1. Shape coexistence in the neutron-deficient, even-even 182-188 Hg isotopes Katarzyna Wrzosek – Lipska, Nick Bree (KU Leuven)  Motivation  Experimental technique  Coulex analysis  Results  Two-state mixing calculations  Conclusions Annual Brix IAP workshop 2013

2. Shape coexistence in the light Hg isotopes Degree of mixing ? Type of deformation: weakly oblate – spherical – prolate ? → Coulomb excitation 0+0+ 0 2+2+ 352 4+4+ 0+0+ 2+2+ 4+4+ 930 335 549 613 0+0+ 0 2+2+ 4+4+ 0+0+ 2+2+ 4+4+ 375 534 653 1089 367 184 Hg 182 Hg N=104N=206 ‘spherical-weak oblate’ ‘deformed (prolate)’ 184 Hg β 2 ≈-0.15 (2h)β 2 ≈+0.25 (4p-6h)  S. Frauendorf Phys.Lett. B 55 (1975) 365  W. Nazarewicz et al. Phys.Lett.B 305 (1993) 195  M. Bender, P.-H. Heneen, P.-G. Reinhard Rev. of Mod. Phys. 75 (2003) 121  K. Heyde and J. Wood Rev. of Mod. Phys. 83 (2011) 1467 Z=82 J. Elseviers et al. PR C 84 (2011) 034307

3. Miniball θrθr EPEP DSSSD-detector (LAB: 15 0 -52 0 ) 182 Hg 2.85 MeV/u target 112 Cd 2 mg/cm 2 Coulomb excitation of 182,184,186,188 Hg @ 2.85 MeV/A θpθp IsotopeSummer 2007Summer 2008 182 Hg4.9 x 10 3 pps 184 Hg1.0 x 10 3 pps1.0 x 10 5 pps 186 Hg2.0 x 10 5 pps2.5 x 10 5 pps 188 Hg2.5 x 10 5 pps3.1 x 10 5 pps Target 112 Cd 112 Cd, 107 Ag, 120 Sn 114 Cd, 107 Ag, 120 Sn 107 Ag, 120 Sn 112 Cd 182 Hg Energy [MeV] Annular strip no. θ

4. Observed gamma ray yields Summer of 2008: 182 Hg@2.85 MeV/u on 112 Cd target 182 Hg 2 + 1 → 0 + 1 4 + 1 → 2 + 1 2 + 2 → 0 + 1 112 Cd (2 + 1 → 0 + 1 ) 0 352 335 548 613 0+10+1 2+12+1 0+20+2 2+22+2 4+14+1 the K α and K β X rays originating from mercury. in prompt coincidence with a particle Doppler broadened conversion from the observed transitions cannot explain the amount of X rays : N total = 1017(51) N conv = 167(13) N K-vacancy = 129(30) → N left = 721 (60) remaining E0 X rays attributed to the converted 2 + 2 → 2 + 1 transition and the E0 (0 + 2 → 0 + 1 ) deexcitation E0 231 (74)490 (95) Method: N.Bree 2010

5. Observed gamma ray yields Summer of 2008: 182 Hg@2.85 MeV/u on 112 Cd target 182 Hg 2 + 1 → 0 + 1 4 + 1 → 2 + 1 2 + 2 → 0 + 1 112 Cd (2 + 1 → 0 + 1 ) 0 352 335 548 613 0+10+1 2+12+1 0+20+2 2+22+2 4+14+1 mixing between different states → strongly converted 2 + 2 → 2 + 1 transitions: (E. Rapisarda,  decay studies of 182,184 Tl isotopes) 184 Hg: α CE (2 + 2 → 2 + 1 ) = 23(5) 182 Hg: α CE (2 + 2 → 2 + 1 ) = 4.2(8) E0 E2/M1 E0 GOSIA code, Q s (2 + ) in 182-188 Hg Combined analysis of the Coulex data + τ measurements RDDS measurements at Jyvaskyla and ANL (L. Gaffney, M. Hackstein, T. Grahn, A. Petts) + BR and α CE (2 + 2 → 2 + 1 ) (E. Rapisarda) 42(2) ps 37(1) ps PhD thesis of N.Bree

6. Results – E2 matrix elements 2.7(2)1.6(2) 0.60(3) -3.71(6) 1.29(-3; +4) -2.65(15) 1.25(5) -3.14(8) 5.30(44) 1.27(25) -0.89(14) -0.21(2) 1.22(-7; +10) (-0.08; +0.08) -3.5(12) 4.1(-4; +10) -2.7(2) 2.85(6) 3.05(-2;+25) 1.31(1) 2.07(8) 182 Hg 184 Hg 186 Hg 188 Hg PhD thesis of N.Bree

7. Quadrupole deformation parameters in 182-188 Hg Overall deformation ~ β ~ : Triaxiality ~ γ ~ : Quadrupole Sum Rules - relate experimental ME2’s with quadrupole deformation parameters (D. Cline, Ann Rev Nucl Part Sci 36 (1986) 683, K. Kumar, Phys. Rev. Lett. 28 (1972) 249) ~ BE2(2 + i → 0 + 1,2 ) ~ magnitudes and relative signs of,, Q sp (2 + ) A Hg in a good agreement with the Isotope Shift measurements (G. Ulm et al., Z. Phys. A 325 (1986) 247). 0+20+2 0+10+1 0+20+2 0+10+1 triaxiality

8. G.J. Lane et al., NPA 589 (1995) 129 P. J. Brussaard, P.W.M. Glaudemans 1977 |0 + 1 > = α 0 |0 + S > + β 0 |0 + D > |2 + 1 > = α 2 |2 + S > + β 2 |2 + D > 0+S0+S 2+S2+S 0+D0+D 2+D2+D |0 + 2 > = β 0 |0 + S > - α 0 |0 + D > |2 + 2 > = -β 2 |2 + S > + α 2 |2 + D > Two-state mixing model un-mixed mixed A C > 0 D < 0 B Experimental E2 matrix elements can be expressed by:  un-mixed E2 matrix elements (A,B, C, D)  mixing amplitudes (α 0, α 2, β 0, β 2 ) = 0 α J 2 + β J 2 = 1

9. Mixing amplitudes  0 + states remains un-mixed for all 182-188 Hg  2 + states: mixing is changing from 29% up to 98%  4 + states remains deformed for all 182-188 Hg Deduced from the two-band mixing calculations by fitting higher-lying levels using the variable moment of inertia (VMI) model (R. Page): 182 Hg 184 Hg 186 Hg 188 Hg

10. 182 Hg: α 2 2 = 29% 184 Hg: α 2 2 = 51% 186 Hg: α 2 2 = 90% 188 Hg: α 2 2 = 98% α 4 2 = 3% α 4 2 = 4% α 4 2 = 7% α 4 2 = 20% 4 + 1 →2 + 2 2 + 2 →0 + 2 4 + 1 →2 + 1 2 + 1 →0 + 2 2 + 2 →2 + 1 2 + 1 →0 + 2 2 + 2 →0 + 2 2 + 2 →2 + 2 4 + 1 →2 + 2 4 + 1 →2 + 1 2 + 1 →2 + 1 2 + 1 →0 + 2 4 + 1 →2 + 2 2 + 2 →2 + 2 2 + 2 →2 + 1 2 + 2 →0 + 2 4 + 1 →2 + 1 2 + 1 →2 + 1 2 + 1 →0 + 1 fitted un-mixed ME2’s: A = = 1.2 eb B = = 3.3 eb C = = 1.8 eb D = = -4.0 eb 2 + 1 →2 + 1

11. Un-mixed matrix elements: BMF ↔ VMI ↔ RDDS BMF P.-H. Heenen, M. Bender, Y. M. Yao 3.3 5.45 7.12 8.72 10.1 1.2 2.29 3.19 VMI 5.43(22) 6.29(33) 7.17(90) RDDS T. Grahn et al., PRC 80, 014324 (2009). 182 Hg ME2 [eb]

12. Conclusions  E2 matrix elements connecting low-lying 0 + 1,2, 2 + 1,2,3, 4 + 1,2 states in 182-188 Hg were determined.  Quadrupole deformation parameters of the 0 + states extracted for a first time:  0 + ground state weakly deformed (β≈0.15) and of oblate nature  0 + excited state more deformed, triaxiality not excluded  Experimental results can be interpreted within the two-state mixing model:  magnitudes and signs of E2 matrix elements reproduced for 182,186,188 Hg;  properties of the 2 + 1 state in all 182-188 Hg can be fully explained by different mixing amplitudes; continuation of the shape-coexistence studies in the n-deficient Hg isotopes @ HIE-ISOLDE → accepted proposal for 182,184 Hg Future plans:

13. KU Leuven, Belgium P. Van Duppen, M. Huyse, N. Bree, K. Wrzosek-Lipska, N. Kesteloot, L. Gaffney, H. De Witte University of Jyväskylä, Helsinki Institute of Physics, Finland J. Pakarinen, P. T. Greenlees, T. Grahn, P. Rahkila University of Liverpool, U.K. D.T. Joss, P. A. Butler, R. D. Page, G. O’Neil, P. Papadakis University of York, U.K. D.G. Jenkins, A. N. Andreyev CERN-ISOLDE, Switzerland E. Rapisarda, D. Voulot, F. Wenander University of Manchester, U.K. T. E. Cocolios, S. Freeman TU-München, Germany V. Bildstein, R. Gernhäuser, R. Krücken, K. Nowak, D. Mücher TU-Darmstadt, Germany Th. Kröll, M. Scheck, N. Pietralla University of Oslo, Norway A. Goergen, M. Guttormsen, A.C. Larsen, S. Siem CEA-Saclay, France W. Korten, M. Zielinska, M.-D. Salsac, T. Duguet, F. Dechery HIL University of Warsaw, Poland P. J. Napiorkowski, J. Srebrny, K. Hadynska-Klek, L. Prochniak University of Köln, Germany A. Blazhev, J. Jolie, N. Warr, P. Reiter, H. Duckwitz University of Ioannina, Greece N. Patronis Atlanta, U.S.A J. L. Wood U. Gent, Belgium K. Heyde Université Libre de Bruxelles, Belgium P.-H. Heenen CEN, Bordeaux-Gradignan, France M. Bender University of Huelva, Spain J.-E. Garcia Ramos GANIL, France E. Clement, B. Bastin

14. Extra slides

15. Low-energy part of the Coulomb excited level scheme of 182-188 Hg

16. E0 known BR (new decay data) unobserved transitions 184 Hg 36.3 (27) ps 30.9 (11) ps 8.9 (11) ps mean lifetimes, average values: RDDS and Rud et. al (Phys. Rev. Let. 31 (1421) 1973)  CE (2 2 +  2 1 + ) = 23 (5)

17. Experimental campaigns 2008: 2.85 Mev/A on 112 Cd target 0+0+ 2+2+ 4+4+ 0+0+ 2+2+ 4+4+ 0 367 1089 375 534 653 0+0+ 2+2+ 4+4+ 0+0+ 2+2+ 4+4+ 0 352 930 328 549 613 182 Hg 184 Hg

18. Determination of the quadrupole moment of the first excited 2 + state 2+2+ 112 Cd 182 Hg Energy [MeV] Annular strip no. Coulomb excitation of 182 Hg on 112 Cd target Coulex cross-section depends on both and 0+0+ Scanning the c.m. range by gating on different strips! DSSD Q>0 Q=0 Q<0

19. Matrix elements [eb] 182Hg184Hg186Hg188Hg 1.29 (3; 4) 1.27 (5) 1.22 (7; 10)1.31 (1) -3.71 (6) -3.14 (8) -2.7 (18)2.07 (8) 0.60 (3) -0.21 (2) (-0.08 ; +0.08) -2.65 (15) -3.5 (12) 2.3 (5; 69) 1.63 (22; 19) 1.27 (25) 4.2 (6; 13) 2.74 (23; 18) -0.89 (14) (-2.8; +1.9) 2.9 (2; 3) 5.30 (44) 4.1 (4; 10) 5.1 (2; 3) 4.9 (4) 4.9 (5; 14) -0.1 (13; 12) 1.4 (12; 18) -2.7 (22; 48)1.0 (4; 6) 1.2 (7; 12) -2.6 (20) 3.8 (8) 2.85 (6) 8.0 (16) 3.05 (17; 25) |1.1| (3) 0.9 (3)

20. Overall deformation ~ β ~ : Triaxiality ~ γ ~ : Qudrupole sum rules invariants: and Parametrization of the E2 operator

21. J. Srebrny, K. Pomorski, D. Cline et al., Nuclear Physics A 766 (2006) 25–51

22. Two-state mixing model Unperturbated: C >0 |0 + 1 > = α 0 |0 + S > + β 0 |0 + D > |0 + 2 > = β 0 |0 + S > - α 0 |0 + D > |2 + 1 > = α 2 |2 + S > + β 2 |2 + D > |2 + 2 > = -β 2 |2 + S > + α 2 |2 + D > = = = 0 Assumption: = α 0 α 2 A + β 0 β 2 B = -α 0 β 2 A + β 0 α 2 B = α 2 β 0 A - α 0 β 2 B = -β 0 β 2 A - α 0 α 2 B = α 2 β 2 (D-C) < 0 = α 2 2 C + β 2 2 D = β 2 2 C + α 2 2 D α 2 2 + β 2 2 = 1 α 0 2 + β 0 2 = 1 0+S0+S 2+S2+S 2+D2+D 0+D0+D A B D < 0 spherical deformed 0+S0+S 2+S2+S 2+D2+D 0+D0+D A C >0 B D < 0 spherical deformed |0 + 1 > = α 0 |0 + S > + β 0 |0 + D > |0 + 2 > = β 0 |0 + S > - α 0 |0 + D > |2 + 1 > = α 2 |2 + S > + β 2 |2 + D > |2 + 2 > = β 2 |2 + S > - α 2 |2 + D > = α 0 α 2 A + β 0 β 2 B = α 0 β 2 A - β 0 α 2 B = α 2 β 0 A - α 0 β 2 B = β 0 β 2 A + α 0 α 2 B = α 2 β 2 (C-D) > 0 = α 2 2 C + β 2 2 D = β 2 2 C + α 2 2 D α 2 2 + β 2 2 = 1 α 0 2 + β 0 2 = 1 Mixing IMixing II α 2 < β 2 & α 2 2 < 50%α 2 > β 2 & α 2 2 > 50%

23. α02α02 α22α22 α42α42 R.PageJ. D. Richards R.PageJ. D. Richards R.PageJ. D. Richards 182 Hg92%93%29%24.4%3%0.2% 184 Hg95%94.6%51%49%4%2.4% 186 Hg98%97%90%92%7%7.4% Mixing amplitudes 188 Hg99%98%20% deduced from the two-band mixing calculations: 1.fitting higher-lying levels following VMI model (R. Page) 2.study the fine structure in the alpha decay (J. D. Richards, PRC 56 (1997) 1389)

25. Un-mixed matrix elements: BMF vs VMI BMF P.-H. Heenen, M. Bender 3.3 5.45 7.12 8.72 10.1 1.2 2.29 3.19 VMI 6.67 7.8 rot 182 Hg ME2 [eb] 5.28 3.3 rot 1.2 1.92 2.42

26. 1.0 711 1.07 2.78 3.93 5.07 obl. 6.68 5.55 4.24 1.0 711 1.2 1.92 2.42 2.84 obl. 7.8 6.67 5.28 BMF rot. model 186 Hg

27. ME2 (0 + D →2 + D ) 182 Hg 184 Hg 186 Hgaverage BMF fit to 4 + 1 →6 + 1 3.08 eb2.95 eb2.75 eb2.93 eb BMF fit to 6 + 1 →8 + 1 3.15 eb3.05 eb2.83 eb3.01 eb τ (6 + 1 )2.54 eb2.47 eb2.15 eb2.50 eb τ (8 + 1 )2.66 eb2.42 eb1.97 eb2.35 eb ME2 (0 + S →2 + S ) 182 Hg 184 Hg 186 Hgaverage BMF fit to 4 + 1 →6 + 1 1.88 eb1.97 eb1.95 eb1.93 eb BMF fit to 6 + 1 →8 + 1 2.55 eb2.26 eb2.15 eb2.32 eb

28. HIE-ISOLDE experiment – counting rates / shift E0