Symmetry Energy of Nuclear Matter and Properties o

SUNY-NTG-97-10March18,1997SymmetryEnergyofNuclearMatterandPropertiesofNeutronStarsinaRelativisticApproachC.-H.Lee,T.T.S.Kuo,G.Q.LiandG.E.BrownDepartmentofPhysics,StateUniversityofNewYork,StonyBrook,N.Y.11794,USA.ABSTRACTAsymmetricnuclearmatteristreatedintheformalismofDirac-BruecknerapproachwithBonnone-boson-exchangenucleon-nucleoninteraction.Weextractthesymmetryenergycoecientatthesaturationtobeabout31MeV,whichisingoodagreementwithempiricalvalueof304MeV.Thesymmetryenergyisfoundtoincreasealmostlin-earlywiththedensity,whichdiersconsiderablyfromtheresultsofnon-relativisticap-proaches.ThisndingalsosupportsthelinearparameterizationofPrakash,AinsworthandLattimer.Wend,furthermore,thatthehigher-orderdependenceofthenuclearequationofstateontheasymmetryparameterisunimportantuptodensitiesrelevantforneutronstars.Theresultingequationofstateofneutron-richmatterisusedtocal-culatethemaximummassofneutronstar,andwendittobeabout2.1M.Possiblemechanismsforthesofteningoftheequationofstatearealsodiscussed.1IntroductionAlthoughthefactthattheequationofstateofnuclearmattercontainsasymmetryenergytermhasbeenknownsincetheearlydaysofnuclearphysics,theexperimentalandtheoreticalstudyofthesymmetryenergyanditsdensitydependenceisbecominganincreasinglyinterestingtopic,mainlybecauseoftherecentdevelopmentofradioactiveionbeamfacilitiesthatallowonetostudy1thestructureandreactionsofneutron-richnuclei[1,2,3],inwhichthesymmetryenergyplaysanimportantrole.Therecognizationthatthesymmetryenergy,especiallyitsdensitydependence,hasaprofoundeectonthepropertiesofneutronstars[4,5,6,7,8]alsomakestheexperimentalandtheoreticaldeterminationofthisquantityveryrelevantanduseful.Empirically,thesymmetryenergycoecientS2(0)innuclearmatteratthesaturationdensity0canbeextractedfromthesystematicstudyofthemassesofatomicnuclei,basedon,e.g.,theliquiddropletmodel[9,10]orthemacroscopic-microscopicmodel[11,12].This,however,determinesthesymmetryenergyonlyforsmallasymmetryparameter(=(N−Z)=A)andfordensitiesaround0.FromtheexperiencewithsymmetricnuclearmatterweknowthatthedeterminationofthecompressionmodulusKat0doesnotuniquelyconstraintheequationofstateathighdensities.Similarly,thedeterminationofS2(0)doesnotguaranteeanunambiguousdeterminationofsymmetryenergyathighdensitieswhichisneededforthestudyofneutronstarproperties.Thesituationchangeswiththerecentadvancesinthedevelopmentofvariousradioactiveionbeamfacilitiesaroundtheworldthatwillproducenucleiwithlargeneutronexcessnearandbeyondthedrip-line.Thestudyofthestructureoftheseneutron-richnucleiallowsustodeterminethesymmetryenergyforlargeasymmetryparameterandextractpossiblehigher-orderdependenceon.Furthermore,thecollisionsofneutron-richnucleiatrelativisticenergies,duringwhichnuclearmatterwithdensitiesupto(2-3)0iscreated,makeitpossibletostudyexperimentallythedensitydependenceofthesymmetryenergy[13,14].Onthetheoreticalside,thesymmetryenergyhasbeenstudiedovermanyyearsbasedonvariousmodelsandapproaches,whichcanroughlybedividedintophenomenologicalandmicroscopic,eachofwhichcanbesubdividedintorelativisticandnon-relativistic.Hartree-Fock[15]andThomas-Fermi[16]calculationswithSkyrme-typeeectivenucleon-nucleoninteractionshavebeencarriedouttostudyvariousnuclearproperties,includingsymmetryenergy.Thesymmetryenergycoef-cientS0fromthesecalculationsrangesfromabout27to38MeV,andisinagreementwiththeempiricalvalueof304MeV[17].SincethetheparametersintheSkyrmeforcesareadjustedtotnuclearmatterandnitenucleiproperties,thisdegreeofagreementisfullyexpected.Anotherphenomenologicalapproachthathasbeenusedextensivelyinthestudyofnuclearpropertiesisquantumhadrodynamics(QHD)whichisbasedontherelativisticeldtheory[18,19].Thesymmetryenergyinthisapproachhastwocontributions[20,21];onecomesfromthe`kinetic'energydierencebetweensymmetricandasymmetricmatter,andtheotherarisesfrom2theexchangeoftherhomesonwhichcouplestoneutronandprotonwithoppositesign.Thesymmetryenergyinthisapproachrangesfromabout35to40MeV[21,22,23],somewhatlargerthantheempricalvalueof304MeV.Onamoremicroscopiclevel,ithasbeentheultimategoaloftraditionalnuclearphysicstode-scribeinaconsistentwaythepropertiesofnuclearmatter,nitenuclei,andnuclearreactionsfromrealisticnucleon-nucleoninteractionsthatarettedtothenucleon-nucleonscatteringanddeuterondata.Therearebasicallytwoapproachestothis;namely,variational-typeandBrueckner-type.Invariationalcalculations,itiswell-knownthattherealistictwo-nucleonpotentialalone,suchasArgonnev14(AV14)orUrbanav14(UV14),doesnotprovideasatisfactorydescriptionofnuclearmatterproperties[24,25].Aphenomenologicalthree-nucleoninteractionhastobeintroduced,whoseparametersareadjustedsothatthevariationalcalculationswiththetwo-andthree-bodyinteractionsgivecorrectnuclearmattersaturationdensity,bindingenergyandcompressionmod-ulus.Thesymmetryenergycoecientobtainedinthevariationalcalculationsisabout30MeV[24,25].TheBrueckner-typeapproachhasbothnon-relativisticandrelativisticversions,knownasBrueckner-Hartree-Fock(BHF)[26,27]andDirac-Brueckner-Hartree-Fock(DBHF)[28,29,30,31,32],respectively.As