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1Andreas Görgen Atelier ESNT 4.-6.2.2008
Nuclear Shapes, Shape Coexistence, and Electromagnetic Moments
An Experimentalist’s Perspective on the Interaction between Experiment and Theory
Andreas Görgen
DSM / IRFU / SPhNCEA Saclay
2Andreas Görgen Atelier ESNT 4.-6.2.2008
Nuclear deformation
),()(1)( 0 YtaRtR
quadrupole octupole hexadecapole
cos20 a
sin2
12222 aa
0°
-60°-120°
spherical
oblatenon-collective
prolatecollective
oblatecollective
prolatenon-collective
=60°
IEII
IIIIeQs )2(
12
02
5
16M
spectroscopicquadrupole moment
Qs<0
Qs>0
collective non-collective
reduced transitionprobability 12
)2();2(
1
2
12
21
I
IEIIIEB
M
3Andreas Görgen Atelier ESNT 4.-6.2.2008
Coulomb excitation
Nuclear excitation by electromagnetic field acting between nuclei.
b
projectile
targetThe excitation cross section is a direct measure of the E matrix elements.
If
1st order:
iffi IEIa )2()1( M
Ii2nd order:
immffi IEIIEIa )2()2()2( MM
Ii
If
Im
iffffi IEIIEIa )2()2()2( MM
reorientation effect:
If
Ii
Mf
lifetime measurement
5)();2(1
EIIEB if
differential Coulomb excitation cross section
transition probability B(E2)
quadrupole moment Qs
44Ar + 208Pb
4Andreas Görgen Atelier ESNT 4.-6.2.2008
Shape coexistence
oblate prolate
0+ 0+2+
2+
4+
4+
6+
6+ 8+ Configuration mixing:
74Kr
oblpro2
oblpro1
0cos0sin0
0sin0cos0
M. GirodM. Bender et al., PRC 74, 024312 (2006)
electric monopole (E0) transition
)(cossin0)0(0 2obl
2pro12 EM
5Andreas Görgen Atelier ESNT 4.-6.2.2008
Systematics of the light krypton isotopes
Inversion of ground state shape for 72Kr
Coulomb excitation to determine the nuclear shapes directly
0+
2+
6+
0+
4+
710671
612
791
0+
0+
2+
4+
6+
508456
768
558
52
0+
0+
2+
4+
6+
770
424
824
611346
0+
0+
2+
4+
6+
1017
455
858
664562
72Kr 74Kr 76Kr 78Kr
prolate oblate
E. Bouchez et. al., Phys. Rev. Lett. 90, 082502 (2003)
energy of excited 0+ E0 strengths 2(E0) configuration mixing
Mixing of the ground state(two-level mixing extrapolated from distortion of rotational bands)
72 · 10-3 85 · 10-3 79 · 10-3 47 · 10-3 2(E0)
6Andreas Görgen Atelier ESNT 4.-6.2.2008
Coulomb excitation of 74Kr and 76Kr
SPIRAL beams 76Kr 5105 pps74Kr 104 pps
4.7 MeV/u
EXOGAM
Pb
[24°, 55°] [55°, 74°] [67°, 97°] [97°, 145°]
74Kr
Coulomb excitation at sub-barrier energies: purely electromagnetic (‘safe’) multi-step excitation possible differential measurement: d/d
7Andreas Görgen Atelier ESNT 4.-6.2.2008
Matrix elements
24.023.053.0
sQ
4.02.08.0
sQ
3.05.03.1
sQ
21.017.024.0
sQ
9.03.03.0
sQ
)2(
)4(
1
1
I
I
Fit matrix elements (transitional and diagonal)to reproduce experimental -ray yields (as function of ) 14 B(E2) values 5 quadrupole moments
E. Clément et al., PRC 75, 054313 (2007)
first reorientation measurement with radioactive beam
8Andreas Görgen Atelier ESNT 4.-6.2.2008
prolate oblateQs<0prolate
Qs>0oblate
experimental B(E2;) [e2fm4]
Comparison with ‘beyond-mean-field’ calculations
K=2 vibration
E. Clément et al., PRC 75, 054313 (2007)
GCM (GOA) calculationq0, q2: triaxial deformationGogny D1S
M. Girod et al.
prolate oblate
GCM calculationaxial deformationSkyrme SLy6M. Bender et al.PRC 74, 024312 (2006)
9Andreas Görgen Atelier ESNT 4.-6.2.2008
Shape transition in the light krypton isotopes
0+
2+
0+
4+
710671
612
0+
0+
2+
4+
508456
558
52
0+
0+
2+
4+
770
424
611346
0+
0+
2+
4+
1017
455
664562
72Kr 74Kr 76Kr 78Kr
prolate
oblate
Experimental(direct and indirect evidence)
2+2
2+1
TheoryGogny D1S 5D GCM (GOA):M. Girod et al.
2+2
2+1
2+2
2+1
also mixing ofK=0 and K=2states
Skyrme SLy6 GCM: M. Bender et al., PRC 74, 024312 (2006)
10Andreas Görgen Atelier ESNT 4.-6.2.2008
Configuration mixing calculations
protons neutrons
Skyrme SLy6 Gogny D1SBender et al. Girod et al.
very similar single-particle energies no big differences on the mean-field level
Difference #2: generator coordinates
axial quadrupole deformation q0 triaxial quadrupole deformation q0, q2
(exact GCM formalism) Euler angles =(1,2,3) 5-dimensional collective Hamiltonian (Gaussian overlap approximation)
Difference #1: effective interaction
excellent agreement for excitation energies, B(E2), and quadrupole moments inversion of ground-state shape from prolate in 76Kr to oblate in 72Kr reproduced assignment of prolate, oblate, and K=2 states
good agreement for in-band B(E2) and quadrupole moments wrong ordering of states: oblate ground-state shape for 72Kr 78Kr excited states dilated in energy K=2 states outside model
triaxiality seems to be the key to describe prolate-oblate shape coexistence in this region
11Andreas Görgen Atelier ESNT 4.-6.2.2008
The light Se isotopes
Coulexlifetimes J. Ljungvall
387234
367034
346834
Se
Se
Se
70Se 72Se
GCM - Gogny D1S (GOA) calculation reproduces excitation energies B(E2) values over-estimated clarifies shape coexistence and shape transitions in Se
J. Ljungvall et al., PRL in pressB(E2;) [e2fm4]
12Andreas Görgen Atelier ESNT 4.-6.2.2008
Deformation and shape coexistence in N=28 isotones
Ca 40
96.94
Ca 42
0.65
Ca 44
2.08
Ca 46
0.003
Ca 48
0.19
Ar 38
0.07
Ca 50
13.9 s
Ar 40
99.59
Ar 42
32.9 y
Ar 44
11.9 m
Ar 46
8.4 s
Ar 48
0.48 s
S 36
0.015
S 38
170 m
S 40
8.8 s
S 42
1.01 s
S 44
123 ms
S 46
50 ms
Si 34
2.77 s
Si 36
0.45 s
Si 38
>1 s
Si 40
33 ms
Si 42
13 ms
Si 44
10 ms
Mg 32
86 ms
Mg 34
20 ms
Mg 36
3.9 ms
Mg 38
>260 ns
Mg 40
1 msM. GirodBruyères-le-Châtel
44S, 42Si, 40Mg Coulomb excitation dream experiments
neutron-rich Ar isotopes from SPIRAL Coulex of 44Ar (2·105 pps) EXOGAM + DSSD on 208Pb target at 3.68 MeV/u on 109Ag target at 2.68 MeV/u differential measurement: (,Z)
20 22 24 26 28 30
20
18
16
14
12
R. Rodríguez-Guzmán et al, PRC 65, 024304 (2002)axial CGM with Gogny D1S
13Andreas Görgen Atelier ESNT 4.-6.2.2008
Coulomb excitation of 44Ar at SPIRAL / GANIL
Ag target, 35°cm70° Ag target, 70°cm130° Pb target, 30°cm130°
M. Zielińska et al.
2+
1.158
2+ 2.011
76(10)
4.6(8)
136(24)
0+
experiment B(E2;) in e2fm4
(4+) 2.746
Qs=8(3) e fm2
0+
102
156
2+
1.729
2+ 3.597
theory HFB+GCM(GOA)
0
180
4.067
Qs=+7 e fm2
Qs=9 e fm2
Qs=14 e fm2
4+ good agreement for B(E2) and Q spectrum too spread out (collective masses from Inglis-Belyaev approximation)
14Andreas Görgen Atelier ESNT 4.-6.2.2008
Conclusions and Perspectives
Shape coexistence and transitions in light Kr and Se isotopes Direct evidence through experimental quadrupole moments Consistent theoretical description: Importance of triaxiality Comparison with theory allows assigning the character of the states
Quadrupole moments and transition strengths Sensitive probe for ‘beyond-mean-field’ calculations Need to understand discrepancies for B(E2) in Se and Ex in Ar
Experimental investigation of N=Z (68Se, 72Kr) and N=28 (46Ar28, 44S28, …)
Difficult but perhaps not unfeasible Program to measure lifetimes after deep-inelastic collisions
Exogam + Vamos + Plunger: 208Pb + 64Ni in 2008 Agata Demonstrator + Prisma + Plunger: 70Zn + 208Pb LoI for 2009
Coulex of SPIRAL-2 (and HIE-ISOLDE) beams Theory to guide experimentalists, e.g. for beam development
15Andreas Görgen Atelier ESNT 4.-6.2.2008
Collaboration
CEA Saclay – DSM / IRFU / SPhN: E. Clément (Kr Coulex) J. Ljungvall (Se Lifetimes) M. Zielińska (Ar Coulex) W. Korten, A. Obertelli, Ch. TheisenA. Chatillon, E. Bouchez, A. Hürstel, Y. Le Coz
CEA Bruyères-le-Châtel – DIF / DPTA / SPN: M. Girod, J.-P. Delaroche (Theory)
GANIL experiments:Warsaw, Liverpool, GSI, GANIL, Surrey, NBI
Legnaro experiments:Köln, Padova, Legnaro, Oslo, Warsaw
ISOLDE experiments:Liverpool, York, CERN, Leuven, Köln, München, Lund, Warsaw, Edinburgh, Legnaro, Oslo, Padova, Darmstadt, Heidelberg, Manchester
Jeunots
Jeunots ?