1. The excitation and decay of nuclear isomers
2. Isomer decay rates
Phil Walker
CERN and University of Surrey, UK
● issues from yesterday
● isomer types
● isomers and the shell model
● K isomers
● K-isomer decay rates

2. Issues from yesterday 1. Parity mixing in γ decay: 180mHf 8- isomer
J.R. Stone et al., Phys. Rev. C76 (2007) at CERN-ISOLDE
2. Isomer de-excitation by Coulex:
68mCu beam (722 keV, 4 min. isomer) interacting with 120Sn
I. Stefanescu et al., Phys. Rev. Lett. 98 (2007) at CERN-ISOLDE
3. Isomer discovery by laser spectroscopy
80mGa and 80gGa seen with laser spectroscopy (with no decay required)
B. Cheal et al., Phys. Rev. C82 (2010) (R) at CERN-ISOLDE
4. Isomer discovery in a Penning trap
65mFe and 65gFe seen in a Penning trap (with no decay required)
M. Block et al., Phys. Rev. Lett. 100 (2008) at NSCL
5. Longest-lived and shortest-lived ground states
M2 + E2

3. shortest: 19Mg 4 ps, 2p decay [PRL99(2007)182501]
Issues from yesterday
1. Parity mixing in γ decay: 180mHf 8- isomer
J.R. Stone et al., Phys. Rev. C76 (2007) at CERN-ISOLDE
2. Isomer de-excitation by Coulex:
68mCu beam (722 keV, 4 min. isomer) interacting with 120Sn
I. Stefanescu et al., Phys. Rev. Lett. 98 (2007) at CERN-ISOLDE
3. Isomer discovery by laser spectroscopy
80mGa and 80gGa seen with laser spectroscopy (with no decay required)
B. Cheal et al., Phys. Rev. C82 (2010) (R) at CERN-ISOLDE
4. Isomer discovery in a Penning trap
65mFe and 65gFe seen in a Penning trap (with no decay required)
M. Block et al., Phys. Rev. Lett. 100 (2008) at NSCL
5. Longest-lived and shortest-lived ground states
M2 + E2
longest: 128Te 7.2x1024 y, 2β- decay
shortest: 19Mg 4 ps, 2p decay [PRL99(2007)182501]

4. Extreme isomers decay rates vary over at least 32 orders of magnitude
long half-life: Ta, 9–, 75 keV, >1016 y
high spin/energy*: 212Rn, 38+, 13 MeV, 12 ns
low energy: Th, 3/2+, 8 eV, ~10 h?
p rich: Ag, 21+, 5.8 MeV, 300 ms
n rich: Cd, 8+, MeV, 220 ns
high mass: Ds, 10–, 1 MeV, 6 ms
PRC 2006
PLB 2008
PRL 2007
Nature 2006
EPJA 2001
decay rates vary over at least 32 orders of magnitude
* unbound to both p and n emission

5. isomer types energy K traps K β yrast line shape traps yrast traps I
lowest energy
for a given spin I
spin I(I+1)
[Walker and Dracoulis, Physics World (Feb 1994) 39]

6. high-spin isomer types
seniority isomer
K isomer
E4 decay
E3 decay 7h
31y
93Mo
178Hf
yrast traps => long lived

7. high-spin isomer types
seniority isomer
K isomer
E4 decay
E3 decay 7h
31y
93Mo
178Hf
seniority isomer
K isomer
190ns
E1 decay 4s
E2 decay
178Hf
92Mo

8. Isomers and the shell model
Low-lying isomers => single-particle spin differences => test of shell model
(other non-isomeric single-particle states are in principle just as useful for
testing the shell model, but only if they can be identified in the first place)
This is just as true now, in regions of shell changes, as it was historically.

9. neutron h11/2 isomers (β decays)
Z = 48 isotopes
figure from: Huck et al., Phys. Rev. C40 (1989) 1384

10. neutron h11/2 isomers Z = 48 isotopes Nilsson diagram 1.8 s 3.4 h
figure from: Huck et al., Phys. Rev. C40 (1989) 1384

11. neutron (h11/2)-2 10+ isomers (γ decays)
N = 80 isotones
Valiente-Dobon et al., Phys. Rev. C69 (2004)

12. proton and neutron (g9/2)-2 8+ isomers 590 ns 480 ns 220 ns
Jungclaus et al.,
PRL99 (2007)
132501

13. 212Rn 212Rn126 Highest spin isomer I = (38), 12 ns states above 86
triple neutron core excitations
212Rn
12.5 MeV
I = (38), 12 ns
212Rn126
states above
5.4 MeV
204Hg(13C, 5n) 86
CAESAR at ANU
5.4 MeV

14. Segre chart with isomers
K isomers in
deformed
nuclei
adapted from Walker and Dracoulis, Nature 399 (1999) 35

15. 178W bands K isomers and rotational bands in a deformed nucleus
1999
K isomers and rotational bands in a deformed nucleus
178W bands
8.8 MeV
6.6 MeV
data from GAMMASPHERE
at Berkeley: 170Er(13C, 5n)
5.3 MeV
3.7 MeV
Note: 175Hf holds the record for the highest
spin/energy K isomer (see previous lecture)

16. Hf-178 new level scheme ~2Δ ~2Δ 4-quasiparticle isomer at 2.4 MeV72
106
[Smith et al., Phys. Rev. C68 (2003) (R)]

17. Single-particle energies
178Hf has N=106, Z=72, β2~0.25
Single-particle energies
106 72
[F.R. Xu et al.,
Phys. Lett. B435
(1998) 257]
Woods-Saxon potential

18. half-lives vs A multi-quasiparticle K isomers > 5ns 178Hf
• 2-, 3-qp
4-, 5-qp
6-, 7-qp
8-, 9-qp
excludes 2-qp isomers in odd-odd nuclei
Walker, AIP-CP819 (2006) 16

19. K isomers - structure deformed shell model - energies
- transition rates?

20. K-forbidden γ-ray transitions
collective
I=R=8
degree of forbiddenness, ν = ΔK – λ
λ=1 transition is 7-fold forbidden
(ν = 7)
symmetry
I=K=8
axis
non-collective
angular momentum has both magnitude and direction!

21. transition-rate hindrance factors
Weisskopf hindrance
degree of K forbiddenness
reduced hindrance
(hindrance per degree of
K forbiddenness)
contains the physics

22. Weisskopf transition rates

23. partial γ-ray half-life: T1/2
level
isomer
other
branches
100-x-y %
γ-ray branch
x %
electron
branch
y % γ
T1/2 = T1/ /x
level

24. 178Hf Hf-178 new level scheme 72 4-quasiparticle isomer M4 E3 E5 E1
0.005% M4 E3 E5
495-keV gate E1
2-quasiparticle isomer
178Hf M2 72
data from the 8π spectrometer at TRIUMF
[Smith et al., Phys. Rev. C68 (2003) (R)]

25. ↑
Hf-178 hindrances
178Hf
K=8
K=16
E1 M2 E3 M4 E5 ↑

26. Löbner systematics Löbner, Phys. Lett. B26 (1968) 369
Löbner, Phys. Lett. B26 (1968) 369

27. Löbner systematics from the gradients:
for each additional degree of K forbiddenness,
the hindrance increases by a factor of ~100
Löbner, Phys. Lett. B26 (1968) 369

28. 2- and 3-qp E2 reduced hindrances
lower fν => more K mixing
(Coriolis and/or γ deformation)
Walker, J. Phys. G16 (1990) L233
Dracoulis et al., Phys. Rev. C71 (2005)

29. 2- and 3-qp E2 reduced hindrances
increasing deformation
lower fν => more K mixing
(Coriolis and/or γ deformation)
NpNn: product of valence
nucleon numbers, e.g. 174Yb (+)
has Z=70, Np=12; N=104, Nn=22
=> NpNn=264
Walker, J. Phys. G16 (1990) L233

30. 2- and 3-qp E2 reduced hindrances
171Tm
Walker et al.
Phys. Rev. C79
(2009)
increasing deformation
NpNn: product of valence
nucleon numbers, e.g. 174Yb (+)
has Z=70, Np=12; N=104, Nn=22
=> NpNn=264

31. 171Tm 1.7 μs 171Tm isomer ΔE = 11 keV (V=12 eV) Walker et al.
Phys. Rev. C79
(2009)

32. 171Tm 1.7 μs 171Tm isomer chance near-degeneracy of two 19/2+ levels
ΔE = 11 keV (V=12 eV)
171Tm isomer
chance near-degeneracy of two 19/2+ levels
Walker et al.
Phys. Rev. C79
(2009)

33. K-mixing mechanisms ￭ chance near-degeneragies – hard to predict!
￭ Coriolis mixing (rotational – orientation change)
￭ γ tunnelling (vibrational – shape change)
￭ level density (thermal – statistical) K R

34. K-mixing mechanisms ￭ chance near-degeneragies – hard to predict!
￭ Coriolis mixing (rotational – orientation change)
￭ γ tunnelling (vibrational – shape change)
￭ level density (thermal – statistical)
larger deformation (NpNn) => less Coriolis mixing K R

35. f(nu) vs E(K)-E(R)/0.85 4-,5-,7-,9-qp isomers A~180 region
level-density
dependence
E2 and E3 transitions
179Ta (49/2) [Kondev]
Walker et al.,
Phys. Lett.
B408 (1997) 42;
Acta Phys. Pol.
36 (2005) 1055
174Yb (14)
[Dracoulis]
175Hf (57/2)
[Kondev]
increasing level density
(+Δ= 0.9 for odd-mass)

36. Where next?

37. Where next? - need for quantitative theory
- compare with other mass regions
- make and test predictions for exotic nuclei

38. 2-qp E2 reduced hindrances even-even nuclides, Kπ = 6+, 8+, 10+ isomers
244Cm
162Dy: Swan et al.,
Phys. Rev. C83
(2011)
190W: Lane et al.,
Phys. Rev C82
(2010) (R) ● ●
134Ce
increasing deformation
fig. updated from
Walker, Nucl. Phys.
A834 (2010) 22c

39. 170Dy: doubly mid-shell 170Dy ? E2 transitions Kπ = 6+ isomers 172Er ?
P.H. Regan et al.,
Phys. Rev. C65
(2002)
A.K. Rath et al.,
Phys. Rev. C68
(2003)
E2 transitions
Kπ = 6+ isomers
172Er ?
174Yb
predictions

40. K-forbidden γ-ray transitions
Summary
K-forbidden γ-ray transitions
fν dependence: NpNn (E2 transitions, 2-qp)
Coriolis effects
γ tunnelling
level-density (multi-qp)
chance near-degeneracy
theory needed, but predictions possible
n-rich predictions – long-lived isomers

41. K-forbidden γ-ray transitions
Summary
K-forbidden γ-ray transitions
fν dependence: NpNn (E2 transitions, 2-qp)
Coriolis effects
γ tunnelling
level-density (multi-qp)
chance near-degeneracy
theory needed, but predictions possible
n-rich predictions – long-lived isomers
Other decay modes (p, n, α, fission): tomorrow’s lecture/seminar

42. “But you’ve no idea what a difference it makes,
mixing it with other things”
Lewis Carroll, Through the Looking Glass
(Macmillan and Co., London, 1872)

43. γ tunnelling γ = 0o γ = -60o γ = -120o potential energy surface
prolate
γ = -60o
oblate
Narimatsu et al.,
Nucl. Phys. A601
(1996) 69
γ = -120o

44. tunnelling 174Yb (K=6) E2 γ-tunnelling description of K-isomer decay
A~180 region
174Yb (K=6)
see Dracoulis et al.
Phys. Rev. C71
(2005)
isomer→gsb
E2 transitions
Chowdhury et al.,
Nucl. Phys. A485
(1988) 136