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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-2012 Shell structure Experimental evidence for magic numbers close to stability Maria Goeppert-Mayer J. Hans D. Jensen

3 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Experimental single-particle energies 208 Pb 209 Bi E lab = 5 MeV/u 1 h 9/2 2 f 7/2 1 i 13/ keV 896 keV 0 keV γ-spectrum single-particle energies

4 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Experimental single-particle energies 208 Pb 207 Pb E lab = 5 MeV/u γ-spectrum single-hole energies 3 p 1/2 2 f 5/2 3 p 3/2 898 keV 570 keV 0 keV

5 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Experimental single-particle energies 209 Pb 209 Bi 207 Pb 207 Tl energy of shell closure: 1 h 9/2 2 f 7/2 1 i 13/ keV 896 keV 0 keV particle states hole states protonsneutrons

6 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Level scheme of 210 Pb 0.0 keV 779 keV 1423 keV 1558 keV 2202 keV 2846 keV M. Rejmund Z.Phys. A359 (1997), keV (pairing energy) residual interaction ! exp. single particle energies

7 MP-41 Teil 2: Physik exotischer Kerne, SS-2012

8 The 100 Sn/ 132 Sn region, a brief background d 5/2 g 7/2 Naïve single particle filling s 1/2 d 3/2 h 11/2 Z = 50 N=50 g 7/2 s 1/2 d 3/2 h 11/ MeV d 5/2 Single particle energies N=82

9 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 The 100 Sn/ 132 Sn region, isomeric states N=50 g 7/2 s 1/2 d 3/2 h 11/ MeV d 5/2 Single particle energies N=82

10 MP-41 Teil 2: Physik exotischer Kerne, SS-2012

11 Shell Model with residual interactions – mostly 2-particle systems Start with 2-particle system, that is a nucleus doubly magic + 2 Consider two identical valence nucleons with j 1 and j 2 Enormous simplifications of shell model calculations, reduction to 2-body matrix elements Energies of single magic nuclei Behaviour of g-factors g( 41 Ca)= g( 43 Ca)=g( 45 Ca)=g( 47 Ca) Parabolic systematics of intra-band B(E2) values and peaking near mid-shell Preponderance of prolate shapes at beginnings of shells and of oblate shapes near shell ends

12 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Shell Model with residual interactions – mostly 2-particle systems Start with 2-particle system, that is a nucleus doubly magic + 2 Consider two identical valence nucleons with j 1 and j 2 Two questions: What total angular momenta j 1 + j 2 = J can be formed? What are the energies of states with these J values?

13 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Coupling of two angular momenta j 1 + j 2 all values from: j 1 – j 2 to j 1 + j 2 (j 1 = j 2 ) Example: j 1 = 3, j 2 = 5: J = 2, 3, 4, 5, 6, 7, 8 BUT: For j 1 = j 2 : J = 0, 2, 4, 6, … ( 2j – 1) (Why these?)

14 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 How can we know which total J values are obtained for the coupling of two identical nucleons in the same orbit with total angular momentum j? Several methods: easiest is the m-scheme.

15 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Coupling of two angular momenta

16 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Residual interaction - pairing Spectrum 210 Pb: Assume pairing interaction in a single-j shell energy eigenvalue is none-zero for the ground state; all nucleons paired (ν=0) and spin J=0. The δ-interaction yields a simple geometrical expression for the coupling of two particles

17 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Pairing: δ -interaction wave function: interaction: with and A. de-Shalit & I. Talmi: Nuclear Shell Theory, p.200

18 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Pairing: δ -interaction wave function: interaction: with and A. de-Shalit & I. Talmi: Nuclear Shell Theory, p.200

19 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 δ -interaction (semiclassical concept) forand θ = 0 0 belongs to large J, θ = belongs to small J example h 11/2 2 : J=0 θ=180 0, J=2 θ~159 0, J=4 θ~137 0, J=6 θ~114 0, J=8 θ~87 0, J=10 θ~49 0

20 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Pairing: δ -interaction δ-interaction yields a simple geometrical explanation for Seniority-Isomers: E ~ -V o ·F r · tan ( / 2 ) for T=1, even J energy intervals between states 0 +, 2 +, 4 +,...(2j-1) + decrease with increasing spin.

21 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Generalized seniority scheme d 5/2 g 7/2 Naïve single particle filling s 1/2 d 3/2 h 11/2 Z = 50 N=50 g 7/2 s 1/2 d 3/2 h 11/ MeV d 5/2 Single particle energies N=82 The 100 Sn / 132 Sn region

22 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Generalized seniority scheme N=50 g 7/2 s 1/2 d 3/2 h 11/ MeV d 5/2 Single particle energies N=82 The 100 Sn / 132 Sn region

23 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Generalized seniority scheme G. Racah et al., Phys. Rev. 61 (1942), 186 and Phys. Rev. 63 (1943), 367 Seniority quantum number ν is equal to the number of unpaired particles in the j n configuration, where n is the number of valence nucleons. energy spacing between ν=2 and ground state (ν=0, J=0): energy spacing within ν=2 states: independent of n

24 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Generalized seniority scheme Seniority quantum number ν is equal to the number of unpaired particles in the j n configuration, where n is the number of valence nucleons. E2 transition rates: for large n Sn isotopes N particles *N holes

25 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Generalized seniority scheme Seniority quantum number ν is equal to the number of unpaired particles in the j n configuration, where n is the number of valence nucleons. N particles *N holes number of nucleons between shell closures N particles *N holes

26 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Signatures near closed shells Excitation energy Sn isotopesN=82 isotones N=50 isotones

27 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Generalized seniority scheme Seniority quantum number ν is equal to the number of unpaired particles in the j n configuration, where n is the number of valence nucleons. E2 transition rates that do not change seniority (ν=2): Sn isotopes


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