Measurements of shape co-existence in 182,184Hg using Coulomb excitation CERN-ISOLDE (J. Cederkäll, P. Delahaye, D. Voulot, L.Fraile, F.Wenander) CCLRC Daresbury Laboratory (B. Gomez, J. Simpson) University of Edinburgh (T. Davinson, P. Woods) University of Göttingen (K.-P. Lieb) University of Jyväskylä (P.T. Greenlees, P. Jones, R. Julin, S. Juutinen) KU Leuven (M Huyse, O. Ivanov, I. Stefanescu, J. Van de Walle and P. Van Duppen) University of Liverpool (P.A. Butler, I. Darby, T. Grahn, R.-D. Herzberg, A. Hurst, G.D. Jones, D.T. Joss, R.D. Page, E.S. Paul, J. Pakarinen, A. Petts) University of Lund (A. Ekstrom, C. Fahlander) TU-München ( T. Behrens, V. Bildstein, T. Fästermann, R. Gernhäuser, Th. Kröll, R. Krücken, M. Mahgoub, P. Maierbeck) University of Oslo (M. Guttormsen, A.-C. Larsen, S. Siem, N. U. H. Syed) CEA-Saclay (E. Clement, C. Dossat, A. Goergen, W. Korten, J. Ljungvall, Ch. Theisen, M. Zielinska ) University of Sofia (G. Rainovski) HIL University of Warsaw (T. Czosnyka, J. Iwanicki, P. Napiorkowski, J. Srebrny, K. Wrzosek) University of York (D.G. Jenkins, B.S Nara Singh, N.S. Pattabiraman, R. Wadsworth)

Systematics of Hg isotopes From Julin et al. J Phys G 27(2001)R109

Decay Schemes a decay 4p-6h prolate b~ +0.25 2 hole oblate b~ -0.15 t measured

Old theory and isotope shifts Hg isotopes Faessler et al. (1972) Quentin et al. (1973) Nilsson et al. (1974) 182Hg has prolate shape Frauendorf et al. (1975) Bengtsson et al. (1981) 182Hg has weak oblate shape Ulm et al. Z. Phys. A 325(1986)247

Recent theory Nazarewicz et al. PLB305 (1993)195 182,184Hg oblate Yoshida and Takigawa PRC55 (1997)1255 Moreno et al. PRC73 (2006) 054302

Experimental Dilemmas Band-mixing analysis leads to the conclusion that there is little mixing (< 4%) between the bandheads Wauters J et al. Z. Phys. A 345 (1993) 21, Phys. Rev. C 50 (1994) 2768 Analysis if the  hindrance factor data suggests a mixing of ~20% Wauters J et al. Analysis of the E0 strength in 184Hg gives a mixing of 0.5% Heyde K and Meyer RA Phys. Rev. C 37 (1988) 2170 Observed branching ratios for E2 decays in 184Hg is best fitted if the sign of the deformation of the two bands is the same Guttormsen M Phys. Lett. 105B (1981) 99

Advantages of Coulex Coulex will preferentially excite states strongly coupled to the ground state so the oblate excited states will be readily observed and identified Low energy Coulex will measure the sign of the diagonal quadrupole matrix element and hence distinguish between prolate and oblate excitation (Hurst et al, 70Se REX measurement submitted to PRL) The degree of mixing between the oblate and prolate structures is determined directly from the transition matrix elements.

Calculated yields transition transition energy (keV) matrix element trans./diag. (eb) -ray yields 2+1-0+1 oblate 352 -1.32/1.57 57800 2+1-0+1 prolate 1.32/-1.57 45800 4+2-2+1 oblate 578 -2.13/2.02 1360 2+2-0+1 prolate 549 0.13/-1.57 200 100 hours of 5 x 104 ions/s

Request Has been demonstrated that 238U can be charge bred to A/q =4.6 with efficiency of ~ 4% Require 5 x 104 accelerated ions/s 3 shifts to test isobaric purity 3 shifts to set-up REX 6 shifts for 184Hg run 12 shifts for 182Hg run

P2+  <0||E2||2+>2 . [1 - <2+||E2’||2+> f()] Reorientation effect P2+  <0||E2||2+>2 . [1 - <2+||E2’||2+> f()] where  ~ E/(Ebeam)3/2 In our experiment P2+ changes by nearly factor of 2 if <2+||E2’||2+> changes sign

Results: 70Se b2 ~ 0.3 PROLATE OBLATE Value from t measurement Heese et al. 1986 PROLATE OBLATE Reproduce measured yield of 2-0 b2 ~ 0.3