• 270 likes • 423 Views
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.
E N D
The spin-orbit interaction and effective masses in mean field models SPhN Saclay
Dirac equation and Schroedinger equation (1) SPhN Saclay
Dirac equation and Schroedinger equation (2) SPhN Saclay
p+40Ca at 497MeV (left) and 800 MeV (right) SPhN Saclay
DBHF (J. Rong, Z. Ma, NVG (2005)) SPhN Saclay
Differential cross sections and analyzing powers SPhN Saclay
Spin rotation functions SPhN Saclay
Skyrme vs. RMF SPhN Saclay
S.O. potentials: Skyrme-HF vs. RMF SPhN Saclay
S.O. potentials in RMF (Na & Mg) SPhN Saclay
S.O. potentials in RMF (Ni) SPhN Saclay
S.O. potentials in RMF (Sn) SPhN Saclay
S.O. splittings in Ne and Mg SPhN Saclay
Density-dependent Relativistic Hartree-Fock(Wenhui Long, thesis, Orsay 2005) • Lagrangian density where SPhN Saclay
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
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
The isotope shift of charge radii in Pb isotopes SPhN Saclay
Effective Mass(M. Jaminon and C. Mahaux, Phys. Rev.C 40:354, 1989) • Scalar Mass: • Effective Mass SPhN Saclay
What is the sign of M*(n)-M*(p) in Skyrme-HF? SPhN Saclay
Extended Brueckner-HF(Cao, Lombardo, Shen, NVG, 2005) SPhN Saclay
Isospin dependence of masses DBHF: Zhong-Yu Ma, et al, Phys. Lett.B 604(2004)170. SPhN Saclay
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
Density-dependence of masses Fig. 11 Effective mass as function of rb Fig. 12 Scalar mass as function of rb SPhN Saclay
Effective Mass in 208Pb SPhN Saclay
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