Calculate the scattering amplitude f(0) in the first Born approximation for scattering of particles of mass m off a Yukawa potential of the form V(r) = 9 e-ar r (3) where a > 0 is related to the mass of the particle "mediating" this interaction. b) Calculate the total cross-section for scattering off the above potential, still in the first Born approximation. A homogeneous collimated beam of cross-sectional area A with N particles, each of momentum p, hits the Yukawa target. Estimate the number of particles that are back- scattered, that is, they deviate more than 90° from their initial direction. Assume that A is bigger than the total scattering cross section and that the first Born approximation holds.