1. M. Girod, F.Chappert, CEA Bruyères-le-Châtel Neutron Matter and Binding Energies with a New Gogny Force

2. Purpose of our study,  0 =0.16 fm -3 D1S Gogny force does not reproduce the EOS for neutron matter Fit NM with Skyrme forces: PhD E. Chabanat Sly4

3. I) The fit to Neutron Matter EOS New Gogny force: D1N II) Properties of D1N in nuclei Contents

4. I) The fit to Neutron Matter EOS New Gogny force: D1N

5. The Gogny force 14 parameters (Wi, Bi, Hi, Mi,  i ) for i=1,2; t 0, x 0,  W ls

6. 14 parameters 14 parameters 14 equations B.E. and radii: 16 O et 90 Zr G.S. properties 2 pairing matrix elements pairing properties 48 Ca: sym=  2s N -  2s P N-P asymmetry …………. 14 parameters determined parameter « sym » Neutron Matter ? Test of the interaction:  0, E 0, K, E surf, m eff, E sym ….

7. Link between the parameter sym and the Neutron Matter EOS? sym=  2s N -  2s P in 48 Ca

8. Results in neutron matter: D1S, D1N Results in nuclear matter with D1N?

9. Nuclear matter properties D1S-D1N D1SD1N  0 (fm -3 ) 0.1630.159 E 0 /A (MeV)-15.93-15.96 K (MeV)210229 E surf (MeV)20.019.3 m eff 0.700.75 E sym (MeV)32.032.9 W ls (MeV)130115 Results in nuclei with D1N?

10. II) Properties of D1N in nuclei 1) Pairing properties 2) Binding energies

11. II) Properties of D1N in nuclei 1) Pairing properties

12. Pairing properties: D1, D1S, D1N, A odd correlations Pairing gap (Satula et al.)

13. Pairing energy in Sn isotopes

14. Moment of Inertia in 244 Pu

15. II) Properties of D1N in nuclei 2) Binding energies

16. Binding Energies: Sn isotopes  E=E HFB -E exp D1S D1N Neutron Matter fit Drift of Binding Energies ?

17. Binding Energies: more precise study

18. Binding Energies: Sm isotopes  E=E HFB -E exp D1S D1N

19. Binding Energies  B=B HFB -B exp

20. Conclusion Aim: build a new Gogny force which fits Neutron Matter EOS D1N Properties in nuclei: Same pairing properties as D1S if not better (moments of inertia) The drift of B.E. with N has disappeared I) PAIRING II) BINDING ENERGIES (B.E.) Other calculations are being done: beyond mean-field D1N should be soon validated: D1S D1N

21. Acknowledgements Nuclear Structure Theory group: J.F. Berger, M.Girod B.Ducomet, H.Goutte, S.Peru, N.Pillet, V.Rotival

23. Results in neutron matter: D1S, D1N Neutron Matter EOS with Gogny forces:

24. Pairing properties Scattering lengths S=0, T=1: 18.50 fm Experimental value 13.51 fm D1 12.12 fm D1S 10.51 fm D1N Experiment: pairing force ~ bare force (Paris, AV18, ….)

25. Semi-empirical (Weiszäcker) mass formula Empirical values: a v =-15.68, a s =18.56, a c =0.717, a I =28.1 [MeV] Calculation of the coefficients ( a v,a s,a I ) with the built interaction?

26. Pairing properties Full HFB calculation Odd A: blocking approximation is used Deviation with experiment: Blocking approximation B.E. of odd nuclei under-estimated when quasi-particle- vibration coupling present Kuo et al: few hundred keV correction

27. Pairing properties Full HFB calculation Odd A: blocking approximation is used Deviation with experiment: Blocking approximation B.E. of odd nuclei under-estimated when quasi-particle-vibration coupling present Kuo et al: few hundred keV correction

28. Inertia momenta in 232 Th  1

29. Inertia momenta in 232 Th 11 11 22 22

30. Neutron Matter EOS: the variational method  non interacting WF Trial wave-function: kf  f(r ij ) f(r ij ) is varied until E var is minimum Variational procedure:

31.  f(r ij )

32. Pairing properties: D1N, A odd ~200 keV

33. Binding Energies: D1S  B=B HFB -B exp

34. Binding Energies  B=B HFB -B exp

35. Binding Energies: D1S  B=B HFB -B exp

36. Binding Energies  B=B HFB -B exp

37. Binding Energies  B=B HFB -B exp

38. Results in neutron matter: D1S, D1N Neutron Matter EOS with Gogny forces:

39. Pairing properties: D1, A odd ~300 keV Pairing gap (Satula et al.)

40. Pairing properties GS energy HFB correlations Exp. ? Beyond HFB Odd nucleus  E corr Kuo et al.D1D1SD1N  corr [keV] Few ~100~300~200 Corr. HFB GS 1 st excited states  E odd even odd  E even

41. ST sub-spaces