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IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 1
Gamma-ray spectroscopy II
Andreas Görgen
DAPNIA/SPhN, CEA Saclay
F-91191 Gif-sur-Yvette
France
agoergen@cea.fr
Lectures presented at the IoP Nuclear Physics Summer School
September 4 – 17, 2005 Chester, UK
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 2
Outline
First lecture
Properties of γ-ray transitions
Fusion-evaporation reactions
Germanium detector arrays
Coincidence technique
Nuclear deformations
Rotation of deformed nuclei
Pair alignment
Superdeformed nuclei
Hyperdeformed nuclei
Triaxiality and wobbling
Second lecture
Angular distribution
Linear polarization
Jacobi shape transition
Charged-particle detectors
Neutron detectors
Prompt proton decay
Recoil-decay tagging
Rotation and deformation alignment
Third lecture
Spectroscopy of transfermium nuclei
Conversion-electron spectroscopy
Quadrupole moments and transition rates
Recoil-distance method
Doppler shift attenuation method
Fractional Doppler shift method
Magnetic moments
Perturbed angular distribution
Magnetic Rotation
Shears Effect
Fourth lecture Fast fragmentation beams Isomer spectroscopy after fragmentation E0 transitions Shape coexistence Two-level mixing Coulomb excitation Reorientation effect ISOL technique Low-energy Coulomb excitation of 74Kr Relativistic Coulomb excitation of 58Cr Gamma-ray tracking AGATA
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Summary (I) veto
nw=0
nw=1
nw=2
0.015
0.25
0.45I-2
I
I-3I-2
I-4
1
1
1
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Angular correlation
Iiπ
Ifπ Ef
Ei
Eγ ,L,L’,δ
∑+=k
kk PAW )(cos1)( ϑϑ
Ylm(θ,ϕ)
m=+1m=0m=-1
simple example:
0+
0+
1+
30o
30o
90o
30o
90o
90o
30o
),;,(
),;,(
1221
2211
θγθγ
θγθγ
I
IRDCO =
Directional correlation from oriented states
Most transitions following fusion-evaporation reactions have stretched dipole or quadrupolecharacter.
⇒ compare experimental RDCO with values fordipole-dipole, dipole-quadrupole, quadrupole-quadrupole cascades
⇒ often sufficient for spin assignments
∆ l=1
∆ m=0
∆ l=1
∆ m=±1
∆ l=2
∆ m=±2
∆ l=2
∆ m=±1
∆ l=2
∆ m=0
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 5
Angular distribution
∑+
−=
−
−
=I
Im
m
m
mP
'2
2
2
2
2
'exp
2exp
)(
σ
σAlignment of angular momentum after fusion-evaporation reaction:
[ ]),,','(2),,',(2),,,(1
1)(),,',( 2
2 ifkifkifkikifk IILLFIILLFIILLFIIILLA δδδ
ρ +++
=
)(0)1(12)( mPkmImIIII
Im
ii
mI
iiki∑
+
−=
− −−+=ρ
The coefficients Ak depend on the multipolarity L
the mixing parameter δ the population width σ
Iiπ
Ifπ Ef
Ei
Eγ ,L,L’,δ
∑+=k
kk PAW )(cos1)( ϑϑ
σ/I is approximately constant (for a given reaction).Normalize to transition with known multipolarity, e.g. 2+→0+
−++++−=
−+
fii
i
II
ifk III
kLLkLLkILLIILLF if
'
011
')12)(12)(1'2)(12()1(),,',(
1
Ferentz-Rosenzweig coefficients
Clebsch-Gordan
Racah
P(m)
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Example: Angular distribution with EUROBALL
25o angle: ring1 + ring2 (tapered)ring 7 (clusters)
90o angle: ring4 + ring5 (clovers)
25o
All θθθθ
90o
All θθθθ
25o
90o
90o
25o
25o
25o
90o
90o
139La(
29Si,5n)
163Lu with Ebeam= 153 MeV
Average of 8 stretched E2 transitions inTSD1 and TSD2
)2590(
)2525(
)90(
)25(
×
×
W
W
W
W
σ/I = 0.25 ± 0.02
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 7
Measuring the mixing parameter δδδδ
We know σ/I and have assigned Iπ
For wobbling bands, we expect
∆I=1 E2 inter-band transitions.⇒ L=1, L’=2, large δ
W(2
5×× ××9
0)
10% M190% E2
80% M120% E2
43/2+→ 41/2+
Angular distribution cannot distinguish between the two.
⇒ measure the linear polarization to establish electric or magnetic character.
49/2+
37/2+
41/2+
45/2+
47/2+
43/2+
39/2+
35/2+
697
639
579
659
643
626
655
596
534
TSD1 TSD2
Two possible solutions
wobbling
something else
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 8
Linear polarization
linear polarization: fixed direction ofelectric field vector E
E
B k
)0()90(
)0()90(1
°=+°=
°=−°===
ζζ
ζζ
NN
NN
AP
Clover detectors asCompton polarimeters(at 90°in Euroball)horizontal vs. verticalscattering
Compton scattering is sensitive to linear polarization:Klein-Nishina formula
E
k
θ
k’
ζ
−+=
Ωζθ
ω
ω
ω
ω
ω
ωσ 22
2
22
0 cossin2'
''
2
r
d
d
Effect is largest at θ=90°
N(9
0°)
-N(0
°)
electric transitions appear positive,magnetic transitions negative
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 9
Polarization measurement in 163Lu
0.10 ± 0.03579E2
0.13 ± 0.03697
0.06 ± 0.05386
0.05 ± 0.04534
-0.11 ± 0.05349M1
0.05 ± 0.05607inter-band
0.12 ± 0.05626
0.11 ± 0.05643
0.17 ± 0.09659
0.18 ± 0.09673
Eγ )0()90(
)0()90(
°+°
°−°=
NN
NNA
49/2+
37/2+
41/2+
45/2+
47/2+
43/2+
39/2+
35/2+
697
639
579
659
643
626
655
596
534
W(2
5×× ××90)
10% M190% E2
80% M120% E2
43/2+→ 41/2+
positive
positive
⇒ electric
negative
Confirmation of the wobbling modein 163Lu through combined angular distribution and linearpolarization measurement.
S.W. Ødegård et al., Phys. Rev. Lett. 86, 5866 (2001)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 10
Jupiter: T = 9 h 50 min polar / equatorial
axis ~ 15/16
MacLaurin shapes
What happens if we spin a liquid drop ?
It becomes oblate !
MacLaurin shapeafter C. MacLaurin(1698-1746)
But what if we spin really fast ?
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Jacobi shapes
piece of moon rock from Apollo mission
The equilibrium shape changes abruptly to a very elongated triaxial shape rotating about its shortest axis.
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Carl Gustav Jacob Jacobi (1804 - 1851)discovered transition from oblate to triaxial shapesin the context of rotating, idealized, incompressiblegravitating masses in 1834.
In 1961 Beringer and Knox suggested a similartransition in the case of atomic nuclei, idealizedas incompressible, uniformly charged, liquid drops endowed with surface tension.
Liquid drop calculation
Jacobi transition for L > L1
Fission barrier vanishes for L > L2
The Jacobi shape transition in nuclei
W.D. Myers and W.J. SwiateckiActa Phys. Pol. B 32, 1033 (2001)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 13
What is the signature of a Jacobi transition in nuclei ?
sharp decrease of frequency withincreasing angular momentum (giant backbend of the moment of inertia)
frequency of collective rotation is related to the E2 γ-ray energy:
many rotational bands at high spinquasi-continuous transitions
measure the energy of the quasi-continuous ‘E2 bump’as a function of angular momentum
γω E21=h
48Ca + 50Ti @ 200 MeV48Ca + 64Ni @ 207 MeV48Ca + 96Zr @ 207 MeV48Ca + 124Sn @ 215 MeV
series of experiments with Gammasphere
as neutron rich as possible:⇒ higher fission barrier
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 14
108 Compton-suppressedHPGe detectors
Measuring angular momentum with Gammasphere
108 Ge detectors6 x 108 = 648 BGO detectors
increase in false veto signalsreduced Ge efficiency but very high granularity
K M J
K = number of hits = fold
M = γ rays emitted = multiplicity (from response function)J = initial angular momentum (from angular distribution)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 15
Incremental spectra:
Multiplicity (Kav-1) gated spectrum
subtracted from (Kav+1) spectrum
The E2 bump
K measures the angular momentumE2 bump measures rotational frequency
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 16
two modifications:
lower effective moment of inertia at low spin due to pairing
no collective rotation about axially symmetric (MacLaurin) shapes in nuclei,
instead, collective rotations are associated with (mostly) prolate shapes
→ no sharp transition caused by breaking of axial symmetry, but smooth transition
Comparison to liquid drop calculations
D. Ward et al., Phys. Rev. C 66, 024317 (2002)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 17
Charged-particle evaporation 40Ca+40Ca @ 167 MeV
80Zr79Zr1n
78Zr2n
79Y1p
77Yp2n0.18
78Ypn
78Sr2p
76Sr2p2n4.06
77Sr2pn2.95
75Srαn
77Rb3p
2.31
75Rbαp
5.35
76Rb3pn101
74Rbαpn2.49
73Rbαp2n0.01
72Rbαp3n
76Kr4p
74.2
74Krα2p20.3
75Kr4pn132
73Krα2pn
52
72Kr2α
0.37
71Kr2αn0.18
75Br5p
68.2
73Brα3p128
74Br5pn3.23
72Brα3pn38.2
71Br2αp11.4
70Br2αpn6.82
74Se6p
1.57
72Seα4p102
73Se6pn
71Seα4pn0.46
70Se2α2p
94
69Se2α2pn1.57
68Se3α
5.07
73As7p
71Asα5p2.03
72As7pn
70Asα5pn
69As2α3p35.6
68As2α3pn
67As3αp15
76Yp3n
66Ge3α2p8.3
69Geα6pn
68Ge2α4p0.37
67Ge2α4pn
64Ge4α
1.48
65Ge3α2pn
70Kr2α2n
69Br2αp2n
67Se3αn
66As3αpn
cross sections in mb
The nucleus of interest is often only weakly populatedcompared to a large background of other nuclei.
Additional sensitivity from: charged-particle detectors neutron detectors recoil detectors tagging techniques
neutrons are deeply bound, charged-particle evaporationfavored despite Coulomb barrier
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 18
Charged particle detection
∆E E
100µm 1mm
p, α
Si telescope
E
mZ
dx
dE2
∝
stopping power
∆E
E
beam
Italian Silicon Sphere ISISLaboratori Nazionali di Legnaro
30 hexagons12 pentagons
used with GASP and Euroball
Microball, Washington University St. Louis
95 CsI(Tl) Scintillatorsin 9 rings
used with Gammasphere
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 19
Neutron detection
Gammasphere with Microball and Neutron shell(Washington University, St. Louis)
Euroball with Neutron wall (Uppsala University)
can be used to select or veto neutron evaporation most powerful together with charged-particle detection used to study nuclei near N=Z line
isospin symmetry proton-neutron pairing shape coexistence astrophysical rapid-proton capture process
neutrons are separated from γ rays by time of flightand pulse shapes (zero-crossing time)
difficult to distinguish two-neutron hit from scattering
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 20
Prompt proton decay in 58Cu
D. Rudolph et al., Phys. Rev. Lett. 80, 3018 (1998)Eur. Phys. J. A 14, 137 (2002)
28Si(36Ar,αpn)58Cu gate on 1α + 1p +1n σrel = 0.3 % Gammasphere, Microball, Neutron Shell
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 21
Ionisationchamber
Recoil decay tagging
Beam
Filter
γ detectors
Recoils
Identification :
ToF, recoil energy,
characteristic decay
SiliconDSSD
∆E, T E, T
Eγ, T
ToF, ∆E-E
recoil identified
associate
with γ
α decay: Eα, T
same pixel
T ≈ T½
isotope identified
Pin diodes:electrons Planar Ge
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JUROGAM – RITU – GREAT at Jyväskylä
tim
e o
f flig
ht
[a.u
.]
energy in Si detector [a.u.]
fusion-evaporationresidues
scatteredbeam
109Ag(83Kr,3n)189Bi ; 12µb
α energy [keV]
counts
ground state
excited states
α spectrumat focal plane
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 23
Recoil-decay tagging: 189Bi spectra
α energy [keV]
counts
1/2+
9/2-
9/2-
1/2+
3/2+
189Bi
185Tl
6672
6831
71067286
185
284
454
total γ
recoilgate
α gate6672
prompt γ rays at target
13/2+357
Eγ [keV]
cou
nts
α and γ tagging:
α gate: 6672 keV; γ gate: 357 keV
T1/2=667 ms
Trecoil - Tα [s]
T1/2=880 ns
Tγ - Tα [µs]
recoil gated
α gated6672 keV
γ rays at focal plane
A. Hürstel et al.,Eur. Phys. J. A 15, 329 (2002)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 24
189Bi level schemes
1/2+
9/2-
9/2-
1/2+
3/2+
189Bi
185Tl
6672
6831
71067286
185
284
454
Eγ [keV]
cou
nts
α and γ tagging: α gate: 6672 keV; γ gate: 357 keV
9/2-
357880 ms
α gate 7266 keV
A. Hürstel et al., Eur. Phys. J. A 21, 365 (2004)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 25
Systematics of the neutron-deficient Bi isotopes
P. Nieminen et al
Phys. Rev. C 69, 064326 (2004)
9/2-
13/2+
17/2+
21/2+
25/2+
29/2+
357
420
313
375
446
189Bi
9/2-
13/2+
17/2+
21/2+
25/2+
252
198
270
343
187Bi
626
9/2-
13/2+
15/2+
17/2+
19/2+
21/2+
605
323
299
327
320
622
647
193Bi
429
318
279
325
248
597
572
9/2-
13/2+
15/2+
17/2+
19/2+
21/2+
604
191Bi
M1E2M2
A. Hürstel et al.
Eur. Phys. J. A21, 365 (2004)
strongly coupled bands deformation aligned
decoupled bands rotation aligned
large Ω small Ω
Ω Ω
Ω=3/2Ω
=13/
2Ω
=9/2 Ω
=1/2