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Finite Nuclei and Nuclear Matter in Relativistic Hartree-Fock Approach

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. Contents. Introduction and motivations

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Finite Nuclei and Nuclear Matter in Relativistic Hartree-Fock Approach

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  1. Finite Nuclei and Nuclear Matter in Relativistic Hartree-Fock Approach Long Wenhui 1,2, Nguyen Van Giai 2, Meng Jie 1 1School of Physics, Peking University, China 2Institut 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 s-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 p-meson • Pairing force in RHB theory • Proposal: • The effective interactions in RHF approach PK1: PHYSICAL REVIEW C 69, 034319 (2004) • The contributions of p-meson • Different nonlinear mechanism

  5. Lagrangian and Hamiltonian • Lagrangian Density • Hamiltonian Density

  6. Hartree-Fock Approach • y  y0 • Hartree-Fock Trial State • Expectations (see s-meson as representative) • Fierz transformation (n=2, 3, 4)

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

  8. Tab. I Effective Interactions • HF(e): (s, w, r and p)HF A. Bouyssy, J.-F. Mathiot, N. V. Giai, S. Marcos, Phys. Rev. C36-380(1987). • HFSI: (s, w, r and p)HF + s self-interactions P. Bernardos, V. N. Fomenko, N. V. Giai et. al., Phys. Rev. C48-2665(1993). • ZRL1: (s, w, r and p)HF + zero-range self-interactions S. Marcos, L. N. Savushkin, V. N. Fomenko et. al., arXiv: nucl-th/0307063.

  9. Observables • Nuclear Matter: r0, K, EB, asym • Binding energies of the following nuclei: 16O, 40Ca, 48Ca, 56Ni, 68Ni, 90Zr, 116Sn, 132Sn, 182Pb, 194Pb, 208Pb Tab. II Bulk Properties of Nuclear Matter

  10. Tab. III Binding energies and charge radii

  11. Fig.1 The binding Energies of Pb isotopes

  12. Fig. 2 Single Particle Energies of 132Sn

  13. Fig. 3 Single Particle Energies of 208Pb

  14. Fig.4 Charge density distributions

  15. Summary • Programs for RHF approach are constructed • New effective interaction PKA with s-, w-, r-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 p-meson • Density-dependent RHF

  16. Thank you!

  17. Sigma Field • s-meson field • Hamiltonian for s-meson  

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

  19. p-meson • Pseudo-vector coupling • Exchange potential 

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