In this problem, neglect spin and relativistic effects, and use the born approximation (a) suppose an electron scatters off a spherically symmetric potential v(r). write down (or compute if you don't reinernber) the formlula for the born approximation to the scattering amplitude f(9,の, in the form of a one- dimensional radial integral f(θ, φ)-j 0 (some function of r) × v (r) dr (b) now suppose that the electron scatters elastically off a spherically symmetric charge distribution, with charge density rho(r) centered at the origin. (this is not a local potential, but the answer to part (a) may still be useful.) calculate, in the born approximation (that is, to first order in the potential), the scattering amplitude f(0,p) and write it as where q is the momentum transferred between the incident and the scattered electron, and fr(q2) is the rutherford amplitude for scattering off a point charge here α is the fine-structure constant. the function f(q2) is called the "form factor. write an explicit formula for f(q2) in terms of p(r) (c) now specialize to an electron scattering elastically off a uniformly charged sphere, centered at the origin, with radius r and total charge ze. what is f(g2) as a function of q and r? hint: you might want the definite integral e-ursin(qr) dr and み 7 and the indefinite integrals r sin r drsinr- r cos x cos x dx = cos x + x sin x note: the scattering amplitude is defined so that its square is the differential cross section: