Nuclear charge and magnetization density distribution parameters from elastic electron scattering

Electron scattering and nuclear structure

A survey has been made of the differential scattering cross sections for 187-Mev electrons on the even-even nuclei $_{12}\mathrm{Mg}^{24}$, $_{14}\mathrm{Si}^{28}$, $_{16}\mathrm{S}^{32}$, $_{18}\mathrm{A}^{40}$, and $_{28}\mathrm{Sr}^{88}$. It has been possible to separate the elastic scattering from the inelastic in all cases and to resolve the inelastic groups from specific nuclear levels for at least one level in all cases. A simple Born-approximation analysis of the elastic data yields values of the effective radii and surface thicknesses of the nuclear charge densities which (if suitably corrected for failure of the Born approximation) are in substantial agreement with the results of Hahn, Ravenhall, and Hofstadter; i.e., a radius parameter of $c\ensuremath{\cong}1.08 {A}^{\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm (radius to half-maximum of the charge distribution) and a surface thickness of $t\ensuremath{\cong}2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm (thickness from 10% to 90% of the maximum of the charge distribution). Phenomenological analysis of the inelastic scattering along the lines laid down by Schiff yields some tentative multipolarity assignments, and application of some results of Ravenhall yields estimates of (radiative) partial level widths; for the $E2$ transitions these correspond to lifetimes of \ensuremath{\sim}19\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ sec (Mg 1.37 Mev) to \ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ sec (Sr 1.85 Mev). The observed strengths of the transitions are compared to those predicted by Weisskopf theory.

Inelastic and Elastic Scattering of 187-Mev Electrons from Selected Even-Even Nuclei

High-energy photon interactions are discussed in terms of the hadronic structure of the photon, which is expressed by means of a formulation which is akin to, but somewhat more general than, vector-meson-dominance or specific generalized vector-dominance models. Experiments which demonstrate and yield information about this hadronic structure are discussed critically, and the resulting information is carefully evaluated. Special attention is paid to diffractive processes such as the photoproduction of vector mesons and to photon shadowing effects on nuclei. Relationships to other views of photon interactions, such as the parton model and the space-time description, are also discussed; these views are seen to complement the hadronic structure picture rather than to be in conflict. The general overview is that there is ample evidence which shows that the photon's hadronic structure plays a significant role in its interactions. What further work would most significantly enhance the understanding of the hadronic structure of the photon is also pointed out.

The Hadronic Properties of the Photon in High-Energy Interactions

Unraveling hadron structure with generalized parton distributions

With apparatus previously described1,2 we have studied the elastic scattering of electrons of energies 100, 188, and 236 MeV from protons initially at rest. At 100 MeV and 188 MeV, the angular distributions of scattered electrons have been examined in the ranges 60°-138° and 35°-138°, respectively, in the laboratory frame. At 236 MeV, because of an inability of the analyzing magnet to bend electrons of energies larger than 192 MeV, we have studied the angular distribution between 90° and 138° in the laboratory frame. In all cases a gaseous hydrogen target was used.

Electron Scattering from the Proton

Electron Scattering From the Proton

Absolute Cross Section for Electron Scattering from Protons

The elastic scattering of 188-Mev electrons from gaseous targets of hydrogen and helium has been studied. Elastic profiles have been obtained at laboratory angles between 35\ifmmode^\circ\else\textdegree\fi{} and 138\ifmmode^\circ\else\textdegree\fi{}. The areas under such curves, within energy limits of \ifmmode\pm\else\textpm\fi{}1.5 Mev of the peak, have been measured and the results plotted against angle. In the case of hydrogen, a comparison has been made with the theoretical predictions of the Mott formula for elastic scattering and also with a modified Mott formula (due to Rosenbluth) taking into account both the anomalous magnetic moment of the proton and a finite size effect. The comparison shows that a finite size of the proton will account for the results and the present experiment fixes this size. The root-mean-square radii of charge and magnetic moment are each (0.74\ifmmode\pm\else\textpm\fi{}0.24)\ifmmode\times\else\texttimes\fi{}${10}^{13}$ cm. In obtaining these results it is assumed that the usual laws of electromagnetic interaction and the Coulomb law are valid at distances less than ${10}^{\ensuremath{-}13}$ cm and that the charge and moment radii are equal. In helium, large effects of the finite size of the alpha-particle are observed and the rms radius of the alpha particle is found to be (1.6\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm.

Elastic Scattering of 188-Mev Electrons from the Proton and the Alpha Particle

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Electron Scattering from the Proton

Electron Scattering From the Proton

Absolute Cross Section for Electron Scattering from Protons

Elastic Scattering of 188-Mev Electrons from the Proton and the Alpha Particle