1、Isospin Dependence of ROMP & Nucleon Effective MassRHIC物理與低能強(qiáng)子物理討論會(huì)山東威海2004年8月4日7日馬中玉中國(guó)原子能科學(xué)研究院合作者：榮健 陳寶秋 朱志遠(yuǎn) 宋宏秋Contents Introduction Isospin dep. of effective int. Relativistic optical model potential Scattering from exotic nuclei Isospin dependence of effective mass SummeryIntroduction Import

2、ance 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 theoryDBHF approach Relativistic

3、 approaches NN + DBHF Success in NM saturation properties DBHF G Matrix - Nucleon effective int. Information of isospin dependenceDirac 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 t

4、rack of rel. structure GVVgQGG 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 220( )( )( )iiiskkMU kUk220( )iiiskkMUUAsymmetric NM Inconsequential r

5、esults for asymmetric nuclear matter Us U0 isospin dep. with a wrong signS. Ulrych, H. Muether, Phys. Rev. C56(1997)1788220( )iiiskkMUUProjection 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)15 551,G

6、0,sU UNew 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)15GVG Asymmetry Energy0.10.20.30.420304050600.0 0.2 0.4 0.6 0.8 1.00102030405060 E/A(,) - E/A(,0) MeV2 1.0 fm-1 1.2 fm-1 1.4

7、fm-1 1.6 fm-1 1.8 fm-1 DBHF BHF aasym()=E/A(,1)-E/A(,0) MeV fm-33-body forceParabolic behavior increase as the densityMa and Liu PRC66(2002)024321;Liu and Ma CPL 19 (2002)190asyaIsospin dep. NN effective int.DBHF Us U0 ( kF、 ) A G=V+G Us E/A B RMF g g g g density dep. isospin dep. effective int.RDDH

8、: Brockmann, Toki, PRL68(92)3408RDHF: Ma, Shi, Chen, PRC50(94)3170Ma, Liu, PRC 66(2002)024321Finite nuclei-0.15-0.10-0.050.000.05-0.08-0.06-0.04-0.020.00132Sn100Sn68Ni56Ni48Ni208Pb90Zr48Ca40Ca16O RMF.A Ref_nm Ref_fn RMF.B(rcCalc.-rcExpt.)/rcExpt.(E/ACalc.-E/AExpt.)/(E/AExpt.) F.Hofmann, C.M.Keil, H.

9、Lenske, PRC64(01)034314Optical model potential The optical potential of a nucleon the nucleon self-energy in the nuclear medium Nucleon self-energy in the nuclear medium with E 000( , )( )( ).( )Fsvk kkkkk0*02220( )1( )( )( )kvsE MkkkMkkk E E incident energy110100123410100k(p) k (fm-1)E (MeV) = 0.0

10、= 0.3 = 0.6kF = 1.36 fm-1k(n) E (MeV) = 0.0 for free NSimple model RHF in the and model g2/4=7.56 kF =1.36 fm-1 g2/4=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,P + 208Pb at Ep=65

11、 MeV030609012015018010-310-210-1100101102103104105 d/d(mb/sr)Anglep+208Pb Ep=65MeV-1.0-0.50.00.51.0p+208Pb Ep=65MeV P0306090120150180-1.0-0.50.00.51.0p+208Pb Ep=65MeV QAngleMa, Zhu. Gu, Zhuo, Nucl. Phys. A490(88)619Outline the methodGVG ,DBHF(k,kF,)Us(k,kF,)U0(k,kF,)Us(E,r) U0(E,r)LDAE-k self-consis

12、tently , real & imaginary ?Schroedinger type eq. (eliminating small component) Veff , Vs.o. , Vdarwin , Vcoulomb d/d , Ay , QEffective interactions Effective int. HF( ) Us, U0, B/A G Imaginary part of OMPDensity dep. Effec. coupling constants0.10.20246810 g2/4 (fm-3)221()( )()( )1()( )iiiiiisaii

13、satitb xdf xacgf xxgxd Effective int. HF( ) Us, U0, B/A GConstraints:(1 )1( 0 )0iiff1.11.21.31.41.51.6-15-10-505 E/A (MeV)kF (fm-1) = 0.0 1.11.21.31.41.51.6-15-10-505 E/A (MeV)kF (fm-1) = 0.3 1.11.21.31.41.51.6-15-10-505 E/A (MeV)kF (fm-1) = 0.6 Self-Energy of proton and neutron-350-300-250010020030

14、0400200250300100200300400 (a)Usp (MeV) (b)Usn (c)U0p (MeV)Energy (MeV) (d) U0nEnergy (MeV)0, .3, .6, 1208Pb density distribution02468101E-41E-30.010.102468100.00.20.40.6 distribution n (fm-3)R (fm) proton neutronNucleon Density Distributions of 208PbProton self-energies0246810-300-200-1000 Re Us (Me

15、V)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeV0246810-5051015 Im Us (MeV)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeV02468100100200300 Re U0 (MeV)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeV0246810-40-30-20-100 Im U0 (MeV)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeVSchroedinger equivalent potentials0246

16、810-60-40-200 Re Ueff (MeV)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeV0246810-0.6-0.4-0.20.00.2 Re US.O. (MeV)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeV0246810-30-20-100 Im Ueff (MeV)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200 MeV02468100.000.040.08 Im US.O. (fm)R (fm) Ep = 20 MeV Ep = 65 MeV Ep = 200

17、MeV208Pb (p, p)208Pb030609010-1100101102103104105106107108109101010111012 () (mb/sr) (deg)40MeV4547.349.461.46579.9208Pb(p,p)208Pb0306090036912151821201.0185.0155.098.079.965.0 Ay () (deg.)49.4MeV208Pb(p,p)208Pb208Pb (p, p)208Pb at E=65 MeV 0246810-40-30-20-100 Re Veff (MeV) VeffI VeffII0246810-12-9

18、-6-30 Im Veff (MeV)r (fm)0246810-0.6-0.4-0.20.00.2 Re Us.o. (MeV)02468100.000.020.04 Im Vs.o. (MeV)r (fm)Isospin dependence of OMPp+ 208Pb isospin dependence0306090120150180-101 Ay( ) (deg.)10-310-210-1100101102103104105 ( ) (mb/sr) Exp. Veff1 Veff265MeV p + 208PbIsospin dependence of OMP10VATtVV101

19、044VAZNVVVAZNVVnp Isospin dependence of OMP Lane potential difference of proton and neutron OMP501001502002503000102030 =0.1 =0.2 =0.3 =0.5 kF=1.20fm-1 Veff()-Veff(0)/ (MeV)Energy (MeV)kF=1.36fm-1V1=24MeVProton208Pb Lane potential 0123 Lane Potentials (MeV) RMOP Cal. Lane Model(a)0369120.00.30.6 r (

20、fm) RMF(NL3) (N-Z)/A(b)0246810-50-40-30-20-100 ReVcent (MeV)R (fm) n p)exp(11)(0310aArrrfDensity distribution of Ca-isotopes024680.000.030.060.090.12 (fm-3)r (fm) 40Ca 48Ca 60Ca 70Ca2468 r (fm)Neutron distributionProton disributionProperties of Ca-isotopes0246810-0.30.00.30.60.9 in nucleir (fm) 40Ca

21、 48Ca 60Ca 70Ca均方根半徑p (fm)n (fm)40Ca3.37713.328648Ca3.37873.604860Ca3.355124.160170Ca3.66814.4457p+ 60Ca at E=65 MeV 02468-400-300-200-1000100200300 Re U (MeV)Re UsRe U002468-50-40-30-20-100 Re Vcent (MeV)02468-18-12-60612 Im U (MeV)R (fm)Im UsIm U002468-15-10-505 Im Vcent (MeV)R (fm)Importance of i

22、sospin dependence OMP10-1100101102103104 Ay( ) d /d /mb/sr65MeV p + 40Ca-1.0-0.50.00.51.01.5 10-1100101102103104 65MeV p + 48Ca-1.0-0.50.00.51.01.5 10-1100101102103104 65MeV p + 60Ca-1.0-0.50.00.51.01.5 030609010-1100101102103104 /deg. /deg.65MeV p + 70Ca306090-1.0-0.50.00.51.01.5 Calculation with i

23、sospind dep. and isospin indep. OMP Results with isospin dep. OMP are better for stable nuclei. Large difference is observed for exotic nucleiIsospin dep. of effective mass Importance of the isospin depndence reaction dynamics of nuclear collisions by radioactice nuclei neutron-proton differential c

24、ollective 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*npmm*,*,nppnMMMM *0.70.8m*0.50.6sMMU*npmmDefinition of effective mass M* and m* refere to different quantities Jaminon & Mahaux89 m* characterizes the nonlocality of the microscopic potential in space (k-mass) an time (E-mass) derived from analyses of experimental data nonrel. shell mod