Measurement of Spins of Ground States of Radioactive Nuclei

1. Measurement of Spins of Ground States of Radioactive Nuclei Wang, Quan (??)

2. Outline Introduction Important definitions The method of the spin Hamiltonian Experimental Methods

3. Introduction Nucleus properties: Nuclear spin, I Nuclear magnetic dipole moment, �I Nuclear electric quadrupole moment, Q Measurement of Spin, counting the discrete 2I+1 degenerate states Measurement of �I, interaction with external or internal magnetic field No direct measurement of Q

4. Important definitions Nuclear Spin I An integer or half integer denoted by I 2I+1 is the spatial degeneracy of the state Ih is the angular momentum operator Z-component, Iz, is quantized to the 2I+1values (I, I-1, I-2,�, -I) The magnitude of vector I is The largest measured being twelve, the largest inferred is eighteen

5. Important definitions Nuclear Magnetic Dipole Moment

6. Important definitions Nuclear Quadrupole Moment Nuclear Magnetic Octupole And Higher Moments

7. Important definitions Hyperfine Structure Anomaly For two isotopes of the same element, a, the magnetic hyperfine constant, is proportional to the nuclear g-factor. In practice,

8. The method of the spin Hamiltonian Determinations are based on the radio-frequency of paramagnetic atoms in atomic beams and of paramagnetic ions in crystalline fields. Breit-Rabi Hamiltonian:

9. The method of the spin Hamiltonian The system has a total spatial degeneracy of (2I+1)(2J+1). Last two terms represent the direct interaction of the nuclear and electronic magnetic moments with the external magnetic field. If B vanishes, the first two terms only partially remove the degeneracy.

10. The method of the spin Hamiltonian Total angular moment Energy of these states (no B field),

11. The method of the spin Hamiltonian Energy with B field (Week B field), Energy with B field (Strong B field),

12. The method of the spin Hamiltonian Na23 fine & hyperfine structure Fine structure, Hyperfine,