On the Dirac Structure of the Nucleon Selfenergy i

OntheDiracStructureoftheNucleonSelfenergyinNuclearMatterA.Trasobares,A.Polls,A.RamosDepartamentd'EstructuraiConstituentsdelaMateriaUniversitatdeBarcelona,E-08028Barcelona,SpainH.M¨utherInstitutf¨urTheoretischePhysik,Universit¨atT¨ubingen,D-72076T¨ubingen,GermanyAbstractTherelativisticstructureoftheself-energyofanucleoninnuclearmatterisinvestigatedincludingtheimaginaryandrealcomponentswhicharisefromthetermsofrstandsecondorderintheNNinteraction.AparameterizedformofBruecknerGmatrixisusedfortheNNinteraction.TheeectsofthetermsbeyondtheDBHFapproximationonquasiparticleenergiesandtheopticalpotentialfornucleon-nucleusscatteringarediscussed.1IntroductionDuringthelastfewyearstheattemptstoderivetheground-statepropertiesofnuclearsystemsfromarealisticnucleon-nucleon(NN)interaction,havebeenpromotedverymuchbytheunderstandingthatrelativisticeectsmaybenon-negligibleinsuchin-vestigations.TheseideaswereoriginallydevelopedwithinthevariousversionsofthephenomenologicalWaleckamodel[1].TheDiracstructureoftheNNinteractionwithastrongrepulsivecomponentoriginatingfromtheexchangeofthe!vectormesonandanattractivecomponentofmediumrangedescribedintermsofascalarmeson()leadstoaself-energyofthenucleoninthenuclearmediumwhichcontainsalargescalarcomponentsandalargetimelikevectorcomponent0.Thesetwocomponentscompensateeachothertoalargeextentifonecalculatesthesingle-particleenergy.Thisleadstothewellknownfactthatthebinding-energyofnucleiareverysmallascomparedtotherestmassofthenucleonM,afactwhichhasoftenbeenusedtoarguethatrelativisticeectsshouldbesmallinthemany-bodyproblemofnuclearphysics.Theindividualcomponentsoftheself-energysareoftheorderofthenucleonrestmass(typicallyonethirdofM).ThereforethestructureoftheDiracspinorsinthenuclearmediumismodiedtoquitesomeextentascomparedtotheDiracspinorforafreenucleon.ThismediumdependenceoftheDiracspinors,whichaectstheevalua-tionoftheNNinteractioninthemedium,leadstoasaturationmechanismfornuclearmatter.1Thesemoreorlessempiricalmodelsreceivedsupportfromcalculations,whichstartfromarealisticOne-Boson-ExchangemodeloftheNNinteraction[2].InthiscontextrealisticNNinteractionmeansthattheparameterscontainedinthesemodelsaread-justedtodescribetheexperimentaldataoffreeNNscattering.Usingsucharealis-ticNNinteractioninamany-bodycalculationoftheDirac-Brueckner-Hartree-Fock(DBHF)type,resultswereobtainedforthesaturationpointofnuclearmatterwhichwereinquiteagoodagreementwiththeempiricalsaturationpoint[3,4].SuchaDBHFcalculationaccountsfortheeectofcorrelationsontheleveloftheBHFapproxima-tion,i.e.thelowestorderintheholelineexpansion,andallowsfortherelativisticeectswhichwejustoutlined.ThissuccessoftherelativisticfeaturescontainedintheDBHFapproachcouldbeasolutionofanoldproblem:theso-calledCoesterbandphenomenon[5],whichstandsforthefactthatmany-bodycalculationsbasedonvari-ousrealisticmodelsoftheNNinteractionleadtopredictionsforthesaturationpointofnuclearmatter,whicheitherfailtoyieldenoughbindingorpredictasaturationdensitytwiceaslargeastheempiricalvalue.SuchaCoesterbandcanalsobeobservedinnon-relativisticstudiesofnitenuc-lei[6].ThereforeitwasquiteobviousthatattemptshavebeenmadetoincludetherelativisticfeaturesalsoinDBHFcalculationsofnitenuclei.Indeedtheinclusionofrelativisticeectsgaveasubstantialimprovementinthecalculatedbindingenergiesandradiiofnitenuclei[7,8].However,thereremainsstilladiscrepancybetweentheDBHFresultsandtheexperimentalvalues.Ontheotherhanditwasobservedthatanextensionofthenon-relativisticBHFapproachtoadenitionofthenucleonself-energywhichaccountsinasymmetricwaynotonlyfortheparticle-particleladdersincludedintheBruecknerG-matrixbutalsoforthecorrespondinghole-holescatteringtermmayleadtoalargerbindingenergyandalargerradiusthanobtainedintheBHFapproach[9].Asimilarfeature,mov-ingthesaturationpointawayfromtheCoesterbandbyincludinghole-holescatteringterms,hasalsobeenobservedinparticle-particlehole-holeRPAcalculationofnuclearmatter[10,11].Takingaveryoptimisticpointofviewonemayarguethatthecom-binationofrelativisticeectsandhole-holescatteringtermsmayleadtoanimprovedmicroscopicunderstandingofgroundstatepropertiesofnuclearsystems.Intheworkpresentedherewewouldliketoinvestigatetheeectsofparticle-particleandhole-holescatteringtermsontherelativisticstructureofthenucleonself-energy.Forthatpurposeweconsiderthenucleonself-energydenedwithalltermsofrstandsecondorderintheNNinteraction(seeFig.1).Incontrasttoearlierinvestigations[12,13,14,15]weevaluatetheimaginarycontributionstothenucleonself-energyallowingforallpossiblecombinationsofmomentumkandenergyk0.Thereforewecanusedispersionrelationstoevaluatealsotherealpartofthesecondorderdiagrams.WeinvestigateindetailtheeectofthesehigherorderdiagramsontheDiracstructureoftheself-energy.Furthermorewederivefromthisrelativisticself-energyanopticalpotentialtobeusedinaSchr¨odingerequationfornucleon-nucleusscattering.Thetechnicaldetailsforthecalculationoftheimaginarycomponentsintheself-energyarepresentedinsection2.Thedispersionrelationsusedtoevaluatethecorre-spondingrealcomponentsaregiveninsection3.