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**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, nukleare Isomere, Symmetrien 29.6. Schalenstruktur fernab der Stabilität 6.7. Tutorium-3 Klausur

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**Production of Radioactive Ion Beams**

Fragmentation in ~20% of all cases the fragment is excited primary beam time-of-flight through the fragment separator FRS ~300 ns Isomeric states can be investigated!

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**What is a nuclear isomer?**

Nuclear Isomer – a long-lived excited nuclear state (T1/2 > 1 ns) decays by emission of a, b, g, p, fission, cluster The first one discovered by O. Hahn in Berlin in 1921 – decay of 234Pa (70 s) von Weizsacker, A. Bohr & B. Mottelson 1/t ~ Eg 2l+1 |< yf | T | yi >| K=0 J w Jmax J=0 Kmax J j2 j1 j K>0 K=0

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**Gamma-rays and energy levels**

Gamma ray: pure electromagnetic radiation change in charge distribution: electric moments change in current: magnetic moments Ji Emission of a gamma-ray removes energy angular momentum, L one unit L = 1, dipole M1, E1 two units L = 2, quadrupole M2, E2 parity: electric (-1)L magnetic (-1)L+1 coincidence Jf Selection rule: |Ji - Jf| L |Ji + Jf| and 0 0 transitions are forbidden only the lowest multipolarities are probable A Z N X

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**Gamma-ray decay electric multipole magnetic multipole dipole**

quadrupole octupole hexadecapole E1:L=1,yes E2:L=2,no E3:L=3,yes E4:L=4,no E5:L=5,yes M1:L=1,no M2:L=2,yes M3:L=3,no M4:L=4,yes M5:L=5,no

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**Lifetime & internal conversion**

relation between t,T1/2 and l Internal conversion: Energy difference between states carried away by atomic electron: Internal conversion coefficients: Important for heavy nuclei, where inner electron shells are closer to the nucleus Important for low-energy transitions

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**Partial lifetime & transition probability**

γ-ray transition probability: reduced transition probability: contains the nuclear structure information

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**Quadrupole deformation**

12+ deformed nucleus 10+ I 8+ 6+ 4+ 2+ 0+ 156Dy (from spherical shell model)

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**Hindrance factor in gamma-ray decay**

Hindrance Factor: Weisskopf (W): based on spherical shell model potential Nilsson (N): based on deformed Nilsson model potential … usually an upper limit, but … EL ML E1 M1 E2 M2 E3 M3 E4 M4 E5 M5

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**178Hf K-isomers in 178Hf w K>0 K=0**

j2 j1 j K>0 K=0 deformed axially symmetric nuclei K is approximately a good quantum number each state has not only Jp but also K 178Hf

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**K-Isomers – the building blocks**

31y K=0 J Kmax J E1 Ex~2Δp Ex~2Δn 178Hf high-K orbitals near the Fermi surface

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**Magnetic moments in 178Hf Ex~2Δp Ex~2Δn proton neutron**

g(h11/2) = g(g7/2) = g(f7/2) = g(i13/2)=-0.29 g(h11/2 x g7/2; 8-) = g(f7/2 x i13/2) = -0.36 g(8- x 8-; 16+) = → μ = g·I = 5.76 nm Ex~2Δp 7.26±0.16 nm Ex~2Δn Hyperfine Interaction 52 (1989) 79

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**K-isomers: Where to find them?**

Deformed nuclei with axially-symmetric shape Mass 180 region : Yb (Z=70) - Ir (Z=77) w K j1 j2 j High-K orbitals near the Fermi surface : 7/2[404], 9/2[514], 5/2[402] n: 7/2[514], 9/2[624], 5/2[512], 7/2[633]

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**K-selection rule and reduced hindrance**

K-isomer decay usually proceeds by minimizing ΔK Usually not this way! ν = ΔK-L – degree of K-forbiddenness – hindrance factor ΔK=16 K=16 ΔK=8 E3 K=8 ΔK=8 E1 K=0

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**K-selection rule and reduced hindrance**

K-isomer decay usually proceeds by minimizing ΔK ν = ΔK-L – degree of K-forbiddenness – hindrance factor ΔK The solid line shows the dependence of FW on ΔK for some E1 transitions i.e. FW values increase approximately by a factor of 100 per degree of K forbiddenness fν=(Fw)1/ν – reduced hindrance per degree of K-forbiddenness – gives yardstick for “goodness” of K-quantum number E1 FW

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K-isomer in 180Ta 75 keV >1015a !!! 8h The rarest natural isotope: abundance of 0.012%

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**Spin isomers 98Cd E4 ~230 ns ~170 ns**

A. Blazhev et al., Phys.Rev.C69 (2004)

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**Core excited states in 98Cd**

GDS: F.Nowacki, Nuc. Phys. A 704 (2002) 223c ESM: H. Grawe et al., NS98 AIP CP 481 (1999) 177 A. Blazhev et al., Phys.Rev.C69 (2004)

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**possible decay through electron conversion**

Shape isomers Fission isomers discovered by S.M. Polikanov Sov. Phys. JETP 15 (1962) 106 axis ratio: prompt fission delayed fission For even-even nuclei bandheads Iπ = 0+ 0+ → 0+ isomers possible decay through electron conversion spontaneous fission

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**Shape isomers 240Pu 238U(α, 2n)240fPu, Eα = 25 MeV deformation**

1. minimum minimum 5.8±0.3 MeV 5.5±0.3 MeV fission isomer t1/2=3.8 ns 238U(α, 2n)240fPu, Eα = 25 MeV conversion electrons in coincidence with delayed fission axis ratio: 2:1 H. Specht et al. Phys.Lett. B41 (1972) 43

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**Excited states in the 2. minimum of 240Pu γ-ray and electron data**

D. Gassmann et al., Phys.Lett. B497 (2001) 181

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**Manipulating isomeric lifetimes the role of electron conversion**

large α leads to shorter lifetimes of nuclear states 200mPt t1/2 = 14.3 ns Eγ = 51 keV (αtot ~ 100) for fully stripped ions !!! ? 300 ns M. Caamano et al. Eur. Phys. J. A23 (2005) 201

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**Manipulating isomeric lifetimes the role of electron conversion**

γ-spectrum after 180 ns after prompt flash and 300 ns TOF through FRS M. Caamano et al. Eur. Phys. J. A23 (2005) 201

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K quantum number K is the projection of total angular momentum of a nucleon state on the symmetry axis, and can be used to label nuclear states K is a conserved quantum number, if nucleus is axially deformed the system is non-rotating Electromagnetic transitions from a state K1 to a state K2 change K by DK = K2 - K1 Electromagnetic transitions of multipolarity l are forbidden if DK > l

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