1. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 MP-41 Teil 2: Physik exotischer Kerne 13.4.Einführung, Beschleuniger 20.4.Schwerionenreaktionen, Synthese superschwerer Kerne (SHE) 27.4.Kernspaltung und Produktion neutronenreicher Kerne 4.5.Fragmentation zur Erzeugung exotischer Kerne 11.5.Halo-Kerne, gebundener Betazerfall, 2-Protonenzerfall 18.5.Wechselwirkung mit Materie, Detektoren 25.5.Schalenmodell 1.6.Restwechselwirkung, Seniority 8.6.Tutorium-1 15.6.Tutorium-2 22.6.Vibrator, Rotator, Symmetrien 29.6.Schalenstruktur fernab der Stabilität 6.7.Tutorium-3 13.7. Klausur

2. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 2 + systematics Excitation energy (keV) Ground state Configuration. Spin/parity I π =0 + ; E x = 0 keV 2+2+ 0+0+

3. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 4 + /2 + energy ratio: mirrors 2 + systematics Excitation energy (keV) Ground state Configuration. Spin/parity I π =0 + ; E x = 0 keV 2+2+ 0+0+ 4+4+

4. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Evolution of nuclear structure as a function of nucleon number

5. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Collective Vibration In general, forbidden – density change! forbidden – CM moves! OK... λ=0 λ=1 λ=2 λ=3 time

6. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Collective Vibration In general, λ=2: quadrupole vibrationλ=3: octupole vibration

7. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Collective Vibration classical Hamiltonian Binding energy of a nucleus: a V = 15.560 MeV a S = 17.230MeV a C = 0.6970 MeV a A = 23.385 MeV a P = 12.000 MeV constants:

8. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Collective Vibration classical Hamiltonian quantization energy eigenvalue 0 wave function

9. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Collective Vibration classical Hamiltonian differential equation

10. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Second Quantization Hamilton operator rule for boson operators: creation & annihilation operators increase or decrease the number of phonons in a wave function ground state (vacuum) 1-phonon state 2-phonon state

11. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Second Quantization Hamilton operator rule for boson operators: 1-phonon energy:

12. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Second Quantization Hamilton operator rule for boson operators: 2-phonon energy: etc.

13. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Second Quantization Hamilton operator rule for boson operators: 2-phonon state: normalization (approximation):

14. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Second Quantization Hamilton operator rule for boson operators: 2-phonon state: normalization:

15. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Collective Vibration

16. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Example of vibrational excitations (E-E ground state) n=1, = 2, 2+ phonon n = 2, = 2, J = 0+, 2+, 4+ ħ 2 2ħ 2 3ħ 2 multiple = 2 phonon states, ideally degenerate 3- state?

17. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Second Quantization Hamilton operator rule for boson operators: 2-phonon state: reduced transition probability:

18. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Reduced transition probabilities 2-phonon state 3-phonon state

19. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Reduced transition probabilities 1-phonon state 2-phonon state 3-phonon state

20. MP-41 Teil 2: Physik exotischer Kerne, SS-2012 The figure shows the experimental energy levels for the nucleus 106 Pd. Find the energy of the first excited 2 + state. Level energy (vibrator model): Ground state level: First excited 2 + level (N=1, J π =2 + ): Second excited 2 + level (N=2, J π =2 + ): Energy of the second exited 2 + state Energy of the first exited 2 + state