Extended energy density functionals and ground-state correlations in nuclei

1. Extended energy density functionals and ground-state correlations in nuclei Jacek Dobaczewski University of Warsaw & University of Jyväskylä European Radioactive Ion Beam Conference. June 6-11 2010, Lamoura (France)

2. Outline • Introduction – energy and particle-number scales in nuclear physics. • Nuclear energy density functional. • Adjustment of the NLO functional (Skyrme) to the experimental single-particle energies. • N3LO energy density functional. • Fast RPA and QRPA + Arnoldi method • Negele-Vautherin density-matrix expansion • Gogny-equivalent Skyrme functional. • New UNEDF functionals. • Separable pairing.

3. Energy scales in nuclear physics G. Bertschet al., SciDAC Review 6, 42 (2007) Nuclear Structure

4. Mean-Field Theory ⇒ Density Functional Theory • Nuclear DFT • two fermi liquids • self-bound • superfluid • mean-field ⇒ one-body densities • zero-range ⇒ local densities • finite-range ⇒ gradient terms • particle-hole and pairing channels • Has been extremely successful. A broken-symmetry generalized product state does surprisingly good job for nuclei.

5. SciDAC 2 Project (USA) • Building a Universal Nuclear Energy Density Functional • Understand nuclear properties “for element formation, for properties of stars, and for present and future energy and defense applications” • Scope is all nuclei, with particular interest in reliable calculations of unstable nuclei and in reactions • Order of magnitude improvement over present capabilities • Precision calculations • Connected to the best microscopic physics • Maximum predictive power with well-quantified uncertainties • FIDIPRO Project (Finland) http://www.unedf.org/ http://www.jyu.fi/accelerator/fidipro/

6. Nuclear Energy Density Functional

7. M.V. Stoitsov, et al., Phys. Rev. C68, 054312 (2003)

8. = Fits of s.p. energies EXP: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 Singular value decomposition M. Kortelainenet al., Phys. Rev. C77, 064307 (2008)

9. Derivatives of higher order: Negele & Vautherin density matrix expansion B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008)

10. Numbers of terms in the density functional up to N3LO B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008) Eq. (28) ≡ density dependent CC Eq. (30) ≡ density independent CC

11. Energy density functional for spherical nuclei (I) B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008) Phys. Rev. C 81, 029904(E) (2010)

12. Energy density functional for spherical nuclei (II) B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008) Phys. Rev. C 81, 029904(E) (2010)

13. Program HOSPHE Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry B.G. Carlssonet al., arXiv:0912.3230

14. Program HOSPHE Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry HFODD B.G. Carlssonet al., arXiv:0912.3230 HOSPHE

15. Fits of s.p. energies – regression analysis EXP-1: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 NLO EXP-2: M.G. Porquet et al., to be published B.G. Carlssonet al., to be published • NM: • Nuclear-matter • constraints on: • saturation density • energy per particle • incompressibility • effective mass

16. Fits of s.p. energies – regression analysis EXP-1: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 N2LO EXP-2: M.G. Porquet et al., to be published B.G. Carlssonet al., to be published • NM: • Nuclear-matter • constraints on: • saturation density • energy per particle • incompressibility • effective mass (Galilean invariance)

17. Fits of s.p. energies – regression analysis EXP-1: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 N3LO EXP-2: M.G. Porquet et al., to be published B.G. Carlssonet al., to be published • NM: • Nuclear-matter • constraints on: • saturation density • energy per particle • incompressibility • effective mass (Galilean invariance)

18. Fast RPA and QRPA + Arnoldi method J. Toivanenet al., Phys. Rev. C 81, 034312 (2010)

20. Fast RPA and QRPA + Arnoldi method 0+ J. Toivanenet al., Phys. Rev. C 81, 034312 (2010) 132Sn 2+

21. QRPA timing Scaling properties • Spherical QRPA+Arnoldi scales linearly with the size of the single-particle space W. • Deformed QRPA+Arnoldi expected to scale quadratically, that is, as W2 • Standard QRPA scales quartically, that is, as W4 ! • Future plans: • Full implementation and testing of the spherical QRPA + Arnoldi method in the code HOSPHE with new-generation separable pairing interactions. Systematic calculations of multipole giant-resonance modes to be used in the EDF adjustments. • Deformed QRPA + Arnoldi method implemented in the code HFODD. Systematic calculations of b-decay strengths functions and b-delayed neutron emission probabilities to be used in the EDF adjustments.

22. Phenomenological effective interactions

23. Negele-Vautherin density-matrix expansion J. Dobaczewski, et al., J. Phys. G: 37, 075106 (2010) Based on the Negele-Vautherin density-matrix expansion, we have derived the NLO Skyrme-functional parameters corresponding to the finite-range Gogny interaction. The method has been extended to derive the coupling constants of local N3LO functionals

24. Negele-Vautherin density-matrix expansion J. Dobaczewski, et al., J. Phys. G: 37, 075106 (2010)

25. Convergence of density-matrix expansions for nuclear interactions (diect term) B.G. Calsson, J. Dobaczewski, arXiv:1003.2543

26. Convergence of density-matrix expansions for nuclear interactions (exchange term) B.G. Calsson, J. Dobaczewski, arXiv:1003.2543

27. SciDAC 2 UNEDF Project (USA) • Building a Universal Nuclear Energy Density Functional • Understand nuclear properties “for element formation, for properties of stars, and for present and future energy and defense applications” • Scope is all nuclei, with particular interest in reliable calculations of unstable nuclei and in reactions • Order of magnitude improvement over present capabilities • Precision calculations • Connected to the best microscopic physics • Maximum predictive power with well-quantified uncertainties • FIDIPRO Project (Finland) http://www.unedf.org/ http://www.jyu.fi/accelerator/fidipro/

28. UNEDF Skyrme Functionals M. Kortelainen, et al.,arXiv:1005.5145

29. UNEDF Skyrme Functionals M. Kortelainen, et al.,arXiv:1005.5145

30. P. Veselý, et al., to be published, 10th International Spring Seminar on Nuclear Physics Vietri Sul Mare, May 21-25, 2010

32. Present FiDiPro group members Jacek Dobaczewski Petr Veselý Pekka Toivanen Gillis Carlsson Alessandro Pastore Francesco Raimondi Nicolas Michel Jussi Toivanen

33. Mean-field equations

34. Fit residuals for centroids of SO partners (SkP) Before After n L n L Before After M. Kortelainenet al., to be published

35. Fit residuals for splittings of SO partners (SkP) Before After n L n L Before After M. Kortelainenet al., to be published

36. N3LO in the chiral perturbation effective field theory W.C. Haxton, Phys. Rev. C77, 034005 (2008)

37. EFT phase-shift analysis D.R. Entem and R. Machleidt, Phys.Rev. C68 (2003) 041001 np phase parameters below 300 MeV lab. energy for partial waves with J=0,1,2. The solid line is the result at N3LO. The dotted and dashed lines are the phase shifts at NLO and NNLO, respectively, as obtained by Epelbaum et al. The solid dots show the Nijmegen multi-energy np phase shift analysis and the open circles are the VPI single-energy np analysis SM99.

38. Energy density functional up to N3LO B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008)