Question

Obtain the form factor F(q) for electron scattering from an extended nucleus of radius R and charge Ze with constant charge density. Show that the minima occur when the condition tan qR = qR, is satisfied

Answer 1

Inside the nucleus the electron sees the potential as given by (1) corresponding to constant charge distribution, while outside it sees the shielded potential given by (2). The scattering amplitude is given by

The angular distribution no longer decreases smoothly but exhibits sharp maxima and minima reminiscent of optical diffraction pattern from objects with sharp edges. The minima occur whenever the condition tan qR = qR, is satisfied. This feature is in contrst with the angular distribution from a smoothly varying charge distribution, such as Gaussian, Yakawa, WoodSaxon or exponential, wherein the charge varies smoothly and the maxima and minima are smeared out, just as in the case of optical diffraction from a diffuse boundary of objects characterized by a slow varying refractive index.