Technical University Munich Isovector properties of covariant DFT's and their influence on static and dynamic properties of neutron distributions ISTANBUL-06 Trento ECT*, Aug. 7, 2009 Peter Ring Technical University Munich 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Density functional theory Density functional theory in nuclei: Density functional theory Slater determinant density matrix Mean field: Eigenfunctions: Interaction: Extensions: Pairing correlations, Covariance Relativistic Hartree Bogoliubov (RHB) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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)=(0+,0) (J,T)=(1-,0) (J,T)=(1-,1) sigma-meson: attractive scalar field omega-meson: short-range repulsive rho-meson: isovector field 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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,… 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 Point-coupling models with derivative terms: ρ σ ω gσ(ρ) gω(ρ) gρ(ρ) 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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009 ρ σ ω

Neutron skins: Na NL3 most of the non-linear models (NL1, NL3, …) overestimate the neutron skins 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

2 MeV/fm3 < p0 < 4 MeV/fm3 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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Ground state properties of finite nuclei DD-ME1 Ground state properties of finite nuclei Binding energies, charge isotope shifts, and quadrupole Deformations of Gd, Dy, and Er isotopes. Charge isotope shifts in even-A Pb isotopes. 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm Masses: 900 keV Lalazissis, Niksic, Vretenar, P.R., PRC 71, 024312 (2005) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Relativistic (Q)RPA calculations of giant resonances Sn isotopes: DD-ME2 effective interaction + Gogny pairing Isovector dipole response protons neutrons Isoscalar monopole response 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

U. Garg: Monopole-resonance and compressibility U. Garg et al, Proceedings INPC2007), Tokyo, June 3-8, 2007 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

comparison with ab initio calculations: DD-ME2 (Lalazissis et al) ab initio (Baldo et al) neutron matter DD-ME2 (Lalazissis et al) nuclear matter see talk of X. Vinas 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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). 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

can we fit directly the potentials ? 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) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

G-Matrix representation in r-space: Tamagaki + Takatsuka potential various densities: kf = 1.0 fm-1 kf = 1.4 fm-1 kf = 1.8 fm-1 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) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

OME-potentials are fitted for r > 0.8 fm: G-Matrix OME-potential density kf = 1.4 fm-1: 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

comparison with other theories other theories density dependence of g for constant masses hadron field theory (from rel. Brueckner) DD-ME1 phenomenological 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Asymmetry energy S2(ρ): G-Matrix present model DD-ME1 empirical values: 30 MeV £ a4 £ 34 MeV 2 MeV/fm3 < p0 < 4 MeV/fm3 -200 MeV < DK0 < -50 MeV 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Equation of state (neutron matter): EOS neutron matter DD-ME1 present model FP Gogny (GT2) G-Matrix asymmetry energy G-Matrix present model DD-ME1 no isovector property of the correlated system has been used for the fit 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Neutron skin and collective phenomena: Relativistic QRPA with the same functionals Soft dipole mode (pygmy resonances) Spin-isospin modes (GT – IAR) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Soft dipole modes and neutron skin ρ(r,t) = ρ0 (r) + δρ(r,t) δρ r 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Dipole-strength in neutron-rich Sn isotopes Th. Aumann: Dipole-strength in neutron-rich Sn isotopes Electromagnetic-excitation cross section Photo-neutron cross section stable A PDR GDR Ecentr [MeV] sum rule fraction [%] Γ 124Sn - 15.3 4.8 116 130Sn 10.1 (0.7) 7.0 (3.0) 15.9 (0.5) (1.8) 145 (19) 132Sn 9.8 4.0 (3.1) 16.1 (0.8) 4.7 (2.2) 125 (32) 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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

neutron skin deduced from pygmy strength Rn-Rp δr Rn – Rp : 130Sn: 0.23 ± 0.04 fm 132Sn: 0.24 ± 0.04 fm LAND Sn isotopes A.Krasznahorkay et al. PRL 82(1999)3216 A. Klimkiewicz, N. Paar, et al, submitted to PRL 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

complex configuration and width : th: Litvinova et al, PRC 79, 054312 (2009) exp: Adrich et al, PRL 75, 132501 (2005) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Spin-Isospin Resonances: IAR - GTR Z,N Z+1,N-1 spin flip s isospin flip t 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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: 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

GTR GT-Resonances N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, 054303 (2004) experiment 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Isobaric Analog Resonance: IAR N. Paar, T. Niksic, D. Vretenar, P.Ring, PR C69, 054303 (2004) experiment 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

Conclusions 1 ------- Conclusions: 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 ! Conclusions 1 ------- 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009

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) 7.8.2009 ECT*, Trento: The Lead Radius Experiment and Neutron Rich Matter, Aug 2-7, 2009