Isospin Dependence of ROMP & Nucleon Effective Mass

1. Isospin Dependence of ROMP & Nucleon Effective Mass RHIC物理与低能强子物理讨论会 山东威海 2004年8月4日－7日 马中玉 中国原子能科学研究院 合作者：荣健 陈宝秋 朱志远 宋宏秋

2. Contents  Introduction  Isospin dep. of effective int.  Relativistic optical model potential  Scattering from exotic nuclei Isospin dependence of effective mass Summery

3. Introduction  Importance of isospin dependence in many aspects: exotic nuclei; astrophysics; heavy ion collision etc.  Isospin dependence of quantities asymmetric energy as function density effective interaction effective mass etc.  Less knowledge from experiments  Study from a fundamental theory

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

5. Dirac structure of G Matrix Bethe-Salpeter equation 3-dimensional reduction: (RBBG) Self-consistent calculations G ? Us, U0  Dirac eq.  s.p. wf G matrix --- do not keep the track of rel. structure

6. 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

7. 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

8. 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

9. 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

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

11. Isospin dep. NN effective int. • DBHF  Us U0 ( kF、 ) A • G=V+G Us E/AB •  RMF •  •  • gg g g density dep. • isospin dep. effective int. RDDH: Brockmann, Toki, PRL68(92)3408 RDHF: Ma, Shi, Chen, PRC50(94)3170 Ma, Liu, PRC 66(2002)024321

12. Finite nuclei F.Hofmann, C.M.Keil, H.Lenske, PRC64(01)034314

13. Optical model 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

14. Simple model  RHF in the  and  model g2/4=7.56 kF=1.36 fm-1 g2/4=10.11 B/A=-15.75MeV Real part : Hartree-Fock Imaginary part: polarization work in the symmetric nuclear matter ZY Ma, P Zhu. YQ Gu, YZ Zhuo, Nucl. Phys. A490(88)619 s,w s,w

15. P + 208Pb at Ep=65 MeV Ma, Zhu. Gu, Zhuo, Nucl. Phys. A490(88)619

16. Outline the method DBHF σ’,ω’ δ’,ρ’ σ,ω,η δ,ρ,π LDA Us(k,kF,β) U0(k,kF,β) Us(E,r) U0(E,r) Σ(k,kF,β) real & imaginary ? ρ , β E-k self-consistently Schroedinger type eq.(eliminating small component) Veff , Vs.o. , Vdarwin , Vcoulomb dσ/dΩ , Ay , Q

17. Effective interactions  Effective int. HF(   )  Us, U0, B/A  G  Imaginary part ofOMP

18. Density dep. Effec. coupling constants  Effective int. HF(   )  Us, U0, B/A  G Constraints:

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

20. 208Pb density distribution

21. Proton self-energies

22. Schroedinger equivalent potentials

23. 208Pb (p, p)208Pb

24. 208Pb (p, p)208Pb at E=65 MeV Isospin dependence of OMP

25. p+ 208Pb isospin dependence

26. Isospin dependence of OMP Isospin dependence of OMP Lane potential difference of proton and neutron OMP V1=24MeV Proton

27. 208Pb Lane potential

28. Density distribution of Ca-isotopes

29. Properties of Ca-isotopes

30. p+ 60Ca at E=65 MeV

31. Importance of isospin dependence OMP  Calculation with isospind dep. and isospin indep. OMP  Results with isospin dep. OMP are better for stable nuclei.  Large difference is observed for exotic nuclei

32. Isospin dep. of effective mass  Importance of the isospin depndence reaction dynamics of nuclear collisions by radioactice nuclei neutron-proton differential collective flow,isospin equil. neutron star properties  Nothing is known experimentally about Non-relativistic models: dep. on models RMF: consistent with Exp. B.A.Li nucl-th/0404040

33. Definition of effective mass  M* and m* refere to different quantities Jaminon & Mahaux’89  m* characterizes the nonlocality of the microscopic potential in space (k-mass) an time (E-mass) derived from analyses of experimental data nonrel. shell model or optical model

34. Dirac and Lorentz mass  RMF Us Uo are constant in energy Dirac mass (scalar mass) Schroedinger equivalent potential Lorentz mass (vector mass) not related to a non-locality of the rel. potentials Us Uo should be of momentum and energy dependence

35. DBHF  Scalar mass in DBHF :  Vector mass:  Isospin dep. of OMP is consistent with Lane pot.

36. Summary  Isospin dependence of the ROMP is studied from the DBHF  New decomposition of G matrix is adopted G=V+G ROMP for finite nuclei EME and LDA  Isospin dep. of OMP is important for the reaction of radioactive nuclei  Isospin dep. of effective mass

37. Thanks