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Covariant density functional theory for collective excitations in nuclei far from stability

Covariant density functional theory for collective excitations in nuclei far from stability. Kazimierz Dolny, Sept. 24, 2005. Peter Ring. Technische Universität München. Rotional Excitations. Vibrational Excitations. Content. Covariant Density Functional Theory.

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Covariant density functional theory for collective excitations in nuclei far from stability

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  1. Covariant density functional theory for collective excitations in nuclei far from stability Kazimierz Dolny, Sept. 24, 2005 Peter Ring Technische Universität München XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  2. Rotional Excitations Vibrational Excitations Content Covariant Density Functional Theory * Parametrization of the Lagrangian * Superdeformed band in Hg-region * Giant resonances GMRundGDR * Pygmy-resonances PDR *pn-QRPA and spin-isospin modes: IAR, GTR XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  3. density matrix Slater determinant Mean field: Eigenfunctions: Interaction: Density fuctional theory Extensions: Covariance, Pairing correlations Relativistic Hartree Bogoliubov (RHB) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  4. Rho-meson: isovector field Omega-meson: short-range repulsive Covariant density functional theory Nucleons are coupled by exchange of mesons through an effective Lagrangian (EFT) (J,T)=(0+,0) (J,T)=(1-,0) (J,T)=(1-,1) Sigma-meson: attractive scalar field XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  5. for the nucleons we find thestaticDirac equation Static RMF theory for the mesons we find theHelmholtz equations No-sea approxim. ! XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  6. Relativistic Hartree Bogoliubov (RHB) Ground-state properties of weakly bound nuclei far from stability Unified description of mean-field and pairing correlations chemical potential quasiparticle energy Dirac hamiltonian quasiparticle wave function Gogny D1S pairing field XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  7. Effective 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) new g  g(r(r)) DD-ME1,DD-ME2 XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  8. Nuclear matter: E/A=-16 MeV (5%), ro=1,53 fm-1 (10%) K = 250 MeV (10%), a4 = 33 MeV (10%) Nuclei used in the fit for DD-ME2 XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  9. g2 g2 aρ How many parameters ? 7 parameters symmetric nuclear matter: E/A, ρ0 finite nuclei (N=Z): E/A,radii spinorbit o.k. Coulomb (N≠Z): a4 K∞ density dependence: T=0 T=1 rn - rp XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  10. Nuclear matter equation of state Neutron Matter XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  11. Symmetry energy saturation density empirical values: 30 MeV£a4£34 MeV 2 MeV/fm3< p0 < 4 MeV/fm3 -200 MeV< DK0 < -50 MeV XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  12. rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm Lalazissis, Niksic, Vretenar, Ring, PRC 71, 024312 (2005) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  13. Ground state properties of finite nuclei Binding energies,charge isotope shifts, and quadrupole Deformationsof Gd, Dy, and Er isotopes. Charge isotope shifts in even-A Pb isotopes. DD-ME1 XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  14. Superheavy Elements: Qa-values Exp: Yu.Ts.Oganessian et al, PRC 69, 021601(R) (2004) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  15. Rotational Motion: Vibrational Motion: A,B ~ δ2E/δρδρ ground-state density drph drhp Excited States: Time dependence: XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  16. Cranked RHB XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  17. Time-dependent RMF:breathing mode, 208Pb: K∞=211 K∞=271 K∞=355 XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  18. 2+-excitation in Sn-isotopes: A. Ansari, PLB (2005) in print XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  19. constraining the nuclear matter compressibility RMF models reproduce the experimental data only if 250 MeV £ K0£ 270 MeV Isoscalar Giant Monopole Resonance: IS-GMR The ISGMR represents the essential source of experimental information on the nuclear incompressibility XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  20. constraining the nuclear matter symmetry energy the position of IVGDR is reproduced if 34 MeV £ a4£ 36 MeV Isovector Giant Dipole Resonance: IV-GDR the IVGDR represents one of the sources of experimental informations on the nuclear matter symmetry energy XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  21. IV-GDR in Sn-isotopes DD-ME2 XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  22. XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  23. XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  24. Evolution of IV dipole strengthin Oxygenisotopes RHB + RQRPA calculations with the NL3 relativistic mean-field plus D1S Gogny pairing interaction. Transition densities What is the structure of low-lying strength below 15 MeV ? Effect of pairing correlations on the dipole strength distribution XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  25. Mass dependence of GDR and Pygmy dipole states in Sn isotopes. Evolution of the low-lying strength. Isovector dipole strength in 132Sn. Nucl. Phys. A692, 496 (2001) GDR Distribution of the neutron particle-hole configurations for the peak at 7.6 MeV (1.4% of the EWSR) Pygmy state exp XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  26. Pygmy-Resonance in deformed 26Ne XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  27. IV Dipole Strength for 208Pb and transition densities for thepeaks at 7.29 MeV and 12.95 MeVPRC 63, 047301 (2001) Exp GDR at 13.3 MeV 208Pb Exp PYGMY centroid at 7.37 MeV In heavier nuclei low-lying dipole states appearthat are characterized by a more distributed structure of the RQRPAamplitude. XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  28. Isoscalar dipole compression - toroidal modes Isoscalar GMR in spherical nuclei -> nuclear matter compression modulus Knm. Giant isoscalar dipole oscillations -> additional information on the nuclear incompressibility. ISGDR strength distributions Effective interactions with different Knm. Compression mode The low-energy strength does not depend on Knm! Phys. Lett. B487, 334 (2000) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  29. Toroidal motion: ISGDR transition densities for 208Pb (NL3 interaction) 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: XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  30. Toroidal dipole strength distributions. Vretenar, Paar, Niksic, Ring, Phys. Rev. C65, 021301 (2002) Velocity distributions in116Sn XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  31. p n Spin-Isospin Resonances: IAR - GTR Z+1,N-1 Z,N spin flip s isospin flip t XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  32. Spin-Isospin Resonances: IAR and GTR proton-neutron relativistic QRPA charge-exchange excitations π and ρ-meson exchange generate the spin-isospin dependent interaction terms the Landau-Migdal zero-range force in the spin-isospin channel (g’0=0.55) S=1 T=1 J = 1+ S=0 T=1 J = 0+ GAMOW-TELLER RESONANCE: ISOBARIC ANALOG STATE: XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  33. GT-Resonances GTR N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, 054303 (2004) experiment XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  34. Isobaric Analog Resonance: IAR IAR N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, 054303 (2004) experiment XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  35. Neutron skin and IAR/GRT The isotopic dependence of the energy spacings between the GTR and IAS direct information on the evolution of the neutron skin along the Sn isotopic chain XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  36. allowed β-decay : * Important points: - the tail of the GT-strength distribution at low energies - the position of specific single particle levels (i.e. effective mass) - effective pairing force in the T=1 and T=0 channel. - in simple QRPA the lifetimes are too big • * Possible methods to improve the results: • coupling to surface vibrations (difficult and beyond mean field) • - use of a tensor coupling in the ω-channel (one phenom. param.) • - T=0 pairing force with Gaussian character (one phen. parameter) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  37. enhanced value of the effective mass increased density of states around the Fermi surface T. Niksic et al, PRC 71, 014308 (2005) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  38. The nucleon effective mass m*: m*representsa measure of the density of states around the Fermi surface nonrelativistic mean-field models effective mass: m*/m=0.8±0.1 Dirac mass: mD=m+S(r) relativistic mean-field models effective mass: m*=m-V(r) conventional RMFmodels spin-orbit splittings + nuclear matter binding 0.55m ≤ mD ≤0.60m small density of states -> overestimated-decay lifetimes 0.64m ≤ m*≤ 0.67m XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  39. Reduction of the spin-orbit in neutron-rich nuclei Radial dependence of the spin-orbit term of the single neutron potential Lalazissis, Vretenar, Poeschl, Ring, Phys. Lett. B418, 7 (1998) The spin-orbitpotential originates from the addition of two large fields:the fieldof the vector mesons (short range repulsion), andthe scalar field of the sigma meson (intermediateattraction). Energy splittings between spin-orbit partner states weakening of the effective single-neutron spin-orbit potentialin neutron-rich isotopes reduced energy spacings between spin-orbit partners XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  40. tensor omega-nucleon coupling enhances the spin-orbit interaction scalar and vector self-energies can be reduced T. Niksic et al, PRC 71, 014308 (2005) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  41. N≈82 region: Cadmium isotopes:1g9/2 level is partially empty T=0 pairing has large influence on the 1g7/2->1g9/2 transition which dominates the -decay process T. Niksic et al, PRC 71, 014308 (2005) XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  42. An increase of the T=0 pairing partially compenstates for the fact that the density of states is still rather low T. Niksic et al, PRC 71, 014308 (2005) G. Martinez-Pinedo and K. Langanke, PRL 83, 4502 (1999) h9/2->h11/2 XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  43. Conclusions • Covariant density functionals are adjusted • to ground state properties of finite nuclei. • Time-dependent mean field theoryprovides a • parameter-free theory for excited states • - rotational spectra (cranked RHB-theory) • - vibrational excitations (rel. quasiparticle RPA) • Applications: • - GMR: 250 < K < 270 • - GDR: 32 < a4 < 34 • - IAR, GTR: pion, Migdal term, -> neutron skin XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  44. Open Problems: Fock terms and tensor forces: - why is the first order pion-exchange quenched? Vacuum polarization: - renormalization in finite systems Correlations: - Projection on particle number and angular mom. - Generator coordinates Complicated Configurations: -particle-vibrational coupling (effective mass) -width of giant resonances XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

  45. Colaborators: A Ansari (Bubaneshwar) G. A. Lalazissis (Thessaloniki) D. Vretenar (Zagreb) N. Paar D. Pena de Arteaga T. Niksic A. Wandelt XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 2005

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