hadrons have different eigenvolumes. In the case when all the mesons are point-like while all the baryons have an effective hardcore radius of 0.3 fm, the temperature dependence of has a broad minimum in the temperature range of 155−210 MeV, with a fit quality comparable to the minimum in the point-particle case. A very similar result is obtained when only baryon–baryon eigenvolume interactions are considered, with the eigenvolume parameter taken from the previous fit to the ground state of nuclear matter. Finally, when we apply the eigenvolume corrections with a mass-proportional eigenvolume , fixed to a particular hardcore proton radius rp, we observe a second minimum in the temperature dependence of , located at significantly higher temperatures. For instance, at rp = 0.5 fm, the fit quality is better than in the point-particle HRG case in a very wide temperature range of 170−320 MeV, which creates uncertainty in the temperature determination from the fit to the data of 150 MeV. These results show that thermal fits to the heavy-ion hadron yield data are very sensitive to the modeling of the short-range repulsion eigenvolume between hadrons, and that the chemical freeze-out temperature can only be extracted from the LHC hadron yield data with sizable uncertainty.

Proton radius from electron-proton scattering and chiral perturbation theory

We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).

Low- and intermediate-temperature proton-conducting electrolytes

We consider the main achievements and problems in the field of proton-conducting solid electrolytes. Because of the extremely small proton radius, mechanisms of proton transport differ drastically from those for other ions. This review examines general aspects of proton transport in low- and intermediate-temperature proton-conducting solid electrolytes, such as hydrated acids, acid salts, and bases and anhydrous acid salts. Proton transport in these materials is due to a sequence of rotations of proton-containing groups and proton hops between them.

Perturbative QCD and beyond: Azimuthal angle correlations in deuteron-deuteron scattering from Bose-Einstein correlations

In this paper, we found within the framework of perturbative QCD, that in deuteron-deuteron scattering the Bose-Einstein correlations due to two parton showers production, induce azimuthal angle correlations, with three correlation lengths: the size of the deuteron ($R_D$), the proton radius ($R_N$), and the size of the BFKL Pomeron which, is closely related to the saturation momentum ($R_c \sim 1/Q_s$). These correlations are independent of the values of rapidities of the produced gluons (long range rapidity correlations), for large rapidities ($\bas |y_1 - y_2| \geq 1$), and have no symmetry with respect to $\phi \to \pi - \phi$ ($ \vec{p}_{T1} \to - \vec{p}_{T1}$). Therefore, they give rise to $v_n$ for all values of $n$, not only even values. The contributions with the correlation length $R_D$ and $R_N$ crucially depend on the non-perturbative contributions, and to obtain estimates of their values, requiries a lot of modeling, while the correlations with $R_c \sim 1/Q_s$ have a perturbative QCD origin, and can be estimated in the ColorGlass Condensate (CGC) approach.

Review of experimental and theoretical status of the proton radius puzzle

The discrepancy between the measured Lamb shift in muonic hydrogen and expectations from electron-proton scattering and regular hydrogen spectroscopy has become known as the proton radius puzzle, whose most "mundane" resolution requires a $> 5 \sigma$ shift in the value of the fundamental Rydberg constant. I briefly review the status of spectroscopic and scattering measurements, recent theoretical developments, and implications for fundamental physics.

The proton radius puzzle

The FAMU (Fisica degli Atomi Muonici) experiment has the goal to measure precisely the proton Zemach radius, thus contributing to the solution of the so-called proton radius “puzzle”. To this aim, it makes use of a high-intensity pulsed muon beam at RIKEN-RAL impinging on a cryogenic hydrogen target with an high-Z gas admixture and a tunable mid-IR high power laser, to measure the hyperfine (HFS) splitting of the 1S state of the muonic hydrogen. From the value of the exciting laser frequency, the energy of the HFS transition may be derived with high precision (~ 10-5) and thus, via QED calculations, the Zemach radius of the proton. The experimental apparatus includes a precise fiber-SiPMT beam hodoscope and a crown of eight LaBr3 crystals and a few HPGe detectors for detection of the emitted characteristic X-rays. Preliminary runs to optimize the gas target filling and its operating conditions have been taken in 2014 and 2015-2016. The final run, with the pump laser to drive the HFS transition, is expected in 2018.

Dispersion theoretical analysis of the nucleon form factors

We review the achievements of the project C.2 , that deals with a dispersion theoretical analysis of the nucleon form factors. We have analyzed the world data for the space-like and time-like form factors to extract nucleon radii and vector meson coupling constants. Our proton charge radius r P E ≃ 0.85 fm has gained prominence in the so-called proton radius puzzle, see Ref. [1]. We also have analyzed the strong energy dependence of the e + e − → pp amplitude at the nucleon-antinucleon threshold, two-photon exchange effects and isospin violation in the isovector nucleon form factors.

Contribution ofσmeson exchange to elastic lepton-proton scattering

Lepton mass effects play a decisive role in description of elastic lepton-proton scattering when the beam's energy is comparable to the mass of the lepton. The future MUSE experiment, which is devised to solve the "Proton Radius Puzzle", is going to cover the corresponding kinematic region for a scattering of muons by a proton target. We anticipate that helicity-flip meson exchanges will make a difference in comparison of elastic electron-proton versus muon-proton scattering in MUSE. In this article, we estimate the $\sigma$ meson exchange contribution in the $t$-channel. This contribution, mediated by two-photon coupling of $\sigma$, is calculated to be at most $\sim 0.1 \%$ for muons in the kinematics of MUSE and it is about 3 orders in magnitude larger than for electrons because of the lepton-mass difference.

Charge, proton and neutron systems and matter radii of N ≈ Z odd-mass nuclei using a particle-number projection approach in the T = 1 pairing case

The charge radii, the proton and neutron systems radii, as well as the matter radii of [Formula: see text] odd-mass nuclei are studied using a particle-number projection approach in the neutron–proton (np) isovector ([Formula: see text]) pairing case. Expressions of the proton and neutron systems quadratic radii are first established within a projection after variation method (i.e., of PBCS type) using a recently proposed wave function for odd-mass nuclei. It is checked that they reduce to the ones obtained in the like-particles pairing case. The new expressions are then used to study numerically the various radii of nuclei such as [Formula: see text] and [Formula: see text], using the single-particle energies of a Woods–Saxon mean-field. It is shown that the few available experimental data are satisfactorily described by means of the present work approach. Furthermore, it appears that the np pairing and projection effects on the various radii are small on average in the case of odd-mass nuclei. However, the relative discrepancies with the values when only the pairing between like-particles is taken into account or the values obtained before the projection may reach up to 3% or 4% for some nuclei.

Update on the impact of the proton radius on the neutron star radius

We present the new result of our investigation on the extraction of proton radius and the impact of different proton radii on the radius of neutron star, after correcting the mistake in the previous calculation of the proton radius. The new value of the extracted proton radius is 0.864 fm. The effect of this correction on the calculated neuron star radius is trivial.

On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle

We present an improved determination of the $\pi\pi$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $\pi\pi\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $\pi\pi$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius.

Chiral effective theory methods and their application to the structure of hadrons from lattice QCD

For many years chiral effective theory (ChEFT) has enabled and supported lattice QCD calculations of hadron observables by allowing systematic effects from unphysical lattice parameters to be controlled. In the modern era of precision lattice simulations approaching the physical point, ChEFT techniques remain valuable tools. In this review we discuss the modern uses of ChEFT applied to lattice studies of hadron structure in the context of recent determinations of important and topical quantities. We consider muon , strangeness in the nucleon, the proton radius, nucleon polarizabilities, and sigma terms relevant to the prediction of dark-matter–hadron interaction cross-sections, among others.

Deducing the proton energy configuration

<p class="abstract">Articles published prior to 1994 by various authors indicate a mass energy sequence for the pion, muon, and electron in the ratios 4: 3: 2 respectively with increments of about 35.3 MeV, with the electron “rest mass” energy rotationally relativistic at α<sup>-1</sup>m<sub>e</sub>c<sup>2</sup>, ~ 70 MeV. Considering 35.3 MeV rotationally relativistic by α<sup>-2/3</sup> (≈ 26.58) extends the sequence to include the proton mass energy at 938 MeV, i.e. 26.58 <em>x</em> 35.3 MeV = 938.274 MeV. This observation leads to describing the proton as a single EM wave propagating in a toroidal path with volume contracted by α and thereby exhibiting unit charge in the far field, and evidencing partial charges in the near field consistent with the UUD quarks of the Standard Model. As with quantum chromodynamics (QCD), over 99% of the proton rest mass is relativistic in nature. A value for the proton radius is obtained within the empirical uncertainty<span lang="EN-IN">s. </span></p>

High-Precision Ramsey-Comb Spectroscopy at Deep Ultraviolet Wavelengths.

High-precision spectroscopy in systems such as molecular hydrogen and helium ions is very interesting in view of tests of quantum electrodynamics and the proton radius puzzle. However, the required deep ultraviolet and shorter wavelengths pose serious experimental challenges. Here we show Ramsey-comb spectroscopy in the deep ultraviolet for the first time, thereby demonstrating its enabling capabilities for precision spectroscopy at short wavelengths. We excite ^{84}Kr in an atomic beam on the two-photon 4p^{6}→4p^{5}5p[1/2]_{0} transition at 212.55nm. It is shown that the ac-Stark shift is effectively eliminated, and combined with a counterpropagating excitation geometry to suppress Doppler effects, a transition frequency of 2 820 833 101 679(103)kHz is found. The uncertainty of our measurement is 34 times smaller than the best previous measurement, and only limited by the 27ns lifetime of the excited state.

Deuteron joins proton as smaller than expected

A new measurement of the muonic deuterium nucleus further complicates the proton radius puzzle.

Laser Spectroscopy of Muonic Hydrogen and the Puzzling Proton

Laser spectroscopy of muonic hydrogen atoms, μp, has revealed a proton root-mean-square (rms) charge radius rE that is an order of magnitude more accurate than the CODATA world average from elastic electron–proton scattering and precision spectroscopy of regular (electronic) hydrogen. Interestingly, though, the value of rE from μp is 4%, or 7 combined standard deviations smaller than the CODATA value of rE. This discrepancy has been coined “proton radius puzzle”. We summarize the experiment and give a brief overview of the theory in muonic hydrogen. Finally we discuss some possible scenarios for the resolution of the “proton radius puzzle”.