Nucleon Effective Mass in the DBHF

1. 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

2. 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

3. 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 Us, U0 are energy indep. Our work Relativistic approach  DBHF

4. 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

5. 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

6. Dirac mass •  Relativistic approach • Effective mass is usually defined as • M* = M – UsDirac 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

7. Dirac and Lorentz mass  RMF Us Uo are constant in energy Us= 375±40 MeV Ring’96 ~0.60±0.04Dirac mass (scalar mass)  Schroedinger equivalent equation Schroedinger equvalent potential , Lorentz mass

8. 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.

9. DBHF approach  Relativistic approaches NN + DBHF Success in NM saturation properties  DBHF G Matrix ––- Nucleon effective int. Information of isospin dependence

10. 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 ? Us, U0  Dirac eq.  s.p. wf G matrix --- do not keep the track of rel. structure Extract the nucleon self-energy with proper isospin dep.

11. 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

12. 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

13. Isospin dep. of Nucleon self-energy Single particle Green’s function Tt : isospin operator Direct terms isoscalar isovector Exchange terms isoscalar isovector

14. Nucleon potential The optical potential of a nucleon thenucleon self-energy in the nuclear medium Nucleon self-energy in the nuclear medium with E > 0 k – E E incident energy

15. Self-Energy of proton and neutron ＝0, .3, .6, 1

16. Isospin dep. of effective mass in RMF Dirac Lorentz Neutron-rich asymmetric NM (RMF) , ,  Taking account of isovector scalar meson  , , ,  Us Uo should be of momentum and energy dependence

17. Nucleon self-energy in DBHF In neutron-rich matter Us Uo of neutrons stronger than of protons

18. DBHF  Dirac mass in DBHF :  Lorentz mass:  Isospin dep. of OMP is consistent with Lane pot. B.A.Li nucl-th/0404040 Ma, Rong, Chen et al., PLB604(04)170

19. 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

20. Thanks

22. GUs Uo Single particle energy R.Brockmann, R. Machleidt PRC 42(90)1965 Momentum dep. of Us & U0 are neglected works well in SNM, inconsistent results in ASNM wrong sign of the isospin dependence

23. Asymmetric NM Inconsequential results for asymmetric nuclear matter  Us U0 isospin dep. with a wrong sign S. Ulrych, H. Muether, Phys. Rev. C56(1997)1788

24. 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

25. Asymmetry Energy 3-body force Parabolic behavior increase as the density Ma and Liu PRC66(2002)024321;Liu and Ma CPL 19 (2002)190

26. Dirac and Lorentz mass  RMF Us Uo 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.

27. Nucleon effective mass