(i) Given the proton to be a uniformly charge sphere of radius R = 1 fm, determine the first order energy shift, making reasonable approximations. How accurate should the first order theory be in this case?
(iii) Once again do the calculations for a muon (mass = 106 MeV/c2) in orbit around Pb nucleus (Z = 82, A = 207) with uniform and spherical-shell charge density distributions. Assume the nuclear radius scales like R ~ A1/3. How accurate should the first order theory be in this case?
The potential energy outside the nucleus is:
U(r) = - kq^2/r r > r_0
Were k is the Coloumb constant.
The charge inside the sphere as a ...
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