1. Finite Nuclei and Nuclear Matter in Relativistic Hartree-Fock Approach Long Wenhui 1,2, Nguyen Van Giai 2, Meng Jie 1 1 School of Physics, Peking University, China 2 Institut de Physique Nucleaire, Universite Paris-Sud, France

2. Contents  Introduction and motivations  Theoretical Framework  Numerical Calculations  Results and Discussions  Summary

3. Introduction  Relativistic Hartree-Fock (RHF) Without self-interactions A. Bouyssy, J.-F. Mathiot, N. V. Giai, S. Marcos, Phys. Rev. C36-380(1987). With  -meson self-interactions P. Bernardos, V. N. Fomenko, N. V. Giai et. al., Phys. Rev. C48-2665(1993). With zero-range self-interactions S. Marcos, L. N. Savushkin, V. N. Fomenko et. al., arXiv: nucl-th/0307063.  Advantage of RHF approach More fundamental theory Nuclear structure: spin-orbit interaction

4. Motivations  RMF theory and RHF approach Hartree  Hartree-Fock Contributions of  -meson Pairing force in RHB theory  Proposal: The effective interactions in RHF approach PK1: PHYSICAL REVIEW C 69, 034319 (2004) The contributions of  -meson Different nonlinear mechanism

5. Lagrangian and Hamiltonian  Lagrangian Density  Hamiltonian Density

6. Hartree-Fock Approach     0  Hartree-Fock Trial State  Expectations (see  -meson as representative)see  -meson as representative  Fierz transformation (n=2, 3, 4)

7. Radial Dirac Equation  Dirac Equation  G and F separations

8. PKA938.5586.70711.57613.5373.1840.0-38.96241.967 HF(e)938.9440.07.230211.21002.62901.00270.0 HFSI939.0412.07.094211.43202.62901.0027-67.18-14.61 ZRL1939.0497.88.369512.14202.62901.0027-29.64651.00 Tab. I Effective Interactions  HF(e): ( , ,  and  ) HF A. Bouyssy, J.-F. Mathiot, N. V. Giai, S. Marcos, Phys. Rev. C36-380(1987).  HFSI: ( , ,  and  ) HF +  self-interactions P. Bernardos, V. N. Fomenko, N. V. Giai et. al., Phys. Rev. C48-2665(1993).  ZRL1: ( , ,  and  ) HF + zero-range self-interactions S. Marcos, L. N. Savushkin, V. N. Fomenko et. al., arXiv: nucl-th/0307063.

9. Observables  Nuclear Matter:  0, K, E B, a sym  Binding energies of the following nuclei: 16 O, 40 Ca, 48 Ca, 56 Ni, 68 Ni, 90 Zr, 116 Sn, 132 Sn, 182 Pb, 194 Pb, 208 Pb 00 EBEB Ka sym M*M* Empirical data0.166±0.018-16.±1.240±5032.±8. PKA0.150-15.99276.1529.510.54 HF(e)0.149-16.40465280.56 HFSI0.14-15.7525035.00.61 ZRL10.155-16.3925035.00.58 Tab. II Bulk Properties of Nuclear Matter

10. Tab. III Binding energies and charge radii 16 O 40 Ca 48 Ca 56 Ni 68 Ni 90 Zr 116 Sn 132 Sn 182 Pb 194 Pb 208 Pb 127.6342.1416.0484.0590.4783.8988.71102.91411.71525.91636.4 PKA127.7342.2416.2473.6586.3784.6984.41103.51412.21526.21635.9 HF(e)89.8272.8340.8666.01401.9 HFSI118.9333.2405.6772.21618.2 ZRL1117.9333.2408.5780.31632.8 2.7303.4783.4794.2704.6255.4425.504 PKA2.7323.4443.5503.8473.9304.3044.6504.7505.3925.4615.502 HF(e)2.733.47 4.265.50 HFSI2.733.48 4.265.52 ZRL12.713.443.494.255.49

11. Fig.1 The binding Energies of Pb isotopes

12. Fig. 2 Single Particle Energies of 132 Sn

13. Fig. 3 Single Particle Energies of 208 Pb

14. Fig.4 Charge density distributions

15. Summary  Programs for RHF approach are constructed  New effective interaction PKA with  -,  -,  -mesons and nonlinear high order terms is obtained  Better descriptions for nuclear matter and finite nuclei are obtained.  Perspective Isotopic shifts hard equation of state Contributions of  -meson Density-dependent RHF

16. Thank you!

17. Sigma Field   - meson field  Hamiltonian for  -meson  

18.  Multipole Expansion of the propagator  Potential Energy and Self-Energy Potential Energy and Self-Energy

19.  -meson  Pseudo-vector coupling  Exchange potential 