Calculating Nilsson levels. In full generality, calculating the Nilsson orbitals for nuclei with arbitrary deformation involves heavy computational work. However, it is easy and illustrative to calculate the lowest states, i.e. p1/2 and p3/2 to first order in deformation, in a simplified three-dimensional harmonic oscillator model. a. Our unperturbed potential will be V(r) = -V0 + m w2 r2 . Derive the general expression for w, such that the potential crosses zero at the radius R of a nucleus of atomic weight A (i.e. R = r0 A1/3 ). Evaluate this expression for V 0 = 55 MeV, r 0 = 1.4 fm, A = 16, and m is the mass of the proton or neutron