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The spin-orbit interaction and effective masses in mean field models

The spin-orbit interaction and effective masses in mean field models. Dirac equation and Schroedinger equation (1). Dirac equation and Schroedinger equation (2). p+40Ca at 497MeV (left) and 800 MeV (right). DBHF (J. Rong, Z. Ma, NVG (2005)). Differential cross sections and analyzing powers.

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The spin-orbit interaction and effective masses in mean field models

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  1. The spin-orbit interaction and effective masses in mean field models SPhN Saclay

  2. Dirac equation and Schroedinger equation (1) SPhN Saclay

  3. Dirac equation and Schroedinger equation (2) SPhN Saclay

  4. p+40Ca at 497MeV (left) and 800 MeV (right) SPhN Saclay

  5. DBHF (J. Rong, Z. Ma, NVG (2005)) SPhN Saclay

  6. Differential cross sections and analyzing powers SPhN Saclay

  7. Spin rotation functions SPhN Saclay

  8. SPhN Saclay

  9. Skyrme vs. RMF SPhN Saclay

  10. S.O. potentials: Skyrme-HF vs. RMF SPhN Saclay

  11. S.O. potentials in RMF (Na & Mg) SPhN Saclay

  12. S.O. potentials in RMF (Ni) SPhN Saclay

  13. S.O. potentials in RMF (Sn) SPhN Saclay

  14. S.O. splittings in Ne and Mg SPhN Saclay

  15. SPhN Saclay

  16. Density-dependent Relativistic Hartree-Fock(Wenhui Long, thesis, Orsay 2005) • Lagrangian density where SPhN Saclay

  17. Density-dependence of Coupling constants Fig. 4 Isovector channels Fig. 3 Isoscalar channels • Contributions from the exchange terms • Isospin properties and exchange terms • Density-dependences of r-N and p-N SPhN Saclay

  18. Root mean square deviations from the data S. N.: Selected Nuclei in Tab. 6 Iso. : Isotope shift of Charge radii in Pb isotopes S. O.: Spin-Orbit splittings in 16O, 40Ca, 48Ca, 56Ni, 90Zr, 132Sn, 208Pb SPhN Saclay

  19. The isotope shift of charge radii in Pb isotopes SPhN Saclay

  20.   Effective Mass(M. Jaminon and C. Mahaux, Phys. Rev.C 40:354, 1989) • Scalar Mass: • Effective Mass  SPhN Saclay

  21. What is the sign of M*(n)-M*(p) in Skyrme-HF? SPhN Saclay

  22. Extended Brueckner-HF(Cao, Lombardo, Shen, NVG, 2005) SPhN Saclay

  23. Isospin dependence of masses DBHF: Zhong-Yu Ma, et al, Phys. Lett.B 604(2004)170. SPhN Saclay

  24. Momentum dependence of masses Filled symbols: Effective Mass Open symbols: Scalar Mass (Dirac Mass) E. N. E. van Dalen, et al, arXiv: nucl-th/0502064 SPhN Saclay

  25. Density-dependence of masses Fig. 11 Effective mass as function of rb Fig. 12 Scalar mass as function of rb SPhN Saclay

  26. Effective Mass in 208Pb SPhN Saclay

  27. Summary • The s.o. component of Skyrme forces is too restrictive. • It can be extended (like SkI4) if one work with energy functionals, not forces. • The s.o. of RMF predicts a definite decrease of splittings for increasing (N-Z). • The s.o. of DDRHF looks promising, more study needed. • Effective masses: EBHF and DBHF agree that M*(n)>M*(p) when N>Z • This prediction disagrees with RMF, agrees with DDRHF. • As for Skyrme-HF it depends on the parametrization! SPhN Saclay

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