New-generation functionals

1. New-generation functionals Jacek Dobaczewski University of Warsaw & University of Jyväskylä In collaboration with: Gillis Carlsson, Markus Kortelainen, Jussi Toivanen, and Marcin Borucki, Alessandro Pastore, Francesco Raimondi, Pekka Toivanen, and Kazuhito Mizuyama, Rayner Rodriguez-Guzman UNEDF Annual Workshop, Pack Forest (WA) June 22-25, 2009

2. Nuclear Energy Density Functional

3. How to extend the nuclear energy density functional beyond the current standard form? Quest for the spectroscopic-quality functional • Density dependence of all the coupling constants • Derivatives of higher order up to N3LO: • Products of more than two densities, for example:

4. = 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)

5. Fits of single-particle energies Before After M. Kortelainenet al., Phys. Rev. C77, 064307 (2008)

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

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

8. How to extend the nuclear energy density functional beyond the current standard form? Quest for the spectroscopic-quality functional • Density dependence of all the coupling constants • Derivatives of higher order up to N3LO: • Products of more than two densities, for example:

9. I. Density dependence of all the coupling constants M. Kortelainenet al., to be published

10. Fit to single-particle energies SLy5 RMS deviation (MeV) PRELIMINARY M. Kortelainenet al., to be published Number of parameters

11. RMS deviation of single-particle energies (MeV) M. Kortelainenet al., to be published

12. PRELIMINARY Stability of the Hartree-Fock solutions K. Mizuyamaet al., to be published

13. How to extend the nuclear energy density functional beyond the current standard form? Quest for the spectroscopic-quality functional • Density dependence of all the coupling constants • Derivatives of higher order up to N3LO: • Products of more than two densities, for example:

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

15. Energy density functional for spherical nuclei (I) B.G. Carlssonet al., C 78, 044326 (2008)

16. EXP-1: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 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

17. Galilean invariance EXP-1: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 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

18. Galilean invariance EXP-1: M.N. Schwierz, I. Wiedenhover, and A. Volya, arXiv:0709.3525 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

19. Fast RPA and QRPA + Lanczos method http://www.jyu.fi/static/fysiikka/saariselka09/ presentations/Toivanen.pdf

20. VAP symmetry restoration by the Lipkin method

21. Thank You

22. Spares

23. II. Derivatives of higher order up to N3LO B.G. Carlssonet al., C 78, 044326 (2008)

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

25. Energy density functional for spherical nuclei (II) B.G. Carlssonet al., Phys. Rev. C 78, 044326 (2008)