1. The Shell Model of the Nucleus 4. Applications – nuclear spin [Sec. 6.1 and 6.3 Dunlap]

2. Switching to the nucleus Even for large A and large l one is not going to get a big splitting. This was not able to change the magic numbers. Mayer, Jensen, Haxel and Suess knew this – they had done this calculation – it had no effect on the magic numbers. What they discovered was that this relativistic Spin Orbit energy was being swamped by another Spin-Orbit energy that was coming from a non-relativistic source.

3. The Full Energy Level diagram of the SHELL MODEL 2 4 2 6 4 2 8 6 4 2 10 Remember the occupancy of each level nl j is (2j+1) – only depends on j The parity of each level nl j is only depends on l + - + + - + + + - - + + - + PARITY -

4. Predicting nuclear spins UNDERSTANDING j-j COUPLING One nucleon in a j-state Two nucleons in same j-state A B Both the states A and B (and any other m j substate) is ok by Pauli Principle. But state B is the lower energy state – because the strong interaction averaged over space is maximized. HIGHER ENERGY STATE LOW ENERGY STATE

5. Predicting nuclear spins SPIN OF EVEN- EVEN NUCLEI One nucleon in a j-stateTwo nucleons in same j-state CORROLARY: If a nucleus has an even number of neutrons – then these will couple to give spin zero If a nucleus has an even number of protons – then these will couple to give spin zero If a nucleus has N=EVEN, and Z=EVEN then J=0

6. Predicting nuclear spins SPIN OF ODD- EVEN NUCLEI One nucleon in a j-state2 nucleons in same j-state3 nucleons in same j-state CORROLARY: Since all EVEN-EVEN configurations are J=0 states – it follows that any EVEN-ODD nucleus must be getting its spin J from the single unpaired nucleon

7. Neutron and Proton levels The potential as seen by a proton is different – especially in large nuclei – there is a Coulomb “tail” outside the nucleus and a “bump” in the center. This does not effect the lower energy levels up to magic (special) number 50. 8 2 2 8 20 28 50 82

8. Neutron and Proton levels For large nuclei (Z>50) there can be some subtle changes in the energy level sequencing due to the Coulomb potential. parity

9. PREDICTING NUCLEAR SPINS

10. Predicting nuclear spins NuclideJJ comment 0+0+ stable 10 5 y E.C. 0+0+ stable 0+0+ 165d  - 0+0+ stable 4.5d  - 0+0+ stable

11. PREDICTING NUCLEAR SPIN – Lead isotopes L=4

12. PREDICTING NUCLEAR SPIN – Lead isotopes

13. Excited states of 41 Ca 1 ?

14. Excited states of 17 O and 17 F NOTE: As far as the strong force is concerned these two nuclei are THE SAME! The strong force does not distinguish n and p. But the EM force does.