MP41 Teil 2 Physik exotischer Kerne 13 4

MP-41 Teil 2: Physik exotischer Kerne 13. 4. 20. 4. 27. 4. 4. 5. 11. 5. 18. 5. 25. 5. 1. 6. 8. 6. 15. 6. 22. 6. 29. 6. 6. 7. 13. 7. Einführung, Beschleuniger Schwerionenreaktionen, Synthese superschwerer Kerne (SHE) Kernspaltung und Produktion neutronenreicher Kerne Fragmentation zur Erzeugung exotischer Kerne Halo-Kerne, gebundener Betazerfall, 2 -Protonenzerfall Wechselwirkung mit Materie, Detektoren Schalenmodell Restwechselwirkung, Seniority Tutorium-1 Tutorium-2 Vibrator, Rotator, Symmetrien Schalenstruktur fernab der Stabilität Tutorium-3 Klausur 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 MP-41 Teil 2: Physik exotischer Kerne, SS-2012

Experimental single-particle energies γ-spectrum single-particle energies 1 i 13/2 1609 ke. V 2 f 7/2 896 ke. V 1 h 9/2 0 ke. V MP-41 Teil 2: Physik exotischer Kerne, SS-2012 208 Pb → 209 Bi Elab = 5 Me. V/u

Experimental single-particle energies γ-spectrum 208 Pb single-hole energies 3 p 3/2 898 ke. V 2 f 5/2 570 ke. V 3 p 1/2 0 ke. V MP-41 Teil 2: Physik exotischer Kerne, SS-2012 → 207 Pb Elab = 5 Me. V/u

Experimental single-particle energies particle states 209 Bi 2 f 7/2 1609 ke. V 896 ke. V 1 h 9/2 0 ke. V 1 i 13/2 209 Pb energy of shell closure: 207 Tl 207 Pb hole states protons neutrons MP-41 Teil 2: Physik exotischer Kerne, SS-2012

Level scheme of 210 Pb 2846 ke. V 2202 ke. V 1558 ke. V 1423 ke. V exp. single particle energies 779 ke. V 0. 0 ke. V -1304 ke. V (pairing energy) residual interaction ! M. Rejmund Z. Phys. A 359 (1997), 243 MP-41 Teil 2: Physik exotischer Kerne, SS-2012

The 100 Sn/132 Sn region, a brief background Single particle energies Z = 50 g 7/2 d 5/2 s 1/2 d 3/2 h 11/2 d 3/2 s 1/2 d 5/2 g 7/2 N=82 N=50 h 11/2 Naïve single particle filling MP-41 Teil 2: Physik exotischer Kerne, SS-2012 Me. V 2. 6 2. 2 1. 6 0. 5 0

The 100 Sn/132 Sn region, isomeric states Single particle energies h 11/2 d 3/2 s 1/2 d 5/2 g 7/2 MP-41 Teil 2: Physik exotischer Kerne, SS-2012 N=82 N=50 Me. V 2. 6 2. 2 1. 6 0. 5 0

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 Ø Enormous simplifications of shell model calculations, reduction to 2 -body matrix elements Ø Energies of single magic nuclei Ø Behaviour of g-factors g(41 Ca)= g(43 Ca)=g(45 Ca)=g(47 Ca) Ø Parabolic systematics of intra-band B(E 2) values and peaking near mid-shell Ø Preponderance of prolate shapes at beginnings of shells and of oblate shapes near shell ends 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? 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, … ( 2 j – 1) MP-41 Teil 2: Physik exotischer Kerne, SS-2012 (Why these? )

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

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

Residual interaction - pairing Ø Spectrum 210 Pb: Ø 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. Ø The δ-interaction yields a simple geometrical expression for the coupling of two particles MP-41 Teil 2: Physik exotischer Kerne, SS-2012 8 6 4 2 0

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

δ-interaction (semiclassical concept) q for θ = 00 belongs to large J, and θ = 1800 belongs to small J example h 11/22: J=0 θ=1800, J=2 θ~1590, J=4 θ~1370, J=6 θ~1140, J=8 θ~870, J=10 θ~490 MP-41 Teil 2: Physik exotischer Kerne, SS-2012

Pairing: δ-interaction 8 6 4 2 0 δ-interaction yields a simple geometrical explanation for Seniority-Isomers: DE ~ -Vo·Fr· tan (q/2) for T=1, even J energy intervals between states 0+, 2+, 4+, . . . (2 j-1)+ decrease with increasing spin. MP-41 Teil 2: Physik exotischer Kerne, SS-2012

Generalized seniority scheme Single particle energies h 11/2 d 3/2 s 1/2 d 5/2 g 7/2 N=82 N=50 Me. V 2. 6 2. 2 1. 6 0. 5 0 The 100 Sn / 132 Sn region 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 jn configuration, where n is the number of valence nucleons. energy spacing between ν=2 and ground state (ν=0, J=0): independent of n energy spacing within ν=2 states: independent of n G. Racah et al. , Phys. Rev. 61 (1942), 186 and Phys. Rev. 63 (1943), 367 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 jn configuration, where n is the number of valence nucleons. E 2 transition rates: for large n ≈ Nparticles*Nholes Sn isotopes 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 jn configuration, where n is the number of valence nucleons. ≈ Nparticles*Nholes number of nucleons between shell closures MP-41 Teil 2: Physik exotischer Kerne, SS-2012

Excitation energy Signatures near closed shells Sn isotopes N=82 isotones N=50 isotones 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 jn configuration, where n is the number of valence nucleons. E 2 transition rates that do not change seniority (ν=2): Sn isotopes MP-41 Teil 2: Physik exotischer Kerne, SS-2012