Precise proton radii from electron scattering

Abstract

We summarize various analyses of the world data on elastic electron scattering for the determination of the most precise charge rms-radius of the proton. We also present the Zemach moments needed for the interpretation of atomic HFS structure and µ-X-ray experiments.Résumé : Nous passons en revue différentes analyses faites à travers le monde des données de diffusion élastique d'électrons afin de déterminer de la façon la plus précise possible le rayon RMS du proton. Nous présentons également les moments de Zeemach requis dans l'interprétation de la structure atomique HFS et des expériences rayons X.[Traduit par la Rédaction]

Hydrogen-deuterium isotope shift: From the1S−2S-transition frequency to the proton-deuteron charge-radius difference

“…An analysis of the world scattering data for the proton leads to a value of r p = 0.895(18) fm (Refs. [14][15][16]), which is in good agreement with the recommended value derived from the 2006 CODATA adjustment of the fundamental constants r p = 0.8768(69) fm (Refs. [11,13]) .…”

“…III. A detailed account of the corrections that contribute at the current level of accuracy is important as it enables theorists and experimentalists to compare the proton-deuteron radius difference derived from high-precision spectroscopy of hydrogen to scattering data [14][15][16], based on a transparent listing of theoretical contributions. Finally, in Sec.…”

A critical compilation of experimental data on spectral lines and energy levels of hydrogen, deuterium, and tritium

“…In this way, it was found that the contributions of the measured H and D frequency intervals to the adjusted values of the fundamental constants are significant for only three constants: the proton charge radius R p , the deuteron charge radius R d , and the Rydberg constant R 1 . In the least-squares determination of these three constants [6,24] there are three degrees of freedom to fit 25 input values (23 frequency measurements in H and D and two direct measurements of R p and R d using electron-proton and electron-deuteron elastic scattering [172,173]). The two 1S-2S measurements by Hänsch et al [115] (1S-2S frequency in H) and Huber et al [152] (H-D isotope shift of the 1S-2S frequency) having sub-kilohertz uncertainties exactly determine two of these three degrees of freedom.…”

Proton root-mean-square radii and electron scattering

“…Problematic in particular is the fact that the (e,e) data sensitive to proton finite size are the ones in the region of momentum transfer q = 0.6-1.2 fm −1 [13]; the determination of the rms radius involves an (implicit or explicit) extrapolation to q = 0. Difficulties due to large-r tail.…”

“…For sake of easier comparison, we use the same data, but only up to q max = 2 fm −1 ; this is entirely sufficient as the data below 2 fm −1 are the only ones sensitive to the rms radii [13]. The data have been fitted with a four-parameter Pade parametrization for G e and G m .…”