(a) Determine the differential cross section dσ/dΩ in the Born approximation for scattering from the potential energy 2μV(r)/ℏ2=γδ(r−a) (see Problem 13.12). Show the explicit dependence of dσ/dΩ on θ.
(b) Evaluate dσ/dΩ in the low-energy limit. Show that the differential cross section is isotropic. What is the total cross section?
(c) Use the condition for the validity of the Born approximation at low energy (see Problem 13.3) to establish that your result in (b) for the total cross section agrees with that given in Problem 13.12 in the appropriate limit.