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ElectronScatteringforNuclearandNucleonStructure Thescatteringofhigh-energyelectronsfromnuclearandnucleontargetsprovidesamicroscopeforexaminingthestructureofthesetinyobjects.Thebestevidencewehaveon whatnucleiandnucleonsactuallylooklikecomesfromelectronscattering.Thisbook examinesthemotivationforelectronscatteringanddevelopsthetheoreticalanalysisof theprocess.Itdiscussesourcurrenttheoreticalunderstandingoftheunderlyingstructure ofnucleiandnucleonsatappropriatelevelsofresolutionandsophsitication,andsummarizespresentexperimentalelectronscatteringcapabilities.Onlyaworkingknowledgeof quantummechanicsandspecialrelativityisassumed,makingthisasuitabletextbookfor graduateandadvancedundergraduatecourses.Itwillalsoprovideavaluablesummary andreferenceforresearchersalreadyworkinginelectronscatteringandotherareasof nuclearandparticlephysics.
johndirkwaleka obtainedhisPhDinnucleartheoryfromtheMassachusettsInstitute ofTechnologyin1958.HewasprofessorofPhysicsatStanfordUniversityfrom1966to 1987andthenwentontobecomeScientificDirectoroftheContinuousElectronBeam AcceleratorFacility(CEBAF)from1986to1992.HeisnowGovenor’sDistinguished CEBAFProfessorofPhysicsattheCollegeofWilliamandMary.Hisresearchinterests covertheoreticalnuclearandsub-nuclearphysics,inparticularnuclearstructure,the relativisticnuclearmany-bodyproblem,strongcouplingQCD,andelectroweakinteractions withnuclei.Hehaspublishednumerouspapersonnuclearphysics,andin1996the AmericanPhysicalSocietyrecognizedhisworkwiththeawardoftheBonnerPrize.He haslecturedonelectronscatteringthroughouttheUnitedStatesandEurope.
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CAMBRIDGEMONOGRAPHSON PARTICLEPHYSICS, NUCLEARPHYSICSANDCOSMOLOGY GeneralEditors:T.Ericson,P.V.Landshoff
1.K.Winter(ed.): NeutrinoPhysics
2.J.F.Donoghue,E.GolowichandB.R.Holstein: DynamicsoftheStandardModel
3.E.LeaderandE.Predazzi: AnIntroductiontoGaugeTheoriesandModernParticle Physics,Volume1:ElectroweakInteractions,the‘NewParticles’andthePartonModel
4.E.LeaderandE.Predazzi: AnIntroductiontoGaugeTheoriesandModernParticle Physics,Volume2:CP-Violation,QCDandHardProcesses
5.C.Grupen: ParticleDetectors
6.H.GrosseandA.Martin: ParticlePhysicsandtheSchr ¨ odingerEquation
7.B.Andersson: TheLundModel
8.R.K.Ellis,W.J.StirlingandB.R.Webber: QCDandColliderPhysics
9.I.I.BigiandA.I.Sanda: CPViolation
10.A.V.ManoharandM.B.Wise: HeavyQuarkPhysics
11.R.Fruhwirth,M.Regler,R.K.Bock,H.GroteandD.Notz: DataAnalysis TechniquesforHigh-EnergyPhysics,secondedition
12.D.Green: ThePhysicsofParticleDetectors
13.V.N.GribovandJ.Nyiri: QuantumElectrodynamics
14.K.Winter(ed.): NeutrinoPhysics,secondedition
15.E.Leader: SpininParticlePhysics
16.J.D.Walecka: ElectronScatteringforNuclearandNucleonStructure
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ELECTRONSCATTERINGFOR NUCLEARANDNUCLEON STRUCTURE JOHNDIRKWALECKA
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Preface Inthesummerof1986IleftStanfordUniversity,after26yearson thefaculty,toassumethejobofScientificDirectorattheContinuous ElectronBeamAcceleratorFacility(CEBAF)nowknownastheThomas JeffersonNationalAcceleratorFacility(TJNAF).Thisfacility,funded bytheDepartmentofEnergyandlocatedinNewportNews,Virginia providesahigh-energy,high-intensity,high-duty-factorelectronaccelerator forstudyingtheinternalstructureofnucleiandnucleons.Ithaslongbeen atoppriorityforthefieldofnuclearphysicsintheUnitedStates.Each yearIgaveaphysicslectureseriesatthesite.Theinitialseriesonelectron scatteringwasbasedonasetoflecturesIhadgivenatArgonneNational Laboratoryinthewinterof1982–1983.AsScientificDirector,Iwas continuallycalledupontomakepresentationsonthistopic.Thisbookis basedbothonthelectureseriesonelectronscattering,andonthemany presentationsIhavegivenonthissubjectovertheyears.
Thescatteringofhigh-energyelectronsfromnuclearandnucleontargets essentiallyprovidesamicroscopeforexaminingthestructureofthesetiny objects.Thebestevidencewehaveonwhatnucleiandnucleonsactually looklikecomesfromelectronscattering.Anintensecontinuouselectron beamwithwell-definedenergyprovidesapowerfultoolforstructureinvestigations.Inclusiveexperiments,whereonlythefinalelectronisdetected, examinestaticandtransitionchargeandcurrentdensitiesinthetarget. Coincidenceexperiments,whereotherparticlesaredetectedtogetherwith thescatteredelectron,providevaluableadditionalinformation.
Inelectronscatteringexperimentswherethemomentumoftheinitial andfinalelectronarewell-defined,avirtualquantumofelectromagnetic radiationisproducedwhichinteractswiththetarget.Theenergyof thisquantumisdeterminedbytheenergytransferfromtheelectron, andthemomentumofthequantumfromthemomentumtransfer.The electromagneticinteractioniswell-understood;theinteractioniswiththe
local,staticanddynamicchargeandcurrentdensities.Thescattering crosssectionisdeterminedbythefour-dimensionalFouriertransformof thesequantities.Foragivenenergytransfertothetarget,onecanvary thethree-momentumtransferbyvaryingthemomentumvectorofthe finalelectron.OnethenmapsouttheFouriertransformofthespatial densities,andbyinversionoftheFouriertransform,onedeterminesthe spatialdistributionofthedensitiesthemselves.Thewavelengthwithwhich thetargetisexaminedisinverselyproportionaltothethree-momentum transfer.Inelectromagneticstudiesinnuclearphysicsonefocusesonhow matterisputtogetherfromitsconstituentsandondistancescales ∼ 10fm to ∼ 0.1fmwhere1fm=10 13 cm.Particlephysicsconcentratesonfiner andfinerdetailsofthesubstructureofmatterwithexperimentsathigh energywhichinturnexploremuchshorterdistances.Tocarryoutsuch studies,oneneedselectronacceleratorsofhundredsofMeVtomanyGeV.
Atheoreticaldescriptionofthenuclearandnucleontargetsisrequired tointerprettheexperiments.Theappropriatedescriptionemployeddependsonthedistancescaleatwhichoneexaminesthetarget.Imagine thatonelooksattheearthfromspace.Theappropriatequantitiesused todescribetheseobservations,theappropriate degreesoffreedom,are macroscopicones,thelocationandshapeofcontinents,oceans,clouds, etc.Whenonegetscloser,finerdetailsemerge,trees,houses,cars,people, andthesemustbeincludedinthedescription.Atthemicroscopiclevelof observations,itistheatomicandsubatomicdescriptionwhichisrelevant. Itisthusself-evidentthat
Theappropriatesetofdegreesoffreedomdependsonthe distancescaleatwhichweprobethesystem.
Atthemacroscopiclevel,onedescribesnucleiintermsofproperties suchassize,shape,charge,andbindingenergy.Furtherrefinementdescribes,forexample,thespatialdistributionofthecharge.Afinerand moredetaileddescriptionisobtainedusingnucleons,protonsandneutrons,asthedegreesoffreedom.The traditional approachtonuclear physicsstartsfromstructurelessnucleonsinteractingthroughstatictwobodypotentialsfittedtotwo-bodyscatteringandbound-statedata.These two-bodypotentialsaretheninsertedinthenon-relativisticmany-body Schr ¨ odingerequationandthatequationissolvedinsomeapproximation —itcanbesolvedexactlyforfew-bodysystemsusingmoderncomputing techniques.Electromagneticandweakcurrentsarethenconstructedfrom thepropertiesoffreenucleonsandusedtoprobethestructureofthe nuclearsystem.
Althoughthistraditionalapproachtonuclearphysicshashadagreat manysuccesses,itisclearlyinadequateforanunderstandingofthenuclearsystemonamoremicroscopiclevel.Amoreappropriatesetof
Preface xi
degreesoffreedomthenconsistsofthe hadrons,thestrongly-interacting mesonsandbaryons,wherebaryonnumber,astrictlyconservedquantity,countsthenumberofnucleonsthatnowexhibitinternalstructure anddynamics.Therearemanyargumentsthatonecangiveinsupportofthispicture.Forexample,thelong-rangepartofallmodern two-nucleonpotentialsconsistsoftheexchangeofmesonsincluding π with(J π ,T )=(0 , 1),σ (0+ , 0),ω (1 , 0),and ρ(1 , 1).Weknowthat atlongrangetheforcebetweentwonucleonscomesfrommesonexchange.Moreover,thefirstexcitedstateofthenucleon,theΔ(1232)with (J π ,T )=(3/2, 3/2),wasfirstsuccessfullydescribedasaresonancearising frompion–nucleondynamics.Asafurtherexample,oneofthesignificant achievementsinthefieldofelectromagneticnuclearphysicsinrecentyears hasbeentheunambiguousidentificationofexchangecurrents,additional currentspresentinthenuclearsystemarisingfromtheflowofcharged mesonsbetweenthenucleonsinthenucleus.
Inanyextrapolationawayfromthetraditionalnuclearphysicsapproach,itisimportanttoincorporategeneralprinciplesofphysicssuch asquantummechanics,specialrelativity,andmicroscopiccausality.The onlyconsistenttheoreticalframeworkwehavefordescribingsucharelativistic,interacting,many-bodysystemisrelativisticquantumfieldtheory basedonalocallagrangiandensity.Itisconvenienttorefertorelativistic quantumfieldtheoriesofthenuclearsystembasedonhadronicdegrees offreedomas quantumhadrodynamics (QHD).
Atastillfinerlevel,wenowknowthatthehadronsarethemselves compositeobjectsmadeupofquarksheldtogetherbytheexchangeof gluons.Wenowhaveatheoryofthestronginteractionsbindingquarks andgluonsintotheobservedhadrons.Thistheoryisbasedonaninternal colorsymmetryandisknownas quantumchromodynamics (QCD).The theoryofQCDhastwoabsolutelyremarkableproperties.Thefirstis asymptoticfreedom,whichroughlystatesthatatveryhighmomenta,or veryshortdistances,therenormalizedcouplingconstantforthebasic processesinthetheorygoestozero;asaconsequence,onecando perturbationtheoryinthisregime.Thesecondpropertyis confinement. Thebasicunderlyingdegreesoffreedominthetheory,quarksandgluons, donotexistasasymptotic,free,scatteringstatesinthelaboratory.They existandinteractonlyinsidehadrons.Youcannotholdasinglequark,or singlegluoninyourhand.Therearestrongindicationsfromlatticegauge theory,whereQCDissolvedatafinitenumberofspace-timepoints, thatconfinementisindeedadynamicpropertyofQCDarisingfromthe nonlineargluoncouplings.Ultimately,nucleonandnuclearphysicsare thestudyofstrong-couplingQCD.
Asfortheotherbasicforcesinnature,surelyoneofthegreatintellectualachievementsofoureraistheunificationofthetheoriesof
Preface electromagnetismandoftheweakinteractions.Itisessentialtocontinue toputthistheoryoftheelectroweakinteractionstorigoroustestsandfully exploreitsconsequences.Nucleiandnucleonsprovideuniquelaboratories inwhichtoconductsuchtestsandexplorations.
Thecurrentpictureofthenucleusinthe standardmodel isthatofa boundsystemofbaryonsandmesons,whichareinturnconfinedtriplets ofquarksandofquark–antiquarkpairs,respectively.Theelectroweak interactionsofleptons(electronsandneutrinos)withthenucleusare mediatedbythephotonandtheheavyweakvectorbosons,the Z 0 and W ± .Theelectroweakinteractionscoupledirectlytothequarks;thegluons areabsolutelyneutraltotheelectroweakinteractions.Thuseverytimeone studiesanucleargammadecay,forexample,oneisdirectlyprobingthe quarkstructureofthenucleus.Oncethequarkisstruck,itisnota quarkthatisemittedfromthetarget,butahadron.Nucleiaretheideal laboratoriesforstudyingthisprocessof hadronization.
AnothertrulyremarkablepropertyofQCDisthattheeffectivedegrees offreedomatlowenergyandlongwavelengths are thehadrons,the baryonsandmesons.
Inthisbook,themotivationforelectronscatteringisexaminedin somedetail.Thetheoreticalanalysisoftheprocessisdeveloped,asisour currenttheoreticalunderstandingoftheunderlyingstructureofnucleiand nucleonsatappropriatelevelsofresolutionandsophistication.Selected examplesaregiven,presentexperimentalcapabilitiesaresummarized,and futuredirectionsarepreviewed.
Inpart1ofthisbookmodernpicturesofthenucleusandnucleonare surveyed.Asanintroductiontoelectronscattering,theopticalanalogyis developed.Thevirtuesofelectronscatteringaredescribedandaqualitative overviewofthenuclearresponsesurfacesininclusiveelectronscattering presented.Theargumentsforcoincidenceexperimentsarethengiven.
Inpart2,ageneraltheoreticalanalysisofelectronscatteringisdeveloped,startingfromadiscussionoftheelectromagneticinteractionwithan arbitrarylocalizedquantummechanicalsystem.Thisincludesamultipole decomposition.Therelativisticelectronsofinterestherearedescribedby theDiracequation,andthenecessarytoolsaredeveloped.Acovariant analysisofthescatteringofanelectronbynuclearandnucleontargets isthencarriedout.Boththeexcitationofdiscretetargetstatesandoneparticleemissioncoincidenceexperimentsareanalyzed.Ananalysisof deep-inelasticscattering(DIS)experiments,wherethefour-momentum transfersquaredandenergytransferbothgrowlarge,butwithafixed ratio,ispresented.Thissectionendswithageneralanalysisofparity violationininclusivepolarizedelectronscattering.
Sinceelectronsarechargedandlight,theybynecessityradiateduringthescatteringprocess.Thisisoneofthetechnicalcomplicationsof
Preface xiii electronscattering.Thisradiationaswellastheaccompanyingvirtual electromagneticeffectsaredescribedby quantumelectrodynamics (QED); part3presentsabriefreviewoftheessentialsofQED.
Part4presentsexperimentalandtheoreticalresultsforselectedexamples.Theseexamplesarechosentoillustratethewidevarietyofincisive informationthatcanbeobtainedaboutthestructureofnucleiandnucleons,theinfluenceelectronscatteringhashadonthedevelopmentof ourpicturesofthesesystems,therolevariouslaboratoriesthroughoutthe worldhaveplayedinthesedevelopments,and,quitefrankly,thebeauty ofthisbranchofphysics.Theoreticalbackgroundintraditionalnuclear physics,relativisticmeanfieldtheory,thequarkmodel,QCD,andthe standardmodelisdevelopedinsufficientdepththatthereadercanindeed workthroughtheexamplesindetail.
Inpart5,futuredirectionsforthefieldarediscussed,buildingonthe evolvingTJNAFprogram,butincludingotherworld-widedevelopments atbothintermediateandveryhighenergy.
Nineappendixesareincludedwhichexploresomeofthemoreinterestingandimportanttechnicalaspectsofthissubject.
Thebookassumesonlyaworkingknowledgeofquantummechanics andspecialrelativityanddevelopsthetheoreticalanalysisinaselfcontainedfashionuptocurrentlevelsofsophistication.Itisbasically aimedatfirst-yeargraduatestudentsandadvancedundergraduatesin physics,althoughitshouldbeaccessibletoothersinthenaturalsciences. Parts1and5canbereadbyawideraudienceinterestedinunderstanding theessentialsofthesubject.Thebookshouldserveeffectivelyasatext forspecialtopicscoursesonthissubjectorasasupplementaltextfor nuclearorparticlephysicscourses.Itshouldalsoserveasasummaryand referenceforresearchersalreadyworkinginelectronscatteringaswellas thoseinotherareas.
ThismanuscriptwastypedbytheauthorinLATEX,fromwhichthe bookisprinted.Figuresarereproducedbypermission.
Williamsburg,Virginia April22,2001
JohnDirkWalecka
Governor’sDistinguishedCEBAF ProfessorofPhysics CollegeofWilliamandMary
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Part1 Introduction https://www.cambridge.org/core/terms https://www.cambridge.org/core/product/161621932DE0F04F7AB163175154152D
Motivation Thismonographisconcernedwiththestudyofnuclearandnucleon structurethroughthescatteringofhighenergyelectrons.Thehistoryof thisfieldiswellsummarizedintheproceedingsofthe Conferenceon35 YearsofElectronScattering heldattheUniversityofIllinoisin1986to commemoratethe1951experimentofLyman,Hanson,andScott;this experimentprovidedthefirstobservationofthefinitesizeofthenucleus byelectronscattering[Ly51,Il87].Hofstadterandhiscolleagues,working intheHighEnergyPhysicsLaboratory(HEPL)atStanfordUniversity inthelate1950’s,beautifullyandsystematicallyexhibitedtheshapeof thechargedistributionsofnucleiandnucleonsthroughexperimentsat highermomentumtransfer[Ho56,Ho63].Subsequentexperimentalwork atHEPL,theBatesLaboratoryatM.I.T.,SaclayinFrance,NIKHEF inHolland,andbothDarmstadtandMainzinGermany(aswellas otherlaboratories),utilizingparalleltheoreticalanalysis[Gu34,Sc54,Al56, de66,Ub71],clearlyexhibitedmoredetailedaspectsofnuclearstructure. Experimentsathigherelectronenergiesandmomentumtransfersatthe StanfordLinearAcceleratorCenter(SLAC)byFriedman,Kendall,and Taylor,togetherwiththeoreticaldevelopmentsbyBjorken,forthefirst timedemonstratedthepointlikequark–partonsubstructureofnucleons andnuclei[Bj69,Fr72].Thisworkplayedakeyroleinthedevelopment ofmoderntheoriesofthestronginteraction.Majoreffortstodayat CEBAF,theContinuousElectronBeamAcceleratorFacility(nowknown asTJNAF,theThomasJeffersonNationalAcceleratorFacility)inthe U.S.,Bates,Mainz,SLAC,DESYinGermany,andCERNinGeneva (usingmuons)contributetothedevelopmentofourunderstandingof nucleiandnucleons.
Inpart1wediscussmodernpicturesofthenucleusandnucleon, startingwithnon-relativisticnucleonsinteractingthroughstaticpotentialsandproceedingtoquarksandgluonswithinteractionsdescribed
bystrong-coupling quantumchromodynamics (QCD).Asanintroduction toelectronscattering,theopticalanalogyisdeveloped.Thevirtuesof electronscatteringaredescribedandaqualitativeoverviewofthenuclear responsesurfacesininclusiveelectronscatteringpresented.Thearguments forcoincidenceexperimentsarethengiven.
Inpart2,ageneraltheoreticalanalysisofelectronscatteringisdeveloped,startingfromadiscussionoftheelectromagneticinteractionwithan arbitrarylocalizedquantummechanicalsystem.Thisincludesamultipole decomposition.Sinceelectronsarerelativistichere,theyaredescribedby theDiracequationandthenecessarytoolsaredeveloped.Acovariant analysisofthescatteringofanelectronbyanucleartargetisthencarried out.Boththeexcitationofdiscretetargetstatesandone-particleemissioncoincidenceexperimentsareanalyzed.Ananalysisofdeep-inelastic scattering(DIS)experiments,wherethemomentumtransfersquaredand energytransferbothgrowlarge,butwithafixedratio,ispresented. Thissectionendswithageneralanalysisofparityviolationininclusive polarizedelectronscattering.
Sinceelectronsarechargedandlight, theybynecessityradiateduringthescatteringprocess.Thisisoneofthetechnicalcomplicationsof electronscattering.Thisradiationaswellastheaccompanyingvirtual electromagneticeffectsaredescribedby quantumelectrodynamics (QED); part3presentsabriefreviewoftheessentialsofQED.
Part4presentsexperimentalandtheoreticalresultsforselectedexamples.Theseexamplesarechosentoillustratethewidevarietyofincisive informationthatcanbeobtainedaboutthestructureofnucleiandnucleons,theinfluenceelectronscatteringhashadonthedevelopmentofour picturesofthesesystems,andtherolevariouslaboratoriesthroughoutthe worldhaveplayedinthesedevelopments.
Inpart5,futuredirectionsforthefieldarediscussed,buildingonthe evolvingTJNAFprogram[Wa93,Wa94],butincludingotherworld-wide developmentsatbothintermediateandveryhighenergy.
Oneofthemostattractiveandpowerfulaspectsofthefieldofelectron scatteringforthestructureofnucleiandnucleonsisthatexperimental andtheoreticaldevelopmentshavealwaysprogressedhandinhand,with eachreinforcingtheother.
Westartthismonographwithamoredetaileddiscussionofthemotivationforstudyingthestructureofnucleiandnucleonsthroughthe scatteringofhighenergyelectrons.
Letusgobacktothebeginning.Whydowedonuclearphysics?Why isnuclearphysicsinteresting?Firstofall,thenucleusisauniqueform ofmatterconsistingofmanybaryonsincloseproximity.Alltheforcesof naturearepresentinthenucleus—strong,electromagnetic,weak,and evengravityifoneincludescondensedstellarobjectswhicharenothing
morethanenormousnucleiheldtogetherbythegravitationalattraction. Thenucleusprovidesamicroscopiclaboratorytotestthestructureof thefundamentalinteractions.Furthermore,thenucleusmanifestsremarkablepropertiesasastronglyinteracting,quantummechanical,relativistic, many-bodysystem.Inaddition,mostofthemassandenergyinthevisibleuniversecomesfromnucleiandnuclearreactions.Also,wenowknow therearenewunderlyingdegreesoffreedominthenucleus,quarksand gluons,interactingthroughremarkablenewforcesdescribedbyquantum chromodynamics(QCD).Thesinglenucleonitselfisnowacomplicated nuclearmany-bodysystem.Theelectromagneticpropertiesofnucleons andnucleiprovidebenchmarkswithwhichtotestourunderstandingof strong-couplingQCDandthequarksubstructureofmatter.Moreover, nuclearphysicsiscrucialtotheunderstandingoftheuniverse,forexample:theearlyuniverse,formationoftheelements,supernovae,andneutron stars.Insum,nuclearphysicsisreallythestudyofthe structureofmatter Whereisnuclearphysicsgoing?Thenuclearsciencecommunityinthe U.S.recentlyunderwentoneofitsperiodiclong-rangeplanningexercises undertheleadershipoftheNuclearScienceAdvisoryCommittee(NSAC) andtheDivisionofNuclearPhysics(DNP)oftheAmericanPhysical Society(APS).Inthereportentitled NuclearScience:ALong-RangePlan [NS96]theheadingsinpartIIon TheScientificFrontiers capturethe presentfrontiers:
1.NuclearStructureandDynamics:ExploringtheLimits
2.TotheQuarkStructureofMatter
3.ThePhasesofNuclearMatter
4.FundamentalSymmetriesandNuclearAstrophysics
Picturesofthenucleus Wecurrentlypossessthreelevelsofunderstandingofthenucleuswithin thefollowingframeworks[Wa95]:
(I) Traditional,Non-Relativistic,Many-BodySystems [Fe71].Thisapproachusesstatictwo-bodypotentialsfittotwo-nucleonscatteringand bound-statedata.Thesepotentialsaretheninsertedinthenon-relativistic Schrodingerequation,andthatequationisthensolvedinsomeapproximation;withfew-nucleonsystemsandlarge-scale computingcapabilities,the equationscannowbesolvedexactly.Electroweakcurrentsconstructed fromthepropertiesoffreenucleonsarethenusedtoprobethenuclearsystem.Althoughthisapproachhashadagreatmanysuccesses [Bl52,Ma55,Bo69,Fe71,de74,Pr75,Fe91,Wa95],itisclearlyinadequate foramoredetailedunderstandingofthenuclearsystem.
(II) RelativisticMany-BodySystems.Amoreappropriatesetofdegreesoffreedomfornuclearphysicsconsistsofthe hadrons,thestrongly interactingmesonsandbaryons.Therearemanyargumentsonecan giveforthis.Forexample,thelong-rangepartofthebestmoderntwonucleonpotentialsisgivenbymesonexchange,predominantly π with (J π ,T )=(0 , 1), σ (0+ , 0), ρ(1 , 1)and ω (1 , 0)[La80,Ma89].Furthermore,oneofthesuccessesofelectromagneticnuclearphysicsistheunambiguousdemonstrationoftheexistenceofexchangecurrents,additional electromagneticcurrentsinthenucleusarisingfromtheflowofcharged mesonsbetweennucleons.Inaddition,onedailyseescopiousproduction ofmesonsfromnucleiinhigh-energyaccelerators.
Theonlyconsistenttheoreticalframeworkwehavefordescribingsucha strongly-coupled,relativistic,interacting,many-bodysystemisrelativistic quantumfieldtheorybasedonalocallagrangiandensity.Itisconvenient torefertorelativisticquantumfieldtheorymodelsofthenuclearsystem basedonhadronicdegreesoffreedomas quantumhadrodynamics (QHD).
Fig.2.1.Nucleusasastrongly-coupledsystemofcoloredquarksandgluons; electroweakinteractionwithalepton.
Moregenerally,onecanviewsuchfieldtheoriesas effective fieldtheories fortheunderlyingtheoryofQCD[Se86,Se97].
(III) Strongly-CoupledColoredQuarksandGluons.Ourdeepestlevelof understandingofnucleons,andthenucleusfromwhichtheyaremade,is asastrongly-coupledsystemofquarksandgluons(Fig.2.1).TheirinteractionsaredescribedbyaYang–Millstheory[Ya54]basedonaninternal colorsymmetry(QCD).Thistheoryhastworemarkableproperties:itis asymptoticallyfree,whichmeansthatatveryhighmomenta,orveryshort distances,therenormalizedcouplingconstantbecomessmall.Thishas severalconsequences.Forexample,itimpliesthatwhenintheappropriate kinematicregime,onescattersfromessentiallyfreepoint-likeobjects.In fact,itwastheexperimentalobservationofthisphenomenonindeep inelasticscattering(DIS)thatdrovetheoriststohuntforasymptotically freetheories[Gr73a,Gr73b,Po73,Po74].Furthermore,whenthecoupling issmall,onecandoperturbationtheory.Themanyhigh-energysuccesses of perturbativeQCD nowprovideconvincingevidencethatQCDistruly theunderlyingtheoryofthestronginteractions.
Whenonescattersaleptonfromanuclearsystem,theelectroweak interactiontakesplacethroughtheexchangeofoneoftheelectroweak bosons(γ,W ± ,Z 0 ),asillustratedinFig.2.1.Thesebosonscoupledirectly tothequarks;thegluonsare absolutelyneutraltotheelectroweakinteractions.Thuseverytimeoneobservesagammadecayorbetadecayofa nucleusornucleon,oneisdirectlyobservingthequarkstructureofthese systems!
ThesecondremarkablepropertyofQCDis confinement,whichmeans thattheunderlyingdegreesoffreedom,quarksandgluons,neverappearas asymptotic,freescatteringstatesinthelaboratory.Youcannotholdafree quarkorgluoninyourhand.Quarksandgluons,andtheirstrongcolor interactions,areconfinedtotheinteriorofthehadrons.Atlowmomenta, orthelargedistancesappropriatefornuclearphysics,therenormalized couplinggrowslarge.QCDbecomesastrong-couplingtheoryinthislimit.
8 Part1Introduction Thereareconvincingindicationsfromlatticegaugetheory(LGT),where strong-couplingQCDissolvedonafinitespace-timelattice[Wi74],that confinementisindeedadynamicalpropertyofQCDarisingfromthe nonlineargluoncouplingsdictatedbylocalcolorgaugeinvarianceinthis non-abelianYang–Millstheory.
Someoptics Toobtaininsightintotheelectronscatteringprocess,weappealtosome elementaryoptics,withwhichthereaderiscertainlyfamiliarfroman introductoryphysicscourse.Ifonelooksthroughatelescopeatastar, orshinesalaserthroughapinhole,onedoesnotreallyobserveapoint oflight,butactuallyadiffractionpatternwithabrightdiscatthecenter andaseriesofconcentricringswithdiminishingintensity.Iftheradius oftheaperturethroughwhichthelightpassesis a,andthewavelengthof theincidentlightis λ1 ,thentheangle θ tothefirstdiffractionminimum ofthecentral Airydisc isgivenby
Here θ ismeasuredfromthecentralray,startingattheaperture.Now introducetheincidentwavenumber k1 and“momentumtransfer” κ
Equation(3.1)canthenberewrittenas
Thisrelationhasamarvelousconsequence.Supposeoneshineslight fromalaserofgivenwavelengthonapinhole,andprojectstheresulting diffractionpatternonascreenbehindthepinhole.Theangletothefirst minimumcanbedeterminedbymaking macroscopicmeasurements of thedistanceofthescreenfromtheapertureandthetransversedistance onthescreenouttothefirstminimum.Equation(3.3)thenallowsone todeterminetheradius a ofthepinhole. Onecanmeasurearadiusof arbitrarilysmallsizeifonlythemomentumtransferislargeenough! The
Fig.3.1.OpticalpathlengthwithrespecttocentralrayinFraunhoferdiffraction.
Fig.3.2.The“momentumtransfer” κ = k1 k2 .
momentumtransferisinverselyproportionaltothewavelength.Thusto obtainlargemomentumtransfer,onehastogotoshortwavelength.One evidentlyneedsawavelengthcomparabletothesizeoftheapertureto makethismeasurement.
Letusextendthesesimpleconsiderations.InFraunhoferdiffractionone hasanincidentplanewaveandanoutgoingplanewaveinthedirection ofobservationasillustratedinFig.3.1.Theopticalpathlengthofan arbitraryraywithrespecttothecentralrayisevidentlygivenfromthis figureas
where ˆ k1 and ˆ k2 areunitvectorsintheincidentandoutgoingdirections respectively.Herethemomentumtransfer κ isdefinedby(Fig.3.2)
Sincethelengthsoftheincomingandoutgoingwavenumbersareidentical
