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Nuclear models

Nuclear models. Our approach…. Look at data that motivates the model Construct a model Make and test predictions from the model. Models we will consider…. Independent particle shell model. Collective models. Fermi gas model. Shell Model - data. 2p separation energy (between isotones).

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Nuclear models

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  1. Nuclear models

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

  3. Shell Model - data 2p separation energy (between isotones) Becomesmuch smallerafter 8, 20, 28, 50, 82, 126 2n separation energy (between isotopes)

  4. T Shell Model - data ARn   + A-4Po 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Ravg

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

  6. Spin-orbit potential 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)

  7. Shell Model Q.M. good quantum numbers

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

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

  10. Systematics…

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

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

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

  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

  16. Nuclear magnetic moments

  17. Nuclear magnetic moments Consider the case: …some algebra happens here…

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

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

  20. Proton: Neutron: Nuclear magnetic moments

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