1. Nuclear models

2. Models we will consider… Independent particle shell model Look at data that motivates the model Construct a model Make and test predictions from the model Our approach… Collective models Fermi gas model

3. Shell Model - data 2p separation energy (between isotones) Becomes much smaller after 8, 20, 28, 50, 82, 126 2n separation energy (between isotopes)

4. Shell Model - data A Rn   + A-4 Po TT Sudden rise at N = 126 Neutron capture cross section   Very small  at N = 28, 50, 82, 126 Abrupt change in nuclear radius at N = 20, 28, 50, 82, 126  R  R avg

5. Shell Model - data And, the observation of discrete photon energies E  emitted from nuclear de-excitation T  show sharp discontinuities near N,Z of 28, 50, 82, 126 BE for last n added: sharp discontinuities near, 50, 82, 126 e.g., (d,p), (n,  ), ( ,n), (d,t) reactions

6. Shell Model Assume that the nucleons move (independently) in a potential, V, created by the other nucleons in the nucleus. Assume that the problem can be addressed by the non- relativistic Schrodinger quantum mechanics. Assume that the potential, V, is spherically symmetric and therefore only a function of r, V(r) Spin-orbit potential

7. Shell Model Q.M. good quantum numbers

8. Shell Model Multiplicities -- 2 spin states different states = Energy difference (splitting) increases with

9. Shell Model energy levels Energy splitting increases with Spectroscopic state multiplicity

10. Systematics…

11. Nuclear magnetic moments Intrinsic (measured) dipole magnetic moments L is orbital angular momentum for single nucleon M is nucleon mass max z-axis projection

12. Nuclear magnetic moments From electron case, you expect to have for this fermion -- Does not agree with measurement Measured dipole magnetic moments

13. Nuclear magnetic moments And, by the same analysis, one gets -- Measured dipole magnetic moments

14. Nuclear magnetic moments Consider nuclei with odd A. Assume that the pairing interaction causes the “core” of paired nucleons to have net I = 0. Assume that the induced magnetic dipole moment is due to the last unpaired nucleon. Use this to estimate the nuclear magnetic dipole moment - within this model.

15. Nuclear magnetic moments

17. Consider the case: …some algebra happens here…

18. Nuclear magnetic moments Consider the case: But, if

19. Nuclear magnetic moments Consider the case: Four cases to consider: both cases shown here for odd proton & odd neutron But, if

20. Nuclear magnetic moments Proton: Neutron: