1. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 1 ISTANBUL-06 Kazimierz Dolny, Sept. 25, 2008 Technical University Munich Peter Ring Covariant density functional theory for masses and fission barriers

2. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 2 Content Calculation of masses Relativistic density functional theory Conclusions Fission barriers

3. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 3 Slater determinant density matrix Mean field:Eigenfunctions:Interaction: Density functional theory in nuclei D.Brink D.Vautherin Skyrme Extensions: Pairing correlations, Covariance Relativistic Hartree Bogoliubov (RHB)

4. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 4 The Walecka model is used as a vehicle to implement a covariant density functional theory through an effective Lagrangian. (J ,T)=(0 +,0) (J ,T)=(1 -,0)(J ,T)=(1 -,1) Sigma-meson: attractive scalar field Omega-meson: short-range repulsive Rho-meson: isovector field Covariant density functional theory

5. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 5 Density dependence Three relativistic models: Meson exchange with non-linear meson couplings: NL1,NL3,TM1,.. DD-ME1,DD-ME2 Boguta and Bodmer, NPA. 431, 3408 (1977) Lalazissis, Koenig, Ring, PRC 55. 540 (1997) R.Brockmann and H.Toki, PRL 68, 3408 (1992) Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (2005) Manakos and Mannel, Z.Phys. 330, 223 (1988) Buervenich, Madland, Maruhn, Reinhard, PRC 65, 44308 (2002) PC-F1,…. Meson exchange with density dependent coupling constants: Point-coupling models with density dependent coupling constants: g(ρ)g(ρ) G(ρ)G(ρ) 8 parameters

6. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 6 Conclusions 1 ------- Conclusions: Nuclear matter data (from masses) - binding energy E/A - saturation density ρ 0 - surface energy a s - symmetry energy a 4 (- compressibility ???) Specific finite nuclei: spherical - binding energies, - radii - spherical closed shell or single closed shell - no single particle energies! How to avoid shell effects? - fit to deformed nuclei (at the beginning) - fit to fission barriers (future) Ab initio ? (far future) - fit to exact calculations for nuclear matter - fit to exact calculations for half infinite nuclear matter - problem of accuracy Stragegies to determine the parameters:

7. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 7 parameterizatio n DD-ME: parameterization of denstiy dependence PHENOMENOLOGICAL: saturation density MICROSCOPIC: Dirac-Brueckner calculations g()g() g()g() g()g() Typel and Wolter, NPA 656, 331 (1999) Niksic, Vretenar, Finelli, Ring, PRC 66, 024306 (2002) Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (05) 4 parameters for density dependence

8. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 8 number of param. How many parameters ? symmetric nuclear matter: E/A, ρ 0 finite nuclei (N=Z): E/A, radii spinorbit for free Coulomb (N≠Z): a4 a4 density dependence: T=0 K∞K∞ 7-8 parameters r n - r p T=1 g2g2 g3g3 aρaρ

9. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 9 Masses: 900 keV rms-deviations: masses:  m = 900 keV radii:  r = 0.015 fm Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (2005) 256 No: 1899.21 (1889.65) MeV ΔE = 560 keV → 0.3 ‰

10. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 10 SH-Elements Superheavy Elements: Q  -values Th: G.A Lalazissis et al, PRC 71, 024312 (2005) Exp: Yu.Ts.Oganessian et al, PRC 69, 021601(R) (2004)

11. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 11 U. Garg: Monopole-resonance and compressibility c ≈ -1

12. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 12 Symmetry energy empirical values: 30 MeV  a 4  34 MeV 2 MeV/fm 3 < p 0 < 4 MeV/fm 3 -200 MeV <  K 0 < -50 MeV saturation density Lombardo

13. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 13 Pb: GMR/GDR DD-ME2 G.A. Lalazissis et al, PRC 71, 024312 (2005)

14. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 14 GMR in Sn Isoscalar Giant Monopole in Sn-isotopes Isoscalar GMR in spherical nuclei → nuclear matter compression modulus K nm. Theory: Lalazissis et al Exp: U. Garg, unpublished Sn isotopes: DD-ME2 / Gogny pairing

15. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 15 Giant resonances in deformed nuclei: IVGDR in 100 Mo Exp: Rossendorf pygmy:

16. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 16 IV-GDR K=0 - K=1 - ρ 0 + δ ρ(t) isovector-dipole response in 100 Mo

17. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 17 pygmy modes in 100 Mo

18. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 18 fission barriers + binding energies DD-ME2/D1S

19. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 19 Gogny D1S: 20% -> 1.5 MeV constant G: 20% -> 2.5 MeV Stepien, Szymanski, PLB 26, 182 (1968) Rutz, Bender, Reinhard et al, PLB 468, 1 (1999) Samyn, Goriely, Pearson, PRC 72, 044316 (2005) Staszczak, Dobaczewski, Nazarewicz, Int. J.Mod. Phys.E Fission barrier depends on pairing:

20. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 20 Simplified pairing energy functional: Gogny: separable: Y. Tian, Z.Y. Ma, P.R.

21. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 21 Determination of the function P(r) in nuclear matter perfect agreement for nuclear matter P(r) Gaussian form P(r) obtained by mapping

22. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 22 In finite nuclei: comparison with Gogny:

23. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 23 dynamic results for the new force: comparison with Gogny:comparison with experiment: A. Ansari PLB 623, 37 (2005)Y. Tian, Z.Y. Ma, P.R. (2007)

24. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 24 investigation of the bare force: there is room left for phonon-exchange force Sn Pb

25. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 25 Comparison of δ-force and separable force with Gogny D1S: matrix elements: pairing field Δ nn'

26. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 26 Conclusions 1 ------- Conclusions: Relativistic density functionals - provide a high quality description of nuclear structure at low costs Density dependence is essential - in the isoscalar (NL3) and in the isovector channel (DD-ME2) Masses are comparable with modern mass models Fission barriers depend on the pairing - on the pairing strength, but also on the form of pairing Ab initio determination of the nuclear density functionals - in principle possible by fitting the density dependence to nuclear matter calculations - however problems with accuracy. Conclusions:

27. www.ph.tum.de XV Nuclear Physics Workshop Kazimierz 2008: "75 years of nuclear fission" Sept. 25, 2008 27 Colaborators: S. Karatzikos (Thessaloniki) G. A. Lalazissis (Thessaloniki) Z.Y. Ma (Beijing) T. Niksic (Zagreb) D. Pena (Orsay) Y. Tian (Beijing) D. Vretenar (Zagreb)