Two-Body Correlations and Pairing Localization in Open Shell Nuclei

1. Two-Body Correlations and Pairing Localization in Open Shell Nuclei Nicolae Sandulescu Institute of Physics and Nuclear Engineering, Bucharest G. Bertsch INT – Seattle N. Pillet CEA- Bruyeres-le-Chatel P. Schuck IPN -Orsay Collaboration:

2. Two-particle correlations in halo nuclei: 11Li .. T. Nakamura et al, PRL96(2006)252502 K. Hagino, H.Sagawa,J.Carbonell,P.Schuk, PRL 99, 2007

3. Two-body correlations in open shell nuclei: general definitions • two-body density • two-body correlations • two-body correlations • in configuration space • two-body correlations in BCS comnmonly associtated to pair transfer amplitude describes correlations between two generic nucleons k is not the wave function of the collective Cooper pair

4. Two-Body Correlations and Pairing Localization in Open Shell Nuclei Main Issues • Pairing correlations: surface/bulk localization ? • What is the size of correlated pairs ? “In nuclei, the pairs cannot be localized within dimensions smaller than the nuclear radius R ”. (A. Bohr et B. R. Mottelson, Nuclear Structure, vol II) • Dependence of correlations on pairing tratment ? • influence of pair fluctuations • structure of pairs in BCS and in exact models • What are the effects of (strong) two-body correlations ? - enhancement of pair transfer - soft dipole/octupole modes ? next talk by Matsuo

5. θ Localization of pairing correlations in open shell nuclei • pairing tensor in coordinate representation : • HFB equations calculations with Gogny force D1S • coherence length N. Pillet, N. S, P. Schuck; PRC76, 2007

6. volume mixed surface Localization of pairing correlations: Sn isotopes N. Pillet, N. S, P. Schuck; PRC76, 2007

7. Pairing localization: Skyrme-HFB calculations Vpair =V0[1-h(r/r0)a]d(r-r’) N. S, P. Schuck, X. Vinas, PRC 71 (2005) 054303

8. Single- particle wave functions: Sn isotopes

10. Pairing field in Sn isotopes N. S, P. Schuck, X. Vinas, PRC 71 (2005) 054303

11. Pairing localization : generic features Coherence length N. Pillet, N. S, P. Schuck; PRC76, 2007

12. Coherence length in Ca and Sn isotopes N. Pillet, N.S., P. Schuck, PRC76, 2007

13. Probability distribution

14. Uncorrelated Probability Distribution

15. The Effect of Parity Mixing N. Pillet, N.S., P. Schuck, PRC76, 2007

16. Parity mixing : generic features

17. Particular case of 36Ca Comparison with 22O Importance of choosing a large configuration space, not restricted to the major shell Results and analysis for 3 isotopic chains

18. Parity mixing in deformed nuclei

19. http://www-phynu.cea.fr

20. Pairing localization in 152Sm Preliminary results N. Pillet, N.S, P. Schuck, J.F. Berger, in preparation

21. Pairing localization in 152Sm Preliminary results

22. How much depend the correlations on pairing treatment ?

23. Correlation Energies in Sm isotopes one can reduce the error by restricting to a smaller space ! G. Dussel, S. Pittel, J. Dukelsky, P. Sariguren, PRC 2007

24. Solutions of pairing Hamiltonian • BCS (identical collective pairs) • PBCS • Exact solution (non-identical collective pairs) R. W. Richardson and N. Sherman, Nucl. Phys. 52 (1964)221

25. Correlation Energies in BCS and PBCS BCS PBCS N. S , G. Bertsch, arXiv 2008

26. Two-body correlations in configuration space Npair =8 weak coupling intermediate coupling strong coupling N. S , G. Bertsch, arXiv 2008

27. Pair transfer amplitudes in BCS and PBCS weak coupling intermediate coupling strong coupling Npair =8 g=0.42 g=0.32 g=0.87

28. Two-body correlations and pair wave function pairing tensor pair wave function BCS, PBCS exact model Npair =8 measure of correlations N. S , G. Bertsch, arXiv 2008

29. L. Cooper, 2007 (Meeting on 50 years of BCS)

30. Probability distribution inside nuclei for 120Sn N. Pillet, N.S., P. Schuck, PRC76, 2007 BCS-BEC transition in the surface of nuclei ?

31. Bosonic character of two-body correlations two-body operator : testing the bosonic character I) analyse the average II) analyse the action on PBCS state: bosonic behaviour: N=8, g=0.87

32. Summary and Conclusions • localization properties (surface/volume) depends essentially on • s.p.states closer to chemical potential and less on pairing force • small coherence length (2-3 fm) in the nuclear surface • two-body correlations associated to the pair wave function • look similar in BCS and PBCS • pair transfer amplitudes are underestimated by BCS • in the exact model all pairs are different and their collectivity • depends on the position of their energies with respect to the • chemical potential proper description for loosely bound nuclei !?

33. Thanks for your attention !

35. BCS-to-BEC crossover from the exact BCS solution G. Ortiz, J. Dukelsky, Phys Rev A72(2005)043611

36. Wave function of Cooper pairs: BCS L. Cooper, 2007 (Meeting on 50 years of BCS)

37. “Wave function of Cooper pairs”: Legget A. Legget, 2007 (Meeting on 50 years of BCS)

38. Condensation Fraction in Sm Isotopes G. Dussel, S. Pittel, J. Dukelsky, P. Sariguren, PRC 2007

39. Pairing Gaps N. S , G. Bertsch, arXiv 2008

40. Uncorrelated Probability Distribution

41. Particular case of 36Ca Comparison with 22O Importance of choosing a large configuration space, not restricted to the major shell Results and analysis for 3 isotopic chains

42. Condensation Fraction for N=8 pairs