Consider a beam of particles with flux F (number per unit area per unit time) incident on a scattering center. A detector of area dA is placed at angle θ and distance r from the scatterer.
(a) Show that the number of particles per unit time entering the detector is dN˙=F(dσ/dΩ)dΩ.
(b) Express dσ/dΩ in terms of the scattering amplitude f(θ).
(c) For a spherically symmetric potential, show that dσ/dΩ depends only on θ.