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

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

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 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 Covariant density functional theory Omega-meson: short-range repulsive Rho-meson: isovector field

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, for the nucleons we find the static Dirac equation for the mesons we find the Helmholtz equations No-sea approxim. ! Static RMF theory

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Effective density dependence: non-linear potential: density dependent coupling constants: g  g (  r)) NL1,NL3.. DD-ME1,DD-ME2 Boguta and Bodmer, NPA. 431, 3408 (1977) R.Brockmann and H.Toki, PRL 68, 3408 (1992) S.Typel and H.H.Wolter, NPA 656, 331 (1999) new

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Nuclei used in the fit for DD-ME2 Nuclear matter: E/A=-16 MeV (5%),  o =1,53 fm -1 (10%) K = 250 MeV (10%), a 4 = 33 MeV (10%)

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, How many parameters ? symmetric nuclear matter: E/A, ρ 0 finite nuclei (N=Z): E/A, radii spinorbit o.k. Coulomb (N≠Z): a4 a4 density dependence: T=0 K∞K∞ 7 parameters r n - r p T=1 g2g2 g2g2 aρaρ

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Symmetry energy empirical values: 30 MeV  a 4  34 MeV 2 MeV/fm 3 < p 0 < 4 MeV/fm MeV <  K 0 < -50 MeV saturation density

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, rms-deviations: masses:  m = 900 keV radii:  r = fm Lalazissis, Niksic, Vretenar, Ring, PRC 71, (2005)

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

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Excited States: Time dependence: Rotational Motion: Vibrational Motion: ground-state density  ph  hp A,B ~ δ 2 E/δρδρ

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

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

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Isoscalar Giant Monopole Resonance: IS-GMR The ISGMR represents the essential source of experimental information on the nuclear incompressibility constraining the nuclear matter compressibility RMF models reproduce the experimental data only if 250 MeV  K 0  270 MeV

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Isovector Giant Dipole Resonance: IV-GDR the IVGDR represents one of the sources of experimental informations on the nuclear matter symmetry energy constraining the nuclear matter symmetry energy 34 MeV  a 4  36 MeV the position of IVGDR is reproduced if

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

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

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

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Mass dependence of GDR and Pygmy dipole states in Sn isotopes. Evolution of the low-lying strength. Isovector dipole strength in 132 Sn. GDR Nucl. Phys. A692, 496 (2001) 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, Pygmy-Resonance in deformed 26 Ne

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, IV Dipole Strength for 208 Pb and transition densities for the peaks at 7.29 MeV and MeV PRC 63, (2001) Exp GDR at 13.3 MeV Exp PYGMY centroid at 7.37 MeV In heavier nuclei low-lying dipole states appear that are characterized by a more distributed structure of the RQRPA amplitude. 208 Pb

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

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Toroidal dipole strength distributions. Velocity distributions in 116 Sn Vretenar, Paar, Niksic, Ring, Phys. Rev. C65, (2002)

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Spin-Isospin Resonances: IAR - GTR Z,N Z+1,N-1 isospin flip  spin flip  pn

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 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 GAMOW-TELLER RESONANCE: ISOBARIC ANALOG STATE: S=1 T=1 J  = 1 + S=0 T=1 J  = 0 + (g’ 0 =0.55)

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

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

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

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

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

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, DD-ME1DD-ME1 * m D /m m * /m tensor omega-nucleon coupling enhances the spin-orbit interaction scalar and vector self-energies can be reduced T. Niksic et al, PRC 71, (2005)

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, 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, (2005) N≈82 region:

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, An increase of the T=0 pairing partially compenstates for the fact that the density of states is still rather low h 9/2 ->  h 11/2 G. Martinez-Pinedo and K. Langanke, PRL 83, 4502 (1999) T. Niksic et al, PRC 71, (2005)

XII. International Workshop Maria and Pierre Curie, Kazimierz Dolny, Conclusions Covariant density functionals are adjusted to ground state properties of finite nuclei. Time-dependent mean field theory provides a parameter-free theory for excited states - rotational spectra ( cranked RHB-theory) - vibrational excitations (rel. quasiparticle RPA) Applications: - GMR: 250 < K < GDR: 32 < a 4 < 34 - IAR, GTR: pion, Migdal term, -> neutron skin

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