P. ArumugamCentro de Física das Interacções Fundamentais and Departamento de Física, Instituto Superior Técnico,

Lisbon, Portugal

S.K. Patra, P.K. Sahu, B.K. SharmaInstitute of Physics, Bhubaneswar, India

X. Vinãs, M. Centelles, Tapas SilUniversitat de Barcelona

Ladek Zdroj

28-Feb-2008

2Outline

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

3Quantum 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

4EFT motivated RMF: E-RMF

5The Energy Density Functional

6Some 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, 054904 (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, 024314 (2001); PRC 63, 044321 (2001).

Superheavy nucleiT. Sil et al, PRC 69, 044315 (2004).

Reaction cross-sections in stable and unstable nucleiSharma et al, JPG 32, 2089 (2006); Shukla et al, PRC 76, 034601 (2007)

7Bulk properties of some nuclei

82n-separation energies

9Cluster & Halo structures

Arumugam et al, PRC 71, 064308 (2005)

Sharma et al, JPG 32, L1 (2006)

11Li

10Neutron 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/0607039v1 (2006),

Horowitz and Piekarewicz PRC 64, 062802R (2001)

11Dirac potentials at high density

12Energy at high densities

Coester band R. Brockmann and R. Machleidt, PRC 42, 1965 (1990).

13EoS is symmetric nuclear matter

Arumugam et al, PLB 601, 51 (2004).

14EoS in Neutron Matter

Arumugam et al, PLB 601, 51 (2004).

15Neutron Star Properties

Arumugam et al, PLB 601, 51 (2004).

16Phase transitions in nuclear matter

Arumugam et al, PLB 601, 51 (2004).

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18Recent work

Quark-Hadron phase transitions within E-RMF

Sharma, Panda and Patra, PRC 75, 035808 (2007).

Full octet of Baryons in the Lagrangian

No mixed phase with original G2 parameter set

G2* (G2): K = 300 (215), mN*/mN = 0.7 (0.664),

saturation properties were used to fix other constants

Unpaired quark matter & Color flavor locked quark matter

Many questions remain open

19Summary & 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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