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New-generation functionals

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,

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New-generation functionals

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  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)

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