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MP-41 Teil 2: Physik exotischer Kerne, SS-2012 MP-41 Teil 2: Physik exotischer Kerne 13.4.Einführung, Beschleuniger 20.4.Schwerionenreaktionen, Synthese.

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Presentation on theme: "MP-41 Teil 2: Physik exotischer Kerne, SS-2012 MP-41 Teil 2: Physik exotischer Kerne 13.4.Einführung, Beschleuniger 20.4.Schwerionenreaktionen, Synthese."— Presentation transcript:

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 Tutorium Vibrator, Rotator, Symmetrien 29.6.Schalenstruktur fernab der Stabilität 6.7.Tutorium Klausur

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

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

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 = MeV a S = MeV a C = MeV a A = MeV a P = 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


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