1. 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)

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

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

4. 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

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

6. 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

7. 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.

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

9. 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

10. 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

11. 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