1. 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

2. 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!

3. 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

4. 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

5. 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

6. 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

7. Partial lifetime & transition probability
γ-ray transition probability:
reduced transition probability:
contains the nuclear structure information

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

9. 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

10. 178Hf K-isomers in 178Hf w K>0 K=0j2 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

11. K-Isomers – the building blocks
31y
K=0 J
Kmax J E1
Ex~2Δp
Ex~2Δn
178Hf
high-K orbitals near the Fermi surface

12. 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

13. 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]

14. 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

15. 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

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

17. Spin isomers 98Cd E4 ~230 ns ~170 ns
A. Blazhev et al., Phys.Rev.C69 (2004)

18. 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)

19. 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

20. 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

21. Excited states in the 2. minimum of 240Pu γ-ray and electron data
D. Gassmann et al., Phys.Lett. B497 (2001) 181

22. 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

23. 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

25. 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