The low-energy Born approximation to the amplitude for electron scattering from a neutron is proportional to the volume integral of the potential energy of interaction between the electron and the neutron,

(a) Write a formula for V_E(r) if ρ_N(s) is the charge density of the neutron and φ(s) is the electrostatic
potential of the electron.

(b) Suppose that ρN(s) = ρ_N(|s|) and that φ(s) varies slowly over the region of space occupied by the neutron’s charge distribution. Show that the scattering amplitude gives information about the second radial moment of the neutron charge density:

Transcribed Image Text:

f(0) = m rh? fd³r d³r Vg(r).