On the role of the effective interaction in quasi-

arXiv:nucl-th/9710033v115Oct1997ONTHEROLEOFTHEEFFECTIVEINTERACTIONINQUASI–ELASTICELECTRONSCATTERINGCALCULATIONSEduardoBauer∗DepartamentodeF´ısica,FacultaddeCienciasExactas,UniversidadNacionaldeLaPlata,LaPlata,1900,Argentina.AntonioM.LallenaDepartamentodeF´ısicaModerna,UniversidaddeGranada,E–18071Granada,Spain.AbstractTheroleplayedbytheeffectiveresidualinteractioninthetransversenu-clearresponseforquasi–freeelectronscatteringisdiscussed.TheanalysisisdonebycomparingdifferentcalculationsperformedintheRandom–PhaseApproximationandRingApproximationframeworks.Theimportanceoftheexchangetermsinthisenergyregionisinvestigatedandthechangesonthenuclearresponsesduetothemodificationoftheinteractionareevaluated.Thecalculatedquasi–elasticresponsesshowclearindicationoftheirsensibil-itytothedetailsoftheinteractionandthisimposesthenecessityofamorecarefulstudyoftheroleofthedifferentchannelsoftheinteractioninthisexcitationregion.PACSnumber:21.30.+y,25.30.Fj,21.60.JzTypesetusingREVTEX1I.INTRODUCTIONAnaspectofgreatimportanceinnuclearstructurecalculationsatanyexcitationenergyconcernswiththeroleoftheeffectiveinteraction.Atlowenergiesthisproblemhasgeneratedaconsiderablebodyofworkinthelasttwentyyears.Onthecontrary,thisisaquestionnotstudiedyetindeepintheliteratureforhigherenergies.Giantresonancesshowanintricatemixtureofmultipolaritiesandthestudyofhowtheinteractionaffectsitisadifficulttask.Inthequasi–elasticpeakregion,theproblemofthelongitudinalandtransverseseparationhasoccupiedmostoftheinvestigationscarriedouttillnowandthediscussionoftheeffectsduetochangesintheeffectiveinteractionhavenotbeenconsideredindetail.Asanexample,wementiontheconsiderablenumberofRandom–PhaseApproxima-tion(RPA)typecalculationsperformedinthisenergyregion,muchofthemusingresidualinteractionswhichincludebasicallyazero–rangetermplusmeson–exchangepotentialscor-respondingtoπ,ρand,eventually,othermesons[1]–[9].Animportantpointconcerningtheinteractionreferstothevalueschosenfortheparametersenteringinthezero–rangepiece.However,andtothebestofourknowledge,onlyinRef.[9]acertaindiscussionrelativetotheeffectsofvaryingtheseparameterscanbefound.Infact,thecommonpracticeistopickaninteractionfromtheliterature,whichusuallycorrespondstoaparameterizationfixedforlowenergycalculations,andafterwardsuseittoevaluatequasi–freeobservablessometimeswithouttakingcareoftheeffectivetheoryinwhichtheinteractionwasadjusted.Itisobviousthat,toacertainlevel,doubtfulresultsarepossiblebecauseoftheknownlinkbetweeneffectivetheoryandinteraction.Inthisworkwewanttoaddressthisquestionandinvestigateifdifferentparametrizationsoftheinteractioncanproducenoticeabledifferencesintheresultsandtheextenttowhichtheuseofaninteractionfixedforagiveneffectivetheoryaffectstheresultsobtainedwithinadifferentone.InSec.IIwegivethedetailsabouttheeffectivetheoriesandinteractionsusedtoperformthecalculations.InSec.IIIweshowanddiscusstheresultswehaveobtained.2Finally,wepresentourconclusionsinSec.IV.II.EFFECTIVETHEORIESANDINTERACTIONSThefirstinteractionweconsiderinthisworkistheso–calledJ¨ulich–StonyBrookinter-action[10]whichisaneffectiveforcewidelyusedforcalculationsinthequasi–elasticpeak.Itisgivenasfollows:VIres=VLM+Vπ+˜Vρ.(1)HereVLMisazero–rangeforceofLandau–Migdaltype,whichtakescareoftheshort–rangepieceoftheNNinteraction:VLM=C0[g0σ1·σ2+g′0σ1·σ2τ1·τ2].(2)Ontheotherhand,afinite–rangecomponentgeneratedbythe(π+ρ)–mesonexchangepo-tentialsisalsoincluded.Thetildein˜Vρmeansthatthebareρ–exchangepotentialisslightlymodifiedinordertotakeintoaccounttheeffectoftheexchangeofmoremassivemesons.Inparticular,afactorr=0.4ismultiplyingthefinite–rangenon–tensorpieceofthepotential(seeRef.[10]fordetails).Thisforcewasfittedtoreproducelowenergymagneticpropertiesintheleadregion(specifically,magneticresonancesin208Pbandmagneticmomentsandtransitionprobabilitiesintheneighboringnuclei).ThecalculationswereperformedintheframeworkoftheRPAandWoods–Saxonsingle–particlewavefunctionswereusedintheconfigurationspace.Thevaluesg0=0.57andg′0=0.717(withC0=386.04MeVfm3)werefoundtobeadequatetodescribethepropertiesstudied.Aspreviouslystated,thisinteractionhasbeenconsideredindifferentcalculationsinthequasi–elasticpeak(seee.g.[9]).TheproblemarisebecausesomeofthemhavebeendonewithintheFermigas(FG)formalism,withlocaldensityapproximationtodescribefinitenuclei,intheringapproximation(RA),wheretheexchangetermsarenottakenintoaccount,andwiththefullunmodifiedρ−exchangepotential.Underthesecircumstances,3thepossibleeffectsinthenuclearresponsesduetotheinconsistencybetweenthemodelandtheeffectiveinteractioncouldbenon–negligible.Thisispreciselythefirstaspectwewanttoinvestigate.TodothatwecomparetheresponsesobtainedwiththeJ¨ulich–StonyBrookinteractionwiththosecalculatedwithasecondeffectiveforceoftheform:VIIres=VLM+Vπ+Vρ,(3)byconsideringthesamevaluesforthezero–rangeparametersinbothcases.TheforceinEq.(3)onlydiffersfromVIresintheρ-potentialwhich,inthiscase,doesnotincludeanyreductionfactor.BothRPAandRAeffectivetheoriesareusedtoanalyzetheresults.Asecondquestionofinteresttousistodeterminehowthechangeofthezero–rangeparametersaffectstheresponsescal