Structure properties of even-even actinides at normal- and super-deformed shapes

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. 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. 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: 226-236Th, 228-242U, 232-246Pu, 238-250Cm, 238-256Cf, 242-258Fm, 250-262No.

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. Theory HFB under constraints Variational principle : <H- zZ -nN-iiQi-Jz>] = 0 Where H = i Ti + 1/2 ijVij Vij is the nucleon-nucleon effective interaction D1S of GOGNY <Z or N>= Z or N <Qi>= qi <Jz > = (I(I+1))1/2 Qi isQ20 ~ r2 Y20 or Q22 ~ r2 (Y22 +Y2-2)

6. Blocking Neutron and proton 2QP excitations Trial state : qij>= +i +jq> Minimisation : <qijH - zZ - nNqij>] = 0 2QP energies : Eij2QP = <qijHqij> - <qHq> Calculations with and without breaking time reversal symmetry

7. 5D GCM + GOA Pot. Energy, InertiaandZPEcalculatedfrom HFB

8. WKB Method Shape isomer decays: -back and fission half-lives (s) T(,f) = 2.87 10 -21 (1+ exp(2S(,f)) / E0 S = L {2Bs(s) [ V(q(s)) – E0]}1/2 ds E0 = assault energy (MeV); Bs(s) = collective masse; s = curvilinear coordinate

9. 250 No

17. SD ground states ?

18. ND Multipole moments SD

19. ND p/n multipole moments SD

20. 2QP ND

21. 2QP SD

22. ND spin isomers

23. SD spin isomers

24. SD collective levels

25. SD 0+ collective levels

26. Inner barriers

27. 0+ states of Pu Isotopes : A determination of inner barrier heights

28. ND moments of inertia

29. ND moments of inertia

30. ND moments of inertia

31. ND moments of inertia

32. SD moments of inertia

33. SD moments of inertia 240 U Shape evolution with rotation

34. Half-lives Fission -back

35. Third well at ID

36. Mean deformations of collective states in the 0-2plane

37. Mean deformations of collective states in the 0-2plane Localisation of ID states

38. ID Collective wave functions

39. Third well spectroscopy

40. B00 Potential Band structure in the shallow ID well is governed by collective masses

41. Conclusion and outlook 1/2 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. Conclusion and outlook 2/2 Next: Even-odd and odd-odd heavy actinides : g.s. properties, spin isomer energies and half-lives