Shape coexistence in neutron-rich Sr isotopes: Coulomb excitation of 98 Sr

1. Shape coexistence in neutron-rich Sr isotopes:Coulomb excitation of 98Sr Emmanuel Clément IN2P3/GANIL – Caen France INTC-P-216 Addendum IS451 Andréas Görgen CEA-Saclay Irfu/SPhN France

2. Evidence for shape competition around N=60 • The nuclear deformation is one of the fundamental property of a nucleus • The n-rich Sr, Zr isotopes present one of the most impressive deformation change in the nuclear chart • Experimental values like level scheme, dr², and identification of isomers are measured since decade in this nuclei but no direct measurement of the deformation in excited states was reported so far • Remain extremely challenging for theoretical model • Systematic of 2+1 state • Observation of 0+2 state • B(E2; 0+1 2+1) measurement • Quadrupole moment

3. Evidence for shape competition around N=60 40 • The 2+1 state in Zr is described predominantly by n excitation • In Sr isotopes, 2+1 might be created by p and n excitation  higher B(E2) • 0+2 state created by 2p-2h excitation across Z=40 1g7/2 ll 3s1/2 ll 1g7/2 2d5/2 ll 1g ll ll 2d5/2 50 50 0+2 1g9/2 2p1/2 40 2p • Beyond N=60, the tensor force participates to the lowering 0+2 state and to the high collectivity of 2+1 state. Same mechanism than N=28, 20 for 42Si and 32Mg 1f5/2 ll ll ll 0+1 ll ll 2p3/2 1f 28 • But in the current valence space, need higher effective charge to reproduce the known B(E2)  p and n orbital from the core or higher shells. Q0 ?? p n K. Sieja et al PRC 79, 064310 (2009)

4. Evidence for shape competition around N=60 h11/2 g9/2 from core g7/2 • 9/2+ isomer identified  ng9/2[404]  extruder neutron orbital from 78Ni core • Create the N=60 deformed gap • pg9/2 <-> nh11/2 influence ? 2d5/2 • Clear evidence for neutron orbital playing an important role in the shape transition • Established sign for extruder or intruder orbital • Search for isomer in odd neutron Sr and Zr A. Jokinen WOG workshop Leuven 2009 W. Urban, Eur. Phys. J. A 22, 241-252 (2004)

5. Shape coexistence in the mean field approach P. Möller et al Phys. Rev. Lett 103, 212501 (2009) • Large area of competing minima • Prolate, oblate or spherical states within small energy range • In Sr and Zr : possible coexistence between nearly spherical and deformed minima ? shape coexistence

6. Shape coexistence in the mean field approach HFB Gogny D1S E [MeV] Both deformations should coexist at low energy • Shape coexistence between highly deformed and quasi-spherical shapes All theoretical calculations predict an onset of quadrupole deformation at the neutron number N=60 but differ for excitation energy, collectivity and deformation • Important constraints for theories : • E (2+1), E (0+2), r²(E0), B(E2), Q0

7. Evidence for shape competition around N=60 – Experimentally N=58 N=60 t = 7(4) ps  Nearly spherical ground state Highly deformed rotational band b≈ 0.4

8. Evidence for shape competition around N=60 – Experimentally 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  gradual shape change ? N=58 N=60 The measurement of transition strength and intrinsic quadrupole moments are sensitive probe to understand the complex shape coexistence in Sr isotopes  Coulomb excitation

9. IS451 Beam production 2007 run Production Suffered of a low beam intensity (105pps in the proposal)‏ Low efficiency of the post-acceleration (low energy part ~1.9% ; linac 70%)‏ First Sr beam at REX-ISOLDE We choose the molecular extraction as 96Sr19F+ to not suffer from the Rb contamination HRS A= 115 UCx Target 96Rb ( Trap HS ) …. off‏ 7 to 1.3 105 96Sr19F+/C Separator A/Q = 4.17 Molecular extraction EBIS 96Sr23+ REX-beam 2.87 MeV/u 1 to 0.5 ~104pps PSB Proton beam 115In

10. Coulomb excitation at Miniball ~ 20 W.u (almost the same than the N=58 94Kr – D Mucher ISWK 2009) Qs < +34 efm²  b< 0.14 • 7 clusters of MINIBALL • Annular segmented silicon detector for particles detection • Coulomb excitation on 120Sn and 109Ag • Coulex normalisation possible through the target gamma line • Differential and integrated cross section • The mean deformation is null as its B(E2) is rather large  Quasi vibrator character • The large B(E2) might indicate a large contribution of the protons • Shell Model & Mean Field calculations under study • B(E2) and even more the Qs are extremely sensitive probe

11. 98Sr case : highly deformed ground state • Different situation in 98Sr • Weakness of the Z=40 gap  multi particle-hole excitation beyond Z=40 • Strong deformed gap at N=60 gap due to the ng9/2 extruder • Highly deformed prolate shape ? Value of Qs ? (test for both theoretical approach) • Low lying 0+  215 keV : Mixing of wave function high r²(E0) but almost perfect rotor • Inversion of configuration • Measurement of the Qs in the rotational ground state band • Try to populate the 2+2 state N=60

12. Experimental details Coulomb excitation cross section en [b] Yield measurements were performed on-line in 2007: Yield 2007 Low energy 2009 Low energy 3.7 10596Sr19F+/μC 1.9%  0.5 to 1 104 pps 5 to 7% 3.104 pps 1.3 10598Sr19F+/μC 0.3 104 pps 1.104 pps

13. Conclusion Coulomb excitation at low energy offers an unique opportunity to understand the complex scenario of shape change in Sr isotopes • Measurement of the diagonal matrix element in the 2+1 4+1 6+1 states • Measurement of the transitional matrix elements related to the 2+2 Highly complementary with the IS485 experiment defended by D. Mücher and collaborators Additional Requested beam time : 10 Shifts +14 remaining from 2007 21 Shifts for radioactive beam 3 Shifts for setup (stable beam)

15. From D. Mücher Isolde Workshop 2009

16. Evidence for shape competition around N=60 N. Marginean PRC 80, 021301(R) (2009)

17. Evidence for shape competition around N=60 – Experimentally But almost a perfec rotor and b(E2) ratio gives a small mixing N=58 N=60 r(E0)² = 210(31) m.u. r(E0)² = 51(5) m.u. r(E0)² is directly linked to deformation and mixing configuration

19. Ag target : no differential cross section but normalization of the first ME Sn target : Target normalization & differential cross section measurement IgSr/IgSn Area covered by the previous measurement t= 7(4) ps Coulex calculation with only 2 ME without minimization Pure prolate Diagonal ME =0 Pure oblate qcm