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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Beam-target double-spin asymmetry in quasielastic electron scattering off the deuteron with CLAS

The deuteron plays a pivotal role in nuclear and hadronic physics, as both the simplest bound multinucleon system and as an effective neutron target. Quasielastic electron scattering on the deuteron is a benchmark reaction to test our understanding of deuteron structure and the properties and interactions of the two nucleons bound in the deuteron. The experimental data presented here can be used to test state-of-the-art models of the deuteron and the two-nucleon interaction in the final state after two-body breakup of the deuteron. Focusing on polarization degrees of freedom, we gain information on spin-momentum correlations in the deuteron ground state (due to the D-state admixture) and on the limits of the impulse approximation (IA) picture as it applies to measurements of spin-dependent observables like spin structure functions for bound nucleons. Information on this reaction can also be used to reduce systematic uncertainties on the determination of neutron form factors or deuteron polarization through quasielastic polarized electron scattering. Furthermore, we measured the beam-target double-spin asymmetry (A || ) for quasielastic electron scattering off the deuteron at several beam energies (1.6–1.7, 2.5, 4.2, and 5.6–5.8GeV), using the CEBAF Large Acceptance Spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility. The deuterons were polarized along (or opposite to) the beam direction. The double-spin asymmetries were measured as a function of photon virtuality Q 2 (0.13–3.17(GeV/c) 2 ), missing momentum (p m =0.0–0.5GeV/c), and the angle between the (inferred) spectator neutron and the momentum transfer direction (θ nq ). We compare our results with a recent model that includes final-state interactions (FSI) using a complete parametrization of nucleon-nucleon scattering, as well as a simplified model using the plane wave impulse approximation (PWIA). We find overall good agreement with both the PWIA and FSI expectations at low to medium missing momenta (p m ≤0.25GeV/c), including the change of the asymmetry due to the contribution of the deuteron D state at higher momenta. At the highest missing momenta, our data clearly agree better with the calculations including FSI. Final-state interactions seem to play a lesser role for polarization observables in deuteron two-body electrodisintegration than for absolute cross sections. Our data, while limited in statistical power, indicate that PWIA models work reasonably well to understand the asymmetries at lower missing momenta. In turn, this information can be used to extract the product of beam and target polarization (P b P t ) from quasielastic electron-deuteron scattering, which is useful for measurements of spin observables in electron-neutron inelastic scattering. But, at the highest missing (neutron) momenta, FSI effects become important and must be accounted for.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Electron density dependence of intensity ratio for FeXXII extreme ultraviolet emission lines arising from different ground levels in electron beam ion trap and large helical device

Extreme ultraviolet (EUV) spectra of highly charged iron ions in a wavelength range of 100-300 A have been observed from two different plasma sources of the Tokyo Electron Beam Ion Trap (Tokyo-EBIT) with a monoenergetic electron beam and a Large Helical Device (LHD) with Maxwellian electron energy. The excitation process of the spectral lines is compared between the two plasmas, and it is found that the excitation process for Fe XIX - Fe XXII ions is clearly different. Namely, the EUV emission lines from the EBIT plasma are only dominated by electron impact excitation connected to the ground state, but the excitation mechanism is not so simple in the LHD plasma. The difference in the excitation process is studied by measuring the intensity ratio of EUV emission lines (114.412 A [1s{sup 2}2s2p{sup 2} {sup 2}P{sub 3/2}{yields}1s{sup 2}2s{sup 2}2p {sup 2}P{sub 3/2}]/117.144 A [1s{sup 2}2s2p{sup 2} {sup 2}P{sub 1/2}{yields}1s{sup 2}2s{sup 2}2p {sup 2}P{sub 1/2}]) arising from different ground levels in the Fe XXII ions. The line intensity ratio has an extremely small value of 0.2 in the EBIT plasma with a low beam current of 30 mA and a beam energy of 2 keV, while the ratio varies with the electron density n{sub e} in the LHD plasmas, i.e., 0.35 for n{sub e} = 1 x 10{sup 13} cm{sup -3} and 0.65 for n{sub e} = 4 x 10{sup 13} cm{sup -3}. Here, the electron density of the EBIT plasma is estimated to be smaller than 10{sup 12} cm{sup -3} and the electron temperature of the LHD plasmas is 2 keV. The dependence of the line intensity ratio on the observed electron density is analyzed for both the EBIT and the LHD plasmas using several collisional-radiative (CR) models. The present experimental data can easily be reproduced by the analysis when the thermal proton impact excitation is taken into account. The importance of the proton impact excitation is also experimentally verified by injecting an iron pellet into the LHD plasmas and changing the ratio of the proton density to the electron density.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Saturation of a floating potential of an electron emitting electrode with increased electron emission: A one-dimensional kinetic model and particle-in-cell simulation

A bounded plasma system is studied by a one-dimensional kinetic model and particle-in-cell computer simulation using the XPDP1 code. Three particle species are injected into the system from a planar source, which are the singly charged positive ions and the cool and the hot electrons. All the particle species are injected with half-Maxwellian velocity distributions with different temperatures. From the collector, the emitted electrons are injected, also with a half-Maxwellian velocity distribution, but with a much lower temperature than the cool electrons. As electron emission from the collector is increased, the floating potential of the collector increases also until the boundary of space charge limited emission is achieved. In the simulation, the emission can be increased further and it turns out that the floating potential of the collector remains constant in spite of the increased electron emission. The model on the other hand is valid only up to the boundary of space charge limited emission. The predictions of that limit and of the respective floating potential of the collector by the model are in very good agreement with the simulation. As the criterion for comparison of the model and the simulations propose the matching of the potential, electric field, and density profiles obtained from the simulation and from the numerical solution of the Poisson equation. The matching of potential and electric field profiles is usually almost perfect. On the other hand, the numerical solutions of the Poisson equation give larger ion density at the source and emitted electron density at the collector than obtained from the simulation, but the matching of the particle densities around the inflection point of the potential between the model and the simulation is excellent for all 4 particle species. The same is valid also for the hot electron density at the source. If the potentials and the electric fields are read from the simulation and inserted into the model equations, one obtains an over-determined system of 4 equations for 3 unknown parameters: the ion and the hot electron density at the source and the emitted electron density at the collector. A solution of such a system with the method of least squares is presented. The errors obtained by such a solution can be considered as a measure of how well does the model describe the simulated system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The effect of driven electron-phonon coupling on the electronic conductance of a polar nanowire

A semi-classical model is proposed to explore the effect of electron-phonon coupling on the coherent electronic transport of a polar chain which is confined between two rigid leads in the presence of an external electric field. To this end, we construct the model by means of Green's function technique within the nearest neighbor tight-binding and harmonic approximations. For a time-periodic electric field, the atomic displacements from the equilibrium positions are obtained precisely. The result is then used to compute the electronic transport properties of the chain within the Peierls-type model. The numerical results indicate that the conductance of the system shows interesting behavior in some special frequencies. For each special frequency, there is an electronic quasi-state in which the scattering of electrons by vibrating atoms reaches maximum. The system electronic conductance decreases dramatically at the strong electron-phonon couplings and low electron energies. In the presence of damping forces, the electron-phonon interaction has a less significant effect on the conductance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

COLLISIONLESS ELECTRON–ION SHOCKS IN RELATIVISTIC UNMAGNETIZED JET–AMBIENT INTERACTIONS: NON-THERMAL ELECTRON INJECTION BY DOUBLE LAYER

The course of non-thermal electron ejection in relativistic unmagnetized electron–ion shocks is investigated by performing self-consistent particle-in-cell simulations. The shocks are excited through the injection of a relativistic jet into ambient plasma, leading to two distinct shocks (referred to as the trailing shock and leading shock) and a contact discontinuity. The Weibel-like instabilities heat the electrons up to approximately half of the ion kinetic energy. The double layers formed in the trailing and leading edges then accelerate the electrons up to the ion kinetic energy. The electron distribution function in the leading edge shows a clear, non-thermal power-law tail which contains ∼1% of electrons and ∼8% of the electron energy. Its power-law index is −2.6. The acceleration efficiency is ∼23% by number and ∼50% by energy, and the power-law index is −1.8 for the electron distribution function in the trailing edge. The effect of the dimensionality is examined by comparing the results of three-dimensional simulations with those of two-dimensional simulations. The comparison demonstrates that electron acceleration is more efficient in two dimensions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Electronic phase transitions in f-electron metals at high pressures: Synchrotron x-ray spectroscopic studies on Gd to 100 GPa

Unusual phase transitions driven by electron correlation effects occur in many f-electron metals (lanthanides and actinides alike) from localized phases to itinerant phases at high pressures. The dramatic changes in atomic volumes and crystal structures associated with some of these transitions signify equally important changes in the underlying electronic structure of these correlated f-electron metals. Yet, the relationships among the crystal structure, electronic correlation and electronic structure in f-electron metals have not been well understood. In this study, utilizing recent advances in third generation synchrotron x-ray spectroscopies and high-pressure diamond-anvil cell technologies, we describe the pressure-induced spectral changes across the volume collapse transition in Gd at 60 GPa and well above. The spectral results suggest that the f- electrons of high-pressure Gd phases are highly correlated even at 100 GPa - consistent with the Kondo volume collapse model and the recent experimental evidence of strong electron correlation of {alpha}-Ce.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Imaging single electrons to enable the generation of ultrashort beams for single-shot femtosecond relativistic electron diffraction

The generation and control of relativistic electron beams well suited for ultrafast electron diffraction application has rapidly advanced, greatly benefiting from the overlap in techniques and expertise with the accelerator community. However, imaging the diffracted MeV electrons with high detection efficiency has remained an under-explored area. In this paper, we report on a quantitative study of the imaging of MeV electrons using a detection system consisting of a phosphor screen, a lens-coupling optics, and a charge-coupled device camera. It is shown that every MeV electron in the beam yields a signal well above the camera noise. With this detection efficiency, only {approx}10{sup 5} electrons per pulse are needed to obtain a high quality single-shot diffraction pattern from a crystalline sample. We measured that such a low charge beam can be as short as 30 fs rms. Further, we discuss the possibility of compressing these electron beams to sub-5 fs rms bunch length by velocity bunching using a short high gradient rf accelerating structure scheduled to be installed next year at the UCLA Pegasus Laboratory. This opens the possibility of single-shot determinations of structural changes in many ultrafast physical processes like nonequilibrium phonon dynamics or relaxation pathways in systems with strong electron-phonon coupling.

43 PARTICLE ACCELERATORS↗
DOE OSTI2018

Nanoscale Lacing by Electrons

The ability to harness the optical or electrical properties of nanoscale particles depends on their assembly in terms of size and spatial characteristics which remains challenging due to lack of size focusing. Electrons provide a clean and focusing agent to initiate the assembly of nanoclusters or nanoparticles. Here an intriguing route is demonstrated to lace gold nanoclusters and nanoparticles in string assembly through electron-initiated nucleation and aggregative growth of Au(I)-thiolate motifs on a thin film substrate. This size-focused assembly is demonstrated by controlling the electron dose under transmission electron microscopic imaging conditions. The Au(I)-thiolate motifs, in combination with the molecularly mediated alignment, facilitate the interstring electrostatic and intrastring aurophilic interactions, which functions as a molecular template to aid electron-initiated 1D lacing. The findings demonstrate a hierarchical route for the 1D assemblies with size and spatial tunable catalytic, optical, sensing, and diagnostic properties.

Cheng, Han-Wen↗
DOE OSTI2021

Modulating the Electron Affinity of Small Bipyridyl Molecules on Single Gold Nanoparticles for Plasmon-Driven Electron Transfer

Developing controlled platforms for plasmon-driven chemistry is of great importance in catalytic reactions at the nanoscale. We report anion radical formation for five bipyridyl complexes of varying degrees of electron affinity utilizing optically fo-cused intraband (594 nm) and interband (532 nm) pump excitation of single gold nanoparticles. The surface-enhanced Raman scattering (SERS) of anion radicals for the five non-resonant adsorbed molecules 2,2’-bipyridine (22BPY), 4,4’-bipyridine (44BPY), trans-1,2-bis(4-pyridyl)ethylene (BPE), 1,2-bis(4-pyridyl)acetylene (BPA), and 1,2-bis(4-pyridyl)ethane (BPEt) were detected using localized surface-plasmon resonance (LSPR) excitation with 785 nm. The electron affinity of the five bipyridyl complexes were determined using electrochemistry. Molecules with low electron affinity experienced high-er instances of radical anion formation under a plasmon-coupled intraband electron transfer excitation (594 nm) whereas molecules with high electron affinity showed a preference for anion radical formation under direct interband electron trans-fer excitation (532 nm). The lowest unoccupied molecular orbital (LUMO) energy levels for low electron affinity surface-bound molecules (22BPY, BPEt) are on average ~0.43 eV higher for high electron affinity surface-bound molecules (BPA, BPE, 44BPY) as calculated using time-dependent density functional theory, elucidating the importance of plasmon coupling to energy levels that facilitate charge transfer pathways. We also show the ability to ‘activate’ high vs low electron affinity single nanoparticles with the choice of pump excitation wavelength. The findings show the complex interplay between molecular electron affinity, orbital overlap with the density of states of the plasmonic metal, and excitation energetics of the pump laser wavelength. Potential applications of this work include enhanced control over molecular scale catalysis, biosensor design, and solar energy capture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Electronic–Vibrational Coupling and Electron Transfer

This Feature Article describes our recent work on implementing pump-degenerate four-wave mixing for studying electronic vibrational coupling in solid-state systems and in particular in interfacial electron transfer systems. Interfacial electron transfer (ET) reactions constitute key physical phenomena central to a variety of light-induced energy transport and conversion processes such as vision, photocatalysis, photovoltaics, energy storage, molecular electronics, etc. Heterogeneous material systems like organic/inorganic interfaces are of particular interest due to the variety of possible modifications to their properties. Although ET dynamics has been studied intensively in heterogeneous systems, many questions remain unanswered. The significance of electronic–vibrational coupling and coherence is one aspect that has yet to be fully explored. It is well-known that ET between a molecule and a semiconductor can be accompanied by vibrational excitation due to Franck–Condon overlap of the excited state and cation. The energy necessary for exciting these high-energy vibrational modes is taken from the excess energy of the transferred electron and leads to an ET spectrum. This spectrum carries information that is associated with the vibrational wavepacket that is involved in the ET process, including the coherent beating that results from periodic attempts to overcome the transition state. The dynamics of the wavepacket, and in particular its coherence time, provides insight into the strength of the coupling between electron donor and acceptor states and the adiabaticity of the process. This information is important but not readily available for interfacial ET systems comprising a large number of possible electron acceptor states because neither the rate of the reaction nor the electronic spectrum allows unambiguous assignment. These recent studies give access to vibrational wave packet dynamics triggered by ET reaction and have the potential to allow direct measurement of Huang–Rys parameters and study fundamental properties of interfacial ET like the adiabaticity and the amount of coherence—electronic and vibrational—in the system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Structural origins of the electronic properties of materials via time-resolved infrared spectroscopy

Time-resolved mid-infrared (TRIR) spectroscopy offers new opportunities to investigate how the molecular and structural properties of optoelectronic materials influence their electronic and transport states. This capability emerges from the ability to measure low energy electronic transitions in the mid-infrared that are related to delocalized states in materials and to simultaneously detect the vibrational properties of the materials that influence those states. Furthermore, the ability to simultaneously measure electronic and vibrational transitions in materials offers unprecedented opportunities to correlate structural dynamics of materials with their electronic and transport properties. Here, these capabilities are introduced by first describing the basic principles of TRIR spectroscopy used to examine electronic processes in materials. Then, several applications of TRIR spectroscopy are described in which measurements of the vibrational spectra of electronic excited states are probed as a means to correlate the structural properties of materials with the delocalization of their electronic states. In one example, exciton localization mechanisms in organic semiconductors are probed through vibrational spectra of the molecules in their excited states and correlated with their crystalline packing arrangements. Another example highlights the use of TRIR spectroscopy to examine singlet fission reaction dynamics through a combination of low energy electronic transitions and the vibrational spectra that are unique to the electronic states involved in the reaction. Finally, the use of TRIR spectroscopy to investigate charge carrier localization mechanisms in lead-halide perovskites is described, followed by an outlook of future applications of the technique in optoelectronic materials research.

36 MATERIALS SCIENCE↗
DOE OSTI2019

A benchmark photoelectron spectroscopic and theoretical study of the electronic stability of [B12H12]2-

We report a joint benchmark study on the electronic stability of closo-dodecaborate [B12H12]2- employing negative ion photoelectron spectroscopy and high level electronic structure methods. The photoelectron spectra of [B12H12]2-, measured at 266, 193 and 157 nm, yield the Adiabatic and Vertical Detachment Energies (ADE and VDE) of this dianion at 0.93 ± 0.05 eV and 1.15 ± 0.05 eV, respectively, along with a ~ 3 eV Repulsive Coulomb Barrier (RCB) against electron detachment. Theoretical calculations at various levels of electronic structure theory confirm the high stability of this dianion. The ADE and VDE values calculated at the CCSD(T)/aug-cc-PVQZ level are 0.92, and 1.16 eV, in excellent agreement with the experimental benchmark values. The comparison between the experimental and the theoretical values obtained at different levels of theory indicate that the PBE0 density functional represents a cost-effective method of sufficient accuracy to describe the molecular properties of this dianion and associated compounds. The theoretical RCB was modelled after the electrostatic potential (ESP) and point charge method (PCM) along three different detachment pathways, viz. along the B-H bond, perpendicular to a B-B bond, and normal to a B-B-B triangle. It was found that detachment of the electron along the B-H bond is preferred, as this pathway is associated with RCBs between 2.3 eV (PCM) and 3.3 eV (ESP), values that bracket the experimental estimate of ~ 3 eV.

Apra, Edoardo↗
DOE OSTI2019

The electron canonical battery effect in magnetic reconnection: Completion of the electron canonical vorticity framework

A widespread practice in studying magnetic reconnection is to examine the electron momentum equation. Here, we present an alternative, ab initio framework that examines the motion of the electron canonical vorticity, which is the curl of the electron canonical momentum. The competition between just two terms—the convective term and the electron canonical battery term—determines the dynamics of electron canonical vorticity and equivalently the electron physics down to first principles. To demonstrate the power of this approach, the growth, saturation, stability, and morphology of the electron diffusion region are explained within the electron canonical vorticity framework. The framework provides a clear distinction between reconnection models where the frozen-in property of the magnetic field is violated by electron inertia and by pressure tensor effects such as electron viscosity.

25 ENERGY STORAGE↗
DOE OSTI2020

Neutralization of ion beam by electron injection: Accumulation of cold electrons

Ion beam charge neutralization by electron injection is a complex kinetic process. Recent experiments show that the resulting self-potential of the ion beam after neutralization by plasma is much lower than the temperature of plasma electrons [Stepanov et al., Phys. Plasmas 23, 043113 (2016)], indicating that kinetic effects are important and may affect the neutralization of the ion beam. We performed a numerical study of the charge neutralization process of an ion beam making use of a two-dimensional electrostatic particle-in-cell code. The results show that the process of charge neutralization by electron injection is composed of two stages. During the first stage, the self-potential of the beam is higher than the temperature of injected electrons (T e /e) and all injected electrons are captured by the ion beam. During the second stage, hot electrons escape from the ion beam and the beam self-potential (φ) decreases because cold electrons slowly accumulate resulting in the beam self-potential φ to become much lower than Te/e in agreement with previous experimental observations at Princeton Advanced Teststand. We also determined that the resulting φ scales as φ~√T e , in agreement with previous experimental observations from Gabovich's group. In addition, the results show that the transverse position of the electron source has a great impact on ion beam neutralization. A slight shift of the electron source as relevant to the ion thrusters leads to a large increase in the beam self-potential because of an increase in potential energy of injected electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

High-resolution planar electron beam induced current in bulk diodes using high-energy electrons

Understanding the impact of high-energy electron radiation on device characteristics remains critical for the expanding use of semiconductor electronics in space-borne applications and other radiation harsh environments. Here in this paper, we report on in situ measurements of high-energy electron radiation effects on the hole diffusion length in low threading dislocation density homoepitaxial bulk n-GaN Schottky diodes using electron beam induced current (EBIC) in high-voltage scanning electron microscopy mode. Despite the large interaction volume in this system, quantitative EBIC imaging is possible due to the sustained collimation of the incident electron beam. This approach enables direct measurement of electron radiation effects without having to thin the specimen. Using a combination of experimental EBIC measurements and Monte Carlo simulations of electron trajectories, we determine a hole diffusion length of 264 ± 11 nm for n-GaN. Irradiation with 200 kV electron beam with an accumulated dose of 24 × 10 16 electrons cm -2 led to an approximate 35% decrease in the minority carrier diffusion length.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Near-infrared noise in intense electron bunches

This article investigates electron bunch density fluctuations in the 1 −10 μ⁢m wavelength range, focusing on their impact on coherent electron cooling (CEC) in hadron storage rings. In this study, we compare the shot-noise model with experimental observations using bandwidth-filtered near-infrared optical transition radiation (OTR) photodiode signals, where the transverse bunch size is much larger than the OTR wavelength of interest. The relativistic electron bunch (𝛾 ≈ 50) parameters are close to those proposed for the coherent electron cooler in the electron-ion collider (EIC) project. Preliminary feasibility experiments were conducted, and the noise factors are presented, supported by particle tracking. No major density fluctuations or effective cooling rate decrease were revealed for EIC CEC design parameters. Additionally, longitudinal-space-charge-induced microbunching for the chicane-compressed bunch was observed with coherent OTR enhancements up to 100 times, providing further calibration of the measurement method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Electronic and structural ground state of heavy alkali metals at high pressure

Here, alkali metals display unexpected properties at high pressure, including emergence of low symmetry crystal structures, that appear to occur due to enhanced electronic correlations among the otherwise nearly-free conduction electrons. We investigate the high pressure electronic and structural ground state of K, Rb, and Cs using x-ray absorption spectroscopy and x-ray diffraction measurements together with ab initio theoretical calculations. The sequence of phase transitions under pressure observed at low temperature is similar in all three heavy alkalis except for the absence of the oC 84 phase in Cs. Both the experimental and theoretical results point to pressure-enhanced localization of the valence electrons characterized by pseudo-gap formation near the Fermi level and strong spd hybridization. Although the crystal structures predicted to host magnetic order in K are not observed, the localization process appears to drive these alkalis closer to a strongly correlated electron state.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Proton radius from electron scattering data

Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle. Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. Methods: We make use of stepwise regression techniques using the F-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. Results: Starting with the precision, low four-momentum transfer (Q 2 ) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the F-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on GE from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-Q 2 data on G E to select functions which extrapolate to high Q 2 , we find that a Pad´e (N = M = 1) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, G E (Q 2 ) = (1 + Q 2 /0.66 GeV 2 ) -2 . Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extreme low-Q 2 data or by use of the Pad´e approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering result and the muonic hydrogen result are consistent. Lastly, it is the atomic hydrogen results that are the outliers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗