22.101 Applied Nuclear Physics (Fall 2004) Problem Set No. 5 Due: Oct. 25, 2004 Problem 1 (a) Sketch the energy levels of nucleons as given by two central force potentials, an infinite spherical well and a parabolic well (see Fig. 9.5). Explain the spectroscopic notation used in labeling each level, and how is degeneracy of each level determined. What is the significance of these results concerning the stability of nuclei? (b) Sketch the energy levels of nucleons given by a shell-model potential with spinorbit coupling (see Fig. 9.6), and explain the notation. What new features do you get with this model compared to the two models in part (a)? Problem 2 Explain the operation of angular momentum addition in general, where one adds two angular momentum operators, L and S, to form a total angular momentum operator j, j = L + S. Apply your explanation to the particular case where L and S are the orbital and spin angular momentum operators of a nucleon respectively. Problem 3 On the basis of the single-particle shell model with spin-orbit coupling (Fig. 9.6), predict the ground-state spin and parity of the following nuclides: Li6, N14, Mn55, Nb93, Xe131, Au197, Pb207, Bi209 Compare your results with experimental data (e.g., Nuclide Chart); in the case of any discrepancy between your predictions and experiments, give an explanation.