P. Arumugam Centro de Física das Interacções Fundamentais and Departamento de Física, Instituto Superior Técnico, Lisbon, Portugal S.K. Patra, P.K. Sahu, B.K. Sharma Institute of Physics, Bhubaneswar, India X. Vinãs, M. Centelles, Tapas Sil Universitat de Barcelona Ladek Zdroj 28-Feb-2008

2 Outline Mean Field Theory Quantum Hadrodynamics EFT motivated Relativistic Mean Field (E-RMF) Theory Finite Nuclei Bulk properties  justifying the fit & overall description Halo & Clustering  precision of evaluated density distributions Neutron skin  Neutron stars Infinite Matter EoS at high densities Neutron star properties Liquid-gas phase transition Conclusions

3 Quantum Hadrodynamics (QHD) Earlier QHD studies were based on renormalizable models  No scalar-vector & vector-vector interactions “Standard” RMF models Non-linear  Use effective coupling constans  renormalizability ??? Modern approach to renormalization Cutoff in derivative expansions All non-renormalizable couplings consistent with the underlying symmetries of QCD are allowed

4 EFT motivated RMF: E-RMF

5 The Energy Density Functional

6 Some applications of E-RMF Pion-nucleus scattering B. C. Clark et al, PLB 427, 231 (1998). Nuclear spin-orbit force R. J. Furnstahl et al, NPA 632, 607 (1998). Asymmetric nuclear matter at finite temperature (with G1) P. Wang, PRC 61, (2000). Effect of new nonlinear couplings on the nuclear matter and finite nuclear properties M. Del Estal et al, NPA 650, 443 (1999); PRC 63, (2001) ; PRC 63, (2001). Superheavy nuclei T. Sil et al, PRC 69, (2004). Reaction cross-sections in stable and unstable nuclei Sharma et al, JPG 32, 2089 (2006); Shukla et al, PRC 76, (2007)

7 Bulk properties of some nuclei

8 2n-separation energies

9 Cluster & Halo structures Arumugam et al, PRC 71, (2005) Sharma et al, JPG 32, L1 (2006) 11 Li

10 Neutron skin in heavy nuclei Uncertainty in neutron radius measurement ~ 0.2 fm !! Only few popular Skyrme parameters relevant for finite nuclei are chosen. Piekarewicz nucl-th/ v1 (2006), Horowitz and Piekarewicz PRC 64, R (2001)

11 Dirac potentials at high density

12 Energy at high densities Coester band R. Brockmann and R. Machleidt, PRC 42, 1965 (1990).

13 EoS is symmetric nuclear matter Arumugam et al, PLB 601, 51 (2004).

14 EoS in Neutron Matter Arumugam et al, PLB 601, 51 (2004).

15 Neutron Star Properties Arumugam et al, PLB 601, 51 (2004).

16 Phase transitions in nuclear matter Arumugam et al, PLB 601, 51 (2004).

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18 Recent work Quark-Hadron phase transitions within E-RMF Sharma, Panda and Patra, PRC 75, (2007). Full octet of Baryons in the Lagrangian No mixed phase with original G2 parameter set G2* (G2): K  = 300 (215), m N * /m N = 0.7 (0.664), saturation properties were used to fix other constants Unpaired quark matter & Color flavor locked quark matter Many questions remain open

19 Summary & Conclusions E-RMF: Systematic inclusion of new interaction terms under the guidance of EFT techniques No forcing of any change in the parameters initially determined from a few magic nuclei Results for finite nuclei are as good as any best model or even better Soft EOS both around saturation and at high densities which is consistent with measurements of kaon production flow of matter in energetic heavy-ion collisions observed neutron star masses and radii Liquid-gas phase transition is understood but questions remain open with Quark phase and G2* E-RMF approach can be considered as a salient step towards a unified theory for finite nuclei as well as for infinite nuclear matter

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