Brueckmann, H.

Kluge, W.

Schaenzler, L.

English

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Juni 1967Institut für Experimentelle KernphysikExperimental Investigations of the ReactionsR(d, 2p)n and D(d, dp)n with 50 Me V DeuteronsR. Brückmann, W. Kluge, L. SchänzlerKFK 608Als Manuskript vervielfältigtFür diesen Bericht behalten wir uns alle Rechte vorGESELLSCHAFT FüR KERNFORSCHUNG MA~.H.KARLSRUHEJuly 1967KERNFORSOHUNGSZENTRUM KARLSRUHEKFK 608Institut für Experimentelle KernphysikExperimental investigations of the reactions p(d,pp)nand d(d,dp)n with 50 MeV deuteronsH. Brückmann, W. Kluge, L. SchänzlerGesellschaft für Kernforschung m.b.H. KarlsruhePaper presented at the Symposium on Light Nuclei,Few-Body-Problems and Nuclear Forees, Brela, Yugoslavia,June 26. - July 5, 1967AbstractA collimated beam of 51.5 MeV de~terons from the Karlsruheisochronous cyclotron was used to investigate the threeparticle reactions p + d -.. n + p + P and d + d ---"d + P + n.The two emitted protons or the proton and the deuteron,respectively, were detected in coincidence with two scintil-lation counters.The experimental data for the reaction p(d,pp)n exhibit apronounced peak due to final state interaction between theoutgoing neutron and one proton (the proton angles werechosen to be e lab= 400 and e lab= 250 accordingly). Theanalysis shows that this final state interaction is domi-nated by the virtual singulet state of the deuteron. Theextracted n-p scattering length is lasl = (19 ± 2.5)f.In the investigation of the reaction d(d,dp)n the angleswere chosen so as to observe predominantly the processwhere the neutron in the target deuteron acta as a'spectator' particle. The analysis in terms of the Chew-Lowextrapolation procedure yields a straight line intersectingthe En-axis at -(0.95 ± 0.15) MeV (En , energy of the spec-tator neutron). The extrapolated d-p cross section is(14 ± 5) mb/sr. The value obtained from an independentmeasurement of elastic deuteron-proton scattering i8(32 ± 3) mb/sr.- 2 -The experimental investigation of two of the simplest threeparticle reactions namely the reactions p + d -p n + p + Pand d + d ----&pd + P + n is of great interest from twodifferent points of view:a) The general understanding of reactions with three particlesin the exit channel requires more detailed experimentaldata on these reactions.b) The corresponding reaction n + d-. n + n + p involvingtwo outgoing neutrons is one of the main tools to provideinformation about the neutron-neutron force. However theneeded connection between a two particle interaction andthe results which con be obtained from a three particlereaction can only be checked experimentally in thosecases, where the two particle interaction is known froman independent experiment. The mentioned reactionsp + d -"n + p + p and d + d ---. d + P + n are weIlsuited to this basic task.The experimental results published hitherto for these reactionsprovide evidence of three different reaction models to betaken into account [ 1 - 8 ]:1) The three nucleons populate the available phase spacestatistically.2) The process can be treated as a quasifree scatteringbetween two particles; one nucleon acts only as aI spectator I •3) A final state interaction between two nucleons characterisesthe reaction.The experimental conditions for our investigations wereselected in such a way that we observed predominantly aneutron - proton final state interaction in the reactionp + d-+n + p + p. In the second reaction d + d-.d + P + nthe parameters were chosen to study predominantly a quasifreedeuteron-proton scattering.A collimated beam of 51.5 MeV deuterons from the Karlsruheisochronous cyclotron was used to bombard a gas targetfilled with hydrogen or deuterium.. The two emitted protonsor the proton and the deuteron were detected in coincidencewith two scintillation counters. T.he angles with respeet tothe beam axis were 03 and Q4 (Fig. 1).- 3 --- --The momentum P3 and P4 01' t~ outgoing particles wascoplanar with the momentum P1 01' the projectile deuteron.The energies 01' two particles (E3 and E4) are registered,and each event is thus kinematically completely defined.The energy and the direction 01' the third particle(the neutron) as weIl as the relative energies betweentwo outgoing particles are calculated.Large distances between the target and the detector(L3 = 70 cm, L4 = 92 cm) allowed a particle identificationby using time-of-flight technique [ 9 J. These Iargedistances were also convenient to achieve the necessarysmall resolution 01' D. Q4 = ±. 0.50 and ß 03 = ±. 0.750 •The coincident events were registered in a two dimensional4096 channel analyser.Final state interaction in the reaction p + d -... n + p + pThe requirement for a study 01' the neutron-proton finalstate interaction is that one wants E45 (the relativeenergy between one proton and the neutron) to becomezero along the kinematically allowed curve E4 = f(E3).For our experiment this condition fixed 94 to 25°after 03 had been chosen to be 400 in the laboratorysystem. The point, where E45 1s zero corresponds to themaximum allowed value 01' E39Fig. 2 shows on the left a map di,splay of the experimentaldata with E3 as abscissa and E4 as ordinate in an arrayof 32 x 128 channels. Most 01' the registered eventspopulate the kinematically allowed curve E4 = f(E3).A distinct peak appears in the region where E3 reachesits maximum allowed value. This peak is assigned to afinal state interaction between one outgoing proton andthe neutron. The right hand side of Fig. 1 shows theprojection onto the E4 axis. For comparison the full linerepresents the normalized phase space.- 4 -The aim of the following interpretation of the experi-mental results is to achieve more insight into then-p final state interaction. The analysis of these datashould directly show the S-matrix pole of the deuteronsingulet state. One should also be able to comparethree particle results with values obtained from thecorresponding two particle reaction, namely the freen-p scattering.The cross section for the 3 particle reaction may bewritten aswhere I is the channel spin and S the total spin ofthe two particles experiencing the final state interaction,and gSI and q (03' 04' E4 ) are the statistical factorsdue to spin and space respectively.The contribution of the virtual singulet deuteronstate to be final state interaction can now be describedby writing I~12 as__B;;.....__ /2k + i ae's(2)Here, k is the internal momentum within the n-p systemand -i~s characterizes the position of the pole ofthe S-matrix (see, for instance, Watson [10J).In order to check the pole character of the matrixelement,it is convenient to plot the quantitytN7~F)-1' versus the relative energy Enp • N'is thenumber of counts per dE4 interval. The phase spacefactor PSF is proportional to ~(03' 04' E4 ) and isnormalized to the eXperimental däta.- 5 -Fig. 3 shows such a plot for our experimental data.Within the statistical errors the plotted points arerepresented fairly weIl b~ a straight line intersecting112 Zthe abscissa at Eo = - 2": . The value obtained forE is E = -(120 ± 30)KeV. This would correspond to ao 0 +scattering length of lasl = (19 - 2.5)f. This value,obtained from the investigation of the n-p final stateinteraction, may be compared with the scattering lengthknown from the n-p singulet cross section which isa s = -(23.73 ± O.007)f.The following conclusions can be drawn from our experiment:1) The final state interaction as observed in ourexperiment is dominated by the virtual singuletstate of the deuteron.2) The extracted scattering length as appears to besmaller than the value known from the n-p crosssection. If this result will be confirmed by anexperiment with improved statistics it might beexplained by an influence of the triplet boundstate or by an interference effect. Only apartof' this interference between the A and B termof equation (2) has the same E dependence as thepure B term.Quasielastic scattering in the reaction d + d ........ d + P + nA quasielastic scattering process where one particleacts only as a 'spectator' particle can be observedin the laboratory system in two different ways. Eitherthe 'spectator' is part of the projectile nucleus('projectile spectator') or it is part of the targetnucleus ('target spectator'). TUe difference arisesonly because two detectors have to be used at fixedpositions in the laboratory. This can be outlined ina discussion of two examples. The neutron in a deuteronis assumed to act as a spectator particle in botaexamples.- 6 -In the reaction d + P _n + p + p the neutron actsas a projectile spectator, if this reaction is inducedby accelerated deuteron. The spectator neutron willcarry away about half the primary energy and the twocoincident protons will be found in the lab.systemunder angles where (03 + 04) is near 900 • For suchcombinations of angles the kinematically allowed curvecontracts to a very small circle and finally becomesa point. The spectator peak is always located in thecorner of low E3 and E4 values. This situation is notfavourable to the study of the quasielastic scatteringprocess. Fig. 4 shows an experimental result for thisexample. Deuterons with an energy of 51.5 MeV were usedto bombard a hydrogen target. The angles of the twoo 0proton counters have been 03 = 40 and 04 = 40 •On the other hand a 'target spectator' neutron 1sconsidered. There the neutron is left over with onlyits internal momentum distribution from the deuteronand almost the total energy is available for the twoparticles to be detected in coincidence. The spectatorpeak will be located in the neighbourhood of the lineE3 + E4 = E1 -~' (~is the binding energy of thedeuteron). This configuration should be preferred ofone wants to investigate mainly effects of quasielasticscattering. Fig. 5 shows our experimental result forthe reaction d + d -- d + P + n. A broad 'target spectator'peak is clearly visible. The ~~gles were chosen so thatthe neutron energy E5 reaches down to zero along thekinematically allowed curve (03 = 400, 0 4 = 250 )A projection of the data onto the E4 axis 1s shown onthe right of Fig. 5. The dashed curve represents thenormalized phase space.- 7 -For analysis the Chew-Low theory [11,5] was used.Within the assumption of this theory the three particlecross section for a pure spectator mechanism can bewritten aswhere the phase space factor is labelIed q (E4 ) andC is a constant containing the masses, the initialmomentum, and the normalization factor of the deuteronwave function. The matrix element1f 12= I< P1 1 - Psi V I P3 I P4 > 12represents a multiple of the free elastic deuteron-protonscattering only at the position of the pole whereE5 is E5 = P52/2 m5 = - E:s/2 (indices according to Fig.1)"It should be noticed that a measurement of the threeparticle cross section at the pole can never be realizedexperimentally, because the spectator energy E5 wouldhave to be negative at this point. The fourth factor inthis expression results from the internal momentumdistribution within the deuteron. Here ~ denotes thebinding energy of the deuteron.In the comparison of our experimental result with thetheoretical predictions two aspects were regarded. Ina first step only a test for the pole cha~er wascarried out. For this purpose it is convenient to plotthe quanti ty VP~F I versus the spectator energy En •Here N denotes the number of events registered perchannel and PSF is the normalized phase space factor.A pure pole character as predicted in formula (3) wouldresult in a straight line intersecting the En axisat ...1.1 MeV ..- 8 -Fig. 6 shows our data plotted for the test of the polecharacter. Within statistics the points are loeated ona line crossing the axis at -(0.95 ± 0.15) MeV. It canbe concluded, that the shape of the three particle crosssection is dominated by the pole term wh1ch 1s causedby the internal momentum distribution in the deuteron.The second aspect in the interpretation aims atextracting the elastic deuteron-proton cross sectionfrom the measured three particle cross section. As wasoutlined before,an extrapolation procedure has to beused to evaluate the matrix element Ifl 2 at theunphysical point, where En is equal to -EB/2. For thisanalysis we assumed that the pole term of equation (3)is exactly valid and we are able then to plot thequantity Ifl 2 as a function of En • The dashed curve inFig,. 5 proportional to the phase spaee factor was assumedto be a background which can be subtracted. The obtainedplot !f1 2 in units of mb/sr versus En"iS shown in Fig. 7.The points denote numbers from the lower half and thecrosses numbers from the upper half of the experimentalcurve N versus E4 • Only a few points are labeled withthe statistical errors. As can be seen, most of the plottedvalues can be represented by a straight line. Only thepoints at high neutron energy En which are marked withcrosses do not fit this line. The reason ,for thisdiscrepancy might be a final state interaction betweenthe deuteron and the proton which increases the countingrate at these high values of E4 • (Additional events inthe same energy region were observed clearly in aseparateexperiment, where other angles were used). For the extra-polation into the unphysical region the straight lineis used and this yields a value of (14 ± 1) mb/sr forthe free elastic proton-deuteron cross section.The error contains only the statistical uncertainty.The absolute accuracy is estimated to be ± 5 mb/sr.- 9 -By using this matrix element 1~12 as a linear functionof En this interpretation describes the shape of thespectatorpeak as shown for comparison in the lowerpart of Fig. 7. Significant deviations are only seenin the region of high E4 values where another mechanismcontributes to the cross section.To compare the d-p cross section extracted ~rom thethree particle reaction with a value obtained framfree deuteron-proton scattering the d-p differentialcross section was measured separately. The result isshown in Fig. 8. From this measurement a value o~(32 ± 3) mb/sr is obtained for the angles used in thecoincidence experiment. The comparison shows that theseresults dif~er by a factor of about two. For an explanationof this dif~erence more experimental data are needed andthe extrapolation procedure has to be examined in detail.In the course of a further study o~ simple three particlereactions we plan to repeat the experiments described.The aim is to obtain much better statistics and to checkall quantities which have an influence on the absolutecalibration of the three particle cross section. Theinvestigation of the neutron-neutron interaction inreactions like n + d-.n + n + p will follow afterexperience has been gathered with reactions involvingonly the n-p interaction.... 10 -R e f e ren ces1) W.D. Simpson, J.D. Bronson, W.R. Jackson, G.C. Philips,Rev. Mod. Phys. 22, 523, (1965)P.F. Donovan, Rev. Mod. Phys. 22, 501, (1965)vI. Slaus, J.W. Verba, J.R. Richardson, R.F. Carlson,L.S. August, Phys. Lett. ~, 358, (1966)4) R.J. Griffiths, K.M. Knight, Nucl. Phys. 2,i, 56, (1964)5) A.F. Kuckes, R. Wilson, P.F. Cooper, Ann. Physe .12.,193, (1961)6) R.F. Carlson, Rev. Mod. Phys. 22, 531, (1965)W.D. Simpson, Ph.D. Thesis, Rice University Houston,Texas 19658) H. Brückmann, W. Kluge, L. Schänzler, Phys. Lett. 24B,649, (1967)H. Brückmann, Habilitationsschrift Technische HochschuleKarlsruhe 1966H. Brückmann, E.L. Haase, W. Kluge, L. Schänzler(to be published)10) K.M. Watson, Phys. Rev. 88, 1163, (1952)11) G.F. Chew, F.E. Low, Phys. Rev. 112, 1640, (1959)- 11 -Captions o~ ~iguresFig. 1:Schematic drawing o~ the experimental arrangement.Coincidences between the two detector output signalsare registered.Fig.2:Experimental data ~or the reaction p + d~n + p + p.A map display for the two protons (with energies E3 and E4 )registered in coincidence is shown on the le~t. T.he dataprojected onto the E4 axis and the normalized phase space~actor are shown on the right.Fig. 3:Analysis o~ the pole character o~ the ~inal state inter-action peak. The straight line intersects the abszissaat Enp= -(120 ± 30) KeV.Fig. 4:Experimental data ~or the reaction p + d~n + p + p. Mapdisplay o~ events where two reaction products were registeredin coincidence (with energies E3 and E4 ). The proton-protoncoincidences are populating a small circle. On this circlea projectile spectator peak can be seen. The angles were03 = 400 and 04 = 400 •Fig. 5:Data for the reaction d + d-..d + P + n. The map displayshows proton-deuteron coinc~4e~ces. ~~re ~4 denotee thedeuteron energy and E3 the proton energy. The data projectedonto the E4 axis and the normalized phase space factor areshow-n on the right.- 12 -Fig. 6:Chew-Low plot for the data shown in Fig. 5. The straightline fit intersects the En-axis at En = -(0.95 ± 0.15) MeV.Fig. 7:The upper part shows the matrix element Ifl 2 plottedversus the neutron spectator energy En • A straight -lineextrapolation to En = -1.1 MeV yields (14 ± 1) mb/sr forthe differential cross section in elastic deuteron-protonscattering. In the lower part the shape of the spectatorpeak resulting from this fit is compared with the experi-mental data shown in Fig. 5.Fig. 8:Differential cross section for elastic deuteron-protonscattering.(D--(3)detector Igas ta~et80mmFaraday6 3~51.5 MeVdeuterons 6 4SCQtte~chamberdetector IrsUts defining theactive target volumeand the solid anglesFig. 1•·.·.. . .7.5p(d ,pp)nEd= 51.5 MeV93 =40°94 =25°5.02.5..••..•..•..•..•." .. .••••....·'. .•••••••••••••·.••••••-..••••• •...• ••••• ••••••••••-...• •• •••..• ••••••••••••••••••••....•••-........-.........•. ...·....· .....••••••.... ...........•••..... .. ,............•••e •••e' •••••. ...... .•••..••...........•• •••. ....e •• '.•........••••••..••••..103020[MeV]•..•. . ..... .. .. .. ... . . .. " ... .... . .. . ..- .....•...... .•• •••• ••••• •• e ••••••••... . ...·10 20Fig. 2ooNoo~a.c&AIc >- G»a. :ea. It) 0 0.0 It) 0~ ,..."It) ~ N11 11 II-A. ." (') 'lt&AI (J) (J)Fig. 3Fig. 4~>G) >~ G) 0 0~ ~ 0 1ft.. C .. "ut - 1ft- II II.a A. • a.- tJ>""E 0 " 1ft tJ>r-.I CI!) ..." II II IIw" - "" tJ>CI!) 0"a w"c." 0"~CI!)c:"....Cl!)b 0-"~>G)~··..~.,.. .•••••••••••••••••..•• 0• 0o ••o ••··.·.....o •o .0·.·...• ••o ••........ .. .. .. ..... .... . .............. ..•....•............... .. .....••. ....0 •·.....••·.···.._....·.·..·.·..·..·.·.·........·..........•••••_.............111 .....E---_~-----------_-----------'o.. o"Fig. 5C'>l11I •t!J,...+~0- CA-I - >• A. •0 ." ~.. 10 00I ~ ~ 10 0,..• ." 10 C'I •• - II II 11.c 0 " " A-U 11I (!) (!)----~~---------_rO,...I~Iz ~------,~-~------T~-------Fig. 615105IfI2f~~]'~)t"~~ - x, lCXj-.,.~• x l(e e e}..t lC'''~~o 1N/channel400 +------1f----+----+----+-----+----l----_+_100 t------1---+---f'----+----+----;-p.....-----------,f-----_+_200 +----l----+-~___fT'-+----+--~---+---t-----+-300 f-------1r----+-----+----f------I--''r-----+---I-----1-ol----t--===L=:.=.=!=====:.:t:=.::==:t-=~=:l~~~40 35 30 25 20 15 MeV Ed1.5 0.75 0.20 0 0.20 0.75 1.5 MeV EnFig. 7100 ~CM 15050oIH(d,d)HEd =51,5 MeV............'" ...'" l." I'" ". I'. 11'., ..,. I.". ,,\ .I\ I"'.. /''-..,.,I1 I010100dadQ[~~r]CMFig. 8

Experimental investigations of the reactions H(d, 2p)n and D(d, dp)n with 50 MeV deuterons

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Experimental investigations of the reactions H(d, 2p)n and D(d, dp)n with 50 MeV deuterons

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