Shape coexistence in neutron-rich Sr isotopes:Coulomb excitation of 96Sr

Emmanuel ClémentCERN-PH, Geneva

Andréas GörgenCEA-Saclay DAPNIA/SPhN France

INTC-P-216CERN-INTC-2006-033

M. Girod, CEA

Shapes of exotic nuclei

Prolate

Oblate

Quadrupole deformation of the nuclear ground states

oblate and prolate shapes static moment prolate, oblate or spherical states within small energy range

shape coexistence

deformed nuclei B(E2)

n-rich Sr and Zr isotopes

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

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

E (0+2), ²(E0), B(E2), Q0 …

Mixing of wave function GCM

HFB Gogny D1SM. Girod CEA Bruyères-le-Châtel

… but differ for deformation parameter and excitation energy

96Sr is a transitional nucleus

Shape coexistence between highly deformed and quasi-spherical shapes

E [

MeV

]

Both deformations should coexist at low energy

Evidence for shape coexistence in Sr and Zr

>0 : deformed state <<1 : Quasi-spherical

The first evidence is the energy of the 2+1 state

N=58

Level scheme established by spectroscopic experiments

N=58

N=60

= 7(4) ps Nearly spherical ground state Highly deformed rotational band ≈ 0.4

Evidence for shape coexistence in Sr

Ground state band

(E0)² = 53 m.u.

N=58

N=60

(E0)² = 180 m.u.

Evidence for shape coexistence in Sr

Excited configuration

(E0)² is directly linked to deformation and mixing configuration

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)

Lifetime compatible with = 0.25

Evidence for shape coexistence in Sr

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

Recent results :

N=58

N=60

Lifetimes compatible with = 0.25

≈ 0.4

The measure of transition strength and intrinsic quadrupole moments is essential to understand the complex shape coexistence in Sr isotopes Coulomb excitation

Evidence for shape coexistence in Sr

Experimental details

First Sr beam at REX-ISOLDE need new development

Molecular beam has shown the efficiency of this technique in term of purity and intensity…

see 70Se case (A. Hurst et al. Isolde workshop and users meeting 2005/2006)

PSB

n-converter

UCx Target

5.7 106

96Sr/C

Molecular extraction 96Sr19F

Separator

96Rb

Trap

EBISSlow extraction

Separator

115In

96Sr REX-beam2.9 MeV/u 105 pps for 2CProton beam

• Ba beam for IS411, Krücken et al.• 78Sr D. Bandyopadhyay et al. this INTC

The proposed Se beam development has strong synergies :

MINIBALL SET UP

REX beam 120Sn

Coulomb excitation on 120Sn target :

Compromise between cinematic and coulex cross section Coulex normalisation possible through the Sn gamma line Cross section between 29.5 and 147.5 deg in center of mass

(differential cross section)

Classical set up composed by : The 8 clusters of MINIBALL Stripped silicon detector for particles detection

(Doppler correction and differential cross section)

Coulomb excitation cross section

Improve the B(E2) 0+1->2+

1: 7(4) ps

Extract the diagonal matrix element

Establish the properties of the ground state band

Establish the set of transitional matrix elements at low spins

Extract diagonal matrix elements

Understand the structure at low spin of the deformed configuration(s)

Coulomb excitation cross section

Coulomb excitation analysis : GOSIA* *D. Cline, C.Y. Wu, T. Czosnyka; Univ. of Rochester

yields as function of scattering angle: differential cross section Least squares fit of matrix elements (transitional and diagonal) Experimental spectroscopic data

Lifetimes Branching ratios

7(4)ps

167(17) ps9.7(1.4) ns

< 9 ps

Coulomb excitation analysis : GOSIA* *D. Cline, C.Y. Wu, T. Czosnyka; Univ. of Rochester

yields as function of scattering angle: differential cross section Least squares fit of matrix elements (transitional and diagonal) Experimental spectroscopic data

7(4)ps

167(17) ps9.7(1.4) ns

< 9 ps

Lifetimes Branching ratios

Spectroscopic data limit the number of degrees of freedom

Conclusion

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

Requested beam time :

Improvement of the B(E2,2+1 0+

1) value

Measure of the B(E2) related to the 0+2,3 and 2+

2,3 states

Measure of the diagonal matrix element of the 2+1 state

Measure of the diagonal matrix elements of the 2+2 and 2+

3 states

21 Shifts of radioactive beam3 Shifts for setup (stable beam)

Precise comparisons with HFB+GCM calculations will be undertaken(P.H Heenen, M. Bender, … )

Collaboration

E. Clément, J. Cederkäll, P. Delahaye, L. Fraile, F. Wenander, J. Van de Walle, D. Voulot,

PH Department, CERN, Geneva, Switzerland

A. Görgen, C. Dossat, W. Korten, J. Ljungvall, A. Obertelli, Ch. Theisen, M. Zielinska,

DAPNIA/SPhN, CEA Saclay, France

T. Czosnyka, J. Iwanicki, J. Kownacki, P. Napiorkowski, K. Wrzosek, HIL, Warsaw, Poland

P. Van Duppen, T. Cocolios, M. Huyse, O. Ivanov, M. Sawicka, I.Stefanescu, IKS Leuven, Belgium

S. Franchoo, IPN Orsay, France

F. Dayras, G. Georgiev, CSNSM Orsay, France

A. Ekström, Department of Physics, Lund University, Sweden

M. Guttormsen, A.C. Larsen, S. Siem, N.U.H. Syed, Department of Physics, University of Oslo, Norway

P.A. Butler, A. Petts, Oliver Lodge Laboratory, University of Liverpool, UK,

D.G. Jenkins, Department of Physics, University of York, UK,

V. Bildstein, R. Gernhäuser, T. Kröll, R. Krücken, TU München, Germany

P. Reiter, N. Warr , IKP Köln, Germany

96Sr – 98Sr

Coulomb excitation and reorientation effect

1er order:

B(E2)

2+

0+

a(1)

2+

0+

a(1) a(2) a(2)

2nd order: Reorientation effect

Q0

d dRuth Pif=dif d__ __

if IEIa )2()1( M

j

ijjf IEIIEIa )2()2()2( MM ifff IEIIEIa )2()2()2( MM

Example: differential Coulex cross sectionfrom 74Kr SPIRAL experiment:distinguish between prolate and oblate shapes

I(4+)/I(2+)