Diffusion d'électrons de haute énergie et répartition de la charge électrique du noyau

Abstract

The phase-shift η j of the partial wave j depends on the nuclear charge distribution only through the value at the edge of the nucleus of some function γ j ( r), solution of a Riccati equation. We give two methods to calculate this function. These methods are quickly convergent and provide a very precise value of γ j ( r) after one or two iterations only. The zero order approximation (the same in both procedures) can be calculated very simply and is already quite close to the exact value. So far as this zero order approximation is concerned the phase-shift η j depends on the nuclear charge distribution only through the average value of some function I j(κr) weighted by the nuclear charge density. We discuss the sensitivity of the differential scattering cross-section to the details of the nuclear charge distribution. At not too high energies (less than about 100 MeV for heavy nuclei), the angular distribution of the scattered electrons depends mainly of the average values 〈 I j(κr)〉 . Finer details can be reached at higher energies but the static model of the nucleus becomes less founded. In the appendix, we show how the method may be applied to non relativistic nuclear scattering.