Nuclear Instruments and Methods m Physics Research A 335 (1993) 156-164North-Holland

Simultaneous neutron-neutron proton-neutronand proton-proton interferometry measurements

R. Ghetti a, L. Carlén a, M. Crongvist b, B. Jakobsson a, F. Merchez ', B . NorénD . Rebreyend d , M . Rydehell b , O. Skeppstedt ' and L. WesterbergDepartment of Cosmic and Subatomic Physics, Lund University, Lund, Sweden

b Department of Physics, Chalmers Institute of Technology, Gothenburg, Sweden` The Scedberg Laboratory, Uppsala, Sweden"Institute des Sciences Nucleatres, Grenoble, France

Received 11 May 1993

This paper describes a technique to perform simultaneous neutron-neutron, proton-neutron and proton-proton nuclearmterferometry measurements . Experimental arrangements for intermediate energy heavy ion interferometry experiments arepresented and their limitations are investigated . The construction of correlation functions, particularly with respect to normaliza-tion and background corrections is discussed. Some new results on correlation functions from the reaction 30 A MeV °°Ar+ 12Care shown and possibilities to improve the interferometry technique are discussed.

1. Introduction

When light particles are emitted in close proximityin space and time, their wave functions of relativemotion are modified by final state interactions andquantum statistical symmetries. By measuring two-par-ticle correlation functions at small relative momenta itshould be possible to obtain information about thespace-time characteristics of the emitting source [1-9].

Several effects in nuclear reactions lead to correla-tions between emitted particles, but many of them, likemomentum conservation and quasi-elastic scatteringcreate mainly large angle correlations [10,11] . Threeeffects are important for small angle nucleon-nucleoncorrelations [1] : the short range attractive nuclear in-teraction, which creates a positive correlation, the longrange Coulomb interaction and the Pauli exclusionprinciple for identical particles with the opposite ef-fect . At high energies, when the emission is fast, thecorrelation is dominated by the final state interactions(nuclear and Coulomb) . In the proton-proton (pp)case a positive correlation peak appears at relativemomentum q = I p t _P2112 = 20 MeV/c due to theattractive s-wave nuclear interaction disturbed by thelong range repulsive Coulomb interaction which cre-ates an anticorrelation for q = 0 . For the proton-neu-tron (pn) system Coulomb effects are absent and onemay expect a pronounced correlation at q = 0 MeV/cdue to nuclear attraction . The mean field Coulombinteraction with the proton may however obscure this

0168-9002/93/$06 .00 © 1993 - Elsevier Science Publishers B.V . All rights reserved

NUCLEARINSTRUMENTS& METHODSIN PHYSICSRESEARCH

Section A

a

picture and deplete the nuclear interaction peak [12] .Neutron-neutron (nn) correlations should insteadprobe the pure nuclear final state interaction .

At lower energies where true compound nuclei arecreated, the time difference between the emission oftwo nucleons becomes large compared to the scatteringlength ; the effects of the final state interactions be-come negligible and the pure quantum statistical inter-ference can be observed [9,13] .

At intermediate energies it is difficult to asses therelative importance of spatial and time dependenceand there are therefore strong motivations to measuresimultaneously pp, pn and nn correlations . This paperdescribes a technique to perform such measurements .

2. Experimental interferometry technique

The interferometry technique requires measure-ments of the relative momentum (q) between twoparticles (fig. 1) . The relative momentum cannot bemeasured directly but must instead be determined fromsimultaneous measurements (correlations) of p t andp2 . In order to obtain high precision in these measure-ments the detectors must provide good particle identi-fication, good energy- and angular resolution.

The threshold for the relative momentum is deter-mined by the energy threshold of the detected particlesand by the smallest angle between neighbouring detec-tors . It is important to push this threshold to the lowest

R. Ghettc et al. / Simultaneous nn, pn and pp measurements

Fig . 1 . (a) Schematic illustration of two-nucleons correlationin which a nucleon (rl,p1) is detected by detector 1 simulta-neously with the detection of a nucleon (r2, p2) by detector 2.(b) Relative angle (B) and relative momentum (q) between

two particles .

possible value since the final state interaction signatureof the correlation function appears at very small valuesof q, particularly for nn and pn interactions.A wide dynamical range and solid angle coverage

are also desirable characteristics of the detector systemsince large energies (giving high q values) are impor-tant for the normalization of the measured correlationfunction and large solid angle for obtaining good statis-tics . Energy and angular determination should be asprecise as possible in order to minimize the errors in q .

Fig. 2 shows the setup used in our simultaneousmeasurement of pp, pn and nn correlation functions . A

compact Csl array (EMRIC) [14,15] was used for pro-ton detection (section 2.1), a spacious array of largearea liquid scintillators for neutron detection (section2.2) and a combination of the two for pn interferome-try . The CA array was placed 60 cm from the targetcentered at a laboratory angle of 45°. Five hexagonalneutron scintillators were placed 3.5 m from the targetbehind the holes created by removing five Csl crystalsin the proton array, to allow for pn correlation mea-surement . Three of the hexagons were positioned inthe horizontal plane and two above and below thecentral detector at azimuthal angles of ±8°. The dis-tance between neighbouring centers was 50 cm . Sixcylindrical neutron detectors were placed at other an-gles in the horizontal plane with a distance of 73 cmbetween their centers. This setup allowed relative mo-mentum (q) thresholds of 4 MeV/c for pp and pncorrelations and 5 MeV/c for nn correlations.

The experiment was performed with a 30 A MeV40Ar beam, from the SARA coupled cyclotrons, bom-barding 3 mg/cm2 thick "Au, 12C and CH2 targets.The beam frequency was 12 MHz and one burst out oftwo was suppressed . This gave a time interval of 166 nsbetween the bursts which allowed registration of neu-

Cslt-is Hi-5

157

Fig . 2. The experimental setup . The upper part is a top view. CS'1-16 is the Csl array. H 1 5 are the 5 hexagonal liquid scintillatorswith plastic veto detectors (S) in front. They are positioned behind holes created in the Csl array (as shown in the front view in the

lower part of fig . 2) . C1_6 are 6 cylindrical liquid scintillators with a lead absorber in front (Pb) .

15 8

trons with threshold energy of 3 MeV. The intensitywas stabilized around 10 nA and the beam energyresolution (DE/E) was of the order of 2-3 x 10-3 .

2.1 . Proton detection

EMRIC is an array of 25 CsI(TI) scintillators thatcan be used in conjunction with a multiwire propor-tional chamber (MWPC) for a precise position deter-mination . The 25 independent modules fit in a spheri-cal arrangement at 60 em from the target . The activesurface is 4 x 4 cmz and the thickness 10 cm, whichallows detection up to 200 MeV protons. The CsIcrystals are coupled to XP2012 phototubes .

Particles with charge from I to 3, are easily identi-fied with pulse shape analysis [16,17] . Fig. 3a is anexample of the charge and mass resolution that isobtained when plotting the correlation between theslow and fast components of the pulse integrated dur-ing time gates of 400 ns and 4 ws separated by 1 .7 p,s(section 2.3 fig . 5b).

The CsI array allowed us to measure relative anglesin the range 3.8° (angular separation between centersof adjacent modules) to 16.6°, since no MWPC wasused in this particular experiment . Each crystal sub-tended a solid angle of ~z 4.4 msr corresponding to aresolution of the relative angle of OB fi�hm = l .l° .

For a more precise position determination the useof two MWPC planes covering the total CsI area isneeded. The spacing between the wires is 1 mm whichallows a precision of AO = 0.1° (at 60 cm from thetarget) . If a MWPC is used the minimum relative angleis then determined by the frame around the CsI detec-tors ; this is 2 mm wide resulting in a AO of 0.2° .

The energy threshold is low due to the fact that CsIcrystals are not hygroscopic and can be used in air with

R. Ghetto et al. / Simultaneous nn, pn and pp measurements

a thin shield of 10 Win carbon and 10 win Mylar.Outside a standard vacuum chamber (with a 50 winsteel window) the proton energy threshold was 8 MeV.

The relation between the light response of the Csl'sand the particle energy must be established for eachindividual crystal . Two different techniques can beused ; preceeding silicon detectors or time of flight(TOE) measurements . The first technique [18] makesuse of two totally depleted surface barrier detectorswhich are temporary located in front of the CsI'sduring a calibration run. The light particles are identi-fied in the DE-E correlation plot . The response of theAE detector is determined from particles having theminimum energy required to cross both detectors (fromthe semiempirical range-energy relation). Once the cal-ibration of the silicon detector is performed, it isstraightforward to determine the relation between thepulse height in the CsI detectors and the energy de-posited in the AE detector . This gives the CsI responsefunction .

In the TOF technique [14,15], a copper plate stopsthe beam well before the reaction chamber. Lightparticles (p, d, t, a, Li) from the reactions are emittedin a wide range of energies and their TOF is measuredwith two thin plastic scintillators separated by a flightpath of ~ 5 m. These particles are then detected in theCsI detectors and the correlation between the CsIsignal and the TOF provides particle identification andenergy determination (with a resolution of 1-2% in therange 25-100 A MeV) .

The energy resolution of the crystals, estimated byusing protons and a beams of well defined energy, is ofthe order of 2-3% for protons in the range 15-170MeV [14] . Gainshift problems in the pulse-shape dis-criminators caused by high counting rates, temperaturevariations, ac and do input interference signals etc. [19]may deteriorate the energy resolution to 5-10%.

Fig . 3 . (a) Charged particle identification from one Csl(TI) crystal obtained via pulse shape discrimination technique . (b) Neutronand y separation in one neutron detector

2.2. Neutron detection

Liquid scintillators are the most commonly usedneutron detectors in interferometry experiments . Inour experiment stainless steel containers (with wallthickness of 2 mm and coated inside with white reflec-tor paint) filled with Bicron BC-501 organic liquidscintillator were used . The thickness is 15 .6 cm and thediameter is 30 .5 cm for the cylindrical detectors and16 .7 cm (effective cylinder diameter) for the hexago-nally shaped modules (see fig. 2) . The glass window ofthe scintillators was optically coupled to a 12 .7 cmdiameter XP2041 PM tube .

Neutron-gamma separation (fig . 3b) was obtainedvia pulse shape analysis [19] for a wide range of ener-gies (3-200 MeV) .

Charged particles were rejected by using thin plasticveto-scintillator detectors or Pb absorbers placed infront of the neutron detectors .

The energy is determined from a measurement ofthe flight time of the neutron from the target to thedetector . The emission time of the neutron is taken tobe that of the accelerator RF start signal plus a con-stant offset determined from the known flight time of-y-rays hitting the detector . The total time resolution,determined from the width of the y peak, is 3 ns . Thisuncertainty is due partly to the time jitter between theRF signal and the actual interaction (i .e . the durationof the individual beam pulse) and partly to the timingresolution of the detectors .

Our neutron detectors allow energy thresholds aslow as 25 keV equivalent electron energy (ee) corre-sponding to = 0.3 MeV neutrons . In this experimentthe threshold was set at 1 MeV ee by using the Comp-ton edge of 'oCo, corresponding to a neutron energy ofabout 3 MeV [20] .

2.3 . Electronics and data acquisition

The triggering and digitizing electronics is shown infig . 4. For neutrons three data words were recorded foreach hit detector corresponding to time, full energyand tail of the energy signal . For protons slow and fastcomponents of the energy signal were recorded . Theanode signals from the PM tubes were split into threeparts using impedance-matched splitters. One of thesignals was fed into the constant fraction discrimina-tors (CFD) while the other two were fed into individu-ally-gated charge integrating analog to digital QDCs[21] . To ensure the proper timing for neutron detec-tors, the QDCs were gated by a signal generated fromthe overlap of the master trigger and the CFD signalfrom the detector . For neutron detectors, the gate forthe full signal started 20 ns before and the tail gate 50ns after the leading edge of the analog signal (fig . 5a).Both gates were open for 300 Its . For CsI detectors,

R. Ghetti et al. / Simultaneous nn, pn andpp measurements

11 units 16 units

159

Veto

Splitter

CFD

X11

MLU

X 1s

Master Triggei

ANDStrobe

FO

Strobe

stlp

PU

PtSteStirt p

TDCGàte`J

GateQDC

QDC

BC-501

CFD Splitter

QDC

Inhibit

RF

CAMAC

Data Acq.

Fig . 4 . Schematic picture of the electronics setup where sealers,rate dividers etc . have been left out. The following abbrevia-tions have been used in fig . 4 : CFD = constant fraction dis-criminator . QDC = charge-to-digital converter. TDC= time-to-digital converter. MLU= multiplicity and logic unit . FO =logic fan out. GG = gate generator . AND = logic AND. PU =

patter unit .

slow and fast components of the pulse were integratedduring time gates of 400 ns and 4 Ws respectively,separated by 1.7 ws (fig . Sb).

The multiplicity outputs from the multiplicity unitwere added to give the total number of hit detectors .For coincidence data the system was triggered by amultiplicity of 2 or more . The overlap time was set toabout 150 ns to allow coincidences between particleswith different flight times. Singles data were also takenby triggering the system with multiplicity 1 signals,scaled down by a factor 100 with rate dividers (notindicated in fig . 4).

The time to digital converters (TDC) were startedby a signal that is not correlated with the time of thenuclear interaction. To allow the reconstruction of theproper time of flight, the time between the triggersignal and a signal from the cyclotron radio frequencyfield was measured for each event. The TDCs werecalibrated with cable delays, while the zero time wasdetermined from the position of the gamma peak inthe time of flight spectrum .

160

delayedprompt

-260 50

210 350

U~- i

fast slowR

0 0.4

1.7h

a)t( ns)

b)

Fig . 5 . (a) Charge integration of the neutron signal during two300 ns time gates. The first one is opened 20 ns before theleading edge of the pulse, giving the "prompt" value. Thesecond one 50 ns after, giving the "delayed" value. (The plotof the "delayed" versus "prompt" signals is shown m fig . 36) .(b) The Csl(TI) signal is integrated during two time gateswhose timing is adjusted to separate the "fast" and "slow"components of the pulse. (The two-dimensional plot of "slow"

versus " fast" component is shown m fig. 3a).

In addition to the ADC signals, a number of sealers(resident in CAMAC) where read out and stored on 8mm Exabyte tape by a VME based data acquisitionsystem, which also provided the on-line analysis tools .This data acquisition is a modular, flexible, stand-alonesystem utilizing the possibilities of parallel processingoffered by the VME bus. The central CPU is aVMVE147 board from Motorola . The user's interfacefor control and monitoring of the data taking is MS-DOS via an IBM-compatible PC connected to theVME system by a high speed parallel link . The eventsare read from the CAMAC equipment by one proces-sor through a VMX-CAMAC interface and deliveredinto buffers. Output to tape has the highest priorityand in case of idleness, on-line sorting into one- andtwo- dimensional spectra is performed.

3. The correlation functions

3.1 . Normalization

The data analysis in interferometry experiments hasthe goal to construct a correlation function which is asaccurate as possible.

R. Ghent et al. / Simultaneous nn, pn and pp measurements

The two-particle correlation function is given by[221 :

C(q)=kNc(q)Nnc(q)

where N,(q) represents the yield of coincidence eventsand Nnc(q) the yield of uncorrelated events . The nor-malization constant (k) is obtained from the conditionthat C(q) = 1 at large relative momenta and thereforeit is important that accurate measurements are per-formed at least out to q = 100 MeV/c.

The quality of the correlation function depends alsoon the denominator construction . Two different ap-proaches are commonly used [23,241 . In the "singlestechnique" Nnc(q) is constructed from the product ofsingle event distributions provided that they are mea-sured simultaneously, with the same external triggerconditions and with the same device as the true two-particle coincidence yield . This will account for thesame impact parameter distribution, the same geomet-rical constraints and the same efficiencies . In the"event-mixing technique" Nnc(q) is constructed by cor-relating each p 1 -particle with a randomly chosen P2_particle from the total correlation sample and thennormalized to the number of two-particle events in Nc .This method ensures that the uncorrelated distributionincludes the same class of collisions and kinematicalconstraints as the numerator but has the disadvantagethat it may attenuate the very correlations one wishesto measure [25,261 . Fig. 6a shows the Nnc(q) con-

2000

1500

Nnc(q) 1000

500 e. oe

" oo

0 20 40 60 80 100 120 140

al

co o~c "" e " " f f}p~T¢¢ ¢~-11ti60 80 100 120 140

q (MeV/c)

Fig . 6. Neutron-neutron measurement from 40Ar+ 12C reac-tion . (a) Yield of uncorrelated events (N,,(q)) constructedwith "event-mixing" technique (filled dots) and with "singlesproduct" (empty circles) . (b) nn correlation function obtainedwith the "event-mixing" denominator (filled dots) and withthe "singles product" denominator of fig . 6a (empty circles) .

structed from our neutron-neutron 40Ar + 12C datawith "singles product" and "coincidence mixing". Fig.6b shows the nn correlation function obtained with thetwo normalization procedures . The results are verysimilar but with the "event-mixing" technique both thetrue nn correlation peak and the cross-talk "false"correlation (which is most prominent in the region15 <_ q < 40 MeV/c) are slightly suppressed . When thecoincidence data contain very strong correlations the"event-mixing" technique does not completely succeedin decorrelating the events and therefore introduces adistortion in the correlation function . The degree ofdistortion depends on the strength of the correlationand on the available statistics. In the pp case, the twodifferent denominator construction procedures yieldedvery similar correlation functions . This is due to thefact that the pp coincidence data sample contains avery weak correlation and that large statistics is avail-able from the pp measurement.

3.2 . Corrections to the raw data

3.2 .1 . Neutron detection efficiencyIn the nn and pn cases, both Nc and N, c must

contain an energy dependent efficiency correction . Theefficiency of the neutron detectors has been MonteCarlo simulated with the program of ref. [20] whichintroduces all important elastic and inelastic scatteringchannels . The results for hexagonal and cylindricaldetectors are shown in fig . 7, for a fixed energy thresh-old of 3 MeV. The energy dependence of the neutron

R. Chetti et al. / Simultaneous nn, lin and pp measurements

50

40

30

20

10

°0 20 40 60 80 100Energy (MeV)

Fig . 7. Neutron efficiency calculated with the program of [20]for hexagonal (filled squares) and cylindrical (open squares)

liquid scintillator neutron detectors .

detection efficiency originates from the variation of thecross sections for the different reaction mechanismsand from the energy threshold [27] . Similar shapes ofthe energy dependence are obtained with the programMENATE [28] (section 3.2 .2) but a difference up to25% from the results shown in fig . 7 can be found atlow energies .

The total effect of this correction on the correlationfunctions is very small, suggesting that, on the average,the detection efficiency affects the numerator and de-nominator in the same way.

3.2.2. Background correctionsIn the nn correlation function two main sources of

background have been taken into account: neutron

Table 1Cross-talk dependence (% of the total two-neutron coincidence yield) on the neutron energy and on the distance between twodetectors (energy detection threshold of 1.0 McVee)

Table 2Cross-talk dependence (% of the total two-neutron coincidence yield) on the energy threshold for two detectors 45 cm apart

Threshold Neutron energy [MeV][MeVee] 5 10 15 25 40 60 1000 .1 51 .0 73 .1 77 .0 80 .0 80 .7 81 .0 82 .40 .2 32 .6 67.6 73 .4 75 .7 77 .2 77 .5 82 .20 .4 0 .0 48 .2 62.1 67 .1 72 .5 72 .7 78 .70 .6 0 .0 30.9 58.6 62 .9 70 .1 72 .6 75 .90 .8 0 .0 8 .5 53 .2 60 .4 63 .9 67 .2 74 .11 .0 0 .0 0.0 19.5 31 .8 57 .6 64 .4 73 .4

Distance Neutron energy [MeV][cm] 5 10 15 25 40 60 10015 0 .0 90 .7 93 .9 94 .1 96 .2 96 .8 97 .030 0 .0 46 .7 70.4 71 .5 80 .8 83 .3 85 .445 0 .0 0 .0 19 .5 31 .8 57 .6 64 .4 73 .460 0 .0 0 .0 19 .5 25 .1 47 .2 52 .8 57 .375 0 .0 0 .0 18 .3 25 .1 26 .1 29 .0 34 .3

16 2

scattering from one neutron detector into another(cross-talk) and neutron scattering in the CsI array.

Cross-talk [28,29] is the most serious kind of back-ground when a dense array of neutron detectors isused without shielding between them . If a neutron isscattered from one detector into another and recordedin both the event is normally indistinguishable from atrue 2n coincidence and introduces an ambiguity in theresults .

Analytical estimations of the cross-talk are possiblebut full Monte Carlo simulations are generally re-quired (section 3.3, fig . 10). Simulations have beenperformed with the Monte-Carlo code MENATE [28]that introduces the following reaction mechanisms :C(n, 2n), C(n, n' y), C(n, a), C(n, n') 3a, C(n, n),C(n, np), C(n, p) and H(n, np) for neutrons; comptonscattering and photoelectric effect for -y-rays .A qualitative understanding of the cross-talk effect

can be obtained from the simplest possible experimen-tal situation with two neutron detectors. The depen-dence on neutron energy, distance between detectorsand detection energy threshold is shown in tables 1 and2. The figures represent cross-talk probabilities relativeto the total amount of nn events (under the assumptionof a singles/coincidence ratio of 1860 which was de-duced from our experimental data). The calculationsare made for two hexagonal detectors of 20 cm thick-ness and 198.5 CM Z surface area .

Inspection of tables 1 and 2 reveals that :- Due to the delicate scattering kinematics the

amount of cross-talk is strongly energy depen-dent and increases with the neutron energy .

- For a fixed detection energy threshold theamount of cross-talk increases rapidly with de-creasing detector distance (table 1) .

-

For a fixed distance between the detectors, theamount of cross-talk for low energy neutronsvaries rapidly with the energy threshold (table2). Higher detection thresholds reduce thecross-talk problem since cross-talk neutrons havelost energy and easily fall below the detectionlimit.

These results are in good agreement with analyticalcalculations and with the experimental cross-talk valuemeasured with an isotropic 14 MeV neutron source inref. [29] . A complete cross-talk simulation for the ex-perimental setup of fig . 2 has been performed intro-ducing the experimental neutron energy distributions(see fig . 10). The amount of false 2n events generatedfrom cross-talk scattering has been estimated to liearound 10% for Au target and 20% for C target of thetotal nn correlation sample .

The neutron-neutron correlation function in ourcase is disturbed also by neutrons originating fromelastic and inelastic CsI(n, n') scattering in the protondetector array. This contribution has been experimen-

R. Ghetu et al. / Simultaneous nn, pn and pp measurements

2

o C(q). C(q) corrected

0 20 40 60 80 100q (MeV/c)

Fig . 8. Neutron-neutron correlation function from 4()Ar+ 197An raw data . Filled dots : correlation function measured withthe normal setup of fig. 2 . Empty circles : correlation functionmeasured after removing the Csl array from the experimental

area

tally measured in a run during which the CA array wasphysically removed from the experimental area . Fig. 8shows the raw 30 A MeV 40Ar + "'An nn correlationfunction together with the one measured without theCsI array in the experimental area . The effect is no-ticeable only for q values < 10 MeV/c (since else-where the nn correlation function is flat) where thesmall q shift suppresses the nn correlation .

q (MeV/c)

Fig 9. (a) nn- (b) pp- (c) pn-correlation functions measuredfrom 40Ar+ 12C reactions at 30 A MeV. 13 Csl detectors, fourhexagons and two cylindrical liquid scintillators have been

used (see text for more details) .

6

C(q) 4

- ,n) a

2

0 20 40 60 80t

100

q (MeV/c)

1 .2 b)+

C(q) 0.9

0 .6

0 .30 20 40 60 80 100

q (MeV/c)

2 .0 d1 .5

C(q)1 .0

0.50 20 40 60 80 100

Analytical calculations have shown that the effect of(n, n') scattering in the CsI array is negligible for theproton-neutron correlation measurement (less than 1%of the total pn events are affected by it) . Also thecontribution from direct knock-out charge-exchange(p, n) reactions in the CsI detector material producinga false pn correlation is less than 1% .

Finally it should be stressed that other effects, likethe beam halo hitting the target frame etc., may causebackground . A run without target revealed the pres-ence of a background contribution of 5% pp, 4% pnand 2% nn coincidence events .

3.3. Selected experimental results

Final pp, nn and pn correlation functions from 30 AMeV 40Ar + 12C collisions are presented in fig. 9. Theyare constructed from = 8700 nn, 460 000 pp and 149 000pn events detected with 13 CsI modules, four hexago-nal and two cylindrical liquid scintillators (CZ and C3in fig . 2) in the horizontal plane. "Event-mixing" tech-nique has been used for the uncorrelated yield con-struction. All corrections described in sec. 2 have beenmade . The vertical error bars are purely statisticalwhile the errors Oq on the relative momenta havebeen calculated, individually, from the position andenergy uncertainties. For the nn correlation functionthe main contribution to Oq comes from the positionuncertainty. This error has been estimated randomiz-ing the hit position of each neutron homogeneouslyover the front area of the detector. It is less than 2MeV/c due to the small solid angle (= 1 .8 msr) cov-ered by one single hexagonal neutron detector in theexperimental setup. In the proton-proton case, eachCsI crystal covers a solid angle more then twice theone covered by a hexagonal neutron detector . Thetotal Oq due to position and energy calibration uncer-tainties is between 3.0 and 5.5 MeV/c.

3

00 10 20 30 40 50 60

q (MeV/c)

Fig. 10 . "Cross-talk correlation function" obtained fromMonte Carlo simulations with the program of ref. [28] . Thecalculation is normalized to the same number of coincidencesas in fig . 9a . The "event-mixing" denominator (fig . 6a) has

been used as uncorrelated background for this figure .

R. Ghetti et al. / Simultaneous nn, pn and pp measurements 16 3

The curves of fig . 9 exhibit the shape expected froma combination of antisymmetrization effects and finalstate interactions [1,30] . One should notice that:

- The rather large width of the pp correlationfunction may be due to the limited angularresolution . In order to achieve a good resolutionthe use of a MWPC is needed .

- The "bump" observed in the nn correlationfunction in the region 15 < q < 40 is attributedto cross-talk background . The kinematics ofcross-talk events in our experimental setup issuch that the "false" nn coincidences arisingfrom cross-talk all lie in the 15 <q < 40 relativemomentum region, and are therefore clearlyseparated from the true correlation appearing atq < 10 MeV/c .

Fig. 10 shows the "cross-talk correlation function".It is obtained from a complete cross-talk Monte Carlosimulation (see section 3.2 .2) of our experimental setup,done by introducing the experimental neutron energydistribution from the 30 A MeV 40Ar + 12 C data. Themain contribution to the cross-talk comes from theC(n, n')C and C(n, n')3a reactions which produce thetwo peaks of fig . 10 . The calculation is normalized tothe same number of coincidences as in fig . 9a. The"event-mixing" denominator of fig . 6a has been used asuncorrelated yield for the construction of fig . 10 .A physical interpretation of the results in terms of

the underlying reaction dynamics and time-space sourceextension gained from comparison with theoretical cal-culations is discussed elsewhere [30-32].

The experimental results stress the need for mea-surements at very low q values in order to observe theexpected pp anticorrelation and pn and nn correlation .The data analysis [32] has revealed that in our mea-surements the strong q = 0 nn correlation peak comesonly from low energy neutrons (E� < 7 MeV) .

Acknowledgements

The authors wish to thank the Swedish ResearchCouncil for Natural Sciences . Financial support fromStiftelsen Blanceflor Boncompagni Ludovisi f6dd Bildtis gratefully acknowledged by RG.

References

[1] S.E . Koonin, Phys . Lett . B70 (1977) 43 .[21 W.G . Lynch et al ., Phys . Rev. Lett . 51 (1983) 1850 .[3] Z. Chen et al ., Phys . Rev. C36 (1987) 2297 .[4] Z. Chen et al ., Phys . Lett . B186 (1987) 280.[5] J. Pochodzalla et al ., Phys . Rev. C35 (1987) 1695 .[6] J . Pochodzalla et al ., Phys . Lett . B174 (1986) 36 .[7] S. Pratt and M.B . Tsang, Phys . Rev. C36 (1987) 2390 .

164

[8] TC Awes et al ., Phys . Rev. Lett. 61 (1988) 2665 .[9] D. Ardouin et al ., Nucl . Phys . A495 (1989) 57c.

[10] I . Tanihata, S. Nagamiya, S. Schnetzer and H. Steiner,Phys . Lett . 13100 (1981) 121.

[11] J . Knoll and J. Randrup, Phys . Lett . 13103 (1981) 264.[l2] G. Bertsch, P. Damelewicz and H. Schulz, Preprint NBI-

92-75 .[13] W. D6nnweber et al ., Phys . Rev. Lett. 65 (1990) 297[14] J Mistretta, Thesis Unrv of Grenoble ISN 1988 unpubl .[15] F. Merchez et al ., Nucl. Instr. and Meth . A275 (1989)

133.[16] C.J . Crannel et al ., Nucl . Instr. and Meth . 115 (1974) 253[17] J Alarja et al ., Nucl . Instr. and Meth A252 (1986) 352.[18] A. Kristiansson et al ., Nucl . Instr. and Meth . A295 (1990)

359.[19] J . Bialkowski, M. Moszyinski and D. Walski, Nucl . Instr.

and Meth . A275 (1989) 322.[20] R.A. Cecil, B.D . Anderson and R. Madey, Nucl . Instr.

and Meth 161 (1979) 439.

R Ghetti et al. / Simultaneous nn, pn and pp measurements

[21] R. Foglio, A. Patti and J . Pouxe, Internal Report ISN8741(1987) .

[22] G.I . Kopylov, Phys . Lett . 50b (1974) 472.[23] B. Khelfaoui, Thesis Univ . of Grenoble ISN 1991 unpubl .[24] D. Rebreyend et al ., Phys . Rev. C46 (1992) 2387 .[25] M.A. Lisa et al ., Phys. Rev. C44 (1991) 2865 .[26] W.A . Zajc et al ., Phys. Rev. C29 (1984) 2173 .[27] S.E . Arnell et al ., Nucl . Instr. and Meth . A300 (1991)

303[28] P. D6sesquelles et al ., Nucl. Instr. and Meth . A307 (1991)

366.[29] M. Cronqvist et al ., Nucl . Instr. and Meth . A317 (1992)

273[30] V.A Avdeichikov et al ., Lund Univ . Preprint LUIP9201

(1992) .[31] R. Ghetti et al ., Proc. Int. Winter Meeting on Nuclear

Physics, Bormio, Italy, Jan. 1993, ed . I Iori (Univ. ofMilano), in press

[32] M . Cronqvist et al ., submitted to Phys. Rev. Lett