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The Shell Model of the Nucleus 4. Applications – nuclear spin

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

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The Shell Model of the Nucleus 4. Applications – nuclear spin

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  1. The Shell Model of the Nucleus4. 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 + - + 10 2 - 4 6 Remember the occupancy of each level nlj is (2j+1) –only depends on j + - 8 + 2 4 + 6 - The parity of each level nlj is only depends on l 2 - 4 + + 2 PARITY

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

  5. Predicting nuclear spins SPIN OF EVEN- EVEN NUCLEI One nucleon in a j-state Two 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-state 2 nucleons in same j-state 3 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. 8 2 2 8 20 20 28 50 50 82 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. 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

  11. PREDICTING NUCLEAR SPIN – Lead isotopes L=4

  12. PREDICTING NUCLEAR SPIN – Lead isotopes

  13. Excited states of 41Ca ? 1

  14. Excited states of 17O and 17F 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.

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