Isospin dependence and effective forces of the Relativistic Mean Field Model

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

2. 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 Structure of superheavy elements Evolution of shell structure EOS of asymmetric nuclear matter and neutron matter Need for improved isovector channel of the effective nuclear interaction.

3. Covariant density functional theory: system of Dirac nucleons coupled by the exchange mesons and the photonfield through an effective Lagrangian. (J,T)=(1-,0) (J,T)=(0+,0) (J,T)=(1-,1) Rho-meson: isovector field Omega-meson: short-range repulsive Sigma-meson: attractive scalar field:

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

5. 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 constantsg2, g3, ... The parametersare determined from properties of nuclear matter (symmetric andasymmetric) 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: Here, the meson-nucleon couplings T.W.,DD-ME.. are replaced by functions depending on the density r(r)

6. g2 g3 aρ How many parameters ? 7 parameters number of param. symmetric nuclear matter: E/A, ρ0 finite nuclei (N=Z): E/A,radii spinorbit for free Coulomb (N≠Z): a4 K∞ density dependence: T=0 T=1 rn - rp

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

8. Shape coexistence in the N=28 region G.L., Vretenar, Ring, Stoitsov, Robledo, Phys. Rev. C60, 014310 (1999) 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 breaking Shape coexistence Ground-state quadrupole deformation Average neutron pairing gaps

9. Neutron single-particle levels for 42Si, 44S, and 46Ar 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!

10. Proton emitters I Nuclei at the proton drip line: Vretenar, G.L., Ring, Phys.Rev.Lett. 82, 4595 (1999) characterized by exotic ground-statedecaymodes such as the directemission of charged particles and -decayswith large Q-values. Ground-state proton emitters Self-consistent RHB calculations -> separation energies, quadrupole deformations, odd-proton orbitals, spectroscopic factors G.L., Vretenar, Ring Phys.Rev. C60, 051302(1999)

11. Proton drip-line in the sub-Uranium region Possible ground-state proton emitters in this mass region? Proton drip-line for super-heavy elements: How far is the proton-drip line from the experimentally known superheavy nuclei? G.L. Vretenar, Ring, PRC 59 (2004) 017301

12. Paar et al, Phys. Rev. C63, 047301 (2001) 208Pb Pygmy: 208-Pb 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. Among several single-particle transitions, a single collective dipole state is found below 10 MeV and itsamplitude represents a coherent superposition of many neutron particle-holeconfigurations.

13. ME2 Sn Neutron radii RHB/NL3 Na

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

15. PARAMETRIZATION OF THE DENSITY DEPENDENCE MICROSCOPIC: Dirac-Bruecknercalculations of nucleon self-energies in symmetricand asymmetricnuclear matter g saturation density PHENOMENOLOGICAL: g(r) g(r) g(r) S.Typel and H.H.Wolter, NPA656, 331 (1999) Niksic, Vretenar, Finelli, Ring, PRC66, 024306 (2002)

16. Nuclei used in the fit for DD-ME2 Fit: DD-ME2 (%) (%) Nuclear matter: E/A=-16 MeV (5%), ro=1,53 fm-1 (10%) K = 250 MeV (10%), a4 = 33 MeV (10%)

18. Neutron Matter

19. Nuclear Matter Properties

20. rms-deviations: masses: Dm = 900 keV radii: Dr = 0.015 fm Masses: 900 keV G.L., Niksic, Vretenar, Ring, PRC 71, 024312 (2005) DD-ME2

22. SH-Elements Superheavy Elements: Qa-values Exp: Yu.Ts.Oganessian et al, PRC 69, 021601(R) (2004) DD-ME2

24. Isoscalar Giant Monopole: IS-GMR IS-GMR The ISGMR represents the essential source of experimental information on the nuclear incompressibility Blaizot-concept: constraining the nuclear matter compressibility RMF models reproduce the experimental data only if 250 MeV £ K0£ 270 MeV T. Niksic et al., PRC 66 (2002) 024306

25. saturation density Lombardo Isovector Giant Dipole: IV-GDR 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 the position of IV-GDR is reproduced if 32 MeV £ a4£ 36 MeV T. Niksic et al., PRC 66 (2002) 024306

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

28. 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 • DD-ME1,… have also DD in the T=1 channel • better neutron radii • better neutron EOS • better symmetry energy • consistent description of GDR and GMR