1. The problem statement, all variables and given/known data Show that the mean-square charge radius of a uniformly charged sphere (with radius R) is < r^2 > = 3*R^2 / 5 2. Relevant equations < r^2 > = [tex]\int[/tex] [tex]\varphi[/tex]f* r^2 [tex]\varphi[/tex]i dV [tex]\varphi[/tex]f* = exp(-i q dot r) [tex]\varphi[/tex]i = exp(i q dot r) where q = kf - ki and pf = h_bar * kf pi = h_bar * ki r > R: V(r) = -Ze^2 / (4*pi*e0) * 1/r^2 r < R: V´(r) = -Ze^2 / (4*pi*e0*R) * (3/2 - 1/2 * (r/R)^2) Ei = 1/2*m*vi Er0 = J0^2/(2*m*r0^2) + V(r0) or V´(r0) according as r > R or r < R. J0 = Ji = m*vi*b where b is the impact parameter and is b = Ze^2/ (4*pi*e0*m*vi^2) * cot(A/2) for hyperbolic orbits, Ei > 0 3. The attempt at a solution I basically want to know if my approach is correct. I think that I have to find < r0^2 > where r0 is the distance of closest approach to the centre of the charge distribution either inside it (where the electron feels V´(r)) or outside it (where the electron feels V(r)). I've done some calculations using the radial energy equation, trying to solve for r0^2, but the calculations are a mess and I get a feeling I'm going about it all wrong. The problem is from Krane's Introductory Nuclear Physics, Chapter 3, problem 3.1.