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

1. INTC-P-216 CERN-INTC-2006-033 Shape coexistence in neutron-rich Sr isotopes:Coulomb excitation of 96Sr Emmanuel Clément CERN-PH, Geneva Andréas Görgen CEA-Saclay DAPNIA/SPhN France

2. Prolate • deformed nuclei B(E2) • oblate and prolate shapes static moment • prolate, oblate or spherical states within small energy range shape coexistence Shapes of exotic nuclei Oblate M. Girod, CEA Quadrupole deformation of the nuclear ground states

3. n-rich Sr and Zr isotopes All theoretical calculations predict a sudden onset of quadrupole deformation at the neutron number N=60 … but differ for deformation parameter and excitation energy HFB Gogny D1S M. Girod CEA Bruyères-le-Châtel E [MeV] 96Sr is a transitional nucleus • Both deformations should coexist at low energy • Shape coexistence between highly deformed and quasi-spherical shapes • Important constraints for modern nuclear structure theories : • Predicted values of b2 • E (0+2), r²(E0), B(E2), Q0 … • Mixing of wave function  GCM

4. Evidence for shape coexistence in Sr and Zr The first evidence is the energy of the 2+1 state N=58 |b| <<1 : Quasi-spherical |b| >0 : deformed state

5. Evidence for shape coexistence in Sr Level scheme established by spectroscopic experiments • Ground state band N=58 N=60 t = 7(4) ps  Nearly spherical ground state Highly deformed rotational band b≈ 0.4

6. Evidence for shape coexistence in Sr • Excited configuration N=58 N=60 r(E0)² = 53 m.u. r(E0)² = 180 m.u. r(E0)² is directly linked to deformation and mixing configuration

7. Evidence for shape coexistence in Sr N=58 N=60 The highly deformed band 0+32+34+2becomes the ground state band in 98Sr

8. The onset of deformation around N=58 is maybe more gradual Evidence for shape coexistence in Sr C. Y. Wu et al. PRC 70 (2004) W. Urban et al Nucl. Phys. A 689 (2001) Recent results : Lifetime compatible with b = 0.25 N=58 N=60

9. Evidence for shape coexistence in Sr Lifetimes compatible with b = 0.25 N=58 N=60 b≈ 0.4 The measure of transition strength and intrinsic quadrupole moments is essential to understand the complex shape coexistence in Sr isotopes  Coulomb excitation

10. The proposed Se beam development has strong synergies : • Ba beam for IS411, Krücken et al. • 78Sr D. Bandyopadhyay et al. this INTC 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) Separator 96Rb UCx Target 5.7 106 96Sr/mC Trap Molecular extraction 96Sr19F Separator n-converter 96Sr REX-beam 2.9 MeV/u 105 pps for 2mC EBIS Slow extraction Proton beam PSB 115In

11. MINIBALL SET UP • Classical set up composed by : • The 8 clusters of MINIBALL • Stripped silicon detector for particles detection • (Doppler correction and differential cross section) 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)

12. 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

13. Coulomb excitation cross section • 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)

14. 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 < 9 ps 9.7(1.4) ns 167(17) ps 7(4)ps

15. 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 Spectroscopic data limit the number of degrees of freedom < 9 ps 9.7(1.4) ns 167(17) ps 7(4)ps

16. Conclusion Coulomb excitation at low energy offers an unique opportunity to understand the complex scenario of shape coexistence in Sr isotopes • 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 Precise comparisons with HFB+GCM calculations will be undertaken (P.H Heenen, M. Bender, … ) Requested beam time : 21 Shifts of radioactive beam 3 Shifts for setup (stable beam)

17. 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

18. 96Sr – 98Sr

19. Example: differential Coulex cross section from 74Kr SPIRAL experiment: distinguish between prolate and oblate shapes ds dsRuth __ __ Pif = dWif dW Coulomb excitation and reorientation effect Reorientation effect 1er order: 2nd order: 2+ 2+ a(1) a(2) a(1) a(2) 0+ 0+ Q0 B(E2) I(4+)/I(2+)