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Isospin dependence and effective forces of the Relativistic Mean Field Model Georgios A. Lalazissis Aristotle University of Thessaloniki, Greece Georgios A. Lalazissis Aristotle University of Thessaloniki, Greece Collaborators: T. Niksic (Zagreb), N. Paar (Darmstadt), P. Ring (Munich), D. Vretenar (Zagreb)

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Need for improved isovector channel of the effective nuclear interaction. EOS of asymmetric nuclear matter and neutron matter Structure and stability of exotic nuclei with extreme proton/neutron asymmetries Formation of neutron skin and halo structures Isoscalar and isovector deformations Mapping the drip-lines Evolution of shell structure Structure of superheavy elements

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Covariant density functional theory: system of Dirac nucleons coupled by the exchange mesons and the photon field through an effective Lagrangian. (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

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Covariant density functional theory Dirac operator: No sea approximation:i runs over all states in the Fermi sea

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EFFECTIVE INTERACTIONS (NL1, NL2, NL3, NL-Z2, …) model parameters: meson masses m , m , m , meson-nucleon coupling constants g , g , g , nonlinear self-interactions coupling constants g 2, g 3,... The parameters are determined from properties of nuclear matter (symmetric and asymmetric) and bulk properties of finite nuclei (binding energies, charge radii, neutron radii, surface thickeness...) Effective density dependence through a non-linear potential: Boguta and Bodmer, NPA. 431, 3408 (1977) NL1,NL3,TM1.. through density dependent coupling constants: T.W.,DD-ME.. Here, the meson-nucleon couplings are replaced by functions depending on the density r)

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number of param. How many parameters ? symmetric nuclear matter: E/A, ρ 0 finite nuclei (N=Z): E/A, radii spinorbit for free Coulomb (N≠Z): a4 a4 density dependence: T=0 K∞K∞ 7 parameters r n - r p T=1 g2g2 g3g3 aρaρ

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One- and two-neutron separation energies surface thickness surface diffuseness Neutron densities groundstates of Ni-Sn Ground states of Ni and Sn isotopes combination of the NL3 effective interaction for the RMF Lagrangian, and the Gogny interaction with the parameter set D1S in the pairing channel. G.L., Vretenar, Ring, Phys. Rev. C57, 2294 (1998)

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RHB description of neutron rich N=28 nuclei. NL3+D1S effective interaction. Strong suppression of the spherical N=28 shell gap. 1f7/2 -> fp core breakingShape coexistence G.L., Vretenar, Ring, Stoitsov, Robledo, Phys. Rev. C60, (1999) Ground-state quadrupole deformation Average neutron pairing gaps Shape coexistence in the N=28 region

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Neutron single-particle levels for 42 Si, 44 S, and 46 Ar against of the deformation. The energies in the canonical basis correspond to qround-state RHB solutions with constrained quadrupole deformation. Total binding energy curves SHAPE COEXISTENCE Evolution of the shell structure, shell gaps and magicity with neutron number!

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Ground-state proton emitters Self-consistent RHB calculations -> separation energies, quadrupole deformations, odd-proton orbitals, spectroscopic factors G.L., Vretenar, Ring Phys.Rev. C60, (1999) Proton emitters I characterized by exotic ground-state decay modes such as the direct emission of charged particles and -decays with large Q-values. Vretenar, G.L., Ring, Phys.Rev.Lett. 82, 4595 (1999) Nuclei at the proton drip line:

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How far is the proton-drip line from the experimentally known superheavy nuclei? G.L. Vretenar, Ring, PRC 59 (2004) Proton drip-line in the sub-Uranium region Possible ground-state proton emitters in this mass region? Proton drip-line for super-heavy elements:

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Pygmy: 208-Pb Paar et al, Phys. Rev. C63, (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. Among several single-particle transitions, a single collective dipole state is found below 10 MeV and its amplitude represents a coherent superposition of many neutron particle-hole configurations. 208 Pb

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Neutron radii RHB/NL3 Na SnME2

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2. MODELS WITH DENSITY-DEPENDENT MESON-NUCLEON COUPLINGS 2. MODELS WITH DENSITY-DEPENDENT MESON-NUCLEON COUPLINGS A. THE LAGRANGIAN B. DENSITY DEPENDENCE OF THE COUPLINGS the meson-nucleon couplings g , g , g -> functions of Lorentz-scalar bilinear forms of the nucleon operators. The simplest choice: a) functions of the vector density b) functions of the scalar density

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PARAMETRIZATION OF THE DENSITY DEPENDENCE MICROSCOPIC: Dirac-Brueckner calculations of nucleon self-energies in symmetric and asymmetric nuclear matter g PHENOMENOLOGICAL: S.Typel and H.H.Wolter, NPA 656, 331 (1999) Niksic, Vretenar, Finelli, Ring, PRC 66, (2002) g()g() g()g() g()g() saturation density

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Fit: DD-ME2 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%)

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Neutron Matter

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DD-ME2DD-ME1TW-99NL3NL3 * ρ ο (fm -3 ) Ε/Α (MeV) K (MeV) J (MeV) m * /m Nuclear Matter Properties

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Masses: 900 keV rms-deviations: masses: m = 900 keV radii: r = fm G.L., Niksic, Vretenar, Ring, PRC 71, (2005) DD-ME2

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SH-Elements DD-ME2 Exp: Yu.Ts.Oganessian et al, PRC 69, (R) (2004) Superheavy Elements: Q -values

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IS-GMR Isoscalar Giant Monopole: 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 Blaizot-concept: T. Niksic et al., PRC 66 (2002)

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IV-GDR Isovector Giant Dipole: IV-GDR the IV-GDR represents one of the sources of experimental informations on the nuclear matter symmetry energy constraining the nuclear matter symmetry energy 32 MeV a 4 36 MeV the position of IV-GDR is reproduced if T. Niksic et al., PRC 66 (2002) saturation density Lombardo

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Relativistic (Q)RPA calculations of giant resonances Isoscalar monopole response Sn isotopes: DD-ME2 effective interaction + Gogny pairing

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Conclusions: -Covariant Density Functional Theory provides a unified description of properties for ground states and excited states all over the periodic table -The present functionals have 7-8 parameters. -The density dependence (DD) is crucial: NL3 is has only DD in the T=0 channel NL3 is has only DD in the T=0 channel DD-ME1,… have also DD in the T=1 channel DD-ME1,… have also DD in the T=1 channel better neutron radii better neutron radii better neutron EOS better neutron EOS better symmetry energy better symmetry energy consistent description of GDR and GMR consistent description of GDR and GMR

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