Shape coexistence in exotic nuclei studied by low energy coulomb excitation

Emmanuel ClémentCERN-PH, Geneva

M. Girod, CEA

Quadrupole deformation of the nuclear ground states

A=70-80, N=Z

Shapes of exotic nuclei

Static moment measurement (oblate-prolate)

The shape of a nucleus is a fundamental property reflecting the spatial distribution of the nucleonsMagnetic dipole and quadrupole moments are very sensitive to all types of correlations

Important benchmarks for nuclear models / theory

B(E2) measurement

Shape coexistence

Prolate-oblate-spherical shape in a small energy range

n-rich Sr&Zr

n-rich Ar See M. Zielińska’s talk

74Kr

HF

B+

Go

gn

y D

1S

M.

Giro

d e

t a

l.,

To

be

pu

blis

he

d

Deformation parameter

Sin

gle

par

ticu

le l

evel

sch

eme

(MeV

)

Important constraints for modern nuclear structure theories : Predicted values of 2

E (0+2), ²(E0), B(E2), Q0 …

Mixing of wave function GCM

Shapes coexistence in light Kr isotopes

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

72(6) 84(18) 79(11) 47(13)Transition strenght : ²(E0).10-3

E. Bouchez et al. Phys. Rev. Lett., 90 (2003)F. Becker et al., Eur. Phys. J. A 4 (1999)A. Giannatiempo et al., Phys. Rev. C 52

(1995)

2+

1233

2+

918

2000 & 2001 Conversion electron spectroscopy : E0 transition

E. BouchezThèse Université de Strasbourg 1 (2003)

2002 First Coulomb excitation of a radioactive 76 Kr beam @ SPIRAL +EXOGAM

End of 2006 Coherent analysis of all data from 76Kr and 74Kr

2003 Coulomb excitation of a radioactive 74Kr beam @ SPIRAL+EXOGAM

E. ClémentThèse Université de Paris 11 (2006)

Once upon a time ….

F. Becker et al. Nucl. Phys. A 770 (2006)

2000 Coulomb excitation of 78Kr

Complete measure of reduced transition probability B(E2) and static quadrupole moment

E. Clément, A. Görgen, W. Korten et al.Submitted to Phys. Rev. C

2004 Lifetime measurement of 76Kr and 74Kr @ GASP

A. Görgen, E. Clément et al. Eur. Phys. J. A 26, 153 (2005)

In the future Low-energy Coulomb excitation of 72Kr beam development needed

?

14 E2 transitional matrix elements

5 E2 diagonal matrix element 5 E2 diagonal matrix element

18 E2 transitional matrix elements

Transition probability : describe the coupling between states

Spectroscopic quadrupole moment : intrinsic properties of the nucleus

74Kr76Kr

In 74Kr and 76Kr, a prolate ground state coexists with an oblate excited configuration

First direct experimental proof of the shape coexistence in light Kr isotopes

Coulomb excitation analysis with GOSIA

E. Bouchez Thèse SPhN 2003

E. Clément et al. Submitted to PRC

E. Clément Thèse SPhN 2006

For the shape-coexisting states, prolate and oblate wave functions are highly mixed

Weak mixing ≈ quantum rotor

Strong mixing perturbation of the collectivity74Kr

Configurations mixing (1)

Shape coexistence in a two-state mixing model

Configurations mixing (2)

Perturbed statesPure states

Extract mixing and shape parameters from set of experimental matrix elements.

Full set of matrix elements :E. Clément, A. Görgen, W. Korten el al. Submitted to PRC

0.69(4) cos2θ0 0.48(2)

E. Bouchez et al. Phys. Rev. Lett., 90 (2003)

Energy perturbation of 0+2 states

cos2θ0

76Kr 74Kr 72Kr

0.73(1) 0.48(1) 0.10(1)

Model describes mixing of 0+ states well, but ambiguities remain for higher-lying states. Two-band mixing of prolate and oblate configurations is too simple.

Restricted to axial symmetry : no K=2 states

B(E2) values e2fm4

Shape coexistence in mean-field models (2) Skyrme

GCM-HFB (SLy6) M. Bender, P. Bonche et P.H. Heenen, Phys. Rev. C 74, 024312 (2006)

HFB+GCM method Skyrme SLy6 force density dependent pairing interaction

Inversion of oblate and prolate states

Collectivity of the prolate rotational band is correctly reproduced

Interband B(E2) are under estimated Same conclusion for 76Kr

Shape coexistence in mean-field models (3) Gogny

GCM-HFB (Gogny-D1S)J-P. Delaroche et al. In preparation

Axial and triaxial degrees of freedom

HFB+GCM with Gaussian overlap approximationGogny D1S force

Same conclusion for 76Kr

The agreement is remarkable for excitation energy and matrix elements

GCM is a good approach to treat shape coexistence

main differences between the two ‘beyond mean field’ calculations: Skyrme Gogny axial triaxial

• It is important to include the triaxial degree of freedom to describe shape coexistence in light krypton isotopes

K=0 prolate rotational ground state band

K=2 gamma vibrational band

2+3 oblate rotational state

Strong mixing of K=0 and K=2 components for 2+

3 and 2+2 states

Grouping the non-yrast states above 0+2 state in

band structures is not straightforward

Neutron rich Sr & Zr isotopes are accessible by fission of an UCx target

New area of investigation

Coulomb excitation of such nuclei can be performed at REX-ISOLDE

All theoretical calculations predict a sudden onset of quadrupole deformation at the neutron number N=60

HFB Gogny D1SM. Girod CEA Bruyères-le-Châtel

96Sr is a transitional nucleus

E [

MeV

]

Shape coexistence between highly deformed and quasi-spherical shapes

Electromagnetic matrix elements are stringent test for theory

Both deformations should coexist at low energy

Sr and Zr n-rich isotopes around N=60

N=58

N=60

The highly deformed band 0+32+

34+2 becomes the ground state band

in 98Sr

Evidence for shape coexistence in Sr

N=58

N=60

C. Y. Wu et al. PRC 70 (2004)W. Urban et al Nucl. Phys. A 689 (2001)

Recent results :

Lifetime compatible with = 0.25

The onset of deformation around N=58 is maybe more gradual

The measure of transition strength and intrinsic quadrupole moments is essential to understand the complex shape coexistence in Sr isotopes Coulomb excitation Accepted experiment at REX-ISOLDE (IS451)

Evidence for shape coexistence in Sr

Coulomb excitation at low energy offers an unique opportunity to understand the complex scenario of shape coexistence in exotic nuclei

Precise comparisons with HFB+GCM calculations are essential to understand the shape coexistence

Conclusion

• GCM is a good approach to treat shape coexistence.

• It is important to include triaxial degree of freedom.

• Data from n-rich nuclei will provide more insight into shape coexistence.

1CERN, Geneva, Switzerland 7Department of Physics, Lund University, Sweden

2DAPNIA/SPhN, CEA Saclay, France 8Department of Physics, University of Oslo, Norway

3HIL, Warsaw, Poland 9Oliver Lodge Laboratory, University of Liverpool, UK,

4IKS Leuven, Belgium 10Department of Physics, University of York, UK,

5IPN Orsay, France 11TU München, Germany

6CSNSM Orsay, France 12IKP Köln, Germany

1DAPNIA/SPhN, CEA Saclay2Oliver Lodge Laboratory, University of Liverpool3GSI Darmstadt4GANIL

E. Clément,1 A. Görgen,1 W. Korten,1 E. Bouchez,1 A. Chatillon,1 Y. Le Coz,1 Ch. Theisen,1 J.N.

Wilson,1 M. Zielinska,5,1 , J.-P. Delaroche8, M. Girod8, H. Goutte8, S. Péru8, C. Andreoiu,2 F.

Becker,3 J.M. Casandjian,4 W. Catford,9 T. Czosnyka,5 G. de France,4 J. Gerl,3 J. Iwanicki,5 P.

Napiorkowski,5 G. Sletten,6 C. Timis7

5Heavy Ion Laboratory, Warsaw6NBI Copenhagen7University of Surrey8CEA/DIF, DPTA/SPN, CEA Bruyère-le-Châtel

Collaboration

E. Clément1, A. Görgen2 , J. Cederkäll1, P. Delahaye1, L. Fraile1, F. Wenander1, J. Van de Walle4, D. Voulot1, C.Dossat2, W. Korten2, J. Ljungvall2, A. Obertelli2, Ch. Theisen2, M. Zielinska2, J. Iwanicki3, J. Kownacki3, P. Napiorkowski3, K. Wrzosek3, P. Van Duppen4, T. Cocolios4, M. Huyse4, O. Ivanov4, M. Sawicka 4, I.Stefanescu4, N. Bree4, S. Franchoo5, F. Dayras6, G. Georgiev6, A. Ekström7, M. Guttormsen8, A.C. Larsen8, S. Siem8, N.U.H. Syed8, P.A. Butler9, A. Petts9, D.G. Jenkins10, V. Bildstein11, R. Gernhäuser11, T. Kröll11, R. Krücken11, P. Reiter12, N. Warr12 ,