1. Shell Model with residual interactions – mostly 2-particle systems Simple forces, simple physical interpretation

5. 2 – (valence) particle systems Need to consider a more complete Hamiltonian: H = H 0 + H residual H residual reflects interactions not included in the single particle potential. Especially important for valence nucleons. NOT a minor perturbation. In fact, these residual interactions determine almost everything we know about most nuclei, especially e-e nuclides. Start with 2- particle system, that is, a nuclei that are “doubly magic + 2”. H residual is H 12 (r 12 ) Consider two identical valence nucleons with angular momenta j 1 and j 2. Two questions: What total angular momenta j 1 + j 2 = J can be formed, and what are the energies of the states with these angular momenta?

6. Coupling of two angular momenta j 1 + j 2 All values from: j 1 – j 2 to j 1 + j 2 (j 1 = j 2 ) Example: j 1 = 3, j 2 = 5: J = 2, 3, 4, 5, 6, 7, 8 For j 1 = j 2 : J = 0, 2, 4, 6, … ( 2j – 1) (Why these?) /

7. How can we know which total J values are obtained for the coupling of two indentical nucleons in the same orbit with total angular momentum j? Several methods: easiest is the “m-scheme”.

9. Separate radial and angular coordinates