1. ESNT Saclay February 2, 2006 1 Structure properties of even-even actinides at normal- and super-deformed shapes J.P. Delaroche, M. Girod, H. Goutte, J. Libert CEA Bruyères-le-Châtel & IPN Orsay

2. ESNT Saclay February 2, 2006 2 Introduction Contemporary issue: understanding the properties which govern stability of SHEs and synthesis Strategy: 1) present day: dedicated experimental and model studies of structure properties of heaviest actinides 2) Here: model studies extended to A = 226 - 262 Goal: model validations :  reliable extrapolation into the SHE mass region

3. ESNT Saclay February 2, 2006 3 Present work Microscopic model analyses of a huge amount of experimental data at ND and SD shapes. (multipole moments, spin and shape isomers, SD phonons, inner+outer barriers, moments of inertia, shape isomers decay modes) Tools: mean field and beyond mean field methods with D1S force Constrained HFB, blocking Configuration mixing (  = + levels) WKB method Playgrounds: 226-236 Th, 228-242 U, 232-246 Pu, 238-250 Cm, 238-256 Cf, 242-258 Fm, 250-262 No.

4. ESNT Saclay February 2, 2006 4 Outline I. HFB methods: constraints and 2qp blocking Multipole moments, potential energy curves and surfaces, spin isomers II. Configuration mixing (  = + levels) shape isomers, SD phonons outer and inner barriers III. Cranking HFB (Yrast bands) kinetic moments of inertia, alignments IV. WKB method  -back and fission decay modes for shape isomers V. Third potential well at ID deformation : N ~ 154 nuclei VI. Conclusion + outlook

5. ESNT Saclay February 2, 2006 5 HFB under constraints Variational principle : Where H =  i T i + 1/2  i  j V ij Vij is the nucleon-nucleon effective interaction D1S of GOGNY = Z or N = q i = (I(I+1)) 1/2 Q i is Q 20 ~ r 2 Y 20 or Q 22 ~ r 2 (Y 22 +Y 2-2 )  ] = 0 Theory

6. ESNT Saclay February 2, 2006 6 Blocking Neutron and proton 2QP excitations Trial state :  qij > =  + i  + j  q > Minimisation :  ] = 0 2QP energies : E ij 2QP = - Calculations with and without breaking time reversal symmetry

7. ESNT Saclay February 2, 2006 7 Pot. Energy, Inertia and ZPE calculated from HFB 5D GCM + GOA

8. ESNT Saclay February 2, 2006 8 WKB Method Shape isomer decays:  -back and fission half-lives (s) T(  f) = 2.87 10 -21 (1+ exp(2S ( ,f) ) / E 0 S =  L {2B s (s) [ V(q(s)) – E 0 ]} 1/2 ds E 0 = assault energy (MeV); B s (s) = collective masse; s = curvilinear coordinate

9. ESNT Saclay February 2, 2006 9 250 No

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17. ESNT Saclay February 2, 2006 17 SD ground states ?

18. ESNT Saclay February 2, 2006 18 ND SD Multipole moments

19. ESNT Saclay February 2, 2006 19 ND SD p/n multipole moments

20. ESNT Saclay February 2, 2006 20 2QP ND

21. ESNT Saclay February 2, 2006 21 2QP SD

22. ESNT Saclay February 2, 2006 22 ND spin isomers

23. ESNT Saclay February 2, 2006 23 SD spin isomers

24. ESNT Saclay February 2, 2006 24 SD collective levels

25. ESNT Saclay February 2, 2006 25 SD 0 + collective levels

26. ESNT Saclay February 2, 2006 26 Inner barriers

27. ESNT Saclay February 2, 2006 27 0 + states of Pu Isotopes : A determination of inner barrier heights

28. ESNT Saclay February 2, 2006 28 ND moments of inertia

29. ESNT Saclay February 2, 2006 29 ND moments of inertia

30. ESNT Saclay February 2, 2006 30 ND moments of inertia

31. ESNT Saclay February 2, 2006 31 ND moments of inertia

32. ESNT Saclay February 2, 2006 32 SD moments of inertia

33. ESNT Saclay February 2, 2006 33 SD moments of inertia Shape evolution with rotation 240 U

34. ESNT Saclay February 2, 2006 34 Half-lives Fission  - back

35. ESNT Saclay February 2, 2006 35 Third well at ID

36. ESNT Saclay February 2, 2006 36 Mean deformations of collective states in the  0 -  2 plane

37. ESNT Saclay February 2, 2006 37 Mean deformations of collective states in the  0 -  2 plane Localisation of ID states

38. ESNT Saclay February 2, 2006 38 ID Collective wave functions

39. ESNT Saclay February 2, 2006 39 Third well spectroscopy

40. ESNT Saclay February 2, 2006 40 B 00 Potential Band structure in the shallow ID well is governed by collective masses

41. ESNT Saclay February 2, 2006 41 Conclusion and outlook 1/2 I. Mean field and beyond mean field methods implemented with D1S force provide predictions, most of which in good overall agreement with various measurements collected over the years for actinides (including heaviest ones). Complex structure properties of N ~ 154 nuclei at triaxial inner barriers are explained. II. Items to be fixed : collective masses (beyond Inglis Beliaev formula) III.  -vibration energies: quadrupole + hexadecapole modes (?) IV. Pairing / alignment properties at high rotational frequency: effect of octupole correlations ?

42. ESNT Saclay February 2, 2006 42 Conclusion and outlook 2/2 Next: Even-odd and odd-odd heavy actinides : g.s. properties, spin isomer energies and half-lives