第十三屆核結構研討會暨第九次“核結構與量子力學”專題討論會內蒙古·赤峰2010年7月夸克核心的混合星及致密星第三家族特木爾巴根（南陽師范學院）第十三屆核結構研討會暨第九次“核結構與量子力學”專題討論會內1IIntruductionIITheoryIIIThirdFamilyofCompactStarsIIntruduction2Introduction1.HistoryofNeutronStarsStudy2.ModelsforNeutronStar3.PresentsituationsforNeutronStarInvestication4.MotivationIntroduction1.HistoryofNeut3Intro.

--HistoryIn1932,Chadwickdiscovedneutron,andLandaupredictedneutronstarsimmediately

.In1934,Baade

and

ZwickyIn1939,Tolman-Oppenheimer-Volkoff(TOV)equations.In1967,HewishandBelldetectedthefirstpulsar,andknownasrotatingneutronstar.Intro.--HistoryIn1932,4Intro.—ModelsforNSIntro.—ModelsforNS5Intro.--TOVEquations

Oppenheimer-Volkoff(OV)方程：r→距星體中心的距離；p(r)→距中心為r處的壓強；(r)→能量密度；M(r)→半徑為r的球體內的物質的質量。

由物態方程p=p(),給定星的中心密度，由OV方程就可進行數值求解。Intro.--TOVEquationsOppenhe6Intro.–PresentSituationsforNSStudy1.Neutronstarwithhyperons(orwithkaoncondensation):

n,p,e,,

,,,,k-(-)2.Strange(quark)stars:

u,d,s，e3.Hybridstarswithquarkcore:

n,p,e,,

,,,,

u,d,s4.ThirdfamilyofcompactstarsIntro.–PresentSituationsfor7IITheories1HadronicPhase:RMFT2QuarkPhase:MITBagModel，NJLModel,M-D-Dquarkmodel,QMFM,EMQM,D-D-BintheframeworkofMITbagModel

3MixedPhase:Gibbscriterionforphaseequilibriumandglobalelectricchargeneutrality.IITheories1HadronicPhase:8Quarkmodels

1Effectivemassbagmodel(EMBM)K.SchertlerNuclear,C.GreinerPhysicsA616(1997)

2Nambu—Jona-Lasinio（NJL）ModelY.NambuandG.Jona-LasinioPhys.rev.122,124(1961)3Mass-density-dependentQuarkmodel(MDDQM)—

G.X.PengPhys.Rev.C62(025801)

4

Density-dependentbagconstantintheframewokofMITbagmodelQuarkmodels1Effectivemass9IIIHybridsarswithquarkcoreandthirdfamilyofcompactstars

Hadronphase：TM2parametersetsintheframeworkofRMFTTM1,TM2:Y.Sugahara,H.Toki,Relativisticmean-fieldtheoryorunstablenucleiwithnon-linearsigmaandomegaterms,Nucl.Phys.A579(1994)557-572

IIIHybridsarswithquarkco10ThermodynamicalPotencial

ThermodynamicalPotencial11FomulaeforquarkmodelsMass-density-denpendentquarkmodelEffectivemassquarkmodelNJLmodelQuarkcondensationFomulaeforquarkmodelsMass-d12Energydensityandpressure(EOS)Energydensityandpressure(E13EOS-IfBagParameterisDensityDependentEOS-IfBagParameterisDensit14FormulasformixedphaseGibbscriterionforphaseequilibriumChemicalpotencialssatisfyFormulasformixedphaseGibbs15Conservationofbaryonnumberdensity,globalelectricchargeneutralityandtotalenergydensityformixedphasewhereConservationofbaryonnumber16

Calculationalresults

1.GL85,TM2-D-D-BintheframeworkofbagmodelSubmittedtoEPJA,

ChinesePhysicsCVol.332.GL85-NJLModelHP&NP,2006,30(10)3.GL85-MDDQMHP&NP,2006,30(12)4.GL85,TM2-EMBMCommun.Theor.Phys.45(2006)5.GL85—SEBMEur.Phys.J.AVol.38,287-293(2008)Calculationalresults1.GL8517Density-dependentbagparameterDensity-dependentbagparamete18EnergyDensity/BaryonVersusTotalBaryonNumberDensity

EnergyDensity/BaryonVersus19SQMEOS

SQMEOS20HybridstarEOSHybridstarEOS21Mass-radiusrelationofSSMass-radiusrelationofSS22Mass-radiusrelationofhybridstars-ThirdfamilyofcompactstarsMass-radiusrelationofhybrid23PossibleExistenceofTFTM2+EMBMg=0—1.0TFPossibleExistenceofTFTM2+E24PossibleExistenceofTFTM2+EMBM,g=0,B1/4=175-180MeVPossibleExistenceofTFTM2+E25ConclusionsConclusions26結論(續)

以TM2為核物質狀態方程的混合星質量-半徑曲線中，口袋常數B1/4在175MeV-178MeV（g=0）之間或耦合常數在g=0-1(口袋常數B1/4=180MeV時)很小范圍內存在TF。這些計算結果為觀測具有相同質量而不同結構和半徑的雙星提供了理論依據。TF的存在亦是混合星內存在夸克相變的有力證據。

在有效質量口袋模型中,強耦合常