Analysis of angular distribution of proton-neutron FSI in the reaction 2H(p, pn)1H at E0 = 12.5 MeV

LB : 2.B

Nuclear Physics A337 (1980) 365-376; © North-Bollard Publlalürsg Co., Antaterdam Not to be reproduced by photoprint or microSlm without written peamission from the publisher

ANALYSIS OF ANGULAR DISTRIBUTION OF PROTON-NEUTRON FSI IN THE REACTION 2H(p, pn)tH AT Eo = 12S MeV E.ANDRADEt Instituto de Fisica, Universidad National Autdnoma de México . Apdo . Postal2ll-364, México 20, D.F. D. MILJANIt~

Ruder Bo.~kovié Institute, Zagreb, Yugoslavia and G. C. PHILLIPS

T. W. Bonner Nuclear Laboratories ; .Rice University, Houston, Texas, USA Received 19 October 1979 Abstract : The angular dependence of the p-n,final state interaction in the pd -" pup reaction for Eo = 12 .5 MeV is studied. The experimental results are compared with a calculation using the Watson-Migdal model and exact three-body calculations. Both calculations show satisfactory agreement with the data . E

NUCLEAR REACTIONS ZH(p, 2p), E = 12 .5 MeV ; measured pn~oin ; deduced angular dependence of final state interaction. Watson-Migdal, exact three-body models .

1. Introduction In recent gems considerable effort has been put into the experimentâl and theoreticâl investigations of few-body problems [see e.g. review papers in refs . t -s)] . Deuteron break-up by nucleons has received much attention, with the hope of adding some. information to the understanding of the nucleon-nucleon interaction. The first studiesofthesereactions were concernedwith understanding the reaction mechanism. The existing experimental data provide convincing evidence for the following two reaction mechanisms : (i) sequential decay or final-state interaction (FSn, in which a .pair of particles interact in the final state after being produced by the primary interaction ;. (ü) quasi-free scattering (QFS), in which the incoming particle interacts with one of the nucleons with not momentum transfer to the other nucleon of the target deuteron. This paper presents an analysis of an angular distribution of p-n FSI at Epo =. 0 from proton induced deuteron break-up at Eo = 12.5 MeV. The shape of the final-state interaction peak in coincidence spectra (kinematically f Supported in part by La Direcci6n Adjunta de Formacidn de Recutsos Humanos del CONACyT de México. 365

April 1980

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complete experiment) is very sensitive to the low-energy parameters of p-n scattering. The aims of this analysis are: (a) to compare the data with the exact three-body calculations, (b) to obtain information on the relation between the exact three-body calculations and the simple theoretical apprôximation, i.e. with the WatsonMigdal model (WMM) [ref. a)]. The exact three-body calculations are done using the Ebenhöh code (ECM [ref, a)] . Kluge et al. s) have made a similar analysis of the experimental data of diûerent groups on the angular distributiôns of p-n FSI in the reaction pd --~ ppn measured at several bombarding energies . 2. Experimental proced~ue The 12.5 MeV proton beam provided by the Rice University tandem accelerator, of about 20 nA was used to bombard a foil of deuterated polyethylene . The experimental set-up is shown schematically in fig. 1. This set-up was used to measure simultaneously four experiments from the bombardment.of deuterons with protons. Removable Yrering Quarfz

Anti-scattering Sllts Neutron Exit Por Solid State Defector 2

Fig. 1 . Basic schematic of the experiment and the reaction chamber.

One ofthese experiments was themeasurement ofproton-proton coincidence spectra from the pd -~ ppn reaction .performed using two surface-barrier siliwn detectors located at symmetric angles - Bt = 9z = B. Proton-neutron coincidences at - B~ = 9z were detected simultaneously using a liquid scintillator neutron detector that determined the energy of the neutrons by time of flight. These symmetric detection geometries were very convenient in studying the angular distributions of the p-p

ZH(p, Pn)'H

367

and p-n QFS contributions in the deuteron break-up by protons. The results of these measurements were published in ref. 6). The third experiment involved thedetermination of the proton-neutron çoincidence spectra from the pd -. pnp reaction with both counters located at the same angle 62 = 6Q = B. These data are analyzed in this paper. It is obvious that the simultaneous detection of the p-n (QFS and FSI) and p-p (QFS) coincidences from the pd -> ppn reaction allows trustworthy comparison between the three-body cross sections') . In order to be independent of changes in target thickness with time and from errors in the charge measurement, thé fourth experiment, realized simultaneously, was the monitoring of elastically scattered protôns at the scattering angle B l . This peak was .used to normalize the three-body break-up cross sections e). The neutron detector was a N)r218 liquid scintillator 12.7 cm in diameter and 7.6 cm in depth; the scintillator was viewed by an assembly of two Amperex 56 AVP photomultiplier tubes, used in coincidence in order to reduce the background caused by the phototube noise. The detector was shielded as described in ref. ~ and placed outside the scattering chamber at a distance of 2.16 m from the target center . The electronic system for studying the above four experiments on the bombardment of~deuterons with protons is shown in fig. 2. The data were stored in an IBM 1800 . on-line computer utilizing a 8-parameter interface system '°). l:n this experiment 1024channel resolution was chosen in the measurement of each parameter. Using GATE A

Fig. 2. Block âu~gram of electronics : a triangle preamplifier ; AMP, linear amplifier; DDL AMP, double delay line amplifier ; .SCA, timing and single-channel analyzer ; TAC. time to amplitude converter ; GDG, gate and delay generator ; ADC, analog to digital converter ; SCINT ; eciritillator ; PM, photomultiplier ; PSD, pulse-shape discriminator; COIN, coincidence unit ; CRT, cathode ray tube.

36 8

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these facilities it is possible to measure up to eight different experiments simultaneously and to measure, for each one, from one to eight parameters . Associated with each of the experiments, a gate pulse .(tag) is foimed using some electronic logic. This tag is generally recorded on magnetic tape along with the measured parameters of the corresponding experiment . The tag associated with each event of a given experiment is used to . identify the experiment and corresponding measured parameters . The data are reduced by reading the tapé into the computer and applying some specific programming conditions. About 8096 memory words are available for a program to display on a cathode ray tube single spectra or two-dimensional data during the course of the experiment. The four experiments realized simultaneously will be referred to as "gate A, B, C and D", i.e. proton 1-proton 2, proton 1-neutron, proton 2-neutron .coincidences and free-energy spectrum experiments respectively . It was necessary to measure a total of seven parameters with the experiments described above. With reference to fig. 2, the thick lines are concerned with the seven linear signals connected to the ADCs through linear amplifiers . The pârameters associated with gate C for each p-n coincidence event were :the proton energy, relative neutron time of flight (with respect to the proton), dynode and pulse-shape discrimination (PSD) signals: The last two signals from the neutron detector were used for y-ray rejection based on the idea suggested by Alexander and Goulding l t). Moré detailed information about the reduction of the data is given in ref. '). Careful

w

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3

4

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Fig. 3. Neutron detector efïiciency. Thesolidcurve is a theoretical curve(ORNL calculations) normalized using the n'He coincidences from the by 0.83 to fit the experimentally measured effitiencies ~H(d, n)3 He reaction.

(n

attention was paid to the determination of neutron efficiency in order to obtain absolute cross sections for proton-neutron coincidence measurements . The absolute efficiency was determined by the detection of the n-3He coincidences from ZH(d, 3He)n reactions as described in ref. 12). The measured neutron counter efficiency is shown in fig. 3. For neutron energy above 2 MeV the absolute efficiency was determined with an accuracy of approximately 10 ~.

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369

3. Experimental data An advantage of kinematically complete measurement of the pd --> pnp reaction is that the proper choice of the pair of angles allows the reaction to be observed at kinematical conditions where one reaction mechanism is dominating. For small relative energies, Ero, one expects the p-n FSI to bé dominant. Therefore one wants Epo to reach zero along the kinematically allowed curve (locus). The obvious detection geometry is such that proton and neutron are detected at the same angle. The other choice is at the angles for p-p detection where Epa = 0. This geometry was most often used in p-d break-up studies [see refs. 1 z )] . In that .way one avoids neutron detection problems . However, in our case, the first geometry was used by observing. in coincidence proton and neutron going out in the same direction (9P = B o The bombarding energy was .12 .5 MeV and the angular range covered in the measurements was 17 .5 5 B S 45°. The measured coincidence spectra are shown as projections on the proton-energy axis for the proton detected at B p = 90 = B. An overview of the measured spectra is presented in fig. .4 . as a ~

=

~.

N u

8 (DEGREES)

Fig. 4. Proton-neutron coincidence spectra from the reaction p+d ~ p+n+p for Eo = 12 .5 MeV and Bp = Bo = B. The spectra are represented by the solid line through the measured points ; the dotted line represents the relative energy in p-n system .

family of histograms for vârious angles . The p-n relative energy, EPo, is also plotted along with the data. All these spectra are dominated by a peak near zero relative energy in the proton-neutron system. 4. Data analysis In the Watson-Migdal model (WMM), the final-state interaction effects axe taken into account by the modification of â Born approximation calculation by the insertion of the value of the wave function of the relative motion at the origin 3). The T-matrix element is given for an S-wave by D(Ep~ ~

(H°rn) .

(1)

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It is also assumed that the variation of ~ with EP° can be neglected and the only dependence on the relative energy EP° is given by the factor 1lD(EP°). The three-body cross section is then given by d3Q __ 2_ mo . FP°(EPJTs PS, _ (2) ~ dE1 dS~ l dSi z po where F°P = 1/~D(CP°)~z is the p-n enhancement factor, mo and Po are the mass and momentum of the incident proton, respectively, and PS is the three-body phase space factor . In the effective-range approximation the p-n enhancement factor is given by

_

4{kp° +az)rô

where a is given by

kP° is the p-n relative momentum, aP° is the p-n scattering length, and ro, the effective

range. According to eq. (3), the p-n FSI should be limited only to small relative energies and thereby results in a rather sharp peak at zero p-n relative energy . Since the neutron and proton can interact in the singlet or in the triplet state, both singlet and triplet contributions have to be used when considering p-n FSI in the pd -" pnp reaction . Accounting for the final-state interaction of one p-n pair only and using incoherent superposition of the singlet and triplet amplitudes the cross section is written as the sum d3Q _ [X~Fp° ±XP°F`P°] PS. dEPdâèPdSè° X~ and Xp° are factors which are proportional to the production probability of the p-n pair in the singlet and triplet state, respectively : - 2n mo I~,,Iz . po By fitting eq. (5) to experimental data, some authors have extracted values for the parameters ap°, Xp° and Xp°: The extractedwalues of ap°have been in good agreement with the experimental results. The aim of this analysis was to extract relative singlet to triplet contributions, and because of that the p-n scattering parameters were fixed. These parameters, as known from free scattering, are shown in table 1, together with other parameters discussed in the next section. The exact three-body calculations are done using the Ebenhôh code, which solves the three-partàcle Faddeev equationsexactly for separable S-wave, spin-dependent NN interactions 4). For a separable potential v(p', p) _ ~ig(p')g(p) the form factors g(p) used have the ~I,rô

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triplet p-n singlet p-n singlet p-p

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Fig. 5. Proton-neutron coincidence spectra from the p+d -. p+n+p reaction for Eo = 12.5 MeV and B = BP = B". Solid lines represent least squares fits to the experimental points using the Watson Migdal p-n enhancement factors (eq. 5) . The contrebutions from the p-n FSI in the singlet state (dashed line) aad p-n FSI triplet state (dash~otted line) are shown separately.

Yamaguchi form, i.e. N 8(p) = Pz+ßz

~ and N are determined by the normalization condition which .leads to N=

ßK(ß+K) lam,

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The parameters K and .ß are connected with the scattering length an$ the éffective

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range ro by (Kz

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(9)

1 (10) (K-~TOKz) = . apn All the parax~eters used in the calculation are shown in table 1 . 5. Results and disa~ssion

Fig. 5 shows experimental data together with WMM calculations . Relative singlet to triplet contributiôns were extracted by fitting eq. (5) to the experimental data . In this way the singlet and triplet contributions that were obtained are shown separately as well as their sum. Figs. 6aß show the data together with the three-body calculations using the Ebenhöh code. Fig. 7 shows experimental cross sections for Ep° = 0 as a function of the undetected proton c.m. angle together with the three-body calculations . As can be seen, for the backward angles, B~.m. > 115°, the theory overestimates, while for

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2 H(p, Pn)'H

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Fig. 6. Proton-neutron coincidences spectra from the p+d ~ p+n+p reaction for E = 12 .5 MeV and B = Bp = Bo. Solid lines represent the EbenhBh onde calculations . No normalization factor has bcen applied to the calculated value.

PRODUCTION ANGLE 9~R (deq .l

Fig. 7. ~H(p, np) éxperimental cross sections for E~ = 0 as a function of the undetected proton c .m . angle together with BbeahSh code calculations .

> 95° it underestimates the experimental values . Similar results have been obtained for backward angles in â recent study of deuteron break-up at 8.5 MeV [ref. 13)]. Iû the case of sp~tral shapes, three-body calculations in most Cases give satisfactory :agreement. Now a few words should be said about the relationship between the WMM model and the three-body calculations . Previous analysis s) of the p-d break=up data for Ed = 52.3 MeV has shown the applicability of the WMM in the region of dominant n-p FSI. If the WMM is applicable in this present case, the ratios .between the singlet and the triplet contributions, i.e. Xôp Fôp/Xn P Fnp for Epn = 0 as determined by the least square fife to the experimental data, should be equal to the ratios between the squared transition matrix elements for scattering into the sing_ let and triplet states, ie. to. IT'1 2/IT'`I z, obtained from the three-body calculations. In fig. 8 vertical bars represent X~P Far/XôP FôP (with estimated uncertainties), while the curve represents I~IZ/IT`IZ; all for Enp = 0. It can be seen that at this energy the agreement is only qualitative. One can fmd several reasons for this, which all come about the from low incident energy . For example, FSI effects in other nucleon pairs (n-pZ and pl-pz) are not negligible in the region of the n-p FSI peak, especially at forward detection angles. Also at forward detection eagles the undetected proton energy is not high enough that QFS contributions can be neglected. All of these reasons make the main assumption ofWMM invalid here . Fig. 9 summarizes many of the recent results of deuteron break-up studies at low energies. Zhis figure was taken from ref. t), with our result added. It shows peak cross sections for n-p FSI in the proton induced deuteron break-up reaction at 9~ .m . = 90° as a function of incident proton energy. Our result is for B~ .m . = 91 .3°, 6~.m .

2H(P~~Pn)'H

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Fig. 8. Ratios of the singlet to triplet contributions, as obtained from the experimental data using WMM (vertical bars) Xô PF~lXô P FôP and from three-body calculations (curve)~T~~T~~ . Vertical bars represent estimated uncertainties in the WMM ratios .

Fig. 9. Peak cross sections for n-p FSI ion'H(p, 2p)n reaction at ~.m . = 90° as a function of incident proton energy from different measurements [ref. ')] together with our result. The solid ~urve is a calculation with the charge dependent version of the EbenhBh code using exponential form factors.

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and this value was obtained by taking into account the difference in phase space factors for the H(p, np)p and ZH(p, pp)n reactions at Ep = 0. The theoretical curve is the result of a calculation with the charge dependent version of the Ebenhöh code using exponential form factors. It can be seen that oiir result .follows the general trend ofprevious experimental results and theory. This figure shows relatively large dif%rencies (up to 20 ~) in some experimental data at thé same energies . On the theoretical side even improvements in the exact three-body calculations [see e.g. ref. ta)] do not essentially improve the agreement between experiment and theory. This means that there is still a lot of work to be done on deuteron break-up at low energies, both experimentally and theoretically. References 1) B. 5undquist, Proc . Conf. on few body systems and nuclear forces;Graz, 1978 . ed . H. Zingl, M. Haftel and H. Zankel (Springer, Berlin, 1978) vol 2, .p. 267 2) H. Kumpf, H. Moller, J. Mosner and G. Schmidt, Particles and Nucleus (Joint Institute of Nuclear.Research, Dubna) 9 (1978) 412 3) K. M. Watson, Phys. Rev. 88 (1972) 1163 4) W. Ebenhoh, Nucl. Phys. A191 (1972) 97 5) W. Kluge; R. Schlaffer and W. EbenhSh, Nucl . Phys. A228 (1974) 29 6) E. Andrade, V. Valkovic, D. R~dié and G. C. Phillips, Nucl . Phys . A183 (1972) 145 7) E. Andrade, Ph.D. Thesis, Rice University (1972), unpublished 8) A. S. Wilson, M. C. Taylor, J. C. l.egg and G. C. Phillips, Nucl . Phys . A126 (1969) 193 9) D. Rendic; G. S. Mutchler, S. T. Emerson, J. Buchanan, D. E. Velkley, l. Sandier, V. A. Otte, N. M. Bretscher, B. E. Bonner and G. C. Phillips, Nucl. Instr. 99 (1927) 189 10) H. V. Jones and J . A. Buchanan, IEEE Trans. N~17 (1970) 398 11) T. K. Alexander and F. S. Goulding, Nucl. Instr. 13 (1961) 244 12) W. R. Jackson, A. S. Divatia, B. E. Bônner, Ç. Joseph, S. T. Emerson, Y. S. Chen, M. C. Taylor, W. D. Simpson, V. Valkovié, E: B. Paul and G. C. Phillips, Nucl . hutr . SS (1967) 349 13) H. Guratzsch, B. Kahn, H. Kumpf, J. Mosner, W. Neubert, W. Piltz,~G . Schmidt and S. Tesch, Nucl. Phys . A293 (1977) 109 14) J. H. Stuivenberg, Thesis, Vrije Universiteit, Amsterdam 1976