Shape coexistence in exotic nuclei studied by low energy coulomb excitation

1. Shape coexistence in exotic nuclei studied by low energy coulomb excitation Emmanuel Clément CERN-PH, Geneva

2. Shapes of exotic nuclei Quadrupole deformation of the nuclear ground states M. Girod, CEA Magnetic dipole and quadrupole moments are very sensitive to all types of correlations The shape of a nucleus is a fundamental property reflecting the spatial distribution of the nucleons Important benchmarks for nuclear models / theory Static moment measurement (oblate-prolate) B(E2) measurement Prolate-oblate-spherical shape in a small energy range Shape coexistence • A=70-80, N=Z • n-rich Sr&Zr • n-rich Ar  See M. Zielińska’s talk

3. Shapes coexistence in light Kr isotopes HFB+Gogny D1S M. Girod et al., To be published 74Kr Single particule level scheme (MeV) Deformation parameter  • 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. Once upon a time …. 72(6) 84(18) 79(11) 47(13) Transition strenght: ²(E0).10-3 prolate oblate 2000 & 2001 Conversion electron spectroscopy : E0 transition 6+ 6+ 6+ 2000 Coulomb excitation of 78Kr 6+ 791 2+ 2+ 858 824 768 2002 First Coulomb excitation of a radioactive 76 Kr beam @ SPIRAL +EXOGAM 4+ 918 4+ 4+ 0+ 4+ 612 1233 0+ 664 2+ 611 562 558 2003 Coulomb excitation of a radioactive 74Kr beam @ SPIRAL+EXOGAM 346 0+ 0+ 2+ 2+ 1017 2+ 770 710 671 52 455 508 456 424 0+ 0+ 0+ 0+ 2004 Lifetime measurement of 76Kr and 74Kr @ GASP 72Kr 74Kr 76Kr 78Kr • E. Bouchez • Thèse Université de Strasbourg 1 (2003) • E. Clément • Thèse Université de • Paris 11 (2006) ? • F. Becker et al. Nucl. Phys. A 770 (2006) Complete measure of reduced transition probability B(E2) and static quadrupole moment • A. Görgen, E. Clément et al. • Eur. Phys. J. A 26, 153 (2005) 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) End of 2006 Coherent analysis of all data from 76Kr and 74Kr • E.Clément, A. Görgen, W. Kortenet al. • Submitted to Phys. Rev. C In the future Low-energy Coulomb excitation of 72Kr beam development needed

5. Transition probability : describe the coupling between states E. Bouchez Thèse SPhN 2003 Spectroscopic quadrupole moment : intrinsic properties of the nucleus E. Clément Thèse SPhN 2006 E. Clément et al. Submitted to PRC Coulomb excitation analysis with GOSIA 76Kr 74Kr • 14 E2 transitional matrix elements • 18 E2 transitional matrix elements 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 • 5 E2 diagonal matrix element • 5 E2 diagonal matrix element

6. Weak mixing ≈ quantum rotor Configurations mixing (1) • For the shape-coexisting states, • prolate and oblate wave functions are highly mixed Strong mixing  perturbation of the collectivity 74Kr

7. Pure states Perturbed states Extract mixing and shape parameters from set of experimental matrix elements. 76Kr 74Kr 72Kr • Energy perturbationof 0+2 states E. Bouchez et al. Phys. Rev. Lett., 90 (2003) 0.48(1) 0.10(1) cos2θ0 0.73(1) • Full set of matrix elements : cos2θ0 0.69(4) 0.48(2) E. Clément, A. Görgen, W. Kortenel al. Submitted to PRC Configurations mixing (2) Shape coexistence in a two-state mixing model 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.

8. 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 Restricted to axial symmetry : no K=2 states Inversion of oblate and prolate states B(E2) values e2fm4 Collectivity of the prolate rotational band is correctly reproduced Interband B(E2) are under estimated Same conclusion for 76Kr

9. Shape coexistence in mean-field models (3) Gogny The agreement is remarkable for excitation energy and matrix elements GCM-HFB (Gogny-D1S) J-P. Delaroche et al. In preparation K=0 prolate rotational ground state band HFB+GCM with Gaussian overlap approximation Gogny D1S force 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 Axial and triaxial degrees of freedom • 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 Same conclusion for 76Kr

10. New area of investigation All theoretical calculations predict a sudden onset of quadrupole deformation at the neutron number N=60 Neutron rich Sr & Zr isotopes are accessible by fission of an UCx target Coulomb excitation of such nuclei can be performed at REX-ISOLDE

11. Sr and Zr n-rich isotopes around N=60 HFB Gogny D1S M. Girod CEA Bruyères-le-Châtel E [MeV] 96Sr is a transitional nucleus b • Both deformations should coexist at low energy • Shape coexistence between highly deformed and quasi-spherical shapes • Electromagnetic matrix elements are stringent test for theory

12. 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

13. Lifetime compatible with b = 0.25 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 : N=58 N=60 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)

14. Conclusion 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 • 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.

15. Collaboration E. Clément,1A. Görgen,1 W. Korten,1 E. Bouchez,1 A. Chatillon,1 Y. Le Coz,1 Ch. Theisen,1 J.N. Wilson,1M. 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,5P. Napiorkowski,5 G. Sletten,6 C. Timis7 1DAPNIA/SPhN, CEA Saclay 2Oliver Lodge Laboratory, University of Liverpool 3GSI Darmstadt 4GANIL 5Heavy Ion Laboratory, Warsaw 6NBI Copenhagen 7University of Surrey 8CEA/DIF, DPTA/SPN, CEA Bruyère-le-Châtel 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 , 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