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/

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

Thanks

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.

Nucleon effective mass