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

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