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RIKEN-06

RIKEN-06. Beyond Relativistic Mean Field Theory. RIKEN, March 20, 2006. Peter Ring. Technical University Munich. Conclusions and outlook. Relativistic RPA in deformed nuclei - D. Pena Arteaga. Basics of Relativistic Mean Field Theory. A new method to carry out variation after projection

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RIKEN-06

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  1. RIKEN-06 Beyond Relativistic Mean Field Theory RIKEN, March 20, 2006 Peter Ring Technical University Munich RIKEN, March 2006: Mean field theories and beyond.

  2. Conclusions and outlook Relativistic RPA in deformed nuclei - D. Pena Arteaga Basics of Relativistic Mean Field Theory A new method to carry out variation after projection - E. Lopes, R. Rossignoli, J. Sheikh, Applications of Generator Coordinate Method: - T. Niksic, D. Vretenar Coupling of low-lying collective states: - E. Litvinova Content: RIKEN, March 2006: Mean field theories and beyond.

  3. Covariant density functional theory Walecka model Nucleons are coupled by exchange of mesons through an effective Lagrangian (EFT) (J,T)=(1-,0) (J,T)=(0+,0) (J,T)=(1-,1) Rho-meson: isovector field Omega-meson: short-range repulsive Sigma-meson: attractive scalar field RIKEN, March 2006: Mean field theories and beyond.

  4. Point-Coupling Models Point-coupling model σ ω δ ρ J=1, T=1 J=0, T=1 J=1, T=0 J=0, T=0 Manakos and Mannel, Z.Phys.330, 223 (1988) Bürvenich, Madland, Maruhn, Reinhard, PRC 65, 044308 (2002 RIKEN, March 2006: Mean field theories and beyond.

  5. Effective density dependence: Density dependence non-linear potential: NL1,NL3.. Boguta and Bodmer, NPA. 431, 3408 (1977) density dependent coupling constants: R.Brockmann and H.Toki, PRL68, 3408 (1992) S.Typel and H.H.Wolter, NPA656, 331 (1999) T. Niksic, D. Vretenar, P. Finelli, and P. Ring, PRC 56 (2002) 024306 g  g(r(r)) DD-ME1,DD-ME2 RIKEN, March 2006: Mean field theories and beyond.

  6. Three relativistic models: Density dependence Meson exchange with non-linear meson couplings: Boguta and Bodmer, NPA. 431, 3408 (1977) NL1,NL3,TM1,.. Meson exchange with density dependent coupling constants: R.Brockmann and H.Toki, PRL68, 3408 (1992) DD-ME1,DD-ME2 Point-coupling models with density dependent coupling constants: Manakos and Mannel, Z.Phys.330, 223 (1988) PC-1,…. RIKEN, March 2006: Mean field theories and beyond.

  7. No-sea approxim. ! The static limit (with time reversal) static RMF eq. for the nucleons we find thestaticDirac equation for the mesons we find theHelmholtz equations RIKEN, March 2006: Mean field theories and beyond.

  8. TDRMF: Eq. Time dependent mean field theory: No-sea approxim. ! and similar equations for the ρ- and A-field RIKEN, March 2006: Mean field theories and beyond.

  9. breathing mode: 208Pb Monopole motion K∞=211 K∞=271 K∞=355 RIKEN, March 2006: Mean field theories and beyond.

  10. Interaction: Relativistic RPA for excited states RRPA drph, drah Small amplitude limit: ground-state density drhp, drha RRPA matrices: the same effective interaction determines the Dirac-Hartree single-particle spectrum and the residual interaction RIKEN, March 2006: Mean field theories and beyond.

  11. ph Eph ≈ 10 MeV Fermi sea Dirac sea ah-configurations Selfconsistent Symmetries Eah ≈ -1200 MeV ah <ph|Vω|ah> ≈ 0 for vector mesons <ph|Vσ|ah> ≠ 0 for scalar mesons • size of matrix.element • the same quantum numbers possible • large degeneracy P. Ring et al., NPA 694 (2001) 249 RIKEN, March 2006: Mean field theories and beyond.

  12. Pb: GMR/GDR DD-ME2 G.A. Lalazissis et al, PRC 71, 024312 (2005) RIKEN, March 2006: Mean field theories and beyond.

  13. Sn: GDR DD-ME2 DD-ME2 IV-GDR in Sn-isotopes G.A. Lalazissis et al, PRC 71, 024312 (2005) RIKEN, March 2006: Mean field theories and beyond.

  14. IV-GDR in deformed 20Ne IV-GDR in Ne-20 (dots) NL3 RIKEN, March 2006: Mean field theories and beyond.

  15. IV-GDR in 16O IV-GDR in O-16 (test) RIKEN, March 2006: Mean field theories and beyond.

  16. Scissor mode in 20Ne BM1 strength in Ne-20 NL3 RIKEN, March 2006: Mean field theories and beyond.

  17. Scissor mode in 20Ne at E1+=5.66 MeV Scissor in Ne-20 δρ p n Transition density δρ(r,z) NL3 RIKEN, March 2006: Mean field theories and beyond.

  18. 1+ 1+ Spurious modes in 20Ne Spurious modes in Ne-20 1_ Eph=hω NL3 RIKEN, March 2006: Mean field theories and beyond.

  19. Pygmy-Resonance in deformed 26Ne pygmy-resonance in Ne-26 GANIL THEORY preliminary RIKEN, March 2006: Mean field theories and beyond.

  20. Beyond Mean Field Beyond Mean Field * Conservation of symmetries: Projection before Variation * Motion with large amplitude: Generator Coordinates * Coupling to Collective Vibrations - shifts of single particle energies - decay width of giant resonances J. Sheikh and P. Ring, Nucl. Phys. A665 (2000) 71 E. Lopes, PhD thesis, TU München T. Niksic, D. Vretenar, and P. Ring, Phys. Rev. C (2006) in print E. Litvinova and P. Ring, Phys. Rev. C (2006) in print RIKEN, March 2006: Mean field theories and beyond.

  21. Halo wave function in the canonical basis: decomposition of |Li> |CN|2 N 2 4 6 8 10 RIKEN, March 2006: Mean field theories and beyond.

  22. analytic expressions projected HFB-equations (variation after projection): J.Sheikh and P. Ring NPA 665 (2000) 71 Projected density functionals: projected DFT projected denstiy functional: density dependent interactions !!! RIKEN, March 2006: Mean field theories and beyond.

  23. Halo-formation in Ne-isotopes projected Ne-chain pairing energies binding energies rms-radii L. Lopes, PhD Thesis, TUM, 2002 RIKEN, March 2006: Mean field theories and beyond.

  24. Generator Coordinate Method (GCM) GCM-method Constraint Hartree Fock produces wave functions depending on agenerator coordinate q GCM wave functionis a superposition of Slaterdeterminants Hill-Wheeler equation: with projection: RIKEN, March 2006: Mean field theories and beyond.

  25. Energy surfaces in 194Hg: potential surface: Hg-194 RIKEN, March 2006: Mean field theories and beyond.

  26. Norm matrix in GCM details of norm-matrix in GCM RIKEN, March 2006: Mean field theories and beyond.

  27. unprojected GCM (N-dependence) unprojected GCM: N-dependence RIKEN, March 2006: Mean field theories and beyond.

  28. unprojected GCM (Δq-dependence) unprojected GCM: q-steps RIKEN, March 2006: Mean field theories and beyond.

  29. GCM wave functions GCM-wavefunctions: Hg-194 RIKEN, March 2006: Mean field theories and beyond.

  30. J-projected energy surfaces: Hg-194 RIKEN, March 2006: Mean field theories and beyond.

  31. Energy surfaces in 32Mg: potential surface: Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  32. single particle spectra single-particle spectra: Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  33. J-projected potential surfaces J-projected surfaces: Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  34. Gaussian operlap approximation GOA: Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  35. J-projected norm J-projected Norm Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  36. rotational energy corrections rotational energy correction: Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  37. J-projected GCM-spectrum J-projected GCM spectra; Mg-32 RIKEN, March 2006: Mean field theories and beyond.

  38. JGCM-wavefunctions: Mg-32 J-projected GCM wave functions: RIKEN, March 2006: Mean field theories and beyond.

  39. RPA-modes mean field pole part μ + = + μ Particle-Vibrational Coupling:energy dependent self-energy: single particle strength: RIKEN, March 2006: Mean field theories and beyond.

  40. Distribution of single-particle strength in 209Bi fragmentation in 209-Bi RIKEN, March 2006: Mean field theories and beyond.

  41. RIKEN, March 2006: Mean field theories and beyond.

  42. Width of Giant Resonances The full response contains energy dependent parts coming from vibrational couplings. Self energy g – phonon amplitudes (QRPA) ph interaction amplitude RIKEN, March 2006: Mean field theories and beyond.

  43. Decay-width of the Giant Resonances E1 photoabsorption cross section RIKEN, March 2006: Mean field theories and beyond.

  44. GMR in RRPA and RRPA-PC GMR in RRPA+RRPA-PC RIKEN, March 2006: Mean field theories and beyond.

  45. The Giant Dipole Resonance in 208Pb GDR in Pb, RRPA-RRPA-PC RIKEN, March 2006: Mean field theories and beyond.

  46. The Giant Dipole Resonance in 132Sn GDR in Sn, RRPA+RRPA-PC RIKEN, March 2006: Mean field theories and beyond.

  47. GDR: comparison with experiment Energy and Width of GDR RIKEN, March 2006: Mean field theories and beyond.

  48. Conclusions: Conclusions 1 ------- Deformed RPA- and QRPA calculations are now possible. They are very important for nuclei far from stability In transitional nuclei we can do Variation after Projection a new method allows this also in relativistic calculations. Configuration mixing is possible by GCM calculations: - they require angular momentum projection - the numerical effort is large - restriction to axial symmetry at the moment essential The admixture of 2p-1h or 2p-2h states is possible by particle vibrational coupling (PVC). - this leads to fragmentation of the single particle states - enhanced level density at the Fermi surfac - enhancedwidth of giant resonances RIKEN, March 2006: Mean field theories and beyond.

  49. Open Problems: -----Open Problems ------ Simpler parametrizations: - point coupling - simpler pairing Improved energy functional: - Fock terms and tensor forces - why is the first order pion-exchange quenched? - is vacuum polarization important in finite nuclei Conceptual problems: - what is form of the functional, if we go beyond mean field? - density dependence and projection (Egido-poles) - density dependence and symmetries (RPA) RIKEN, March 2006: Mean field theories and beyond.

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