Presentation on theme: "Nucleon Effective Mass in the DBHF 同位旋物理与原子核的相变 CCAST Workshop 2005 年 8 月 19 日－ 8 月 21 日 马中玉 中国原子能科学研究院."— Presentation transcript:
Nucleon Effective Mass in the DBHF 同位旋物理与原子核的相变 CCAST Workshop 2005 年 8 月 19 日－ 8 月 21 日 马中玉 中国原子能科学研究院
Introduction Importance of isospin physics in many aspects: exotic nuclei; astrophysics; heavy ion collision etc. Isospin dependence of many quantities: asymmetric energy as function of density effective interaction; effective mass etc. Effective mass characterizes the propagation of a nucleon in the strongly interacting medium reaction dynamics of nuclear collisions by unstable nuclei neutron-proton differential collective flow, isospin equil. neutron star properties
Introduction Less knowledge of isospin dependence from experiments Study from a fundamental theory NN interaction + SR correlation Many works in non-relativistic and relativistic approaches RMF : success in describing g.s. properties isospin dep. based on stable nuclei U s, U 0 are energy indep. Our work Relativistic approach DBHF
Definition of effective mass In non-relativistic approach effective mass m* describe an independent quasi-particle moving in the nucl. medium characterizes the non-locality of the microscopic potential in space (k-mass) and in time (E-mass) Jeukenne, Lejeune, Mahuax ‘76
Effective mas in non-relativistic appr. Effective mass derived by the two equivalent expression Jaminon & Mahaux’89 It can be determined from analyses of experimental data in nonrel. Shell model or optical model Typical value is m*/m ~ 0.70 ± 0.05 at E = 30 MeV by phenomenological analyses of experimental scattering data
Dirac mass Relativistic approach Effective mass is usually defined as M* = M – U s Dirac mass (scalar mass) describe a nucleon in the medium as a quasi nucleon with effective mass and effective energy, which satisfies Dirac equation. M* and m* are different physical quantities Can not be compared with each other
Dirac and Lorentz mass RMF U s U o are constant in energy U s = 375±40 MeV Ring’96 ~0.60±0.04 Dirac mass (scalar mass) Schroedinger equivalent equation Schroedinger equvalent potential, Lorentz mass
Isospin dep. of effective mass Isospin dependence of effective mss in RMF, Energy dep. of nucleon self-energy is not considered ~0.7 Lorentz mass (vector mass) Lorentz mass not related to a non-locality of the rel. potentials, can be compared with the effective mass in non-relativistic appr. Isospin dep. of Lorentz mass, compare with that in non-rel.
DBHF approach Relativistic approaches NN + DBHF Success in NM saturation properties DBHF G Matrix ––- Nucleon effective int. Information of isospin dependence
Dirac structure of G Matrix Bethe-Salpeter equation 3-dimensional reduction : (RBBG) G=V+VgQG V NN int.(OBEP) g propergator Q Pauli operator Self-consistent calculations important G ? U s, U 0 Dirac eq. s.p. wf G matrix --- do not keep the track of rel. structure Extract the nucleon self-energy with proper isospin dep.
New decomposition of G Decomposition of DBHF G matrix V : OBEP G a projection method (1, ) (1, ) Short range m (g/m) 2 finite E. Shiller, H. Muether, E Phys. J. A11(2001)15
Nucleon self-energy Nucleon self-energy for scattering (k is related with E) Calculated in DBHF by G = V + G Direct Exchange : V OBEP G pseudo meson (1, ) (1, ) : vertex a,b : isospin index single particle Green’s function
Isospin dep. of Nucleon self-energy Single particle Green’s function T t : isospin operator Direct terms isoscalar isovector Exchange terms isoscalar isovector
Nucleon potential The optical potential of a nucleon the nucleon self-energy in the nuclear medium Nucleon self-energy in the nuclear medium with E > 0 k – E E incident energy
Self-Energy of proton and neutron ＝ 0,.3,.6, 1
Isospin dep. of effective mass in RMF Dirac Lorentz Neutron-rich asymmetric NM (RMF) , , Taking account of isovector scalar meson , , , U s U o should be of momentum and energy dependence
Nucleon self-energy in DBHF In neutron-rich matter U s U o of neutrons stronger than of protons
DBHF Dirac mass in DBHF : Lorentz mass: Isospin dep. of OMP is consistent with Lane pot. Ma, Rong, Chen et al., PLB604(04)170B.A.Li nucl-th/0404040
Summary Isospin dependence of the nucleon effective mass is studied in DBHF New decomposition of G matrix is adopted G=V+ G RMF approach with a constant self-energy can not account the isospin dep. of m* properly Isospin dep. of effective mass
G U s U o Single particle energy R. Brockmann, R. Machleidt PRC 42(90)1965 Momentum dep. of U s & U 0 are neglected works well in SNM, inconsistent results in ASNM wrong sign of the isospin dependence
Asymmetric NM Inconsequential results for asymmetric nuclear matter U s U 0 isospin dep. with a wrong sign S. Ulrych, H. Muether, Phys. Rev. C56(1997)1788
Projection method Projection method F. Boersma, R. Malfliet, PRC 49(94)233 Ambiguity results are obtained for with PS and PV Shiller,Muether, EPJ. A11(2001)15
Asymmetry Energy 3-body force Parabolic behavior increase as the density Ma and Liu PRC66(2002)024321;Liu and Ma CPL 19 (2002)190
Dirac and Lorentz mass RMF U s U o are constant in energy ~0.60 Dirac mass (scalar mass) Schroedinger equivalent potential, ~0.70 Lorentz mass (vector mass) Although not related to a non-locality of the rel. potentials, comparable with the effective mass in non-relativistic appr.
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