Brueckmann, H.

Kluge, W.

Matthaey, H.

Schaenzler, L.

Wick, K.

English

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Juni 1970Institut für ExperirxlenteHe KernphysikInvestigation of the Angular Correlation in theThree-Nucleon Reaction d + P ........ P + P + nHo Br üc.krnarm, Wo Kluge, Ho Matthäy, L. Schänzler, x. WiekKERNFORSCHUNGS ZENTRUM KARLSRUHEJuni 1970 KFK 1216Institut für Experimentelle KernphysikInvestigation of the angular correlation in the•three-nucleon reaction d + P + P + P + nH. Brückmann, W. Kluge, H. Matthäy,L. Schänzler and K. WickGesellschaft für Kernforschung m.b.H., Karlsruhe*orally presented at the Washington Meeting on NuclearPhysics April 1970 by H. Matthäy.Bulletin of the AmericanPhysical Society Sero II, Vol. 15, No. 4, 476 (1970)- 1 -AbstractThe reaetion d + p + p + P + n was investigated bykinematieally eomplete experiments at a deuteron bombardingenergy of 52.3 MeV. The aim of a systematie study was toexplore the eontribution of n-p and p-p FSI at many pairsof angles. The data were analyzed using the Watson-Migdaltheory. The n-p and p-p seattering lengths and the eross-seetions for the production of the FSI-pairs in singletand triplet states were extraeted. The seattering lengthsobtained were found to be in good agreement with the valuesknown from free nucleon=nucleon scattering. The resultingangular distributions of the singlet and triplet cross-seetions turn out to be quite different. The elose relationbetween the angular distribution for the triplet cross-seetion and the angular distribution of d-p elastic scatteringis diseussed. In separate runs kinematies were ehanged inorder to obtain the angular distribution of the FSI-pairs intheir em-system.- 2 -I want to present some new results of a systematic investigationof the three-nucleon reaction d + P + P + P + n. This reactionwas studied by coincidence experiments at many pairs of anglesusing the 52 MeV deuteron beam of the Karlsruhe isochronouscyclotron.Our main interest concentrated on a thorough study of the reactionmechanism. Particularly we aimed to establish angular distributionsof the three-nucleon reaction and to test the validity of thetwo_step reaction model rigorously.Fig. 1 shows schematically a basic diagram, representing theessential features of the two-step reaction model. The three-particle reaction is induced by an incoming deuteron and aproton. In the first reaction step a n-p pair with low relativeenergy might be produced. This pair is denoted by d~. The secondreaction step accounts for a final state interaction of then-p pair. Such a finalstate interaction can be observedpredominantly' if the kinematics of the two-detector coincidenceexperiment are chosen properly.As is evidently seen from the diagram such an experiment aimsto answer two main questions. Firstly the angular distributionfor the production of final state interacting n-p pairs can bemeasured as a function of the production angle ed~' Secondlya measurement of the angular distribution in the subsystem ofthe FSI nucleons should verify the reliability of the two-stepreaction model. If the two reaction steps proceed independently,one _ , 4- _ 04-1.-_ .....:J.. _ ...... .-...J .... _",-,: _ ....... 1.-_1.....:,.: .&-.... •e }";;\,; 1.1,;;) l.Iue u. V.L-vu.l.l.\; \,.J.vu V.L-Vua.U.J..J..J. \,:1 tobe J..ndependent ofall variables in the subsystem.Let us nOW turn to the discussion of measurements which werecarried out to investigate the angular distribution of the d*production in the first reaction step. Fig. 2 gives an exampleof two typical map displays obtained in our coincidence experiments,- 3 -The observed events populate the whole kinematieally allowedeurve in the E3, E4 plane. E3 and E4 denote the energies ofthe two eoineident protons. In the upper map displaya strongenhaneement of events is observed at maximum energy E3~ Justat this point the relative energy of the other proton and theneutron is zero.'I'he Lower- map display+is eharaeterized by two final state peaks.It was obtained at the unique kinematieal eondition, wheren-p pairs with zero relative energy ean be observed at twodifferent points of the kinematieal eurve. For the analysis thenumber of coincidence events was projected onto the are length Sof the kinematical curve. The are length S is indicated schematical-ly in the map display.The speetrum resulting from the lower map display is shown infig. 3. Here at this unique kinematical situation two finalstate peaks arise. The data were analysed using the Watsonmodel of FSI. Both the final state interaetion in the singletand thetriplet state have been takeninto aeeount. Thereforethe experimental data allow to evaluate the two produetionprobabilities for the formation of n-p pairs in the singletand the triplet state separately. The upper solid eurve representsthe result of the Watson fit. 'rhe fit agrees exeellently withthe experimental data.. 'I'he different contributions arising fromthe singlet and the triplet states are indieated by thin eurves.Such spectra were measured at ten different pairs of angles.At all these sets of angles n-p pairsenergies reaehing down to zero.The resulting angular distributions for the produetion of singletand triplet pairs with zero relative energy is shown in fig. 4.The three partiele eross-secti6n is given as afunetion of thcproduetion angle ed~.+see fig. 2b- 4 -Evidently the triplet and the singlet angular distributionsexhibit remarkable different shapes. Particularly it shouldbe stressed that the triplet state angular distribution showsa surprising similarity with the angular distribution knownfrom the elastic p-d scattering. Indeed a quantitative relationhas been established which connects the matrix elements of thetwo processes. The cross-section of the three-particle reactionwas calculated from elastic p-d scattering. The result isshown as asolid curve. The agreement with the experimentaldata is excellent.Let us now turn to the second aim of our experiments. We wantedto check the reliability of the two-step reaction model. The",,','+-' f +-" • , +- rI t . , +- r1 11f d t' houl.dpro....,a...,l ... l ... les or ... ue slng... e ... an ..... rlp ...e ........ pro uc lon s.OU...depend on the angle 6d llf only. They should not depend on theinternal angular coordinates of the n-p subsystem. Thereforeangular correlation measurements have been carried out wherethe angle 6dllf has been kept constant but the center of massangle in the subsystem was varied. This means that in thelabQratorysystem the detection angle of thethirdparticlehas to be kept constant while the detection angle 64 of thefinal state interacting proton is varied.Such angular correlation measurements have been carried outand the formulaused in the analysis is shown in fig. 5.The three-particle reaction laboratory cross-section dividedby the phase space factor is given by a sum of singlet ands ttriplet terms. X and X denote the production probabilitiesfor the n-p subsystem in the singlet and triplet state. FS and Ftare the corresponding enhancementfactors. The particularenhancement factor used in this analysis implies the assumptionthat the subsystem is formed in a pure S-state. The value ofXS and Xt were determined experimentally as a function of 64.- 5 -A rather small variation ine 4 corresponds to a very largevariation in subsystem angular coordinate. As is seen evidentlyfrom these experimental results the production probabilitiesare independent on the subsystem angular coordinate. Consequentlythe two-step reaction model turns out to be applicable.The applicability of the two-step reaction model was confirmedfor the n-p FSI. In separate experiments we have studied theproton-proton FSI. Reasonably the model holds in thesamereaction and at identic<fl kinematical conditions also in thesituation where two protons interact in the FS. Therefore oneis able to investigate an anisotropy in the p-p subsystem whichmight be caused by contribution of higher angular momenta inthe Coulomb interaction.Fig. 6 shows an example of a map display for the effect ofp-p FSI. Here the distribution of events on the kinematicalcurve is shown as a runc t Lon of the neutron time-of- flightand the energy of the coincident proton. Contrary to the caseof n-p FSI a deep minimum is observed at zero relative energy.This difference between n-p and p-p FSI is illustrated in fig. 7.Two spectra are shown which were measured to observe p-p andn-p FSI at identical kinematical conditions. The distributionof events in the final state region was projected onto the axisEp' Ep denotes energy of the non final state interacting freeproton. While the n-p FSI exhibits the weil known peak at zerorelativ energy the p-p final state interaction is characterizedby this deep minimum, which is due to Coulomb force. n-p andp-p scattering lengths were obtained which are in very good agree-ment with the values known from free nucleon nucleon scattering.Finally we have investigated the angular distribution in thep-p subsystem by angular correlation measurements. Same of suchresults are shown in fig. 8. One wants to compare the p-p inter-action at different subsystem angles but at the same relativeenergy. Therefore the spectra are given as a function of the- 6 -relative energy Epp or the two protons.The solid eurves indieate least square fits using a modifiedMigdal enhaneement faetor. To eompare the experimental resultswith an isotropie angular distribution in the p-p subsystemthe upper fit is plotted also in the other speetra. Theagreement between the four speetra is quite weIl. A detaileddiseussion shows that the p-p FSI pair is formed in iso statepredominantly but a small anisotropy observed ean be explainedonly by taking into eonsideration higher angular momenta inthe Coulomb interaetion.I want to finish with the eonelusion that the three-nueleonreaetion ean be very weIl explained in terms of the two-stepmodel this holds at least at many partieular kinematiesituations.- 7 -Figure captionsFig. 1Fig. 2Fig. 2bFig. 3Fig. 4Diagram representing schematically the essentialfeatures 01' the two-step reaction model and indicatingthe way to test the model by experiment.Typical experimental map-display taken from theobservation 01' the reaction d+p ~ p+p+n at Ed=52 . 3 MeV.The distribution 01' events on the kinematical locus isshown as a function 01' the energies E3and E4 01' thecoincident protons detected at angles 6 3=42 . 00 64=25. 30•The strong enhancement at maximum energy E3 is due ton-p finalstate interaction (FSI). The arc-length S 01'the kinematically allowed curve is indicatedschematically.Experimental map display taken at symmetrical proton-___ "'!iI ___n- _-,.., __ "",,:..,.0ang~e~ ö3=ö4=~(.( •The spectrum resulting from the projection 01' the datashown in Fig. 2b on the arc-length S. The contribution01' the FSI 01' proton 3 and 4 with the neutron (particle 5)are shown separately for the singlet and the tripletcase.The angular distribution 01' the three-particle productioncross-section 01' final state interacting n-p pairs with(Enp=O) in singlet and triplet state.As abscissa the c.m. production angle Sd· as weIl asthe lab. angle 6p ofthe "free" proton are given. Thesolid curve results from a theoretical calculationconnecting the three-particle cross-section quantitativelyto the cross-section 01' elastic p-d scattering. (Thetriangle denotes a theoretical prediction for thesinglet cross-section at a backward angle).Fig. 5Fig. 6Fig. 7Fig. 8- 8 -The probabilities for the production of final stateinteracting singlet and triplet n-p pairs obtainedfrom an angular correlation measurement. XS and Xt areshown as a function of the lab. detection angle 04 ofthe final state interacting proton, whereas 0d- is keptfixed. The formula used to analyse the experimental datais shown at the top. F S and Ft denote the singlet andtriplet enhancement factors. PpS is the phase-spacefactor.Example of observation of proton-proton FSI in thereaction p+d ~ p+p+n at 0p = 25.30 On = 42.0 0 • Thedistribution of events on the kinematical locus isshownas a function of the proton energy E and Tn thep .neutron time of flight. The gap in the center of theTn axis is caused by use of two time of flight circuits.Cömparison öf n-p and p-p FSI at identical kinematicalconditions. The spectra result from a projection of the ex-perimental data on the proton energy axis Ep • The valuesof the singlet n-p scattering-length and the p-p scatteringlength determined from the spectra are given.Results of the angular correlation measUrement for p-p FSI.The value of the squared three-particle matrixelement(in relative units) as given by the experiment and thecorresponding Watson-Migdal fits (solid curves) are shownas a function of the energy Epp of the protons in their. _ •. _ _ _ _0 _... _.. _ _c , m, sys1;ern. .!:"or compar-ason t ne 1)'., - 1"11; as plot ted alsoin the other spectra (dashed curve). Only the full dotswere included into the fitting-procedure, because for theother points the influence of the spectator-effect cannot bneglected. The minimum relative energy Epp observableat the chosen kinematical conditions is indicated byspecial marks.- 9 -n1st reaction stepAngular distributionof FSI np-pair prod.pp2nd reoction step IAngular distribution -'---------'I in the np-subsystem IFig. 1Fig. 2a- 10 -Fig. 2b1086d-p-e-p-p-nEd=52MeVe3=27.7°fh=27.7°45Slnp(3,Sl2o40S[MeV]50 60 70 80 90I I I ~10 20 30 E3 [MeV]Fig. 3- 11 -42colculoted---tram d-p elastic scattering400' i I a'oo' , '.12'00 I , '.~Oo' ....10 iBpllabnOU~oI i , ,351Fig. 4d3d1 S FS t t+ X'(84 ) FIE np)dSdll 3dß4 • Qps = X(84 ) IEnpl~ XS •XtIBd*=78° I0.6 ! 60.4-t---t------t-4 ,---!_----!--~-0.2r: 2'-,94 9420° 22° 24° 26° 28° 20° 22° 24° 26° 28°Fig. 5- 12 -Fig. 6Ed =52.3 MeV• d+p-d*+p-p+n+po d+p--lHe 2)+n-p+p+no83=42.084=25.30500N100030Ep [MeV]2010Onp= =23.5±O.5 fmopp= -7.5±O.5 tm100300500N700200600400Fig. 7- 13 -Sp= 19.5°Sn=48.3°Qpp=-7.6ff f fH?4200 2 3 46• f1 -~ /tZ It/-" Sp=22.4°4 " =-A Af A =48 ~o/ ' 't f " .... pp ..,...,. ""n ....,/' \2l? ?\~ t'j 1 i0 24 Qpp=-a.3f Sp=25.5°Sn=48.3°24Epp(MeV)32o00 2 3 44 Qpp=-7.9f 8p=28.3°8n=48.3°2Fig. 8

Investigation of the angular correlation in the three-nucleon reaction d+p --> p+p+n

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Investigation of the angular correlation in the three-nucleon reaction d+p --> p+p+n

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