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ISTANBUL-06

ISTANBUL-06. Covariant density functional theory: treatment of the continuum. Saclay, May 20, 2009. Peter Ring. Technical University Munich. Collaborators: E. Litvinova, T. Niksik, D. Pena Arteaga, D. Vretenar, and J.M. Yao. Covariant density functionals.

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ISTANBUL-06

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  1. ISTANBUL-06 Covariant density functional theory: treatment of the continuum Saclay, May 20, 2009 Peter Ring Technical University Munich Collaborators: E. Litvinova, T. Niksik, D. Pena Arteaga, D. Vretenar, and J.M. Yao Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  2. Covariant density functionals Static solutions for the ground state Tensor force ? Conclusions Excited states in the continuum Content - BCS and Hartree-Bogoliubov - Nuclei at the proton drip-line -Treatment of neutron halos in mean field theory - Response formalism - particle vibrational coupling and Pygmy modes Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  3. Walecka model - the basis is an effective Lagrangian with all relativistic symmetries - it is used in a mean field concept (Hartree-level) - with the no-sea approximation (J,T)=(1-,1) (J,T)=(0+,0) (J,T)=(1-,0) sigma-meson: attractive scalar field omega-meson: short-range repulsive rho-meson: isovector field Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  4. ω ω ρ ρ σ σ Point-coupling models with derivative terms: gσ(ρ) gω(ρ) gρ(ρ) Effective density dependence: The basic idea comes from ab initio calculations density dependent coupling constants include Brueckner correlations and threebody forces non-linear meson coupling NL3 gσ(ρ) gω(ρ) gρ(ρ) Manakos and Mannel, Z.Phys.330, 223 (1988) Bürvenich, Madland, Maruhn, Reinhard, PRC 65, 044308 (2002): PC-F1 Niksic, Vretenar, P.R., PRC 78, 034318 (2008): DD-PC1 Typel, Wolter, NPA 656, 331 (1999) Niksic, Vretenar, Finelli, P.R., PRC 66, 024306 (2002): DD-ME1 Lalazissis, Niksic, Vretenar, P.R., PRC 78, 034318 (2008): DD-ME2 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  5. comparison with ab initio calculations: ab initio (Baldo et al) neutron matter DD-ME2 (Lalazissis et al) nuclear matter see talk of X. Vinas Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  6. rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm Masses: 900 keV Lalazissis, Niksic, Vretenar, P.R., PRC 71, 024312 (2005) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  7. U. Garg: Monopole-resonance and compressibility U. Garg et al, Proceedings INPC, Tokyo, 2007 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  8. Covariant density functionals Static solutions for the ground state Tensor force ? Conclusions Excited states in the continuum Content - BCS and Hartree-Bogoliubov -Treatment of neutron halos in mean field theory - Response formalism - particle vibrational coupling and Pygmy modes Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  9. Relativistic potentials continuum V-S ≈ 50 MeV Fermi sea 2m* ≈ 1200 MeV 2m ≈ 1800 MeV Dirac sea V+S ≈ 700 MeV continuum Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  10. Unified description of mean-field and pairing correlations Gogny D1S Relativistic Hartree Bogoliubov (RHB) RHB chemical potential quasiparticle energy Dirac hamiltonian pairing field quasiparticle wave function H. Kucharek, P. R., Z. Phys. A339, 23 (1991) T. Gonzales-Llarena, J. L. Egido, G. A. Lalazissis, P. R., PLB 379, 13 (1996) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  11. Continuum HFB: Continuum HFB for r → ∞ the potenitials do not contribute anymore: And we find the boundary conditions: A. Bulgac, 1980; J.Dobazcewski, H.Flocard, J.Treiner, Nucl. Phys. A422 (1984)103 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  12. BCS-theory Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  13. canonical basis The Bloch-Messiah theorem tells us, that we can diagonalize at the same time the density matrix and the pairing tensor. This basis is called canonical basis (sometimes also natural basis) neither h nor Δ are diagonal in this basis, however their diagonal elements and determine the occupations: and the HFB-wave function has BCS-form in this basis: Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  14. 11Li Neutron halo‘s Neutron halo‘s Mean field theory of halo‘s: (RHB in the continuum) • advantages: • * residual interaction by pairing • * self-consistent description • * universal parameters • * polarization of the core • * treatment of the continuum • problems: • *center ofmass motion • *boudary conditions at infinity Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  15. Densities in Li-isotopes Density in Li-nuclei J. Meng andP. Ring, PRL 77, 3963 (1996) J. Meng andP. Ring, PRL 80, 460 (1998) rel. Hartree-Bogoliubov in the continuum density dependent d-pairing technical: solution of the RHB-equations in r-space with box-boundary conditions Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  16. canonical basis in Li-isotopes canonical basis in Li * eigenstates of the density matrix * wavefunction has BCS-type J. Meng andP. Ring, PRL 77, 3963 (1996) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  17. Giant halo in the Zr region: Giant halo in Zr-nuclei J. Meng andP. Ring, PRL 80, 460 (1998) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  18. Halo wave function in the canonical basis: decomposition of |Li> |CN|2 N 2 4 6 8 10 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  19. Projected Density Functionals and VAP: J.Sheikh and P. R., NPA 665 (2000) 71 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  20. analytic expressions Projected Density Functionals projected DFT projected denstiy functional: density dependent interactions !!! projected HFB-equations (variation after projection): J.Sheikh and P. Ring NPA 665 (2000) 71 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  21. Halo-formation in Ne-isotopes pairing energies binding energies rms-radii L. Lopes, PhD Thesis, TUM, 2002 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  22. Covariant density functionals Static solutions for the ground state Tensor force ? Conclusions Excited states in the continuum Content - BCS and Hartree-Bogoliubov -Treatment of neutron halos in mean field theory - Response formalism - particle vibrational coupling and Pygmy modes Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  23. 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 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  24. 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. R. et al., NPA 694 (2001) 249 Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  25. 208Pb IS-GMR large influence of ahcomponents no influence of ah components IV-GDR Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  26. Linear response theory: Strength function: Response function: without interaction: separable interaction: lin. Bethe Salpeter Eq: Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  27. solution by inversion: in the ph-basis: Treatment of the continuum: Bertsch 1974 single particle Greens function: Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  28. point-coupling: Greens function in r-space: u(r) regular at the origin w(r) outgoing wave at r→∞ Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  29. Applications: E0 peak energy: escape width: Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  30. IV-dipole strength 208Pb neutron threshold: pygmy-region 1.9 % 2.8 % of EWSR Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  31. IV-dipole strength 132Sn neutron threshold: 2.4 % 3.4 % of EWSR Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  32. IV-dipole strength ISGDR toriodal mode (1999) (2000) (2000) (2001) (2002) (2004) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  33. Toroidal motion Toroidal motion ISGDR transition densities for 208Pb (NL3) multipole expansion of a four-current distribution: charge moments magnetic moments electric transverse moments -> toroidal moments toroidal dipole moment:poloidal currents on a torus isoscalar toroidal dipole operator: Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  34. Currents Toroidal dipole strength distributions. Vretenar, Paar, Niksic, Ring, Phys. Rev. C65, 021301 (2002) Velocity distributions in116Sn Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  35. RPA-modes mean field pole part μ + = + μ single particle strength: Particle-vibrational coupling:energy dependent self-energy Density functional theory - Landau-Migdal theory Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  36. E. Litvinova: Energy-dependentself-energy (massoperator) No-sea approximation Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  37. Distribution of single-particle strength in 209Bi fragmentation in 209-Bi Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  38. Single particle spectrum in the Pb region Single particle spectrum 0.71 0.85 1.0 meff 0.76 0.92 1.0 Litvinova, P.R., PRC 73, 44328 (2006) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  39. PVC: induced interaction U(14,23): PVC: induced interaction Self energy g – phonon amplitudes (QRPA) Total Mean Field Pole part p-h interaction amplitude Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  40. The full response contains energy dependent parts coming from vibrational couplings. Self energy ph-phonon amplitudes(QRPA) induced interaction Width of Giant Resonances Litvinova, Tselyaev, P.R., PRC 67, 64308 (2007) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  41. exp Litvinova, Tselyaev, P.R., PRC 78, 14312 (2008) centroid energies for GDR and PDR Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  42. Dipole strength in Sn isotopes Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  43. Parameters of Lorentz distribution* (GDR) 208Pb 132Sn 48Ni 46Fe *Averaging interval: 0-30 MeV Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  44. Litvinova, P.R., Vretenar, PRB 647, 111 (2007) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  45. Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  46. Comparison with experiment : th: Litvinova et al, PRC 79, 054312 (2009) exp: Adrich et al, PRL 75, 132501 (2005) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  47. Conclusions: Conclusions 1 ------- Influence of the continuum on ground states - no influence on magic configurations in stable nuclei - approaching the drip lines there is inflence on pairing - not important in the area of the proton drip line - neutron halos are strongly influenced by pairing in the continuum Theoretical treatment of the continuum for ground states - expansion in an oscillator basis (breaks down for halos) - expansion in a scaled oscillator basis (THO) - expansion in Saxon-Woods functions - solution in r-space (limited to spherical nuclei) Resonances - spectral representation excellent for stable nuclei - in detail there exist differencies for pygmy resonances - rel. continuum-QRPA for nuclei close to neutron drip line still missing Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

  48. Colaborators: T. Niksic (Zagreb) N. Paar (Zagreb) D. Vretenar (Zagreb) S. Karatzikos (Thessaloniki) G. A. Lalazissis (Thessaloniki) E. Litvinova (GSI) V. Tselyaev (St. Petersburg) J. Meng (Beijing) A. Sheikh (Srinagar) D. Peña Arteaga (Orsay) J. Daoutidis (Munich) E. Lopes (BMW) Importance of continuum coupling for nuclei close to the driplines, May 18-20, 2009

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