Nuclear Physics A559 (1993) 347-367 North-Holland

NUCLEAR PHYSICS A

The 4He( y, 2N) reaction measured with tagged photons

S.M. Doran I, I.J.D. MacGregor, J.R.M. Annand, I. Anthony, S.N. Dancer 2, S.J. Hall, J.D. Kellie, J.C. McGeorge, G.J. Miller, R.O. Owens, P.A. Wallace 3

Department of Physics and Astronomy, The Unicersity of Glasgow, UK

B. Schoch 4 and H. Schmieden

Institut fiir Kernphysik, UniL*ersitit Mainz, Germany

S. Klein 5

Physikaiisches lnstitut, Universitiit Tilbtigen, Germany

Received 24 September 1992 (Revised 5 February 1993)

Abstract The results of tagged-photon measurements of the ‘He(y, p&I. “He{?. pn)pn and

4He(y, ppfnn reactions, carried out with photons of energies SO-131 MeV, are presented. The (y. pnId three-body-breakup cross section dominates the four-body-breakup cross section. The three-body-breakup cross section and the corresponding deuteron recoil-momentum spectrum are reasonably accounted for by a mechanism of photon absorption on correlated proton-neu- tron pairs. In contrast the four-body-breakup mechanism appears to have two components: absorption on correlated proton-neutron pairs and a more complex additional component which has a distribution similar to phase space. The data rule out substantial photon absorption on proton-proton pairs.

Key words: NUCLEAR REACTIONS 4He(r, pn) (y, pp), E = 80-131 MeV, measured yield; recoil momentum. deduced o; Natural target, tagged photons. Monte Carlo calculations.

Correspondence to: Dr. I.J.D. MacGregor, Department of Physics and Astronomy, The University of Glasgow, University Avenue, Glasgow G12 8QQ, UK. ’ Present address: Building Research Establishment, East Kilbride, UK. 2 Present address: Rolls Royce, Derby, UK. 3 Present address: Glasgow Polytechnic, Glasgow, UK. 4 Present address: Physikalisches Institut, Universitlt Bonn, Germany. ’ Present address: Siemens, Munich, Germany.

~375-9474/93/$~.~ Q 1993 - Elsevier Science Publishers B.V. AI1 rights reserved

348 S.M. Doran et al. / ‘He(y, 2N)

1. Introduction

At photon energies below the pion-photoproduction threshold the photodisinte- gration of 4He can only populate a limited number of distinct final states. Cross-section measurements can provide information on the strengths of reactions populating each final state and a detailed analysis of the corresponding energy and momentum distributions can reveal information about the reaction mechanisms which are dominant in each case. The present work investigated the 4He(y, pn) and 4He(y, pp> reactions, leading to the three-body pnd and four-body ppnn final states.

There have been many previous studies of the photodisintegration of 4He but most of these have been restricted to the 4He(y, p) reaction. Those which have investigated the photoemission of correlated nucleon pairs are discussed below. The first detailed study of the photoemission of correlated nucleon pairs from 4He was carried out by Barton and Smith [ll who used 280 MeV bremsstrahlung and detected protons and neutrons in the energy range 50 to 150 MeV. They observed that nearly all high-energy protons were emitted in coincidence with neutrons, and established the strong back-to-back angular correlation between the emitted nucle- ons.

Gorbunov and Spiridonov [2] studied the three- and four-body-breakup of 4He using a cloud chamber with a bremsstrahlung beam of 170 MeV. They were only able to analyse 91 4He(y, pd)n events in order to determine the photon energy dependence of the reaction cross section for the three-body-breakup channel, although they used more events to study the angular distributions and correlations between the particles. Their total cross section for this channel is reproduced in fig. 1 along with the results of other measurements discussed below and the results of the present study. The cross section shows a broad peak of - 170 pb at 50 MeV falling to - 40 kb above 100 MeV. From the angular distributions and angular correlations it is clear that a substantial proportion of the events sampled were due to photon absorption on two correlated nucleons, and that this proportion in- creased with photon energy. In contrast the 4He(y, pt> and 4He(y, 3He)n two- body-breakup channels were reported to be characterised by single-nucleon knock- out. For the 4He(y, pp)nn reaction a reasonably constant cross section of N 60 pb was observed above - 35 MeV. The four-body-breakup cross section is shown in fig. 2. Below 75 MeV photon energy the total three- and four-body-breakup cross sections contribute less than 10% of the total photon-absorption cross section, but above this energy they contribute 30%, showing that these channels become more important with higher photon energy.

Arkatov et al. [3] carried out a similar experiment with a 120 MeV bremsstrahlung beam. In this work a total of 2320 events were analysed, allowing cross sections to be evaluated in narrower photon-energy bins and with greater statistical accuracy, than in the work of Gorbunov and Spiridonov. The results of

S.M. Doran et al. / “He(y, 2N) 349

o~‘~~-“~~-“” 0 20 40 60 ,BO 100 120 140

PHOTON ENERGY (MeV )

Fig. 1. The 4He(y, pn)d reaction cross section as a function of photon energy. The solid circles are the

results of the present work, obtained assuming absorption on a proton-neutron pair as described in the

text. The triangles are from Gorbunov et al.. [2], the squares are from Arkatov et al. [3] and the open

circles are from Balestra et al. [4].

120 -

P_

I

p -

.I iii Ii

T -t t P I 1 I 01' I I 1

0 100 200 300 400

PHOTON ENERGY ( MeV)

Fig. 2. The 4H(y, pn)pn reaction cross section as a function of photon energy. The solid circle is the result of the present work, summing the contributions from phase-space absorption and absorption on a

correlated proton-neutron pair as described in the text. The triangles are from Gorbunov et al. [2], the

squares are from Arkatov et al. [3], the open circles are from Balestra et al. [4] and the crosses are from

Emura et al. [5].

350 SM. Doran et al. / ‘He(y, 2 N)

Arkatov et al. for the three-body-breakup channel are also shown in fig. 1. The four body-breakup cross sections obtained were slightly higher than those of the Gorbunov and Spiridonov whereas the 4He(y, pp)nn cross sections were smaller. The authors attribute these differences to some arbitrariness in separating the three- and four-body-breakup events.

Balestra et al. [41 used a diffusion cloud-chamber in a 100 MeV synchrotron beam to study the photodisintegration of 4He. From an analysis of the centre-of- mass breakup angles and the relative energies of the emitted particles they concluded that for photon energies below 60 MeV the main mechanism of the three-body-breakup channel was by photon absorption on two correlated nucleons. The cross sections for the three-body-breakup channel are also shown in fig. 1. The four-body-breakup cross-section measurements, shown in fig. 2, were restricted to photon energies below - 60 MeV. The highest energy data point agrees with Gorbunov et al. and Arkatov et al., although at lower photon energies the cross section is higher.

More recently, studies of the four-body-breakup cross section in the A-reso- nance region have been carried out by Emura et al. [51 who measured the 4He(y, ppnhr reaction using the TAGX spectrometer at the tagged-photon beam of the 1.3 GeV electron synchrotron at the Institute for Nuclear Study, Tokyo. These measurements have reasonably good statistical accuracy and span the photon-energy range 135-455 MeV, just above the photon-energy range of the present measurements. The cross sections obtained rise from zero at the lowest photon-energy bin centered on 155 MeV to - 40 pb at - 400 MeV. As the cross sections for the two-body breakup fall with photon energy this leaves the four- body-breakup channel dominating the other so far measured non-pionic channels (pt, n3He, dd) in the A-resonance region.

The spectra of nucleon momenta obtained in this experiment are not well described by photon absorption on a proton-neutron pair, for photon energies on or below the A-resonance. A further contribution from photon absorption either on proton-proton pairs or on proton-proton-neutron three-nucleon clusters is favoured by the data. The different energy dependence of the four-body-breakup cross section compared to the other channels is also taken as evidence of a contribution from mechanisms other than quasideuteron absorption. This is dis- cussed below in comparison with the results of the present measurement.

The present experiment has substantial advantages compared to the earlier cloud-chamber studies. By using a tagged-photon technique the incident photon energies and fluxes are reliably determined. This contrasts with bremsstrahlung work in which the photon flux has been notoriously difficult to determine, relying either on measuring the total energy of the bremsstrahlung beam or on cross- calibration from other reference reactions. The determination of the incident photon energy in the earlier work was also difficult, being based on kinematic reconstructions from the measured momenta of the charged reaction-products.

S.M. Doran et al. / 4He(y, 2N) 351

This was possible in the 4He(y, pd)n reaction although the resolution obtained was poor. However in the four-body-breakup case only a coarse approximation to the photon energy can be made assuming that the neutrons have the same average kinetic energy as the protons. In the present work the separation of three- and four-body-breakup channels in much clearer than in the previous work and the statistical accuracy of the present experiment is also at least a factor of 2 better than the previous experiments. The one advantages of the previous cloud-chamber studies was the 4~ solid angle subtended by the detectors.

Two main mechanisms have been identified for photon absorption between the giant dipole resonance and the pion production threshold, namely quasifree knockout, in which the photon interacts with a single nucleon, and absorption on correlated proton-neutron pairs. Although quasifree knockout contributes to the exclusive (y, N) reaction channels, its strength decreases rapidly with increasing photon energy. The (y, pn) reaction increasingly dominates the photon-absorption cross section above 100 MeV in light nuclei and measurements in i2C (ref. [6]), 160 (ref. [7]) and 6Li (ref. [8]) d emonstrate that it proceeds by a mechanism in which the photon is absorbed on a correlated proton-neutron pair. It is one of the aims of the present work to study to what extent the three- and four-body-breakup channels in 4He can also be described by such a mechanism.

Theoretical work on (y, NN) reactions has only recently begun to advance beyond the early, and somewhat phenomenological, treatments of Levinger [9] and Gottfried [lo]. Gottfried showed that the (y, pn) reaction cross section can be factorised into two terms, one of which is the probability of finding the two initial nucleons with the correct combined initial momentum, and the other which depends on the short-range correlation between the two nucleons. This result follows from the approximation of zero separation between the nucleon pair which absorbs the photon. In this approach Gottfried related the (y, pn) cross section to that for the photodisintegration of the deuteron, supporting the basic assumptions of the quasi-deuteron model introduced by Levinger [9]. Using the same approxi- mation Boato and Giannini [ll] have extended the factorisation to take account of meson-exchange currents. However recent analyses have revealed the limitations of this approach. Ryckebusch et al. [12] show that the assumptions in Gottfried’s analysis apply fairly well at A-resonance energies but the factorisation is not accurate below 150 MeV where the major contribution to the cross section is due to mesonic photoabsorption rather than mechanisms involving intermediate A

excitation. In a separate analysis of the same type Giusti et al. [13] argue that the (y, pp) reaction has a more direct dependence on short-range correlations than the (y, pn) reaction, since the meson-exchange currents which dominate the (y, pn) process are suppressed to first order in the (y, ppl case.

The study of the (y, NN) reactions in 4He has a special interest compared to the somewhat heavier nuclei on which most recent work has been done, but the interpretation of the 4He data is also more involved. Due to its higher density it is

352 SM. Doran et al. / “He(y, 2N)

likely that short-range correlations will be stronger in 4He than in other nuclei and this may produce an observable influence on the (y, NN) reactions. However no such access to short-range correlations is expected in the present experiment. Higher photon energies are needed before the momentum exchange between the nucleon pair reaches values of importance in short-range interactions.

It is important for the eventual detailed understanding of the photon-absorption mechanism that a microscopic calculation of the photon reaction channels in 4He can be carried out. Unfortunately no such calculation of c-y, NN) reactions has yet been attempted for nuclei heavier than 3He, and the standard quasideuteron analysis is probably less soundly based for 4He than for heavier nuclei. In particular the assumption, that the residual momentum distributions of the two spectator nucleons are the same as their average distribution in the 4He ground state, is questionable. For a few-nucleon system it seems likely that the require- ment that the photon interacts with a closely-spaced pair will select an atypical part of the initial ground state wavefunction both for the struck pair and the spectator nucleons. In 4He the final-state interaction between the generally slow- moving spectator pair is also likely to be important. It may well produce an angular correlation between these nucleons and binding of residual proton-neutron pairs, which could change the relative strengths of the three- and four-body-breakup channels. By contrast final-state interactions between the fast struck nucleons and the spectators should be of negligible importance in 4He. For the ‘*C(y, pn) reaction at similar photon energies it has been shown [141 that the attenuation of the outgoing nucleons is less than 20% and this effect should be still less significant in a much smaller nucleus. In the absence of a more detailed treatment the present data are analysed using the standard quasideuteron approach, in which the pair momentum is obtained from the 4He ground state wavefunction assuming that the spectator pair are on the mass shell at the time of photon absorption and final-state interactions are neglected.

Sect. 2 of this paper reports the details of the experimental measurements and outlines the data analysis procedures. The results and discussion of the measure- ments are presented in sect. 3, and sect. 4 contains a summary and the conclusions drawn from the measurements.

2. Experiment and analysis

The data taken in this experiment were taken at the same time as data on the “jO(y, 2N) reaction described in ref. [71. Most of the experimental apparatus used and the details of the data reduction have been fully described there. The account given here concentrates on those points which differed between the two experi- ments.

353

RASTIC SCINTILLATOR TELESCOPE

Fig. 3. Schematic diagram of the experimental apparatus showing the photon-tagging spectrometer, the plastic-scintillator trigger-detector and the time-of-flight (t.o.f.1 array.

2.1. Experimental apparatus

The experiment was carried out using the Universi~ of Mainz electron mi- crotron MAMI-A. Fig. 3 shows the arrangement of the experimental equipment. The microtron provided a beam of 183 MeV electrons incident on a 25 +rn aluminium radiator which acted as a source of br~msstrahlung photons. The tagged-photon spectrometer 1151 comprised quadrupoie magnet QI and dipole magnets Dl and D2. Magnets D3 and D4 served to remove the main electron beam from the experimental area. The four paths shown through D3 and D4 correspond to different ranges of tagged photons which can be selected by the magnetic fields in Ql, Dl and D2. In this experiment the spectrometer was used to tag photons of energies 80 MeV to 131 MeV with an energy resolution of - 0.5 MeV. The total counting-rate in the spectrometer focal-plane-detector (FPD) was 2 x 10’ per second, The average tagging-efficiency was measured to be 0.373 & 0.011.

The photon beam spot was - 23 mm diameter at the liquid-helium target position. The target-cell consisted of a 6 mm thick elliptical aluminium frame with 125 pm thick Kapton windows and an internal aperture with major and minor axes of 109 mm and 50 mm, respectively. The cell was mounted at 34” to the photon beam in an evacuated target chamber and was surrounded by several layers of 12.5 brn aluminised-mylar insulation foil. It was connected to a commercial 51 dewar for ‘He. The pressure differential across the cell windows caused them to bow

outwards to a maximum thickness of m 15 mm. The effective thickness of the target-cell was determined by a separate experiment which measured the pair-pro- duction yield from the target and compared this with the measured yields from carbon targets of known thicknesses [ 161. The effective number of target nuclei was found to be 4.27 it 0.08 X lO22 cmP2.

A plastic-scintillator telescope-array [17] consisting of two thin AE-layers and one thick E-layer was used to detect protons. The telescope subtended a solid angle of 0.90 sr and covered laboratory angles from 50” to 130”. It was capable of stopping protons of energies up to 120 MeV, had a proton energy threshold of 28 MeV, an energy resolution of N 4% f.w.h.m. at 60 MeV and a f.w.h.m. angular resolution of N 3” in the horizontal plane and N 5” in the vertical plane. The front AE-scintillator was shaped as the arc of a circle of radius 95 mm about the centre of the target and was used to provide a reference time for charged particles leaving the target.

An array of plastic scintillators on the opposite side of the target was used as a time-of-flight (t.0.f.) spectrometer for detecting nucleons correlated in time with the charged-particle trigger. In order to separate neutrons from charged particles a second curved A&detector was placed 95 mm from the target on the t.o.f.-side. The t.o.f. array consisted of 24 plastic-scintillator blocks 0.2 m wide X 1.8 m high X 0.1 m thick [18] placed 3 m from the target and covering laboratory angles from 41” to 139”. The t.o.f. detectors had an intrinsic timing resolution of N 0.5 ns f.w.h.m. and subtended a total solid angle of 0.92 sr. In the analysis, the pulse-height thresholds for the t.o.f. detectors were set at 9.75 MeV neutron energy. The neutron detection efficiencies were calculated using an improved version of the code STANTON [19] and were included in the Monte Carlo code used to calculate overall normalisation factors to be applied to measured data as discussed below. The detection efficiency, averaged over the energies of the detected neutrons, was 10.3%.

The readout of all of the detectors was initiated by a coincidence between the proton detector and the tagged-photon spectrometer.

2.2. Data analysis

The detectors were calibrated and the data analysed broadly as described in ref. [7]. Minor variations and points of importance are described below.

The first data-reduction step was to select protons from a two-dimensional plot of the pulse-height signals in the E-layer of the scintillator telescope against the time difference between the front A&element and the E-layer. The selection of protons from electrons and from some deuterons which survived the first cut was improved by a second cut made on a two-dimensional plot of the pulse height in the rear A&layer against the pulse height in the E-layer.

S.M. Doran et al. / ‘He(y, 2N) 355

Events near the ends of the E-blocks were discarded since they exhibited nonlinearities and poor pulse-height and timing resolution. Together with a cut on events at the ends of the rear A&strips this cut defined the solid angle of the proton detector.

Signals from more than one t.o.f. detector were observed in a significant number of events principally due to random background in these detectors. Some of these events could not be analysed because the t.o.f. detector signals were multiplexed together in groups of four and only the total pulse height from each group was recorded. To keep the analysis simple all events in which more than one t.o.f. detector fired were rejected. A correction was applied to take account of the events rejected. For both prompt and random data sets this correction averaged - 6%.

On the t.o.f.-side, particles which did not fire the t.o.f.-side AE-detector were classed as neutrons. Particles which did fire this AE-detector were identified as being protons or deuterons using a two-dimensional plot of pulse height in the t.o.f. array against particle speed. A two-dimensional cut on this spectrum was used to select protons.

In the analysis only events which make a triple coincidence between the tagger FPD, the trigger detector and the t.o.f. array are of interest. After reduction the data contain some events with a random uncorrelated signal in one or more of these three detectors. The contributions from these random components were measured simultaneously with the time-correlated events and were subtracted as described in ref. [71.

The background from particles which did not originate in the target was obtained from a separate run made with an empty target-cell. This background amounted to about 10% of the target-in-yield and its contribution was subtracted from the final spectra.

The tagger FPD was split into 12 subsections and the data from each subsection were analysed separately. This reduced the number of events which had to be discarded because more than one FPD channel had fired making both the timing of the event and its photon energy ambiguous. Even so a small number of events still had to be discarded. The correction to the cross section for these losses [20] averaged 5% over the 12 FPD subsections.

A further correction was made to account for deadtime in the electronics and computer system. This correction was 1.2%.

2.3. Monte Carlo simulations

A basic aim of this experiment is the comparison of the observed features of the 4He photodisintegration channels with expectations based on two-nucleon absorp- tion mechanisms. In order to make this comparison for integrated quantities such as the initial nucleon pair-momentum distribution or the total photon-absorption

3.56 SM. Doran et al. / ‘He(y, 2N)

cross section, it is necessary to account for nucleon pairs which are not detected due to the limited angular and energy acceptances of the proton-detector telescope and the t.o.f. array. This is done by performing Monte Carlo simulations of the experiment. These simulations are described below and their results are discussed along with the experimental spectra in the next section.

The simulation of two-nucleon absorption was based on the simple quasideuteron model in which the cross section is proportional to the product of the initial pair momentum probability and the deuteron two-body-photodisintegra- tion cross section. The initial momentum distribution of the correlated pair was derived from the momentum distributions of the individual nucleons with respect to the centre-of-mass. Two different nucleon momentum distributions were used, the harmonic-oscillator distribution and one obtained from variational calculations [21]. The harmonic-oscillator parameter p was taken to be 0.403 fm-‘, which gave the correct r.m.s. (charge) radius of 1.67 fm for 4He (ref. [22]). The variational calculations by Schiavilla et al. [21] use realistic hamiltonians which include three-nucleon interactions and give reasonable binding energies and densities for light nuclei and nuclear matter. The results obtained with the Urbana potential were used here. These calculations give a proton momentum distribution which falls more rapidly with momentum than the harmonic-oscillator distribution up to 200 MeV/c, although the differences are small.

The initial three-momenta of the spectator nucleons are each chosen randomly from the momentum-density distribution and added to obtain the total recoil three-momentum. The initial momentum of the correlated nucleon pair is then -Precoi,. The missing energy is fixed at 26.1 MeV for the three-body-breakup channel, but for the four-body-breakup channel it is obtained from the sum of the kinetic energies of the two recoil nucleons. The photon energy is chosen from a bremsstrahlung distribution weighted by the energy-dependent total photon-ab- sorption cross section for deuterium. The photon energy and the missing energy then define the total energy of the two correlated nucleons in the centre-of-mass frame of the photon and the correlated pair.

The nucleon emission angles in the centre-of-mass frame of the correlated pair and the incoming photon were chosen on the basis of the differential cross section for the d(y, p) reaction. In the absence of a better guide the same prescription was used for testing absorption on both proton-proton and proton-neutron pairs.

In deciding whether an event would be detected all possible particle/detector combinations were investigated. Although there is only one possibility in the 4He(y, pn)d rea ction there are four in the 4He(y, pnjpn reaction, since either proton could be detected in the proton detector and either neutron in the t.o.f. array. Similarly in the 4He(y, pp)nn reaction there are two possibilities.

The simulations showed that, as a result of the large Fermi momentum in 4He, the efficiency of detecting nucleon pairs from 4He fell much more rapidly with increasing missing energy and initial pair-momentum than previously found for 160

SM. Doran et al. / ‘He(y, 2N) 357

(ref. [7]). For this reason the simulation results are not used to correct the measured data as was done for 160 but are directly compared with the data.

In order to check whether the agreement obtained between the measured data and the predictions of a two-nucleon absorption model was significant, and not simply due to the insensitivity of the experiment to large values of the initial pair momentum or missing energy, a second set of simulations was carried out using a phase-space distribution for the particles in the final state. The calculations used the CERN multiparticle phase-space code FOWL [23], modified to accept photons as the incident projectiles and to incorporate the bremsstrahlung-weighted d(r, p) cross section as the energy distribution of the photon beam.

One feature of the scintillation-detector response, not included in the Monte Carlo calculation, was the inelastic nuclear interaction of some protons which enter the telescope. Such interactions generally result in a reduced pulse height which shifts those events to higher missing energies. The percentage of events affected [24] is less than 3% at 41 MeV, the average energy of protons from the present reaction. This effect is discussed further in the next section.

3. Results

3.1. 4He(y, pn) reaction

The measured (y, pn> events can be produced by both three-body and four-body breakup of 4He. In the following sections the missing-energy spectrum and recoil-momentum distributions are examined to separate these two channels, extract their cross sections and try to determine the responsible photon-absorption mechanisms.

3.1.1. Missing-energy spectrum Fig. 4a shows the spectrum of missing energies, E, = E, - T, - T, + T&,,

reconstructed event by event from the recorded energies of the tagged photon and the detected nucleons. The recoil kinetic-energy is obtained from Trecoi, = Erecoi, -

Recoil, where Erecoil is the total energy of the undetected particles and Mrecoi, is their invariant mass. The experimental yield represents the relative strength per MeV missing energy, without any corrections for detector acceptances. The units are arbitrary. There are two contributions to this spectrum from the 4He(y, pn)d and the 4He(y, pn)pn reactions. The former reaction has a unique missing energy of 26.1 MeV, smeared only by the 7 MeV f.w.h.m. resolution of the detector arrays. However the extra degree of freedom in the four-body-photodisintegration channel allows a range of missing energies upwards from the reaction threshold at 28.3 MeV.

358 S.hf Doran et al. / 4Hefy, .ZN,l

20 20

MISSING ENERGY f MeV f

(b) 0.020

cl

ii F

; 0.010 a

<

r” f 0.0

MISSING ENER

-0.010

Fig. 4. 4He(y, pn) missing-energy spectrum. In (a) the thick histogram shows the 4HeCy, pn) spectrum. The thin histogram shows the d(y, pn) missing-energy spectrum, shifted and normalised to match the 4He(y, pnM peak and shown for comparison. The histogram in (b) shows the cont~butions from the 4He(y, pn)pn channel calculated by subtracting the two histograms in (a). The solid line is the prediction of photon absorption on a correlated proton-neutron pair, and the dotted line is the prediction of photon absorption on a correlated photon-proton pair, both calculated with harmonic- oscillator wavefunctions. The dashed line is the phase-space prediction. The calculations take account of the detector acceptances. The thresholds for the 4He(y, pnM and 4He(y, pn)pn reactions are shown.

It is clear that the (y, pn) reaction is dominated by the three-body-breakup channel or by four-body-breakup events in which, as a result of final-state interac- tion, the undetected proton-neutron pair emerge at almost the same angle and with similar energies. Such events would generally be expected to have low missing energies, close to the four-body-breakup threshold at 28.3 MeV. The resolution of the present experiment is unable to distinguish such events from three-body-break- up events.

S.M. Doran et al. / 4He(y, 2N) 359

A separation has been attempted between reactions in which the two residual nucleons are bound as a deuteron, or are unbound but have a strong attractive interaction, and reactions in which the two residual nucleons move independently. The separation uses the d(r, pn) missing-energy spectrum obtained with a CD, target, shifted, scaled and superimposed on the helium three-body-breakup peak as shown in fig. 4a. The d(r, pn) reaction has a unique Q-value, and since the charged-particle energy-losses in the CD, and helium targets are very similar, the deuterium peak provides a measure of the experimental missing-energy resolution and peak shape. It is observed that the two peaks differ only in the tail of the distribution at higher missing energies where the four-body breakup of 4He contributes.

Fig. 4b shows the strength of the 4He(y, pn)pn four-body breakup extracted from the difference between these two missing-energy spectra. In the absence of final-state interactions the shape of the four-body missing-energy spectrum can be calculated using the Monte Carlo simulation of the reaction. Fig. 4b also shows the result of this calculation for photon absorption on a correlated proton-neutron pair, for photon neutron pair, for photon absorption on a correlated proton-pro- ton pair in which one struck proton and one spectator neutron are detected and for a phase-space distribution, taking account in all cases of the acceptances of both detector arrays. The calculations for absorption on a proton-neutron pair and on a proton-proton pair both used harmonic-oscillator momentum distribu- tions. The results have been normalised to reproduce the same integrated yield as the experimental spectrum. The spectrum obtained for photon absorption on a correlated proton-neutron pair using variational wavefunctions is not significantly different from the harmonic-oscillator results shown. There is very little difference between absorption on a proton-proton pair and the phase-space distribution, although the results of absorption on a proton-neutron pair do give a distribution which peaks at lower missing energies. However the data are not sufficiently precise to indicate a preference for any particular absorption mechanism.

3.1.2. Recoil-momentum spectra

Further evidence about the nature of the reaction mechanisms for the three- and four-body-breakup channels may be obtained by examination of their recoil- momentum spectra. The experimental data were cut at E, = 35.0 MeV. Data are predominantly due to three-body-breakup below this cut and to four-body-breakup above it.

Fig. 5 shows the recoil-momentum spectrum for the three-body (y, pn)d breakup data, together with the predictions of photon absorption on a correlated proton- neutron pair and the phase-space model. Proton-neutron absorption calculations with both harmonic-oscillator and variational momentum distributions are shown. There is no significant difference between them and both give a reasonably good account of the data, although the fit is not perfect. On the other hand the

360 SM. Doran et al. / 4He(y, 2N)

0 100 200 300 500

RECOIL MOMENTUM ( MeV/c)

Fig. 5. Recoil-momentum spectrum for the 4He(y, pn)d reaction channel. The histogram shows the experimental data for missing energies below 35 MeV. The solid line is the prediction of photon absorption on a correlated proton-neutron pair, calculated with harmonic-oscillator wavefunctions, and the dotted line is the prediction obtained with variational wavefunctions. The dashed line is the

phase-space prediction.

phase-space prediction is considerably different from the data. The data clearly indicate that the principal mechanism for the three-body-breakup channel is one in which the photon interacts with a correlated proton-neutron pair.

The recoil-momentum spectrum for the four-body 4He(y, pnjpn breakup data is shown in fig. 6. The data are compared with the distributions obtained from models of photon absorption on a proton-neutron pair, and on a proton-proton pair, both using harmonic-oscillator wavefunctions, and also with a phase-space distribution. In this case both absorption on a proton-neutron pair and the phase-space distribution give acceptable fits, with the model of abso~tion on a proton-neutron pair giving a slightly better description. However the model of absorption on a proton-proton pair does not agree with the data. The fact that the proton-proton absorption gives a distribution peaking at larger momentum values than the phase-space distribution is understandable because in the former model the undetected proton receives a much larger share of the incident photon momentum. While the results would appear to discount significant absorption on proton-proton pairs they do not provide a clear distinction between absorption on proton-neutron pairs and a phase-space distribution.

31.3. Cross sections The extraction of total cross sections for the three- and four-body-bre~up

channels requires an evaluation of the overall detection efficiency from the Monte

S.M. Doran et al. / 4He(y, 2N) 361

f= 0.020 W

5

c cl

ii 0 010 d

01

,I

00

-0.005 1 RECOIL MOMENTUM ( MeV/c )

Fig. 6. Recoil-momentum spectrum for the 4He(y, pn)pn reaction channel. The histogram shows the

experimental data for missing energies above 3.5 MeV. The solid line is the prediction of photon

absorption on a correlated proton-neutron pair, and the dotted line is the prediction of photon

absorption on a correlated proton-proton pair, both calculated with harmonic-oscillator wavefunctions.

The dashed line is the phase-space prediction.

Carlo simulations as described in section 2.3. The efficiency is strongly dependent on the reaction mechanism assumed.

The data for the three-body-breakup channel were extensive enough to evaluate the reaction cross section in three photon energy bins. The results, obtained for both absorption on a proton-neutron pair and for a phase-space distribution, together with their statistical errors, are given in table 1. The sources of systematic error are given in table 2. The main contribution arises from the uncertainties in the detector thresholds which affect the correction factors used to evaluate the reaction cross sections. This systematic uncertainty is large for the lowest photon energies, but improves markedly as the photon energy increases. No correction has been included for the loss of events which are shifted to higher missing energies due to inelastic interactions of protons in the scintillator as the tail produced is accounted for by fitting the d(r, pn) peak shape which also has a similar high missing energy tail. All other sources of systematic uncertainty are negligible in comparison with those listed.

Table 1 4He(r, pn)d reaction cross sections and their statistical errors

Photon-energy

range (MeV) Photon absorption on a

proton-neutron pair fu,b)

Phase-space

distribution (eb)

80- 97 58.6 f 4.2 228 + 16

97-115 84.6 + 3.4 368 + 15 115-131 91.9 + 3.0 442 f 14

362 S.M. Doran et al. / 4He(y, 2N)

Table 2

Systematic errors

Quantity

detector thresholds

detector efficiencies

tagging efficiency

target thickness

tagger multiplicity correction

t.0.f. multiplexing correction deadtime correction

Total added in quadrature

Systematic error (%I

35.4 (E., = 80-97 MeV)

18.8 (E; = 97-115 MeV)

10.5 (E, = 115-131 MeV) 10.0

2.9

1.9

0.9

0.9

0.2

22.4 (E, = 80-131 MeV)

The photon-energy dependence of the three-body-breakup channel, assuming absorption on a proton-neutron pair, is shown in fig. 1, along with early data from previous cloud-chamber experiments [2-41. The error bars represent only the statistical errors. The cross sections obtained agree in magnitude with the earlier work, where they overlap, but exhibit a trend with photon energy, which is different from the apparent, although poorly defined, trend of the previous data. Even allowing for the systematic uncertainties in the present data, and the difficulties in separating three-body-breakup events from four-body-breakup events in the previous data, the difference remains significant.

There are some grounds for expecting a difference in shape between the previous data and the present work. The 4H(y, pn)d cross sections previously measured [2-41 are much smaller than the total photodisintegration cross section below 80 MeV. It can be concluded from the energy correlation between the proton and neutron in one of these measurements [2] that, particularly below 75 MeV, rather few events have the back-to-back angular correlation typical of a pure two-nucleon process. The two-nucleon component is seen to increase in impor- tance with photon energy but, even above 100 MeV, other mechanisms are still evident. The present measurement is rather insensitive to events in which the proton-neutron pair does not have a strong back-to-back angular dependence and can therefore be taken as defining the trend of the two-nucleon photon-absorption mechanism.

If a phase space model is used to evaluate the 4He(y, pn)d cross section from the present data then the values obtained are greatly in excess of any previous measurement. This supports the conclusion that the large majority of the observed three-body-breakup events arise from a two-nucleon photon-absorption mecha- nism.

For the four-body-breakup channel the average cross section assuming absorp- tion on a correlated proton-neutron pair is 17 + 5 kb over the photon-energy range 80-131 MeV. The result assuming absorption on a proton-proton pair is

S.M. Doran et al. / ‘Hefy% 2N) 363

r 2.3.3 MeV

Fig. 7. Missing-ener~ spectrum for the 4He(y, pp)nn channel. The histogram shows the experimental data. The solid line is the prediction of photon absorption on a correlated proton-neutron pair, calculated with harmonic-oscillator wavefunctions and the dotted line is photon absorption on a correlated proton-proton pair. The dashed line is the phase-space prediction. The threshold for the

4He(y, pp)nn reaction is shown.

30 f 9 kb and that assuming a phase-space distribution is 42 f 12 pb. The larger statistical errors are due to the subtraction process used to extract the four-body- breakup strength. The cross section obtained is larger than a first inspection of the missing-energy spectrum might suggest because its strength is spread in missing energy and the Monte Car10 correction factors increase with missing energy. The effect of three-body events shifted to higher missing energies due to inelastic interactions of protons in the scintillator telescope is largely removed when using the deuterium missing-energy peak to extract the four-body-breakup strength and any residual effect arising from differences between the two reaction thresholds is negligible in comparison with the remaining systematic errors.

3.2. 4He(y, pp) reaction

3.2.1. Mising-energy spectrum The missing-energy spectrum for the 4He(y, pp) reaction is shown in fig. 7

together with the predictions of three separate models. One model assumes absorption on a correlated proton-neutron pair, in which the ejected proton and the spectator recoil-proton are both detected, and accounts well for the shape of the missing-energy spectrum. A second calculation using a phase-space distribution also gives a good description of the missing-energy spectrum, almost indistinguish- able from the first result. This is perhaps not surprising as there is no correlation between the two protons in either of these cases. The third calculation assumes

364 S.M. Doran et al. / ‘He(y, 2N)

0 010

o 0 030

d F

g 0.020

iz d - I” 0 010

-f

00

0 -0.005

RECOIL MOMENTUM ( MeV/c )

Fig. 8. Recoil-momentum spectrum for the 4He(y, pphm reaction channel. The histogram shows the

experimental data. The solid line is the prediction of photon absorption on a correlated proton-neu-

tron pair, calculated with harmonic-oscillator wavefunctions and the dotted line is photon absorption on

a correlated proton-proton pair. The dashed line is the phase-space prediction.

that the photon is absorbed on two correlated protons and gives a very poor description of the spectrum. This appears to rule out significant absorption on proton-proton pairs.

3.2.2. Recoil-momentum spectrum Fig. 8 shows the recoil-momentum spectrum for the 4He(y, pp> reaction. AI1

three models give a reasonable description of the data. This is due to the very strong suppression of the data by the detector threshold effects. These larger for (y, pp) than for (y, pn) because the protons suffer energy losses in the air and have a higher effective threshold in the t.o.f. detectors. This spectrum does not help to distinguish the reaction mechanism in the four-body-breakup channel.

3.2.3. Cross sections The 4He(y, pp) reaction cross section was evaluated in a similar way to the

(y, pn) cross section. If absorption on a correlated proton-neutron pair is as- sumed, an average cross section of 36 _t 3 l.r,b over the photon-energy range 80-131 MeV is obtained, whereas the phase-space distribution gives a value of 29 f 2 ub. The higher value for proton-neutron absorption is understandable as the spectator proton always has a very low energy and consequently a low detection probability.

It will be noted that the four-body-breakup cross section obtained from the

4He(y, PP> data is inconsistent with the cross section obtained from the 4He(y, pn) measurement. One possible explanation is that the four-body-breakup channel proceeds by two mechanisms, partly by absorption on a proton-neutron pair and

SM. Doran et al. / 'Hdy, 2N) 365

partly by a more complicated mechanism for which a phase-space description of the final state is more appropriate. A combination of a cross section of 7.5 _t 7.5 pb for proton-neutron absorption and 22.5 f 7.5 ub for a phase-space mechanism would give the correct measured yields for both the (y, pn) and the (y, pp) reactions. The total cross section obtained in this way is 30 + 3 pb. In this interpretation the phase-space contribution dominates that of the pair absorption mechanism. As discussed previously the TAGX collaboration [5] also found evidence that the four-body-breakup cross section at higher photon energies was not entirely due to absorption on correiated proton-neutron pairs. They suggested either absorption on proton-proton pairs or on three-nucleon clusters. The present results provide some evidence for the importance of other mechanisms but would tend to discount absorption on proton-proton pairs.

The four-body-breakup cross-section value of 30 pb obtained by adding the phase-space and pair absorption contributions is compared with previous measure- ments in fig. 2. The measurements of Gorbunov [2] and Arkatov et al. [3] have large errors but still are not consistent. Our result lies within the range defined by these previous measurements, and is also consistent with the upper limit of 26 pb obtained by the TAGX collaboration [5] at 155 MeV.

4. Summa~ and conclusions

Measurements of the 4He(y, pn)d, 4He(y, pn)pn and 4He(y, pp)nn reactions have been made using tagged photons in the energy range SO-131 MeV. The three-body-breakup channel has a recoil-momentum spectrum which is reasonably well described by photon absorption on a proton-neutron pair. A phase-space distribution fails to give the correct shape. The cross section derived, assuming a pair absorption mechanism, has a magnitude in reasonable agreement with previ- ous cIoud-chamber measurements. If a phase-space distribution is assumed the derived cross section is a factor of N 4 larger and is totally inconsistent with the previous measurements. The data obtained show a rising trend in the cross section from 80 to 131 MeV.

The 4He(y, pn)pn and (y, ppjnn measurements both investigate different as- pects of the four-body-breakup channel but the data do not provide a clear indication of the reaction mechanism. The differences seen in the predicted missing-ener~ distributions or in the recoil-momentum distributions between absorption on correlated proton-neutron pairs and a phase-space distribution are small, so that the data do not even distinguish between these two extremes. They do however exclude significant absorption of photons on a proton-proton pair. Cross sections derived for the four-body-breakup channel depend on the reaction mechanism assumed. Consistency between the (y, pn> and (y, pp) results can only be achieved if both pair-absorption and phase-space mechanisms contribute to the

366 S.M. Doran et al. / 4He(y, 2N)

reaction process. In this case the total cross section obtained is reasonably consistent with previous cloud-chamber measurements.

There is a clear need to study these reactions in greater detail and particularly at higher photon energies where the effects of detector acceptances will be much smaller. The new large-solid-angle detectors with lower energy thresholds planned for use at the new 855 MeV Mainz electron microtron MAMI-B [25,26] will have a more uniform efficiency for nucleon pairs. The resulting improvement in accuracy of the data at larger recoil-momenta and higher missing energies will allow a more precise test of the two-nucleon absorption mechanism and the increased photon- energy range should provide an indication of the contributions of different meson- exchange and A-excitation processes to nuclear photoabsorption.

Support for this work was provided by the United Kingdom Science and Engineering Research Council and the Deutsche Forschungsgemeinschaft. The United Kingdom members of the collaboration wish to thank the Institut fur Kernphysik, Mainz University for the use of its facilities and for assistance received during the course of this experiment. Thanks are also due to the Max Planck Institut fur Chemie, Kernphysikalische Abteilung, Mainz University for making available the liquid-helium dewar used in the present experiment. Two of us (S.M.D. and P.A.W.) are grateful to the Science and Engineering Research Council for providing financial support in the form of research studentships during the period of this work.

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