injectedeaccelerator

MeasurementofpolarizationobservablesinthedpppnreactionatTd2.
0GeVS.
L.
Belostotski,O.
G.
Grebenyuk,L.
G.
Kudin,andV.
N.
NikulinSt.
-PetersburgNuclearPhysicsInstitute,188350,Gatchina,RussiaA.
Boudard,B.
Bonin,M.
Garcon,R.
M.
Lombard,B.
Mayer,andY.
TerrienServicedePhysiqueNucleaire,CEA–Saclay,91191Gif-sur-Yvette,FranceM.
Boivin,E.
Tomasi-Gustafsson,andJ.
YonnetLaboratoireNationalSaturne,CEA–Saclay,91191Gif-sur-Yvette,FranceM.
YounandH.
C.
BhangDepartmentofPhysics,SeoulNationalUniversity,Seoul151-742,KoreaN.
E.
CheungandC.
F.
PerdrisatCollegeofWilliamandMary,Williamsburg,Virginia23185V.
PunjabiNorfolkStateUniversity,Norfolk,Virginia23504J.
Ero,*Z.
Fodor,P.
Koncz,andZ.
SeresKFKIResearchInstituteforParticleandNuclearPhysics,1525Budapest,HungaryReceived29January1997Wehavestudiedthedeuteronbreakupinthep(d,2p)nreactionatTd2.
0GeV.
Inthisexperiment,thevectoranalyzingpowerAY,thetensoranalyzingpowerAYY,andthepolarizationoftheforwardscatteredprotonaremeasuredclosetothequasifreeppscatteringkinematics.
Theseobservablesarepresentedasafunctionoftheneutronmomentumrangingfrom0.
04to0.
45GeV/cintherestframeofthedeuteron.
Markeddeviationsfromtheimpulseapproximationusingconventionaldeuteronwavefunctionsareobserved.
Correc-tionsduetothemultiplescattering,thenalstateinteraction,andtheexcitationarecalculatedinamodelwherethespin-isospinstructureoftheelementaryamplitudesistreatedrigorously.
Withthismodel,areason-ableaccountofthemeasuredpolarizationobservablesisobtained.
Theglobalagreementwithallobservablesis,however,notgoodenoughthatwecanreliablydiscriminatebetweenconventionalwavefunctions.
S0556-28139702507-7PACSnumbers:24.
70.
s,21.
45.
v,25.
10.
s,25.
45.
zI.
INTRODUCTIONThedeuteronisaveryinterestingnucleusasapurecor-relationbetweentheprotonandtheneutron.
Adetailedstudyofitsstructurewillbringinformationonthestronginterac-tionbetweentwoboundnucleonsinspecicquantumstates.
Whilethestaticpropertiesofthedeuteron,suchasbind-ingenergy,radius,andmagneticandquadrupoleelectricmo-ments,arewellknown,thedynamicsofthissystemarelesswelldocumented.
TheknowledgeoftheprobabilityforanucleontohaveaninternalmomentumqinthedeuteronisastrongconstraintfortheNNpotential.
Thelargerthismo-mentum,thesmallertherelativedistancebetweenthetwonucleons.
Astheinternucleondistancedecreases,mesonexchange,andexcitationofthenucleoninternalstructureleadingtoNN*andcomponentsandevennewdynamicaleffectsappear.
Theseultimateeffectsstillunderinvestigationareduetotheincreasingoverlapbetweenthetwonucleon'sthree-quarkbags.
Experimentalinformationfromthepolar-izationobservablesasfunctionsofq,issensitivetosmallcomponentsofthewavefunctionandsocouldhelptodis-entangletheseeffects.
Thekinematicsoftheexclusiveprocessdp→ppniscompletelyspeciedforeachidentiedevent,andscanninginqispossibleassumingthevalidityofplanewaveimpulseapproximationPWIA.
Ameasurementofthevec-torandtensoranalyzingpowerandofpolarizationtransfertooneoutgoingproton,providesfourindependentobservablesofthereactioninadditiontoexistingcross-sectiondata.
Thisredundancywillbeastringenttestforagoodunderstandingofthereactionmechanism.
Experimentallytheanalyzingpowersareratiosofcrosssectionsandoffereasyaccesstosmallprobabilitieswithregardstonormalizationandef-ciencyproblems.
Theusefulnessofpolarized-deuteronbreakupexperimentswasemphasizedandstudiedinseveralpapers1–3.
ThePWIAforthereactionp(d,2p)nunderinvestigationassumesthatoneofthenucleonsinthedeuteronisaspec-tator,beingunaffectedbythebreakupprocess.
Themomen-tumofthisnucleonintheoutgoingchannelboostedtothe*Deceased.
PHYSICALREVIEWCJULY1997VOLUME56,NUMBER1560556-2813/97/561/5014/$10.
00501997TheAmericanPhysicalSocietydeuteronrestframeisinterpretedasitsFermimomentumqorinternalmomentumofthenucleoninthedeuteron.
Hence,intheframeworkoftheIA,itispossibletostudytheinternalmomentumdistribution(q)2u2(q)w2(q).
Withinthesameapproximation,thepolarizationobservablesaresensi-tivetotheratiou(q)/w(q),momentumspacewavefunc-tionsoftheSandDstatecomponentsofthedeuteron,re-spectively.
Thestructureofthedeuteronhasbeenthesubjectofmanyinvestigations,boththeoreticallyandexperimen-tally.
ConventionaltheoreticalstudiesarebasedonmodelsoftheN-Npotential.
Fromthepotential,thewavefunctionofthedeuteronasaboundstateoftheprotonandtheneutronisdeduced.
Amongthenumerousresults,wewillspecicallyusetheBonnwavefunction4andthePariswavefunction5asrepresentativesofreasonablevariationsofvariousphe-nomenologicalpotentials.
Anumberofedelasticscatteringexperimentshavebeenperformedtomeasurethecharge,quadrupole,andmagneticformfactorsseeRef.
6,andreferencesincludedthereinuptoatransferedmomentumof4.
6fm1.
However,thetransverseandlongitudinalstructurefunctions,A(Q2)andB(Q2)havebeenmeasuredupto8and10fm1,respec-tively.
ItshouldbenotedthatifthemomentumtransferinelasticscatteringisQ,thenthecorrespondingvalueofthedeuteroninternalmomentumisqQ/2.
Exclusiveandinclusivedeuteronbreakupreactions,bothprovidinginprincipledirectaccesstothedeuteronwavefunctionhavebeenextensivelyinvestigated.
Therearedatafromtheexclusived(p,2p)n7–15andd(e,ep)n16–18reactions,andalsofromtheinclusivereactionA(d,p)X19–22.
Anexclusiveexperimentonpolarizeddeuteronphoto-disintegrationisinprogressinNovosibirsk23andatNIKHEF24.
InclusivepolarizeddeuteronbreakuphasbeenintensivelyinvestigatedusingDubnaandSaturnepolarizeddeuteronbeams21,22,25–28.
ThesestudieshavedemonstratedthatpolarizationobservablessuchasthetensoranalyzingpowerT20,wereindependentofbeamenergy,andonlyweaklydependentuponthetargetnature,whenanalyzedasafunc-tionofinternalmomentumq,overarangeofdeuteronen-ergiesfrom1.
25to4.
4GeV.
PolarizationtransferdatashowasimilarenergyandtargetindependenceasT20,althoughtheexperimentalevidenceisweaker.
Thevariousreactionsgiveacoherentpictureofthedeu-terondensityandarewellunderstoodintermsoftheIAwithaconventionaldeuteronwavefunctionuptomomentumofabout200MeV/c.
Abovethisqvalue,dependinguponthereactionandthekinematics,theresultsdiffersignicantly.
AftercorrectionstothePWIA,the(q)2from(e,ep)experiment18isinagreementwiththePariswavefunctionupto500MeV/c,whilethe(q)2extractedfrom(p,2p)15agreesbetterwiththeBonnwavefunctioninthesameinternalmomentumrange.
Ininclusivebreakup,withapro-tondetectedintheforwarddirection,amarkedbumporexcessofprobability,isobservedaround320–350MeV/cinthedata,aboveconventionalwavefunctionpredictionsforalltargetsandenergiesofthedeuteronbeam19–22.
Uptonowthisbumpisnotunambiguouslyunderstood.
Newde-greesoffreedominthedeuteronstructurewerealsosug-gested;forexample,KermanandKisslingerfollowedbyothersintroducedandNN*isobariccomponentsinthedeuteronwavefunction29andAbleevetal.
20suggestedsix-quarkeffectsfollowingmanytheoreticalstudies30–32.
Whateverthedeuteronstructure,thePWIAneedstobecomplementedathighinternalmomentabyknowneffectssuchasnalstaterescatteringFSR.
Theoff-shelleffectoftheprotoninthereactiond(e,ep)wasdiscussedinRef.
18.
Theestimatedcorrectiontothecrosssectionwasfoundtobesmallafewpercent.
ThepossibilityofFSRprocesseswasstudied1,8andincludedinmostoftheinterpretations.
Thisaspectisespeciallydetailedin33wheretheexclusived(p,2p)nandinclusivep(d,p)XcrosssectionandtensoranalyzingpowerT20arecomputeduptodoublescatteringbutinacoplanargeometry.
Thevirtualexcitationwasalsodiscussed34,10,forthed(p,2p)ncrosssection,conclud-ingthatitcanbedominantwhenthetwonalprotonsareemittedsymmetricallywithaninvariantmassaroundMNM.
Inotherkinematicsclosertothequasifreescat-tering,thevirtualcontributionwasshown15tohavemodesteffects.
WhenFSRorexcitationplayasignicantrole,itisnotpossibletointerpretthemomentumofthespectatornucleonastheinternalmomentumofthedeuteronconstituentnucle-ons.
Yetthisinterpretationstillprovidesaneasywaytopic-tureanddiscussexperimentalresultswhicharevefolddif-ferentialinathreebodynalstateexperiment.
WeexpectthatpolarizationdatawillprovideatestofthevalidityrangeofthePWIAfromtheuniversalityofobservableswithre-specttoq,aswellasastrongconstraintintheseparationofthereactionmechanismfrompossibleunconventionaldeu-teroncomponents.
InthepresentexperimentthetensorAYYandvectorAYanalyzingpowers,andthepolarizationoftheoutgoingfastprotoninthedp→ppnexclusivereaction,havebeenmeasuredwithpolarizeddeuteronbeamsfromtheSATURNEsynchrotronatLaboratoireNationalSaturneinFrance.
Thecoincidencecrosssectionsmeasuredinthesameexperimentwerepublished35andarethusnotdiscussedinthepresentpaper.
Thetheoreticalmodelusedfortheanalysisofthepolar-izationobservablesissimilartotheoneusedfortheGatchinaunpolarizedpd→ppnexperiment15.
Morede-tailsconcerningthedescriptionofpolarizedobservablesaregiveninSec.
II.
Theexperimentanddatareductionarede-scribedinSec.
III.
InSec.
IV,theresultsarepresentedanddiscussedwithasummaryofthetheoreticalmodelused.
TheconclusionsaredrawninSec.
V.
II.
DESCRIPTIONOFOBSERVABLESInthePWIArst-orderapproximationforthereactionmechanism,thespectatornucleonremainsinthesamespinstateandhasthesamemomentumaspriortothereaction.
Inthisexperimenttheanglesofdetectionforthetwoprotonswerechosentofavorquasifreepp-scatteringevents,leavingtheneutroninthedeuteronasaspectator.
TheamplitudeofthereactioninthePWIAcanbewrittenasFM,1,2,31/21,1/22,1/23,Vpp1,21/2,1M1,3,q,15651MEASUREMENTOFPOLARIZATIONOBSERVABLESIN.
.
.
wherethespinpartofthewavefunctionsisspeciedwithanotationillustratedinFig.
1.
Thedeuteronwavefunctioninmomentumspaceis1M1,3,q1qL0,2uLqYLq11,31M,2wherethesphericalharmonicsYL(q)determinetheangulardependence,and1isthedeuteronspinor.
Theradialdepen-denceoftheSandDstateofthedeuteronarethefunctionsuL(q)tobedenotedinthefollowingasu(q)andw(q),oruandwforshort.
ThecrosssectionoftheexclusivereactionforagivenspinstateMoftheinitialdeuteronisthend5Mdp1d1d2dM121,2,3FM,1,2,32,3wherethenotationdMisintroducedforshortness.
FollowingtheMadisonconvention36thedifferentialcrosssectionforvector(py)andtensor(pyy)polarizationofthedeuteronbeamisd5dp1d1d2py,pyyd5dp1d1d20,0132AYpy12AYYpyy,4withcorrespondingvectorandtensoranalyzingpowersde-nedasAYdM1dM1dM1dM0dM1,5AYYdM1dM12dM0dM1dM0dM1,6andtheunpolarizedcrosssectionasd5dp1d1d20,0ddM1dM0dM13.
7Fromtheseexpressions,onecanderivethefollowingexpres-sionsforthethreeobservablesinthePWIA:AYqPpp2u2w2uw23u2w2nyw2uwu2w2kyk,nPppBY,8AYYq123qY21w22uwu2w2,9ddpp4q2u2w2,10wherekq/qq,nistheunitvectoralongthenormaltotheplaneoftheppscattering,Pppthepolarization,anddppthedifferentialcrosssectionoftheppscattering.
TheexpressionforAY(q)denesastructurefunctionBY(q)forthedeuteron.
Thepolarizationofthefastproton,whichwasalsomea-suredinthisexperiment,isdenedasPNupNdownNupNdown,11wherethenumberoffastprotonsintheupordownspinstateisNupdownMnMdMupdownMnM12,2,3FM,updown,2,32.
12Iftheproportionofincidentdeuteronsineachspinstateisn,n,andn0,thenthevectorandtensorpolarizationofthebeamarepynn,13pyynn2n0,14nnn01,15andthespinstructureofthep(d,2p)namplitudeleadsinIAtoPPpp3BYDpppy/2AYYpyyPpp/213AYpy/2AYYpyy/2,16whereDppisthedepolarizationparameterinfreeppscat-tering.
Thedepolarizationparameterforthep(d,2p)nreac-tioncanbedenedasDvd↑↑d↑↓3d,17withd↑↑12,2,3F1,↑,2,32F1,↓,2,32,18d↑↓12,2,3F1,↑,2,32F1,↓,2,32,19andd1213M,,1,2,3FM,1,2,32.
20FIG.
1.
Notationsforthep(d,2p)nreaction.
ThelettersM,,andirefertothespinmagneticquantumnumberofeachparticle.
5256S.
L.
BELOSTOTSKIetal.
TheDvobservablemeasuresthefractionoffastprotonswiththeirspininthesamedirectionasthedeuteronspin.
IntheIA,thisobservableisequaltoDvBYDpp,21whereBYisthesamedeuteronstructurefunctionwhichwasintroducedearlierinthedenitionofAY;BYhasvaluesintherangefrom1to1.
LabelingthepolarizationofthefastprotonPforanincidentdeuteroninthestate(M1),andPforthestate(M1)theexpressionofDv,follows,DvPP3pyAYPP2.
22CombiningthetwoindependentquantitiesPandPitcanbeshownthatP0PP232AYpyPP2,23whichisthepolarizationofthefastprotonforunpolarizeddeuteronbeam.
IntheIAitisequaltothepolarizationinfreeppscattering:P0Ppp.
24Tosummarize,wenotethatthespinobservablesAY,AYY,andDvarefunctionsoftheratiobetweentheSandtheDstatesataninternalmomentumqxedbythekinematicsintheoutgoingchannel.
IntheIA,themomentumqisthemomentumofthespectatorneutron,inthedeuteronrestframe.
Inthispaperalltheobservablesareshownasfunc-tionsofq,beingsummedupoverotherkinematicvariableswithintheexperimentalacceptance.
Thisrepresentationofobservableswhicharevefolddifferential,doesdisplaythemaindynamicalfeaturesofthereactiontorstorder;thispointwillbefurtherdiscussedinmoredetailinSec.
IV.
Atlargevaluesofq,theIAshouldbecomplementedwithothergraphsincludingFSI,excitation,andsoonseeFig.
2,whichmodifytheobservablessubstantially.
Itfol-lowsthatstrongconstraintsforthecalculationofthereactionmechanismwillresultfromthecomparisonoftheoreticalpredictionswiththefourindependentobservablesAY,AYY,Dv,andP0.
ThetermqYinEq.
9takesintoaccounteventswithppscatteringoutofthehorizontalplaneresultingfromthelargeverticalapertureofthedetectorsinthisexperiment.
ButthePppandDppparametersaredenedonlyforcopla-narppscattering.
Expressionsfortheanalyzingpower,validintheframe-workoftheIA,andsimilartoEqs.
8and9,havebeendiscussedbyWilkin37,andusedforanalysisofinclusivedeuteronbreakupreactiondata21,22andof6Liinclusivebreakupreactiondata38.
However,Eqs.
8and9differfromthembythefactthattheycontainatermdependingonqY.
III.
DESCRIPTIONOFEXPERIMENTANDDATAHANDLINGThepolarizeddeuteronbeamfromtheatomicionsourceHYPERIONisinjectedinthepreacceleratorMIMASandthenintothesynchrotronringSATURNE,whereitisaccel-eratedupto2GeV.
TheextractedbeamistransportedtothetargetpointoftheSPES4spectrometershowninFig.
339.
Thescatteringangle1ofthefastprotonp1wassetto18.
3°bymeansofamovabledipolemagnetupstreamofthetarget.
Therecoilprotonp2wasdetectedincoincidencewiththeprotonp1withinarangeofscatteringangles2from52.
5°to61.
5°withtherecoilspectrometerRSlocatedinthetargetarea.
Thebeamwasstoppeddownstreamfromthetargetinabeamdump.
TheRSdetectorswereprotectedfromadirectviewofthebeamdumpbyaconcretewallof1.
5mthickness.
A.
ThedeuteronbeamandthetargetThebeamwasfocusedonthetargetwithaspotofdimen-sions6mmhorizontallyby2.
2mmvertically.
ThetargetFIG.
2.
TheFeynmandiagramsincludedintothecalculation.
TheexclusivebreakupOisthecoherentsumofrst-orderim-pulseapproximationA,nalstaterescatteringB,andexcita-tionC.
ForgraphsAandB,thetwocircularpermutationsofthenalparticlesarealsocomputed.
ForgraphC,onlythepermutationofnandp1isconsidered.
FIG.
3.
Experimentalsetup:ThemagnetsofthebeamlineandoftheSPES4spectrometerareshownwiththelocationoftheRSarmandofthePOMMEpolarimeter.
Theshadedareasareconcretewalls.
TheRSdetectorsareprotectedfromadirectviewofthebeamstop.
5653MEASUREMENTOFPOLARIZATIONOBSERVABLESIN.
.
.
wasaverticalcylindercelllledwithliquidhydrogen.
Thecellhadadiameterof40mmwithwallsmadeof150m-thickmylar.
Theslowrecoilingprotonsexitedthetargetvacuumchamber38cmawayfromthetargetcellthrougha50mtitaniumwindow.
Thebeamtimestructurewasof0.
4sdurationat3srepetitionperiod.
Thebeamintensitywaslimitedto3.
0109deuteronsperspilltomaintainacceptablevaluesoftheleakagecurrentintheproportionalchambersofRSlo-catedclosetothetarget.
Alsowhendataweretakenclosetothequasielasticpeakthebeamintensitywasfurtherreducedtokeepthedeadtimeofthedataacquisitionsystemreason-ablysmall.
ThereisnodepolarizationofthedeuteronsduringtheaccelerationinSATURNE40,sothatthepolarizationcanbemeasuredat385keVwithalow-energypolarimeter41locatedattheexitoftheionsourcebeforeinjectionintothepreacceleratorMIMAS.
Thepolarizationstateofsuccessivebeamburstswasrepeatedcyclicly,eitherinthetwo-statemodestates2and3,orinthefour-statesmodestates5,6,7,and8.
Successivebeamburstshadadifferentpolar-ization,assummarizedinTableI,togetherwiththemaxi-mumpolarizationdeliveredbytheatomicsourceineachoneofthesestates.
Thedatawereobtainedduringtwoseparateperiodsintwoconsecutiveyears.
Themeasuredpolarizationswerecon-stantduringeachperiodandaregiveninTableIIafterap-propriatenormalization41anddeadtimecorrection42.
Inadditiontothestatisticaluncertaintyfromthebeampolar-izationmeasurements,theestimateofthesystematicerroris6%forthetensorand4%forthevectorpolarization41.
Thedatameasuredduringthetworunshavebeensummedaftercheckingthattheywereconsistentwithinsta-tisticaluncertainty.
B.
TheSPES4spectrometerThespectrometerSPES4isshowninFig.
3;itscongu-rationisdiscussedindetailin39,43.
Atimeofightisobtainedwiththestartfromscintillators1-mmthicknessattheintermediatefocusIF,andthestopgivenbyscintilla-tors3-mmthickinthenalfocusFFFig.
4;thetime-of-ighthasabasedistanceof16.
8mandprovidesexcellenttriggerselectivityforprotons.
Thespectrometermomentumresolutionisp/p103.
Acollimatordenedasolidangleof0.
69msr,withangularacceptancesh1.
04°horizontally,andv2.
17°vertically;themomentumac-ceptancewas4%withoutcuts,extendingto6%withade-creasingsolidangle.
Theangularresolutionafteranalysisofthetrackswas0.
1°fullwidthathalfmaximumFWHMhorizontallyand0.
2°vertically.
Thepolarizationoftheprotonsp1selectedbySPES4ismeasuredwiththepolar-imeterPOMME44.
ThepolarimeterFig.
4measurestheazimuthalasymmetryofp-Cinclusivescatteringfroma31.
2-cm-thickcarbonanalyzerlocatedneartheFFplane.
Protontracksupstreamanddownstreamofthecarbonblockarereconstructedusing6multiwire(XY)proportionalcham-berswithsensitivearea5050cm2forthethreefrontchambersand100100cm2forthethreerearchambers.
ThepolarimeterhasitsowntriggergivenbyacoincidencebetweentheFF,P,andQscintillators.
Thethreefrontcham-bersarealsousedfortheprecisetrackingthatdeterminesthemomentumandscatteringangleattheprimaryliquidhydro-gentarget.
C.
The''recoilspectrometer''RSThe''recoilspectrometer''consistsoftwoX,YmodulesofmultiwireproportionalchambersCH1andCH2,anarrayofsevenscintillationplatesEi,anda74matrixofscin-tillationblocksEijforE,EanalysisFig.
5.
Thedistancesbetweenthetargetpointandthewirechambersarerespec-tively1.
2and2.
7m,whichtogetherwiththe4-mmspacingofthewiresandthemultiplescatteringinthetargetandthetitaniumwindowresultaresolution20.
45°FWHM.
ThesevenplatesoftheEarray,eachof50012510mm3,wereplacedhorizontallyatadistanceof3.
03mfromthetarget.
Eachplateisviewedonbothsidesbyaphotomul-tiplier,andforeachofthematimeandaenergylossinfor-mationarerecorded.
TheEmatrixconsistsof28blocksplasticscintillator120120200mm3,eachofthemviewedbyasinglephotomultiplierandwithchargeinforma-tionrecorded.
D.
CalibrationbyelasticdpscatteringToobtainanabsolutecalibrationoftheanglebetweenSPES4andRS,elastictwo-bodyscatteringdp→pddataTABLEI.
Beampolarizationextremalvalueonthetargetandassociatedbeamstatenumber.
Assignedbeampyy;tensorpy;vectorstatenumberpolarizationpolarization10.
00.
020.
02/330.
02/340.
00.
051.
01/361.
01/371.
01/381.
01/3TABLEII.
Absolutevalueofthebeampolarizationmeasuredduringthetworunswiththestatisticalerror.
Run1Run2pystates230.
6470.
0200.
6330.
007pystates5,6,7,80.
3010.
0170.
3260.
012pyy0.
9470.
0180.
9120.
014FIG.
4.
PolarimeterPOMME:Thehodoscopeofplasticscintil-latorsFiislocatedatthenalfocalizationFFofthespectrometer.
ThePandQilathofplasticscintillatorsareconnectedtophoto-multipliersoneachside.
5456S.
L.
BELOSTOTSKIetal.
wererecordedandanalyzedforseveralSPES4angles,SPES4of7.
0°,6.
5°,and7.
0°.
Inthiscalibration,thedeuteronwasdetectedinSPES4,andtheprotoninRS.
Themeasurementwasextendedtonegativeangleinordertohaveaconstraintforthedeterminationofthe0°valueofSPES4;itwasfoundthatthenominalzeroanglewasshiftedby0.
33°totheleft,theusualscatteringsideinaSPES4experiment.
ForthelargerSPES4valuesof7.
9°,9.
54°,10.
93°,and12.
86°,thecorrelationoftheelasticscatteringdataandthetwo-bodykinematicsconstraintisshowninFig.
6.
Theval-uesdandparethedirectangularmeasurementinSPES4andRSwithrespecttotheircentralaxis.
Fromacomparisonbetweentheexperimentalpointsandthecurve,itwasdeterminedthattheanglebetweentheaxisofSPES4andRSwas75.
0°.
TheelasticscatteringdatawerealsousedtocalibratethetimeofightandtheEandEdetectorsoftheRSforknownprotonenergies.
AmoredetaileddescriptionofallthesecalibrationscanbefoundinRef.
45.
E.
EventselectionThep(d,2p)nreactioneventswereselectedbyrequiringtheappropriatetimingbetweenSPES4andRSrTOF.
TheaccuracyforrTOFwasbetterthan1.
0nsFWHM.
OncetheprotoninSPES4wasidentiedanditsmomentump1re-constructed,rTOFcouldbeconvertedtothetimeofightoftherecoilproton,fromthetargetvertextotheEdetector.
WedenotethisconvertedtimeofightasTOF.
ThisvaluerepresentstheparticlevelocitydetectedbyRSallowingtocalculatetherecoilprotonmomentump2.
The(E,p2)scat-terplotwasusedtoidentifyprotons.
Themomentump2wasusedinsteadofthemeasuredenergyintheEijcounters,becauseabove175MeV,theprotonswerenotstoppinginthe200-mm-thickplasticscintillators.
Thisadditionalinfor-mationEijwasonlyusedtosolveambiguouscases.
Forthedp→p1p2nprocessatagivendeuteronkineticenergyTd,whenp1isdeterminedfromtheSPES4mea-surementand2fromtheRSmeasurement,thereisacor-relationfTd;p1,2,p2,2025betweenp2and2.
Thisequationdenesamaximumscat-teringangle2max(p1,2)andtwopossiblevaluesofp2foragivenscatteringangle2smallerthanthismaximum.
Inthefollowing,thelow-energysolutionLEScorrespondstothelowestvalueofp2andthehigh-energysolutionHEStothehighest.
Thecorrelationisusedtoselectthedp→ppnpro-cessfromtheremainingbackground.
Theangle2ismea-suredbythemultiwireproportionalchamberMWPCofRSandp2bytheTOF,assumingtheRSparticletobeaproton.
Duetomultiplescatteringanddetectionresolutions,thedetectedeventsarespreadaroundthepurekinematicalcor-relation25,evenoutsidethekinematicallimit.
Toover-comethisdifculty,amethodthatminimizestheprobabilityofdeviationfromthethree-bodykinematicswasused.
A''distance''dbetweenthemeasuredeventat(2m,p2m)andtheexpected(2,p2)correlationisdenedd2p2mp22p222m2222,26where2isactuallygivenby2gp1,2,p227derivedfromthecorrelationf.
Theclosestvalue(2c,p2c)isobtainedbyaminimizationofexpression26withrespecttop2.
Thisvalue(2c,p2c)willthendetermineallotherkinemati-calquantitiesassociatedwiththemeasuredeventandcom-patiblewiththedp→ppnthree-bodykinematics.
Acutisalsoappliedontheminimizedd2valuesmallerthan4toselectthedp→ppnreactionandrejectbackground.
ThebackgroundcontaminationwasdeterminedfromFig.
7inaregionoutsidethekinematiclimitsofthedp→ppnreaction.
Inthegure,thecontourwhichisequivalenttotheallowedphasespaceofdp→ppnreactionisshown,butFIG.
5.
RecoilSpectrometerRS:TheRSarmisshownfromthesideontherightpartandfromthebackontheleftpart.
ThedistancebetweenEijscintillatorsandbetweenEscintillatorsisenlargedonthepicture.
Thedistanceisactuallyonlythewrappingpapers.
FIG.
6.
Thecorrelationfromelasticdpscatteringdatausedforcalibration.
5655MEASUREMENTOFPOLARIZATIONOBSERVABLESIN.
.
.
shiftedtolargervalueofTOF.
Theestimatedbackgroundwasaround2%intotal,butitaffectedmostlytheregionoflowcountingratee.
g.
,largeq).
InFig.
8,theestimatedbackgroundandrealp(d,2p)neventsaftersubtractionofthebackground,areshownasafunctionofq.
Fortheselectedeventswithp1andp2determined,themagnitudeofthespectatormomentumqwascalculatedwithatypicalaccuracyof8MeV/crms.
Foragivensetting,theprecisiononqrangesfrom2to30MeV/cinextremecases.
Themeasurementswereperformedatsixdifferentset-tingsofthemagneticeldsinSPES4withcentralvaluesof1.
6,1.
7,1.
8,1.
9,2.
0,and2.
05GeV/c,correspondingtothedifferentdomainsofqlistedinTableIII.
F.
DatahandlingforthepolarizationofthefastprotonOnlyforthoseeventsidentiedasoriginatingfromthedp→ppnreactionwasthepolarimeterPOMMEinformationanalyzed.
Theparticletrajectoriesreconstructedbeforeandafterthescattering,andthereactionvertexinthegraphiteanalyzerwereobtainedfromthefrontandrearchamberscoordinatesFig.
4.
Thethicknessoftheanalyzerwas31.
2cm.
Acutontherangeofthereactionvertextomatchtheactualsizeofthe12Cblockwasrstapplied.
Thedistribu-tionofthecscatteringangleafterthiscutisshowninFig.
9a.
Becausethesmallscatteringanglesaremostlyduetomultiplescatteringandnottoanuclearinteraction,eventswithc2.
5°wererejected.
TheseeventshavenegligibleFIG.
7.
Thecorrelationtoselectthecontaminationsfromback-ground.
Weusedtheeventsinsidethecontourshowntoestimatethecontributionfromthebackground.
FIG.
8.
Theestimatedbackgroundaandrealeventsb.
TABLEIII.
InternalmomentaqfordifferentSPES4settings.
p10,GeV/cq,GeV/c1.
60.
03–0.
201.
70.
04–0.
221.
80.
10–0.
381.
90.
16–0.
412.
00.
22–0.
442.
050.
29–0.
45FIG.
9.
aThedistributionofthescatteringangle(c)aftervertexcut.
Weusedonlytheeventscу2.
5°forthepolarizationanalysis.
bThenaldistributionoftheazimuthalanglec.
5656S.
L.
BELOSTOTSKIetal.
asymmetryandsufferfromabaddeterminationoftheazi-muthalangle(c).
A''conetest''46wasthenapplied.
Thistestrequiresthattheconedenedbycfortherunningeventlieswithintheacceptanceofthepolarimetertocon-siderthisevent.
Itisusedtoeliminatesystematicasymme-triesbyensuringasufcientazimuthalacceptance.
Theef-ciencyofthepolarimeterforthisexperimentwastypically8%.
Theazimuthalangle(c)distributionoftheeventsaftertheconetestisshowninFig.
9b.
Acdistributionwasobtainedforanumberofqvalues.
Togetreasonablestatis-tics,thebinningsizeforqwastakenas0.
05GeV/c.
Foreachevent,thecoefcientsa1Aycccosc,28a2Aycc2,29werecalculatedwithAyc(c)theanalyzingpowerofthein-clusivep12Creactionatthescatteringangle(c).
ValuesofAyc(c)wereobtainedinapreviouscalibrationofthePOMMEpolarimeter44.
Foreachbinofq,thequantitiesa1anda2weresummedforallevents,andtheprotonpolar-izationwasobtainedasPq2a1qa2q.
30ThispolarizationP(P)ismeasuredforthepolarizationstate2respectively3oftheincidentdeuteronbeam.
Rela-tions22and23wereusedtocalcutetheobservables.
ThestatisticaluncertaintyonP0andDvisratherlarge.
InFig.
10eachobservableobtainedfordifferentSPES4mo-mentumisplottedasafunctionofqbutseparatelyforthehigh-andthelow-energysolutionoftheproton.
Withthispartition,qseemsagoodvariableatleasttothelevelofaccuracyoftheexperimentasveriedbya2testbetweenmeasurementsatthesameqvalue.
Mostofthe2perpointaremuchsmallerthan1.
SovaluesobtainedatthesameqbutfordifferentSPES4settingswerecombined.
Theinternalmomentumqisthescalingvariableonlybelow200MeV/c,wheretheIAisknowntobevalid.
Abovethisvalue,thedeviationfromtheIAforP0andDvshouldbesmallerthantheprecisionofthemeasurement.
Thereis,however,anobviousdifferencebetweenthehigh-andthelow-energysolution.
Theycorrespondtodifferentorientationsoftheneutronmomentumqwhichshouldin-duceverydifferentcorrectionstotheIAandthisistherea-sonwhywehavekeptthisdependence.
G.
ObservablesfromselectedeventsAswasmentionedinprevioussections,therearetwoki-nematicalsolutionsandtheobservablesAY,AYY,P0,andDvcanbecalculatedasafunctionofqforeachsolutionseparately.
DenotingthenumberofselectedeventsafterbackgroundsubtractionasNi(q),whereiisthebeampolar-izationstatenumbergiveninTableI,theanalyzingpowersAYandAYYaregivenbyAYq231pyN2qN3qN2qN3q,AYq231pyN5qN6qN7qN8qN5qN6qN7qN8q,31AYYq21pyyN5qN6qN7qN8qN5qN6qN7qN8q,wherethebeampolarizationspyandpyyaredenedinEqs.
13,14,andinTableII.
Expressions31followfromEqs.
4,5,and6.
ThecompletesetofexperimentalvalueswithstatisticalerrorsisgiveninTableIVhighenergyandTableVlowenergyoftherecoilprotonp2).
FIG.
10.
Depolarization(Dv)ofthedp→p1p2nreactionandpolarization(P0)ofthefastproton(p1)asafunctionofq,themomentumoftheneutroninthedeuteronrestframe.
Eachfamilyofsymbolisforagivencen-tralmomentump1detectedinSPES4;thetopguresaandcforthelow-energysolutionofthesecondproton(p2)detectedinRSandthebottomguresbanddforthehigh-energyone.
Thebinninginqis50MeV/c,butthepointsatthesameqvalueareslightlydisplacedtoseethevariouserrorbars.
5657MEASUREMENTOFPOLARIZATIONOBSERVABLESIN.
.
.
IV.
THEORETICALINTERPRETATIONANDDISCUSSIONOFRESULTSA.
ModelusedThekinematicsofthisexperimentisdominatedbythep-pquasielasticscattering.
Nevertheless,then-ptermtakingintoaccountscatteringoftheneuteroninthedeuteronoffthetargetprotonproducingeithertheslowrecoilproton(p2)detectedwithRSorthefastone(p1)detectedbytheforwardspectrometerSPES4wasaddedcoherentlytothemainp-pscatteringtermintheIA.
Thisn-pcontributiontothecrosssectionisrathersmallbutitisnotnegligibleforthepolarizedobservables.
AlltheNNsecond-orderrescatteringtermsFSR'swereincludedtakingintoaccountboththelow-energynalstateinteractionandGlauber-typerescatteringofthefastprotons.
Inaddition,the33excitationdiagramswerealsoevaluated.
TABLEIV.
Measuredvaluesofthetensorandvectoranalyzingpowerandstatisticalrmserrorsasafunctionofq.
Seetextfordetailsandsystematicerrors.
Thistableisfortherecoilingprotonp2ofhighestenergy.
Themomentump1ofthefastprotoninthelaboratoryisspecied.
p1GeV/c)qMeV/c)AYY(AYY)AY(AY)1.
650.
00.
0920.
0320.
2560.
00970.
00.
0930.
0190.
2650.
00590.
00.
1450.
0170.
2550.
005110.
00.
1350.
0200.
2480.
006130.
00.
1840.
0260.
2380.
007150.
00.
2700.
0360.
2100.
011170.
00.
3180.
0510.
1830.
015190.
00.
1920.
0650.
1640.
021210.
00.
0210.
0860.
1290.
028230.
00.
0500.
1040.
1200.
036250.
00.
0140.
1241.
790.
00.
1940.
0180.
2700.
006110.
00.
2510.
0120.
2590.
004130.
00.
2710.
0120.
2490.
004150.
00.
2950.
0140.
2460.
005170.
00.
3570.
0210.
2140.
007190.
00.
4300.
0290.
2100.
010210.
00.
5530.
0380.
1730.
014230.
00.
5570.
0500.
1940.
018250.
00.
4720.
0600.
2030.
022270.
00.
2210.
0281.
8150.
00.
3600.
0250.
2850.
012170.
00.
3890.
0190.
2870.
007190.
00.
4380.
0200.
2580.
007210.
00.
4810.
0230.
2480.
009230.
00.
4900.
0320.
1920.
010250.
00.
5120.
0430.
1640.
013270.
00.
5400.
0570.
1310.
017290.
00.
5590.
0710.
1300.
022310.
00.
4680.
0870.
1320.
0201.
9210.
00.
4240.
0460.
3580.
029230.
00.
3820.
0220.
3040.
009250.
00.
3210.
0210.
2510.
008270.
00.
2700.
0220.
2340.
008290.
00.
1750.
0250.
1800.
009310.
00.
1450.
0310.
1540.
010330.
00.
2040.
0410.
1240.
012350.
00.
1490.
0570.
0830.
015370.
00.
0650.
0760.
0510.
0192.
0290.
00.
0410.
0770.
2700.
039310.
00.
0760.
0360.
2590.
011330.
00.
1260.
0310.
2010.
009350.
00.
1330.
0290.
1720.
009370.
00.
2000.
0300.
1620.
009390.
00.
1220.
0340.
1100.
010410.
00.
2520.
0470.
1440.
014430.
00.
2680.
1020.
1870.
0332.
05350.
00.
1630.
0750.
2370.
028370.
00.
1160.
0470.
1970.
018390.
00.
1210.
0410.
1670.
017410.
00.
2110.
0490.
1510.
020430.
00.
1630.
0940.
1540.
037TABLEV.
Measuredvaluesofthetensorandvectoranalyzingpowerandstatisticalrmserrorsasafunctionofq.
Seetextfordetailsandsystematicerrors.
Thistableisfortherecoilingprotonp2oflowestenergy.
Themomentump1ofthefastprotoninthelaboratoryisspecied.
p1GeV/c)qMeV/c)AYY(AYY)AY(AY)1.
7150.
00.
2930.
021170.
00.
3440.
014190.
00.
3200.
016210.
00.
2810.
021230.
00.
2080.
029250.
00.
2170.
0501.
8170.
00.
2110.
139190.
00.
3500.
0590.
2750.
018210.
00.
3280.
0470.
3110.
012230.
00.
4590.
0480.
2890.
013250.
00.
4450.
0570.
2840.
015270.
00.
4550.
0790.
1930.
021290.
00.
5620.
1060.
1720.
030310.
00.
4700.
1530.
1270.
0451.
9230.
00.
3170.
044250.
00.
4260.
0660.
2920.
017270.
00.
3430.
0510.
2710.
014290.
00.
3270.
0430.
2210.
015310.
00.
3450.
0420.
2040.
018330.
00.
3390.
0490.
1600.
025350.
00.
4000.
0600.
1670.
019370.
00.
1270.
024390.
00.
1120.
0332.
0310.
00.
2380.
0750.
2570.
020330.
00.
1860.
0520.
2230.
016350.
00.
2180.
0490.
1910.
014370.
00.
2990.
0490.
1830.
014390.
00.
2280.
0560.
1460.
015410.
00.
3030.
0730.
1810.
019430.
00.
1680.
1910.
1900.
0362.
05370.
00.
0560.
0720.
2080.
028390.
00.
2260.
0650.
1990.
025410.
00.
1710.
0630.
2230.
026430.
00.
4440.
1040.
2990.
0475856S.
L.
BELOSTOTSKIetal.
Thecalculationsresultspresentedbelowareobtainedbyco-herentsummationoftheIA,FSR,and33excitationdia-grams:MMIAMFSRM.
32AmplitudesMIA,MFSRandMcorrespondtothediagramsA,B,andCshowninFig.
2.
ThespinstructureoftheinputNNamplitudesisincludedintheenergy-dependentphaseshiftanalysisPSAofArndtetal.
47.
FollowingEverett48,inthetrianglediagramB,theNNamplitudesweretakenoutoftheloopintegral,andevaluatedattheoptimumFermimomentum.
However,whenthenucleonpairinteractinginthenalstatehasasmallrelativeenergy,itisnecessaryandpossibletocorrectthisNNamplitudefortheoff-shellbehavioroftheinterme-diatestate49–51:MoffMonfs31,mv2.
33Theformfactorfisafunctionoftheinvariantenergys31ofthepairandofthevirtualmass(mv2e2p2)ofoneoftheintermediatenucleon.
Itspreciseformcanbederivedfromthedeuteronmomentumwavefunctionusingclosure,asinRef.
52.
Thisformfactorwaskeptwithproperpropa-gatorsandverticesintheloopintegralandreplacedbyunityabove200MeV.
TheamplitudeMd→NNhasbeencomputedtakingintoaccounttheone-loopdiagramswiththeN33asintermediatestateandalsothediagramswiththeNscatteringintheS,P,andDwavesparametrizedbytheirphaseshifts.
InordertoavoiddoublecountingwehaveexcludedthenucleonpoleintheNamplitudewhichalreadycontributestotheIAterminEq.
32,andtheP11waveintheNscatteringwhichispartoftheFSRterm.
Finally,theex-changeisalsotakenintoaccountintheinteractionofthetwonucleonsofthed→NNamplitude.
Furtherdetailscanbefoundin53.
Intheframeworkofthismodelaverygooddescriptionoftheexclusiveunpolarizeddifferentialcrosssectionsforthed(p,2p)nreactionstudiedinGatchinahasbeenobtained15.
Itshouldbestressedthatherekinematicsaredevelopedtoincludeeventsoutofthescatteringplane;thecalculationsareintegratedovertheexperimentalapertureofthedetec-tors.
Amorecompletedescriptionofthemodelisinprogressandwillbepublishedsoon.
B.
DiscussionThetensoranalyzingpowerAYYforeachsettingoftheSPES4centralmomentum,andforbothhigh-andlow-energysolutions,isshowninFigs.
11and12.
ResultsofthecalculationswiththedeuteronBonnwavefunctionarealsopresentedinthegures.
Atthe1.
6,1.
7,and1.
8GeV/cset-tings,thetensoranalyzingpowerforthehigh-energysolu-tionshowsgoodagreementwithIAintherange0.
03рqр0.
20GeV/c.
Abovethisregion,thesimpleIAfailsbutisratherwellcorrectedbyadditionaldiagrams.
Thesamebehaviorisobservedatthe1.
8GeV/csettingforthelow-energysolution.
At1.
9,2.
0,and2.
05GeV/cthestrongde-viationofthemeasuredtensoranalyzingpowerfromIAforbothlowandhighT2isnotexplainablebythecalculations.
However,includingsecond-ordertermsrevealstherighttrendwithrespecttotheexperimentalpoints.
AsitfollowsfromEq.
9,inIAtheexperimentalAYYdividedbythefactor13qY2shouldscaleversusqforthetwokinematicsolutionsandalltheSPES4settings.
How-ever,thisisbyfarnotthecase,whichmeansunambigouslythattheIAfailstodescribethedataatqlargerthan0.
2GeV/FIG.
11.
ThetensoranalyzingpowerAYYforthehigh-energysolution.
Theexperimentalpointsarepresentedforthedifferentvaluesofthecentralmomentumdetectedinthemagneticspectrom-eterandasafunctionoftheoutgoingneutronmomentumexpressedinthedeuteronrestframe.
Thehigh-andlow-energysolutionreferstotheenergyoftheslowprotondetectedatthesameangleinRSThecurvesarethecalculationsexplainedinthetext.
Thedashed-dottedlineistheimpulseapproximation,thedashedlinehasinadditiontheFSRcontribution,andthecontinuouslineisthefullcalculationincludinginadditionthevirtual.
FIG.
12.
ThetensoranalyzingpowerAYYforthelow-energysolution.
SamenotationsasinFig.
11.
5659MEASUREMENTOFPOLARIZATIONOBSERVABLESIN.
.
.
c,andnomodicationofthedeuteronwavefunctioncanhelp.
ThevectoranalyzingpowerresultsarepresentedinFigs.
13and14.
Theyexhibitasimilartendency:thefullcalcula-tionsresultinasignicantcorrectiontotheIAabove0.
25GeV/c.
Agoodagreementbetweenthefullcalculationsandtheexperimentalpointsisachievedat2.
0and2.
05GeV/cbothforthehigh-andlow-energysolutions.
Polarizationoftheforward-scatteredprotonsP0andde-polarizationDvarepresentedaveragedovereachSPES4settinginFigs.
15–18.
AgooddescriptionisobtainedforP0whenalldiagramsareincluded,whereasthisisnotthecaseforDv.
EspeciallytheratherhighvalueofDvat220MeV/cisnotreproduced,butthecorrectiontotheIAlooksreasonableathighqmomenta.
TheIAisclosertothedatathanthefullcalculationsforthelow-energybranchespe-ciallyforintermediatevaluesofq.
However,consideringthelargeerrorbarsinthiskinematics,itappearsthatthereisnodecisivediscriminationfromthecalculations.
V.
CONCLUSIONAnextensiveandconsistentsetofdataonpolarizationobservableshasbeenobtainedforthed(p,pp)nthree-bodybreakupofdeuterononhydrogenuptodeuteroninternalmomentaq440MeV/c.
ThevectorAYandthetensorAYYanalyzingpowersex-FIG.
13.
ThevectoranalyzingpowerAYforthehigh-energysolution.
SamenotationsasinFig.
11.
FIG.
14.
ThevectoranalyzingpowerAYforthelow-energysolution.
SamenotationsasinFig.
11.
FIG.
15.
TheforwardprotonpolarizationP0forthehigh-energysolution.
ThenotationofthecurvesarethesameasinFig.
11.
ThecalculationsaredoneconsistentlyasforAYandAYYforeachset-tingofthespectrometerwhilethedataaresummedasexplainedinthetext.
FIG.
16.
TheforwardprotonpolarizationP0forthelow-energysolution.
ThenotationofthecurvesarethesameasinFig.
11.
6056S.
L.
BELOSTOTSKIetal.
hibitalargedeviationfromIAforinternalmomentaqlargerthan200MeV/c.
Theanalyzingpowers,beingratiosofre-actionamplitudes,couldbethoughttobelessmodiedbydistorsionsoftheIAthancrosssections,butthissimplecon-siderationappearsclearlywrong,atleastinthekinematicsinvestigatedhere.
ThedeviationfromtheIAisparticularlylargeforthetensoranalyzingpower.
Onecanconclude,basedontensoranalyzingpowerdataonlythatIAfailstodescribetheAYYdataabove200MeV/c.
Thisconclusioncannotbechangedbymeansofmodicationofthedeuteronwavefunction.
Descriptionofthedataisconsiderablyimprovedatmoderateqwhenconventionalsecond-ordertermsareincludedinthereactionmechanismintheframeworkofthetheoreticalmodeldiscussedabove.
NoticeabledeviationsofthetheoryfromthedatatakeplaceforAYYatlargeq,wheretheres-catteringFSR,thoughshowingtherighttrend,isnotsuf-cienttodescribetheexperimentaldataforthehigh-energykinematicsbranch.
SmallerdeviationsfromIAarefoundforthevectorana-lyzingpowerthanforAYY.
AverygooddescriptionoftheAYdatahasbeenobtainedforallsettingsofthespectrom-eter.
Itshouldbenotedthatoutofplanescatteringistreatedandintegratedovertheexperimentalacceptanceinthecal-culations.
Theexcitationofavirtualisfoundtohaveverylittleeffect,eventhoughtheinvariantenergyofthenucleonpairsissometimesveryclosetoMNM.
However,itshouldbementionedthatthereisonemissinggraphinthemodel;theformationonthetargetproton.
ThepolarizationP0ofthefastprotonmeasuredforthehigh-energybranchisconvincinglyreproducedbythemodel.
Thisisagoodtestfortheunderstandingofthereac-tionmechanism,becausethisobservableisnotsensitiveinrstordertothedeuteronstructure.
Thedepolarizationpa-rameterDvispoorlyreproducedbythemodel.
Toconclude,thepolarizationdataobtainedinthisexperi-menthaveprovidedaseveretestofadetailedmodelofthedp→ppnreactionmechanismaround1GeVpernucleon.
ThemodelhasbeenalreadysuccessfullyusedfordescriptionoftheGatchinaunpolarizedexclusivebreakupdata15.
TheimportanceofcorrectionstotheIAinvariouskinematiccon-ditionsisclearlydemonstratedbothbypolarizedandunpo-larizedexclusiveexperiments.
However,itdoesnotgiveacoherentandprecisepictureofallobservables.
Neverthelesswedonothavemuchfreedomtouseverydifferentdeuteronwavefunctions,takingintoconsiderationthegooddescriptionoftheunpolarizeddeuteronbreakupdataobtainedintheframeworkofthesamemodel.
TheagreementobtainedbetweendataespeciallyAY)andtheorywithaconventionaldeuteronwavefunctionimpliesthatnewdegreesoffreedominthedeuteronstructure,suchassixquarkbag,arenotrevealedinthekinematicregioninvesti-gated.
VI.
ACKNOWLEDGMENTSTheauthorswishtothanktheSATURNEstaffforthequalityofthepolarizeddeuteronbeamprovidedduringtheexperimentandforthemanagementoftheliquidhydrogentarget.
WearegratefultoM.
Rougerfortheconceptionandmanagementofvariouspartsoftheelectronics,subsequentlytakeninchargewithgreatefciencybyJ.
P.
Mouly.
Themanagementofmanypiecesofequipmentfortheexperi-ment,especiallytheRSdetectorswasefcientlyinsuredbyJ.
C.
Lugol,J.
Habault,andJ.
leMeur.
WewouldlikealsotoacknowledgeM.
Strikman,L.
Frankfurt,andJ.
M.
Lagetforfruitfultheoreticaldiscussions.
WealsowishtorememberProfessorJ.
Erodeceasedasaverykindperson,onewhowasveryinterestedinthisphysics,andaninspirationtoallwhoknewhim.
FIG.
17.
ThedepolarizationparameterDvforthehigh-energysolution.
SamenotationsasinFig.
11.
FIG.
18.
ThedepolarizationparameterDvforthelow-energysolution.
SamenotationsasinFig.
11.
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