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ISTANBUL-06

ISTANBUL-06. Isovector properties of covariant DFT's and their influence on static and dynamic properties of neutron distributions. Trento ECT*, Aug. 7, 2009. Peter Ring. Technical University Munich. Content. Density dependence in the isovector channel of covariant density functionals.

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ISTANBUL-06

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  1. ISTANBUL-06 Isovector properties of covariant DFT's and their influence on static and dynamic properties of neutron distributions Trento ECT*, Aug. 7, 2009 Peter Ring Technical University Munich ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  2. Content Density dependence in the isovector channel of covariant density functionals Neutron skin in various models Connection to ab-initio calculations ? Neutron skin and collective phenomena Conclusions The basic goal is to find an optimal functional, which describes the essential facts of nuclear structure properly and to deduce from it the neutron skin ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  3. Mean field: Eigenfunctions: Interaction: Density functional theory in nuclei: Density functional theory Slater determinant density matrix Extensions: Pairing correlations, Covariance Relativistic Hartree Bogoliubov (RHB) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  4. 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 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  5. ω ω ρ ρ σ σ Point-coupling models with derivative terms: 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 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 NL1,NL3,… gσ(ρ) gω(ρ) gρ(ρ) + gradient term 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 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  6. Neutron skins: Na NL3 most of the non-linear models (NL1, NL3, …)overestimate the neutron skins ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  7. Symmetry energy Symmetry energy saturation density empirical values: 30 MeV£a4£34 MeV 2 MeV/fm3< p0 < 4 MeV/fm3 -200 MeV< DK0 < -50 MeV ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  8. 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 the position of IVGDR is reproduced if 32 MeV £ a4£ 36 MeV ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  9. DD-ME1 Ground state properties of finite nuclei Finite nuclei Binding energies,charge isotope shifts, and quadrupole Deformationsof Gd, Dy, and Er isotopes. Charge isotope shifts in even-A Pb isotopes. ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  10. rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm Masses: 900 keV Lalazissis, Niksic, Vretenar, P.R., PRC 71, 024312 (2005) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  11. Relativistic (Q)RPA calculations of giant resonances Sn isotopes: DD-ME2 effective interaction + Gogny pairing Isovector dipole response protons neutrons Isoscalar monopole response ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  12. Isoscalar Giant Monopole Resonances in Sn nuclei R(Q)RPA analysis of compression modes and isovector giant dipole resonances: The compressibility and symmetry energy of nuclear matter: Phys. Rev. C 68, 024310 (2003) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  13. U. Garg: Monopole-resonance and compressibility U. Garg et al, Proceedings INPC2007), Tokyo, June 3-8, 2007 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  14. comparison with ab initio calculations: ab initio (Baldo et al) neutron matter DD-ME2 (Lalazissis et al) nuclear matter see talk of X. Vinas ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  15. Fit to ab-initio results point coupling model is fitted to microscopic nuclear matter: av = 16,04 av = 16.06 av = 16,08 av = 16,10 av = 16,12 av = 16,14 av = 16.16 ρsat= 0.152 fm-3 m* = 0.58m Knm = 230 MeV DD-PC1 A. Akmal, V.R. Pandharipande, and D.G. Ravenhall, PRC. 58, 1804 (1998). ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  16. results for the neutron skin in 208Pb: rn-rp nonlinear meson coupling NL1 0.32 fm NL3 0.28 fm density dependent meson exchange DD-ME1 0.20 fm DD-ME2 0.19 fm point coupling models PC-F1 0.27 fm DD-PC1 0.20 fm ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  17. Microscopic can we fit directly the potentials ? Y. Akaishi (KEK) T. Otsuka (Tokyo) S. Hirose M. Serra† M. Serra, T. Otsuka, Y. Akaishi, P. R., and S. Hirose, Prog.Theor.Phys. 113, 1009 (2005) S. Hirose, M. Serra, P. R, T. Otsuka, and Y. Akaishi, PRC 75, 024301 (2007) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  18. kf = 1.0 fm-1 kf = 1.4 fm-1 kf = 1.8 fm-1 G-Matrix representation in r-space: G-Matrix Tamagaki + Takatsuka potential various densities: the most important contributions to nuclear binding come from 1E and 3E (tensor force) S. Hirose, M. Serra, P. R, T. Otsuka, and Y. Akaishi, PRC 75, 024301 (2007) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  19. OME-potentials are fitted for r > 0.8 fm: OME-potentials G-Matrix OME-potential density kf = 1.4 fm-1: ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  20. comparison with other theories other theories density dependence of g for constant masses hadron field theory (from rel. Brueckner) DD-ME1 phenomenological ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  21. Equation of state (symmetric nuclear matter): EOS symmetric Masses mm(ρ) and coupling constants gm(ρ) for the meson exchange potentials G-Matrix Gogny (GT2) present model (adjusted to GT2) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  22. present model asymmetry energy G-Matrix DD-ME1 Asymmetry energy S2(ρ): empirical values: 30 MeV£a4£34 MeV 2 MeV/fm3< p0 < 4 MeV/fm3 -200 MeV< DK0 < -50 MeV ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  23. present model present model DD-ME1 FP asymmetry energy G-Matrix DD-ME1 EOS neutron matter G-Matrix Gogny (GT2) Equation of state (neutron matter): no isovector property of the correlated system has been used for the fit ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  24. Neutron skin and collective phenomena: Relativistic QRPA with the same functionals Soft dipole mode (pygmy resonances) Spin-isospin modes (GT – IAR) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  25. Soft dipole modes and neutron skin ρ(r,t)= ρ0 (r)+ δρ(r,t) δρ r ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  26. ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  27. Th. Aumann: Dipole-strength in neutron-rich Sn isotopes Electromagnetic-excitation cross section Photo-neutron cross section stable radioactive • PDR • located at 10 MeV • exhausts a few % TRK sum rule • in agreement with theory • GDR • no deviation from systematics P. Adrich et al., PRL 95 (2005) 132501 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  28. PDR strength versus a4, po Th. Aumann: Result (averaged 130,132Sn) : a4 = 32.0 ± 1.8 MeV po = 2.3 ± 0.8 MeV/fm3 RQRPA – DD-ME N. Paar et al. (2007) S(r) : moderate stiffness ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  29. Sn isotopes δr LAND A.Krasznahorkay et al. PRL 82(1999)3216 neutron skin deduced from pygmy strength Rn-Rp Rn – Rp : 130Sn: 0.23 ± 0.04 fm 132Sn: 0.24 ± 0.04 fm A. Klimkiewicz, N. Paar, et al, submitted to PRL ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  30. complex configuration and width : th: Litvinova et al, PRC 79, 054312 (2009) exp: Adrich et al, PRL 75, 132501 (2005) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  31. p n Spin-Isospin Resonances: IAR - GTR Z+1,N-1 Z,N spin flip s isospin flip t ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  32. Spin-Isospin Resonances: IAR and GTR charge-exchange excitations proton-neutron relativistic QRPA 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: ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  33. GT-Resonances GTR N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, 054303 (2004) experiment ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  34. Isobaric Analog Resonance: IAR IAR N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, 054303 (2004) experiment ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  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 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  36. Conclusions: Conclusions 1 ------- We study the density dependence in the isovector channel of covariant density functional theory and discuss its influence on: - symmetry energy - neutron skin - EOS in neutron matter Phenomenological functionals with high precision predict for 208Pb: rn-rp = 0.20 fm Semiphenomenological ab-initio calculations show agreement Properties of specific collective excitations correlate with the neutron skins: - GDR, PDR, Spin-Isospin modes Predictions for densities much higher than saturation density are strongly model dependent ! ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

  37. Colaborators: G. A. Lalazissis (Thessaloniki) E. Litvinova (GSI) V. Tselyaev (St. Petersburg) T. Niksic (Zagreb) N. Paar (Zagreb) D. Vretenar (Zagreb) S. Hirose (Tokyo) M. Serra† Y. Akaishi (KEK) T. Otsuka (Tokyo) ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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