Energy-dependent Lorentz covariant parameterizatio

arXiv:0710.3201v2[nucl-th]3Dec2007APS/123-QEDEnergy-dependentLorentzcovariantparameterizationoftheNNinteractionbetween50and200MeVZ.P.Li1,G.C.Hillhouse2,1,andJ.Meng1,2,3,41SchoolofPhysics,PekingUniversity,Beijing1008712DepartmentofPhysics,UniversityofStellenbosch,Stellenbosch,SouthAfrica3InstituteofTheoreticalPhysics,ChineseAcademyofScience,Beijing100080and4CenterofTheoreticalNuclearPhysics,NationalLaboratoryofHeavyIonAccelerator,Lanzhou730000(Dated:February2,2008)AbstractForlaboratorykineticenergiesbetween50and200MeV,wefocusongeneratinganenergy-dependentLorentzcovariantparameterizationoftheon-shellnucleon-nucleon(NN)scatteringam-plitudesintermsofanumberofYukawa-typemesonexchangesinfirst-orderBornapproximation.ThisparameterizationprovidesagooddescriptionofNNscatteringobservablesintheenergyrangeofinterest,andcanalsobesuccessfullyextrapolatedtoenergiesbetween40and300MeV.PACSnumbers:21.30.-x,13.75.Cs,24.10.Jv1I.INTRODUCTIONWepresentanenergy-dependentLorentzcovariantparameterizationoftheon-shellnucleon-nucleon(NN)scatteringmatrixatincidentlaboratorykineticenergiesrangingfrom50to200MeV.Inparticular,wefocusontherelativisticHorowitz-Love-Franey(HLF)model[1,2,3,4]whichparameterizestheNNscatteringamplitudesasanumberofYukawa-typemeson-exchangeterms.TheoriginalHLFmodelparameterizedppandpnscatteringamplitudesatdiscreteen-ergiesof135,200and400MeV[1,2].Adrawbackoftheinitialrepresentationwasthatseparatefitswereperformedateachenergyresultinginnon-systematicandunphysicaltrendsinthevariousmodelparametersasafunctionofenergy.Thiswasalsoundesirableinthesensethatithinderedmeaningfulcomparisonsoftheoff-shellpropertiesoftheNNscat-teringmatrixatdifferentenergies.ThisproblemwassubsequentlyaddressedbyMaxwellwhodevelopedenergy-dependentparameterizationsoftheNNscatteringamplitudesfortwoenergyranges,namely200-500MeV[3]and500-800MeV[4].Sinceseveralexperimentsatfutureradioactiveionbeamfacilitieswillbeconductedatnucleonenergieslowerthan200MeV,itisessentialtoextendtheHLFmodeltolowerenergiessoastogeneratereliableinputfornuclearreactionmodels.AnattractivefeatureofHLFmodelistheexistenceofasimplerelationship–lackinginconventionalnonrelativisticmodels–betweentheLorentzinvariantNNscatteringampli-tudesandmesonsmediatingtheinteraction.Moreover,thismodelhasaphysicalbasisintheone-boson-exchange(OBE)picture,sincethevaluesoftherealmeson-nucleoncouplingconstants(atenergieshigherthan200MeV)aresimilartothosearisingfrommoresophis-ticatedOBEmodels[1].InadditiontobeingemployedasthebasicNNinteractiondrivingthedominantreactionmechanisminseveralrelativisticscatteringmodelsofnucleon-inducedreactions,theHLFmodelhasalsobeenappliedtoextractrelativisticmicroscopicopticalpotentials[2,5,6,7]forstudyingelasticprotonscatteringfromstablenuclei,aswellasforgeneratingscatteringwavefunctionsforevaluatingtransitionmatrixelementsinvariousrelativisticdistortedwavemodels[5,6].Morespecifically,thelattermicroscopicopticalpo-tentialsaregeneratedbyfoldingtheHLFt-matrixwiththerelevantrelativisticmeanfieldLorentzdensitiesviatheso-calledtρ-approximation.Indeed,oneofthetriumphsofthisfoldingprocedureisthatthemicroscopicpotentials,forenergiesfrom200to400MeV,are2virtuallyidenticaltothecorrespondingglobalphenomenologicalDiracopticalpotentials,whichhavebeenshowntoprovideexcellentquantitativepredictionsofscatteringobserv-ablesforelasticprotonscatteringfromspin-zerostablenucleirangingfrom12Cto208Pbandforincidentenergiesbetween20and1040MeV[8].Oneofthefrontierareasofresearchinnuclearphysicsistounderstandthepropertiesofnucleifarfromthebeta-stabilityline,theso-calledexoticorunstablenuclei.Thesestudiesprovideinsightintothenuclearprocessesthatunderlietheevolutionofthestarsandtheoriginoftheelementsinthecosmos.Indeed,anumberofradioactiveionbeamfacilitiesarecurrentlyunderconstructiontostudyshort-livedrareisotopes.Inparticular,thereareplanstostudyexclusiveproton-inducedproton-knockoutreactions(usinginversekinematics)atfacilitiessuchasRIKENandGSIforbothneutron-andproton-richnucleiatenergieslowerthan200MeVpernucleon.Fortheeventualinterpretationofthesedataitisessentialtohavereliableopticalpotentials.ExistingglobalDiracopticalpotentialshavebeenconstrainedtoreproduceelasticprotonscatteringfromstablenuclei[8],andhencethereisnoreasontobelievethatthesepotentialscanbereliablyextrapolatedforstudiesofunstablenuclei.Ontheotherhand,onecanreadilyextendtheabove-mentionedfoldingproceduretocalculatescatteringpotentialsforproton-inducedreactionsonexoticnuclei.Moreover,thesuccessfulapplicationoftherelativistictρapproximationtodescribeelasticprotonscatteringfromstablenuclei,givesoneconfidenceinextendingthisapproachtostudyprotonscatteringonexoticnuclei.Twobasicingredientsunderlytherealizationofthesefoldingpotentials,namelyasuitableanalyticalrepresentationfortheNNinteractionintheenergyrangeofinterest,aswellasanappropriaterelativisticmodelofnuclearstructure[9].Severalrelativisticmeanfieldnuclearstructuremodelsarecurrentlybeingdevelopedforstudyingthestructureofunstablenuclei[9,10].Inthispaper,however,wefocusondevelopingaHLF-typeparamet