- Email: [email protected]
Differential cross section for the reaction 2H(γ, p)n from 133 to 158 MeV
Nuclear Physics A532 (1991) 617-633 North-Holland
DIFFERENTIAL CROSS SECTION FOR THE REACTION 2H(y, p)n FROM 133 TO 158 MeV P.A. WALLACEI, J.R.M. ANNAND, I. ANTHONY, G.I. CRAWFORD, S.N . DANCER, S.M. DORAN, S.J. HALL, J.D. KELLIE, J .C. MCGEORGE, I.J.D. MACGREGOR, G.J. MILLER and R.O. OWENS Department of Physics and Astronomy, Unnersity ofGlasgow, Glasgow G12 8QQ, UK J. VOGT2 and B. SCHOCH 3 Institut f'ir Kernphysik, Johannes Gutenberg-Universität, D-6500 Mainz, Germany D. BRANFORD Department ofPhysics, Unirersity of Edinburgh, Edinburgh EH9 3JZ, UK Received 29 January 1991 Abstract: The cross section for the reaction 2 H(7, p)n has been measured at laboratory photon energies E; = 133-158 MeV and c.m . angles between 30° and 150° . The reaction was induced by a tagged bremsstrahlung photon beam incident on a liquid deuterium target. The uncertainty in the absolute cross sections is < 5%. There is now reasonable agreement between recent measurements in this energy region and the overall data set now defines the cross section sufficiently well to provide a test of current models of the reaction . E
NUCLEAR REACTION 2 H(7, p), E = 133-158 MeV ; measured absolute 6 (E; . Op ) for Op = 30°-150° .
1. Introduction For more than fifty years the photodisintegration of the deuteron has been used as a test case for the application o', new ideas concerning the nature of the nuclear force. The deuteron as the only two nucleon bound state yields information complementary to that obtained from NN scattering experiments, which have been the basis of most systematic studies of the NN interaction. The concept of a purely NN interaction is of course an approximation with which one attempts to describe the behaviour of a system whose components certainly include mesons, nucleons and nucleonic resonances and in which
I Present address: C.E.N. Saclay, DPhN/SEPN, 91191 Gif sur Yvette Cedex, France . 2 Present address: Saskatchewan Accelerator Laboratory, University of Saskatchewan, Saskatoon . Canada. 3 Present address: Physikalisches Institut der Universität Bonn, D-5300 Bonn 1, Germany. 0375-9474/1991/$3 .50 © 1991 - Elsevier Science Publishers B.V . (North-Holland)
618
P.A . R'allace et al. / 2H(7, p)n
the internal structure of the nucleons may need to be considered explicitly . Given the potential complexity of the dynamics of interacting nucleons, the photodisintegration of the deuteron is a particularly suitable case to treat because of its relative simplicity. The initial wave function is calculable, at least within a given model, and the reaction is influenced more by the nature of the initial photoabsorption mechanism than by the final-state interactions of the outgoing nucleons, which might be the case in a more complex nucleus . However, even for the case of deuteron photodisintegration, it remains unclear how best to proceed to a quantitative understanding of the reaction. There exist a number of theoretical treatments in which the physical content is apparently similar but the predicted cross sections differ by 10-20°®0. Since different formalisms have been employed it is hard to compare the components of the various calculations in a likefor-like fashion. In addition it has been difficult to say to what extent the discrepancies arise from the inclusion or omission of genuine physical effects and to what extent they are due to more `technical' differences in the calculations. In view of the above remarks it is all the more urgent that reliable experimental bench marks should be fixed against which to assess the different model predictions. Unfortunately it has not proved easy to obtain sufficiently accurate data on deuteron photodisintegration for this purpose. The large discrepancies between the existing data sets make it clear that previous workers using bremsstrahlung photon beams encountered severe difficulties in their efforts to suppress background and to obtain a reliable flux normalisation . The ideal solution to both of these problems is that adopted in the present measurement, the use of a tagged photon beam . Measurement of the photon energy as well as that of the emitted proton overdetermines the reaction kinematics and thus permits a very clean rejection of background processes. Furthermore, the photon flux is determined in a very straightforward fashion using a tagging system . It is just that number of photons for which the coincident tagging electron is detected. 2. The experimental system 2.1 . EXPERIMENTAL APPARATUS
The experiment was performed using the Glasgow bremsstrahlung tagging facility') in conjunction with the CW electron beam of the microtron MAMI-A in the Institut filr Kernphysik at Mainz University. An electron beam of energy 183 MeV from the microtron was focussed on a 25 ,um thick aluminium foil radiator. The momenta of the residual electrons following the emission of bremsstrahlung were measured using a magnetic spectrometer whose focal plane was divided into 91 photon energy tagging channels . During the experiment tagged photon beams of intensities between 4 x 106 and 8 x 10 6 per second were produced, spanning the energy range 133-158 MeV with a resolution of 0 .25 MeV. The signals from the 91 electron detectors were grouped and fed to the stop inputs of 6 TDCs. The TDCs were started by a trigger signal from
P.A. Wallace et al. / ZH(v. p)n
619
the plastic scintillator telescope used to detect protons from the deuterium target. To record the photon beam flux, the electron detector signals were combined in groups and fed to 12 scalers. However, since the diameter of the photon beam was restricted by a collimator, it was necessary to evaluate the fraction of tagging electrons whose corresponding photon passed through the collimator cone. This fraction, referred to as the tagging efficiency, was measured at reduced beam intensity by placing a detector in the collimated photon beam and measuring the ratio of tagged photons to tagging electrons. The detector used for this purpose was an SCG 1-C glass scintillator of thickness 12 radiation lengths, which was effectively 100% efficient for 100-200 MeV photons. A correction for the presence of background in the focal-plane detectors was made by repeating the measurement with the bremsstrahlung radiator removed. The tagging efficiency was measured at intervals throughout the experiment . In addition, its relative stability was monitored by observing the ratio between the current in a DC ionisation chamber, placed in the photon beam downstream of the target, and the tagging electron counting rate. During the experiment the tagging efficiency remained stable to ± 1% of its mean value. The deuterium target consisted of a 50 ml cell ofliquid filled from a large low-pressure reservoir of gaseous deuterium by means of a commercial helium cycle refrigerator. The cell was placed in a cylindrical evacuated chamber furnished with a single Kapton window of thickness 100 lim which was large enough to allow the through passage of the photon beam and the outward passage of the emitted protons. The target cell was constructed by glueing 70,um thick Kapton windows on to a 4 mm thick aluminium frame having an oval aperture with major and minor axes 106 mm x 50 mm, respectively . In order to optimise the ratio of thickness of material presented to the incoming beam relative to that encountered by the outgoing protons, the frame was inclined at an angle of 30° to the photon beam axis. When operated at a pressure of 1 .3 atm . the maximum target thickness was 33 mm along the beam axis. The profiles of the cell windows were mapped in detail over a range of cell pressures in order to permit accurate calculation of the average target thickness. The deuterium liquid in the cell was observed to boil gently throughout the experiment because of continuous absorption of radiant heat from its surroundings. The presence of gas bubbles in the target reduced its effective thickness. The density of the liquid/bubble mixture was measured by monitoring the change in the gas pressure in the closed deuterium system, and thus the change in the mass of deuterium in the liquid state, as a function of the volume of liquid/bubble mixture observed in the cell . The correction to the normal deuterium density was found to be (- 5 ± 2) °lo. During the experiment data were taken with the cell both full and empty in order to measure the background from the cell windows. Protons and other particles from the deuterium target were detected in a large solid angle, position sensitive plastic scintillator telescope 2 ) shown in fig. 1 . The telescope consisted of 3 layers of NE 110 plastic scintillators. These were two thin transmission layers (A E1,2 detectors) and a stopping layer (E detector), of thicknesses 1 mm, 3 mm, and 110 mm, respectively. The total frontal area of the E elements
P.A . lVallace et al. / 2H(y, p)n
620
PROTON DETECTOR ELEMENTS
--- AEI SCATTERING CHAMBER WINDOW PHOTON BEAM
---" TARGET CELL
SCATTERING
CHAMBER WALL
2O a a Fig . 1 . Plan view of the experimental system.
405 mm. The A El element was placed close to the target to provide a good tuning signal for the reaction and to discriminate against particles not coming from the target. The J E-, and E layers were constructed as a hodoscope and consisted of five parallel vertical strips and three horizontal blocks of scintillator, respectively, each coupled to two photomultipliers, one at each end. The point of interaction of a particle along the length of an element was obtained from the time difference between the arrivas of the signals at the photomultipliers . The FWHM resolutions of the determination of the horizontal and vertical position of a particle in the plane of the detector were 24 and 41 mm, respectively . At a typical target to detector distance of 50 cm the former figure corresponds to a 0-resolution of 2 .7° FWHM. The signals from the A E, and E sections were used to provide particle identification, and the particle energy was determined from the pulse heights in the E detectors. The total pulse height Q from each detector was evaluated from the geometric mean, Q = Q' Q2, of the signals from the two ends . This procedure compensates for the approximately exponential light attenuation along the length of the scintillator block. Using this technique the pulse-height resolution of the system for protons of energy 40-80 MeV was < 5% FWHM. A hardware threshold set on the weighted sum of the pulse-height signals from the AE, and E detectors was used to veto most of the electron background. Measurements were made at proton emission angles ranging from 30° to 150°. This involved moving the detector twice in order to cover the angular range in 3 overlapping sections of about 7/0' each. The total solid angle subtended by the detector varied from 0.6 to 1 .0 sr depending on its position. vas 10,00 mm x
P.A. Wallace et al. / ZH(7, p)r:
621
2.2. MODELLING OF THE PROTON DETECTOR RESPONSE To obtain accurate results for the deuteron photodisintegration cross section, a reliable treatment of the efficiency and position calibration of the proton detector was needed. For this purpose a Monte Carlo simulation of the experiment was developed 3) . It incorporated proton energy losses in the target and other materials between the target and the E detector blocks, a detailed calculation of the energy loss in each E block including edge effects, nuclear reactions in the scintillators, the non-linearity of the scintillator response as a function of particle energy, and the non-uniform light collection within the scintillator blocks. It also took account of the hardware and software thresholds used during the experiment and the subsequent analysis of the data . To model the distribution of proton production points in the deuterium target, the measured cell shape was sampled using a calculated angular distribution for the photon beam passing through the collimator. The latter was obtained by folding the bremsstrahlung angular distribution with those due to multiple scattering in the radiator and the electron beam convergence at the radiator. Using this Monte Carlo model a pseudo-data set was generated assuming that the initial protons were isotropically distributed but using the kinematics of the 2H(y, p)n reaction . The apparent angular distribution of this pseudo-data as recorded by the detector enabled the evaluation. of efficiency corrections which were applied in the analysis of the real data. The calibration of the position response of the detector was determined by comparison with the results of the Monte Carlo calculation . The solid line in fig. 2a shows the result of a simulation of the horizontal position spectrum in an E element under the applied condition that the incoming proton must pass through the 1st, 3rd or 5th dE-, strip. The histogrammed data in the figure represents a sample of time-difference data scaled linearly to correspond with the position response simulation . Fig. 2b shows a similar result for the vertical position response of a JE2 strip, the applied condition being that only the 1st or 3rd E element should have been triggered by the passage of the proton. The position response thus determined enabled the laboratory 0- and 0-coordinates of the particle's trajectory to be calculated from the x, v-coordinates of
its point of incidence on the face of the detector . In order to check the validity of the Monte Carlo simulation of the detector pulseheight response and also to establish the scale of the energy calibration, a sample of the real deuteron photodisintegration data was processed so as to permit easy comparison with the simulation . Using data from which the electron background, random coincidences and the empty target background had been subtracted as described in the next section, each measured proton could be assumed to have been produced in a 2H(y, p)n reaction and its energy was reconstructed using its measured emission angle and the known photon energy . Fig. 3b displays the spectrum of the differences between this calculated proton energy based on the reconstruction and the measured energy deduced from the pulse heights. When the energy calibration scale is correctly ch-sen a peak centred around 0 MeV is observed, together with a tail mainly due
62 2
P.A. Wallace et al. / 2H(y, p)n
400 600 800 HORIZONTAL COORDINATE (mm)
1000
100 200 300 400 VERTICAL COORDINATE (mm)
500
Fig. 2. The position response of the proton detector (a) in the horizontal direction and (b) in the vertical direction. The histogram is the meas"ired response and the continuous line is the Monte Carlo simulation. to those events in which the proton underwent a nuclear reaction in the scintillator.
The tail also contains events in which the pulse-height signal was degraded because the proton passed through a corner of the E detector without stopping . The solid line in fig. 3b represents the prediction of the Monte Carlo simulation . The simulation is in good agreement with the observed response of the detector both in the prediction
of the resolution of the full energy peak and the extent of the tail . This confirms the validity of the detector calibration over a wide energy range and more importantly the magnitude of the correction which must be made for events in which the detector output pulse does not lie in the full energy peak . The Monte Carlo simulation results were used to calculate the average thickness of the deuterium target weighted by the angular distribution of the photon beam, which was then used in calculating the absolute photodisintegration cross sections . The
P.A. Wallace et al. / 2H(y, p)n
EMEAS
ECALC (
623
MeV
Fig. 3. The measured particle energy spectrum presented on an energy scale, Emeas - EW,, which is referred to the energy calculated assuming 2H(y, p)n kinematics as described in the text. In part (a) the upper curve is before and the lower curve after random background subtraction. Part (b) shows the spectrum after empty target background has been subtracted. The solid line is the result of the Monte Carlo simulation . simutii..iort Also provided a check of the value of the tagging efficiency . The calculated average value for the photon energy range 133-158 MeV was 0.66, in good agreement with the measurement, 0.65 f 0.01 . The directly measured result was, however, used in the data analysis. 3. Data analysis The first step in the data analysis was to discard those events for which more than one electron was recorded in the detectors of a section of the focal plane connected to a single TDC, since the identity and coincidence timing of the tagging electron were ambiguous for such events. This procedure resulted in the loss of some of the genuine
P.A. Wallace et al. / ZH(y, p)n
624
4) tagged events for which a (rate dependent) correction factor was calculated . Once this had been done each event had associated with it an unambiguous photon energy and coincidence timing and therefore a known flight time to the detector, although in the case of the random background events these values were spurious . It was acceptable that, for a given event, candidate tagging elect mns may have appeared in more than one section of the focal plane each connected to a different TDC; each section was treated independently and the "double-counting' of the event was automatically corrected when the random background was subtracted . The next step in the analysis, the identification of protons and the rejection of electron events in the proton detector, was carried out in two stages. The majority of electron events were removed by making a loose cut around the proton ridge in the scatter plot of J E, versus E pulse heights. This was followed by a tighter cut based on the time-of-flight of particles between the JE, and E elements . Fig. 4 is a scatter plot showing time-of-flight versus pulse height for a typical sample of data. The electrons are well separatcd from the protons and the latter are mainly the high-energy products of 2 H( ;,, P) reactions induced by photons in the tagged part of the bremsstrablung spectrum. The data in the proton region were selected for further analysis together with a similar region displaced along the time-of-flight axis, which contains only the random coincidence background. Data selected in this way were then used to generate the energy difference spectra, Em. - Era,, as described in the previous section . Fig. 3a shows a sample of the data at this stage of reduction before and after the subtraction of the random coincidence background . Fig. 3b shows the effect of the subtraction of the genuine tagged background produced with the target cell empty. In the region to the
100 80 z 60 w z
0 0 40 a
20 10
20
30
40
TIME OF FLIGHT (ms)
50
Fig. 4. Scatter plot of pulse height in the proton detector versus flight time from the target used for particle identification . The zero of the time scale is arbitrary.
P.A. Wallace et al. / 2H(y, p)n
625
left of the peak the background is dominant and after the background subtractions the statistical uncertainty is large. For this reason in the final step of the data reduction only those events whose measured proton energy lay within f 10 MeV of the calculated value for a 2 H(7, p)n reaction were accepted and a correction described below was applied for the events lost outside this region. The accepted data in the peak region were binned directly in terms of the angular coordinates, ec.m. and Oc.m., of the centre-of-mass system . The Bc.m. bins were 10° wide covering the range 30°-150°. The 0c.m. limits were set slightly smaller than the physical extent of the proton detector to include only events where the proton energy signal was not degraded by detector edge effects. The data from groups of focal-plane detectors were added to produce M i 2 MeV wide photon energy bins. A sample of pseudo-data generated by the Monte Carlo simulation was analysed, selected and histogrammed in an identical fashion to the real experimental data in order to calculate an efficiency factor for each angle-energy bin which would correct for geometrical acceptance effects, the local value of the detector efficiency for protons in the relevant energy range and the loss of events incurred in the data analysis. Events were lost if the reconstructed proton angle and energy were inconsistent with the 2 H(7, p)n reaction kinematics. On the other hand, the apparent efficiency could be increased if events were wrongly ascribed to a data bin. Generally, however, the net leakage of events from one bin to its neighbour was small. The overall correction factors were typically 8% and never more than 15% at the extreme ends of the angular range covered at each detector setting. The dominant effect generally was the loss of events from the peak region in the energy spectrum due to nuclear interactions, which varied slowly with proton energy, and therefore with the proton angle, from 3% to 11%. The estimated uncertainty in the correction factors was f 2%. The angular distributions thus obtained were combined with the target thickness and the photon beam flux to produce the final cross sections. The effective thickness was given by the density of the deuterium liquid corrected for boiling effects, multiplied by the mean, beam-profile-weighted geometrical thickness . The photon beam flux was defined as the electron flux multiplied by the experimentally determined tagging efficiency. The dead time corrections in the electron scalers were 1-2% depending on the beam intensity . There was an additional correction a) for the discarded events in which more than one electron was recorded in one section of the focal plane. The magnitude of this correction varied with the beam intensity from 5% up to 9% at the highest intensities used. 4. Results 4.1 . THIS EXPERIMENT
The differential cross section data plotted in fig. 5 comprise three overlapping sets of points corresponding to the forward-, middle- and backward-angle proton detector
P.A. Wallace et al. / 2H(y, p)n
626
Et =140 MeV
2 b
C:
150 MeV
f ®
FORWARD ANGLE
POSITION
MIDDLE ANGLE POSITION ® BACK ANGLE o
I
,
POSITION e
I
I
e
80 100 120 140 160 ecm Fig. 5. The 211(p, p)n differential cross section for the three different detector positions. The data obtained with the detector in the forward-, middle- and backward-angle positions are represented as squares, solid circles and triangles, respectively. 0
20
40
60
positions, each identified by different symbols. The error bars shown in the figure are statistical only. The three data sets have been plotted separately because they represent independent nseasurements of the cross section made sequentially with the same apparatus. Their degree of consistency is a measure of the reliability of the methods employed. The consistency actually achieved is reassuring, only a little less good than would be expected given the statistical uncertainties of the measured cross secti.ons. Systematic errors are either common to all the points from a given detector setting or else slowly varying with angle . The estimated magnitudes of the most important sources of systematic uncertainty are target thickness 3%, detector geometry and position calibration 3%, detector efficiency 2%, photon flux 1%. These uncertainties are added in quadrature to obtain the estimated overall systematic uncertainty of 5%. For comparison with other data and with theoretical calculations the weighted means of the data shown in fig. 5 have been calculated and allowance has been made in calculating the errors for the degree of consistency achieved. The results are contained in table 1 .
P.A. Wallace et al. / 2H(y, p)n
627
TABLE 1
Angular differential cross sections for the 2H(y, p)n reaction . The cross sections in the centre-of-mass system are tabulated as a function of the c.m . proton emission angle ec.m . and the laboratory frame photon energy E;, ec.m.
(deg)
35 45 55 65 75 85 95 105 115 125 135 145
(dQ/dQ )c.m. (pb/sr)
Er = 133-145 MeV
E; = 145-158 MeV
4.91 ±0.09 4.76±0.09 4.86±0.09 5.09 ± 0.07 4.73±0.07 4.60 ± 0.07 4.30 ± 0.07 3.87±0.08 3.77 ± 0.09 3.72 ± 0.07 3.18±0.12 3.32±0.17
4.62±0.11 4.65±0.10 4 .76±0.10 4.87 ± 0.07 4.59±0.09 4.48 ± 0.07 4.33 ± 0.08 3.95±0.08 3.79 ± 0.09 3.61 ± 0.09 3.10±0.13 3.25±0.21
4.2. COMPARISON WITH PREVIOUS EXPERIMENTS The present results are compared in fig. 6 with the other recent experiments 5-7 ). The agreement is very much better than that achieved among earlier measurements of the 2H(y, p)n cross section in this energy region . Nonetheless discrepancies beyond the nominal errors are clear. To guide the eye fig. 6 shows separate smooth curves fitted to the present data and to the data points obtained at TRIUMF 5 ) and Frascati 5 ). These cross section shapes differ systematically from each other and from the present data by up to 10%. The angular distribution obtained at MIT by Matthews et al. 7 ) does, however, have a similar shape to the present results. (To facilitate this comparison in fig. 6 the MIT data are multiplied by 0.92. This normalisation is within the combined systematic errors of the two experiments.) It would appear that some of the recent measurements have been affected by undetected systematic errors. The techniques used were quite different in each case. Matthews et al. used a bremsstrahlung beam, which has clearly led to photon flux normalisation errors in the past . This difficulty was avoided by using a geometry in which the full bremsstrahlung cone passed through the deuterium target so that the flux could be calculated from the electron beam charge . A magnetic spectrometer was used for proton detection to reduce background problems. The Frascati measurements used a positron annihilation photon beam with its more favourable spectrum shape peaked at the high-energy end, which was monitored by a
P.A. Wallace et al. / ZH(y, p)n
628
v
bj e,
150 MeV
a
" PRESENT DATA O MIT9D ------
O TRIUMF 86 .
---- ®® FRASCATI 86,89-
0
9
20
1
-
40
'
60
1
1
80
100
1
120
1
140 160
180
()CM
Fig, 6. Differential cross sections for the'-H( , , p)n reaction at E,, = 140 and 150 Met' from this work and three other recent experiments. Solid circles - this work, open squares - TRIUMF 5 ), open and solid triangles - Frascati 6 ), open circles - MIT 7 ). In this figure the MIT data points have been renormalised by a factor of 0.92. The lines are fits to guide the eye. Only statistical errors are shown except in the case of the MIT results, for which the part of the systematic uncertainty which causes angle-to-angle variations was included. pair spectrometer. The experiments 6,' ) both used photon spectra with several different end point energies to provide some internal check on the consistency of the results. The TRIUMF experiment measured the inverse neutron capture reaction, 'H(n, d)y. The problem of neutron flux measurement was circumvented by normalising against the well known pn elastic-scattering cross section. Nonetheless, the experiment is a difficult one in which the determination of the efficiency of the gamma-ray and deuteron recoil detectors is crucial. it k not possible from the internal evidence of the results presented in fig. 6 or from the details given in refs. 5-7 ) to decide which of the recent experiments is most reliable . For this reason the older data 8-12 ) were also re-examined. Although these experiments are open to criticism in several respects, see for example the discussion in ref. 12), the main suspicion has fallen on the photon flux determination. It is worthwhile therefore to see if a consensus can be reached over
P.A. Wallace ei al. / 2H(y. p)n
629
the shape of the angular distribution. Unfortunately this is not the case. The angular distributions from refs . 8-10 ), which differ in magnitude by 35%, do have a similar shape to that obtained at Frascati 6 ) . However, the two other early experiments " .i2) both have a shape at the other extreme of those shown in fig. 6, in agreement with Matthews et al. 7 ) and the present experiment . One concludes that a further improvement in experimental techniques is required to obtain the consistency necessary to pin down the cross section in this energy region to better than 10%. However, the latest data do provide a much better test of the available theoretical calculations than hitherto possible. 5. Discussion There have been many theoretical treatments of the two-body photodisintegration of the deuteron. The most commonly followed theoretical approach to the problem is to perform the calculation in coordinate space using a multipole expansion of the electromagnetic transition operator. The transition matrix elements are calculated only for the lower multipoles, typically up to l = 4, but all partial waves are included in the final state. The treatment of meson exchange current (MEC) effects is facilitated by the use of the Siegert theorem by which the leading terms of the electric transition operators can be expressed '3) in terms of the one-body electric charge density instead of the total electric current operator . The advantage is that these so-called Siegert operators then contain implicitly a large part of the effects of the MEC contained within the `realistic' nuclear potential used to calculate the charge density. The magnetic transition operators and the higher order terms in the electric multipole operators still require MEC contributions to be added explicitly. Although the present photon energy of ti 140 MeV is well below the energy corresponding to the peak of the A-resonance it has become apparent that processes involving the photoproduction of a A in the intermediate state, with associated oneor two-pion exchange to restore the two-body np final state, are already important . The effects are predicted to be responsible for 15-20% of the cross section. There is at present no theoretical consensus as to the appropriate treatment of the propagation of the intermediate-state A in the nucleus. Finally there are effects of relativistic origin which produce significant modifications of the cross section . The most important is a spin-orbit term which must be included in the charge and current operators. This arises from a second order term in the non-relativistic reduction of the electromagnetic hamiltonian for a Dirac particle . In addition the deuteron wave function is modified by dynamical effects, which arise from a relativistic treatment of the NN bound state, and by kinematical corrections, e.g. Lorentz contraction and spin precession, which modify the intrinsic wave function when it is boosted to a moving reference frame 14). An alternative approach 15,16 ) uses a momentum space expansion of the amplitude into S-matrix diagrams representing the interaction of the photon with the nucleon, meson exchange and isobar currents followed by NN7c rescattering .
630
P.A. Wallace et al. / ZH(y, p)n
Both of the above techniques require the use of a realistic potential within which to calculate the initial deuteron wave function. The potentials most frequently used in modern calculations are the Bonn OBEP ") and Paris 18) models. Both give a good account of NN scattering data and of the static properties of the deuteron . However, these properties, such as the electric quadrupole moment, depend largely on the longrange part of the potential (i.e. > 1 .5 fm) which is mediated in both models by the well established one-pion-exchange mechanism . The transitions induced by photons in the present energy range are also sensitive to the shorter range parts of the potential where the two models have a rather different basis. The Siegert operator method is exemplified by the work of the Mainz theory group. Wilhelm et al 19 ) (WiL) present such a calculation performed using both the Bonn OBEP-R and Paris potentials. The calculation includes explicit a and p exchange mechanisms beyond those implicit in the Siegert operators. The impulse approximation is used to treat A currents and the calculation also takes into account the relativistic spin-orbit current . The results are shown in fig. 7a. The difference between the Bonn OBEPR and Paris results is 2-4 over most of the angular range . Only at forward angles is the Bonn prediction appreciably lower than the Paris curve. Also shown in fig. 7a are two more Bonn OBEP-R calculations performed by Schmitt and Arenh6Ve1 2° ) labelled `SchA' and `SchA+Rel' . This comparison gives an idea of the importance of the details of the calculation other than the potential . The SchA calculation differs from that of WiL in using a weaker p coupling constant and in omitting the A-MEC current. Both of these effects lead to a smaller cross section . The SchA -+- Rel calculation includes lowest-order relativistic effects beyond the spin-orbit term which again reduces the cross section over most of the angular range. It can be seen from fig. 7a that these changes produce effects which are at least as large as those produced by changing the potential . However the spread of the recent data is such that it cannot discriminate among the calculations. The calculation of Ying et a1 21) also uses the Bonn potential, but the treatment of the MEC additional to those contained in the Siegert operators uses an approximation which underestimates these contributions 22 ) and produces a result which is 30-50% below the data. Fig. 7b shows a series of calculations performed using the Paris potential . The results of Cambi et a!. 23 ) (CMR ), Jaus and Woolcock 14 ) (JaW) and Laget'6 ) are displayed together with the WiL-Paris calculation shown previously. The differences between WiL, JaW and CMR are essentially due to differences in the treatment of the isobar contributions 22 ) . The calculation of JaW differs from that of WiL in using a weaker yNA coupling and in employing a A-width even below the pion threshold where it should be absent. The CMR calculation employs a static treatment of the A-current which neglects its propagation in the nucleus. The resulting differences in their predictions are fairly large but again because of the spread of the data only the CMR result is clearly excluded . The calculation of Laget, on the other hand, is rather different being based on a Feynman diagram technique . The matrix elements are calculated directly with explicit
P.A. Wallace et al. / 2H(y, p)n
63 1
6 5 4 3 2 E u 5 4 3 2
Fig. 7. Comparison of recent data for the 2 H(7, p) n reaction at E; = 140 MeV with theoretical predictions using (a) the Bonn OBEP-R potential and (b) the Paris potential. References to the theoretical calculations are given in the text. The data are the same as those shown in fig. 6, except that the MIT results are not renormalised. expressions for the current densities. This is in contrast to the previous calculations which all used Siegert operators defined from the one-body charge density. The calculation uses a low-energy expansion of the nuclear electromagnetic currents which is Lorentz invariant to order (Prr/MN ) -2. The current density operators include the relativistic terms corresponding to the corrections introduced into the charge density by the other workers. The interaction is explicitly gauge invariant in the latest version of the calculation 16 ) and consistent wave functions derived from the Paris potential are used. All partial waves are implicitly included in the interaction and the final-state interactions have been calculated for S, P and D waves in the final state. The resultant cross section lies below the data over most of the angular range. Because of the different basis of the calculation it is not possible to say whether any specific feature of the calculation is responsible for the discrepancy.
632
P.A. Wallace et aL / 2N(y, p)n 6. Summary and conclusions
The angular differential cross section for the reaction 2My, p)n has been measured at photon energies between 133 and 158 MeV . The systematic uncertainty of the data is estimated to be 5°ßn and the statistical uncertainties are somewhat smaller. A detailed comparison of this data with that of other recent experiments indicates that our angular distribution shape agrees with that from MIT while the absolute normalisation differs by 8 which is within the combined systematic errors of the two experiments. On the other hand, if the data are compared with those from Frascati and TRIUMF one finds that the absolute magnitudes of the distributions are in reasonable agreement while the shapes differ significantly . We note that all the calculations tend more toward the flatter shape of this data and the MIT experiment rather than the Frascati or TRIUMF distributions which tend to be more sharply peaked around 90° . Taken together, however, the recent data define the shape and magnitude of the cross section to within a band of relative width 10°x. This represents a very considerable improvement upon the situation which existed previously but cannot be regarded as completely satisfactory. The data are good enough to permit criticism of some of the theoretical predictions on the grounds of their treatment of A-resonance and mediumrange MEC effects, but the experimental situation is not yet sufficiently well defined to allow a full evaluation of the theoretical calculations. The authors are grateful to the United Kingdom Science and Engineering Research Council and the Deutsche Forschungsgemeinschaft for supporting this work. The United Kingdom members of the collaboration also wish to thank the Institut fir Kernphysik, Maim University for the use of their facilities and for the assistance received during the course of the experiment . Three of us (P.A.W., S.N.D., and S.M.D.) 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. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)
J.D. Kellie et al., Nucl. Instr. Meth. A241 (1985) 153 I.J.D. MacGregor et al., Nucl. Instr. Meth. A262 (1987) 347 P.A. Wallace, Ph.D. thesis, University of Glasgow (1989), unpublished R.O. Owens, Nucl . Instr. Meth. A288 (1990) 574 J.M. Cameron et aL, Nucl. Phys. A453 (i986) 637 E. DeSanctis et al., Phys. Rev. C34 (1986) 413 P. Levl Sandri et al., Phys. Rev. C39 (1989) 1701 J.L. Matthews et al., to be published E.A. Whalin, B .D . Schriever and A.O. Hanson, Phys . Rev. 101 (1956) 377 R. Kose et al., Z. Phys . 202 (1967) 364 J. Buon et al., Phys . Lett. B26 (1968) 595 lu.A. Aleksandrov et al., Sov. Phys . JETP 6 (1958) 472 P. Dougan, V. Ramsay and W. Stiefler, Z. Phys. A276 (1976) 55 ; A280 (1977) 341 H. Arenh6vel, Z. Phys . A302 (1981) 25
P.A. Wallace et al. / 2H(y, p)n
14) 15) 16) 17) 18) 19) 20) 21) 22) 23)
633
W. Jaus and W.S. Woolcock, Nucl. i'hys. A473 (1987) 667; 685 J.M. Laget, Nucl . Phys. A312 (1978) 265 J.M. Laget, Can. J. Phys . 62 (1984) 1046 and private communication R. Machleidt, K. Holinde and Ch. Elster, Phys. Reports 149 (1987) 1 M. Lacombe et al., Phys . Rev. C21 (1980) 861 P. Wilhelm, W. Leidemann and H. Arenhövel, Few Body Systems 3 (1988) 111 and private communication K.-M. Schmitt and H. Arenhövel, Few-Body Systems 7 (1989) 95 S. Ying, E.M. Henley and G.A. Miller, Phys . Rev . C38 (1988) 1584 M. Sanzone and H. Arenhövel, Few-Body Systems Supplementum 3 (1991) A. Cambi, B. Mosconi and P. Ricci, Phys. Rev. Lett. G48 (1982) 462; J. of Phys. G10 (1984) L11 and private communication
DIFFERENTIAL CROSS SECTION FOR THE REACTION 2H(y, p)n FROM 133 TO 158 MeV P.A. WALLACEI, J.R.M. ANNAND, I. ANTHONY, G.I. CRAWFORD, S.N . DANCER, S.M. DORAN, S.J. HALL, J.D. KELLIE, J .C. MCGEORGE, I.J.D. MACGREGOR, G.J. MILLER and R.O. OWENS Department of Physics and Astronomy, Unnersity ofGlasgow, Glasgow G12 8QQ, UK J. VOGT2 and B. SCHOCH 3 Institut f'ir Kernphysik, Johannes Gutenberg-Universität, D-6500 Mainz, Germany D. BRANFORD Department ofPhysics, Unirersity of Edinburgh, Edinburgh EH9 3JZ, UK Received 29 January 1991 Abstract: The cross section for the reaction 2 H(7, p)n has been measured at laboratory photon energies E; = 133-158 MeV and c.m . angles between 30° and 150° . The reaction was induced by a tagged bremsstrahlung photon beam incident on a liquid deuterium target. The uncertainty in the absolute cross sections is < 5%. There is now reasonable agreement between recent measurements in this energy region and the overall data set now defines the cross section sufficiently well to provide a test of current models of the reaction . E
NUCLEAR REACTION 2 H(7, p), E = 133-158 MeV ; measured absolute 6 (E; . Op ) for Op = 30°-150° .
1. Introduction For more than fifty years the photodisintegration of the deuteron has been used as a test case for the application o', new ideas concerning the nature of the nuclear force. The deuteron as the only two nucleon bound state yields information complementary to that obtained from NN scattering experiments, which have been the basis of most systematic studies of the NN interaction. The concept of a purely NN interaction is of course an approximation with which one attempts to describe the behaviour of a system whose components certainly include mesons, nucleons and nucleonic resonances and in which
I Present address: C.E.N. Saclay, DPhN/SEPN, 91191 Gif sur Yvette Cedex, France . 2 Present address: Saskatchewan Accelerator Laboratory, University of Saskatchewan, Saskatoon . Canada. 3 Present address: Physikalisches Institut der Universität Bonn, D-5300 Bonn 1, Germany. 0375-9474/1991/$3 .50 © 1991 - Elsevier Science Publishers B.V . (North-Holland)
618
P.A . R'allace et al. / 2H(7, p)n
the internal structure of the nucleons may need to be considered explicitly . Given the potential complexity of the dynamics of interacting nucleons, the photodisintegration of the deuteron is a particularly suitable case to treat because of its relative simplicity. The initial wave function is calculable, at least within a given model, and the reaction is influenced more by the nature of the initial photoabsorption mechanism than by the final-state interactions of the outgoing nucleons, which might be the case in a more complex nucleus . However, even for the case of deuteron photodisintegration, it remains unclear how best to proceed to a quantitative understanding of the reaction. There exist a number of theoretical treatments in which the physical content is apparently similar but the predicted cross sections differ by 10-20°®0. Since different formalisms have been employed it is hard to compare the components of the various calculations in a likefor-like fashion. In addition it has been difficult to say to what extent the discrepancies arise from the inclusion or omission of genuine physical effects and to what extent they are due to more `technical' differences in the calculations. In view of the above remarks it is all the more urgent that reliable experimental bench marks should be fixed against which to assess the different model predictions. Unfortunately it has not proved easy to obtain sufficiently accurate data on deuteron photodisintegration for this purpose. The large discrepancies between the existing data sets make it clear that previous workers using bremsstrahlung photon beams encountered severe difficulties in their efforts to suppress background and to obtain a reliable flux normalisation . The ideal solution to both of these problems is that adopted in the present measurement, the use of a tagged photon beam . Measurement of the photon energy as well as that of the emitted proton overdetermines the reaction kinematics and thus permits a very clean rejection of background processes. Furthermore, the photon flux is determined in a very straightforward fashion using a tagging system . It is just that number of photons for which the coincident tagging electron is detected. 2. The experimental system 2.1 . EXPERIMENTAL APPARATUS
The experiment was performed using the Glasgow bremsstrahlung tagging facility') in conjunction with the CW electron beam of the microtron MAMI-A in the Institut filr Kernphysik at Mainz University. An electron beam of energy 183 MeV from the microtron was focussed on a 25 ,um thick aluminium foil radiator. The momenta of the residual electrons following the emission of bremsstrahlung were measured using a magnetic spectrometer whose focal plane was divided into 91 photon energy tagging channels . During the experiment tagged photon beams of intensities between 4 x 106 and 8 x 10 6 per second were produced, spanning the energy range 133-158 MeV with a resolution of 0 .25 MeV. The signals from the 91 electron detectors were grouped and fed to the stop inputs of 6 TDCs. The TDCs were started by a trigger signal from
P.A. Wallace et al. / ZH(v. p)n
619
the plastic scintillator telescope used to detect protons from the deuterium target. To record the photon beam flux, the electron detector signals were combined in groups and fed to 12 scalers. However, since the diameter of the photon beam was restricted by a collimator, it was necessary to evaluate the fraction of tagging electrons whose corresponding photon passed through the collimator cone. This fraction, referred to as the tagging efficiency, was measured at reduced beam intensity by placing a detector in the collimated photon beam and measuring the ratio of tagged photons to tagging electrons. The detector used for this purpose was an SCG 1-C glass scintillator of thickness 12 radiation lengths, which was effectively 100% efficient for 100-200 MeV photons. A correction for the presence of background in the focal-plane detectors was made by repeating the measurement with the bremsstrahlung radiator removed. The tagging efficiency was measured at intervals throughout the experiment . In addition, its relative stability was monitored by observing the ratio between the current in a DC ionisation chamber, placed in the photon beam downstream of the target, and the tagging electron counting rate. During the experiment the tagging efficiency remained stable to ± 1% of its mean value. The deuterium target consisted of a 50 ml cell ofliquid filled from a large low-pressure reservoir of gaseous deuterium by means of a commercial helium cycle refrigerator. The cell was placed in a cylindrical evacuated chamber furnished with a single Kapton window of thickness 100 lim which was large enough to allow the through passage of the photon beam and the outward passage of the emitted protons. The target cell was constructed by glueing 70,um thick Kapton windows on to a 4 mm thick aluminium frame having an oval aperture with major and minor axes 106 mm x 50 mm, respectively . In order to optimise the ratio of thickness of material presented to the incoming beam relative to that encountered by the outgoing protons, the frame was inclined at an angle of 30° to the photon beam axis. When operated at a pressure of 1 .3 atm . the maximum target thickness was 33 mm along the beam axis. The profiles of the cell windows were mapped in detail over a range of cell pressures in order to permit accurate calculation of the average target thickness. The deuterium liquid in the cell was observed to boil gently throughout the experiment because of continuous absorption of radiant heat from its surroundings. The presence of gas bubbles in the target reduced its effective thickness. The density of the liquid/bubble mixture was measured by monitoring the change in the gas pressure in the closed deuterium system, and thus the change in the mass of deuterium in the liquid state, as a function of the volume of liquid/bubble mixture observed in the cell . The correction to the normal deuterium density was found to be (- 5 ± 2) °lo. During the experiment data were taken with the cell both full and empty in order to measure the background from the cell windows. Protons and other particles from the deuterium target were detected in a large solid angle, position sensitive plastic scintillator telescope 2 ) shown in fig. 1 . The telescope consisted of 3 layers of NE 110 plastic scintillators. These were two thin transmission layers (A E1,2 detectors) and a stopping layer (E detector), of thicknesses 1 mm, 3 mm, and 110 mm, respectively. The total frontal area of the E elements
P.A . lVallace et al. / 2H(y, p)n
620
PROTON DETECTOR ELEMENTS
--- AEI SCATTERING CHAMBER WINDOW PHOTON BEAM
---" TARGET CELL
SCATTERING
CHAMBER WALL
2O a a Fig . 1 . Plan view of the experimental system.
405 mm. The A El element was placed close to the target to provide a good tuning signal for the reaction and to discriminate against particles not coming from the target. The J E-, and E layers were constructed as a hodoscope and consisted of five parallel vertical strips and three horizontal blocks of scintillator, respectively, each coupled to two photomultipliers, one at each end. The point of interaction of a particle along the length of an element was obtained from the time difference between the arrivas of the signals at the photomultipliers . The FWHM resolutions of the determination of the horizontal and vertical position of a particle in the plane of the detector were 24 and 41 mm, respectively . At a typical target to detector distance of 50 cm the former figure corresponds to a 0-resolution of 2 .7° FWHM. The signals from the A E, and E sections were used to provide particle identification, and the particle energy was determined from the pulse heights in the E detectors. The total pulse height Q from each detector was evaluated from the geometric mean, Q = Q' Q2, of the signals from the two ends . This procedure compensates for the approximately exponential light attenuation along the length of the scintillator block. Using this technique the pulse-height resolution of the system for protons of energy 40-80 MeV was < 5% FWHM. A hardware threshold set on the weighted sum of the pulse-height signals from the AE, and E detectors was used to veto most of the electron background. Measurements were made at proton emission angles ranging from 30° to 150°. This involved moving the detector twice in order to cover the angular range in 3 overlapping sections of about 7/0' each. The total solid angle subtended by the detector varied from 0.6 to 1 .0 sr depending on its position. vas 10,00 mm x
P.A. Wallace et al. / ZH(7, p)r:
621
2.2. MODELLING OF THE PROTON DETECTOR RESPONSE To obtain accurate results for the deuteron photodisintegration cross section, a reliable treatment of the efficiency and position calibration of the proton detector was needed. For this purpose a Monte Carlo simulation of the experiment was developed 3) . It incorporated proton energy losses in the target and other materials between the target and the E detector blocks, a detailed calculation of the energy loss in each E block including edge effects, nuclear reactions in the scintillators, the non-linearity of the scintillator response as a function of particle energy, and the non-uniform light collection within the scintillator blocks. It also took account of the hardware and software thresholds used during the experiment and the subsequent analysis of the data . To model the distribution of proton production points in the deuterium target, the measured cell shape was sampled using a calculated angular distribution for the photon beam passing through the collimator. The latter was obtained by folding the bremsstrahlung angular distribution with those due to multiple scattering in the radiator and the electron beam convergence at the radiator. Using this Monte Carlo model a pseudo-data set was generated assuming that the initial protons were isotropically distributed but using the kinematics of the 2H(y, p)n reaction . The apparent angular distribution of this pseudo-data as recorded by the detector enabled the evaluation. of efficiency corrections which were applied in the analysis of the real data. The calibration of the position response of the detector was determined by comparison with the results of the Monte Carlo calculation . The solid line in fig. 2a shows the result of a simulation of the horizontal position spectrum in an E element under the applied condition that the incoming proton must pass through the 1st, 3rd or 5th dE-, strip. The histogrammed data in the figure represents a sample of time-difference data scaled linearly to correspond with the position response simulation . Fig. 2b shows a similar result for the vertical position response of a JE2 strip, the applied condition being that only the 1st or 3rd E element should have been triggered by the passage of the proton. The position response thus determined enabled the laboratory 0- and 0-coordinates of the particle's trajectory to be calculated from the x, v-coordinates of
its point of incidence on the face of the detector . In order to check the validity of the Monte Carlo simulation of the detector pulseheight response and also to establish the scale of the energy calibration, a sample of the real deuteron photodisintegration data was processed so as to permit easy comparison with the simulation . Using data from which the electron background, random coincidences and the empty target background had been subtracted as described in the next section, each measured proton could be assumed to have been produced in a 2H(y, p)n reaction and its energy was reconstructed using its measured emission angle and the known photon energy . Fig. 3b displays the spectrum of the differences between this calculated proton energy based on the reconstruction and the measured energy deduced from the pulse heights. When the energy calibration scale is correctly ch-sen a peak centred around 0 MeV is observed, together with a tail mainly due
62 2
P.A. Wallace et al. / 2H(y, p)n
400 600 800 HORIZONTAL COORDINATE (mm)
1000
100 200 300 400 VERTICAL COORDINATE (mm)
500
Fig. 2. The position response of the proton detector (a) in the horizontal direction and (b) in the vertical direction. The histogram is the meas"ired response and the continuous line is the Monte Carlo simulation. to those events in which the proton underwent a nuclear reaction in the scintillator.
The tail also contains events in which the pulse-height signal was degraded because the proton passed through a corner of the E detector without stopping . The solid line in fig. 3b represents the prediction of the Monte Carlo simulation . The simulation is in good agreement with the observed response of the detector both in the prediction
of the resolution of the full energy peak and the extent of the tail . This confirms the validity of the detector calibration over a wide energy range and more importantly the magnitude of the correction which must be made for events in which the detector output pulse does not lie in the full energy peak . The Monte Carlo simulation results were used to calculate the average thickness of the deuterium target weighted by the angular distribution of the photon beam, which was then used in calculating the absolute photodisintegration cross sections . The
P.A. Wallace et al. / 2H(y, p)n
EMEAS
ECALC (
623
MeV
Fig. 3. The measured particle energy spectrum presented on an energy scale, Emeas - EW,, which is referred to the energy calculated assuming 2H(y, p)n kinematics as described in the text. In part (a) the upper curve is before and the lower curve after random background subtraction. Part (b) shows the spectrum after empty target background has been subtracted. The solid line is the result of the Monte Carlo simulation . simutii..iort Also provided a check of the value of the tagging efficiency . The calculated average value for the photon energy range 133-158 MeV was 0.66, in good agreement with the measurement, 0.65 f 0.01 . The directly measured result was, however, used in the data analysis. 3. Data analysis The first step in the data analysis was to discard those events for which more than one electron was recorded in the detectors of a section of the focal plane connected to a single TDC, since the identity and coincidence timing of the tagging electron were ambiguous for such events. This procedure resulted in the loss of some of the genuine
P.A. Wallace et al. / ZH(y, p)n
624
4) tagged events for which a (rate dependent) correction factor was calculated . Once this had been done each event had associated with it an unambiguous photon energy and coincidence timing and therefore a known flight time to the detector, although in the case of the random background events these values were spurious . It was acceptable that, for a given event, candidate tagging elect mns may have appeared in more than one section of the focal plane each connected to a different TDC; each section was treated independently and the "double-counting' of the event was automatically corrected when the random background was subtracted . The next step in the analysis, the identification of protons and the rejection of electron events in the proton detector, was carried out in two stages. The majority of electron events were removed by making a loose cut around the proton ridge in the scatter plot of J E, versus E pulse heights. This was followed by a tighter cut based on the time-of-flight of particles between the JE, and E elements . Fig. 4 is a scatter plot showing time-of-flight versus pulse height for a typical sample of data. The electrons are well separatcd from the protons and the latter are mainly the high-energy products of 2 H( ;,, P) reactions induced by photons in the tagged part of the bremsstrablung spectrum. The data in the proton region were selected for further analysis together with a similar region displaced along the time-of-flight axis, which contains only the random coincidence background. Data selected in this way were then used to generate the energy difference spectra, Em. - Era,, as described in the previous section . Fig. 3a shows a sample of the data at this stage of reduction before and after the subtraction of the random coincidence background . Fig. 3b shows the effect of the subtraction of the genuine tagged background produced with the target cell empty. In the region to the
100 80 z 60 w z
0 0 40 a
20 10
20
30
40
TIME OF FLIGHT (ms)
50
Fig. 4. Scatter plot of pulse height in the proton detector versus flight time from the target used for particle identification . The zero of the time scale is arbitrary.
P.A. Wallace et al. / 2H(y, p)n
625
left of the peak the background is dominant and after the background subtractions the statistical uncertainty is large. For this reason in the final step of the data reduction only those events whose measured proton energy lay within f 10 MeV of the calculated value for a 2 H(7, p)n reaction were accepted and a correction described below was applied for the events lost outside this region. The accepted data in the peak region were binned directly in terms of the angular coordinates, ec.m. and Oc.m., of the centre-of-mass system . The Bc.m. bins were 10° wide covering the range 30°-150°. The 0c.m. limits were set slightly smaller than the physical extent of the proton detector to include only events where the proton energy signal was not degraded by detector edge effects. The data from groups of focal-plane detectors were added to produce M i 2 MeV wide photon energy bins. A sample of pseudo-data generated by the Monte Carlo simulation was analysed, selected and histogrammed in an identical fashion to the real experimental data in order to calculate an efficiency factor for each angle-energy bin which would correct for geometrical acceptance effects, the local value of the detector efficiency for protons in the relevant energy range and the loss of events incurred in the data analysis. Events were lost if the reconstructed proton angle and energy were inconsistent with the 2 H(7, p)n reaction kinematics. On the other hand, the apparent efficiency could be increased if events were wrongly ascribed to a data bin. Generally, however, the net leakage of events from one bin to its neighbour was small. The overall correction factors were typically 8% and never more than 15% at the extreme ends of the angular range covered at each detector setting. The dominant effect generally was the loss of events from the peak region in the energy spectrum due to nuclear interactions, which varied slowly with proton energy, and therefore with the proton angle, from 3% to 11%. The estimated uncertainty in the correction factors was f 2%. The angular distributions thus obtained were combined with the target thickness and the photon beam flux to produce the final cross sections. The effective thickness was given by the density of the deuterium liquid corrected for boiling effects, multiplied by the mean, beam-profile-weighted geometrical thickness . The photon beam flux was defined as the electron flux multiplied by the experimentally determined tagging efficiency. The dead time corrections in the electron scalers were 1-2% depending on the beam intensity . There was an additional correction a) for the discarded events in which more than one electron was recorded in one section of the focal plane. The magnitude of this correction varied with the beam intensity from 5% up to 9% at the highest intensities used. 4. Results 4.1 . THIS EXPERIMENT
The differential cross section data plotted in fig. 5 comprise three overlapping sets of points corresponding to the forward-, middle- and backward-angle proton detector
P.A. Wallace et al. / 2H(y, p)n
626
Et =140 MeV
2 b
C:
150 MeV
f ®
FORWARD ANGLE
POSITION
MIDDLE ANGLE POSITION ® BACK ANGLE o
I
,
POSITION e
I
I
e
80 100 120 140 160 ecm Fig. 5. The 211(p, p)n differential cross section for the three different detector positions. The data obtained with the detector in the forward-, middle- and backward-angle positions are represented as squares, solid circles and triangles, respectively. 0
20
40
60
positions, each identified by different symbols. The error bars shown in the figure are statistical only. The three data sets have been plotted separately because they represent independent nseasurements of the cross section made sequentially with the same apparatus. Their degree of consistency is a measure of the reliability of the methods employed. The consistency actually achieved is reassuring, only a little less good than would be expected given the statistical uncertainties of the measured cross secti.ons. Systematic errors are either common to all the points from a given detector setting or else slowly varying with angle . The estimated magnitudes of the most important sources of systematic uncertainty are target thickness 3%, detector geometry and position calibration 3%, detector efficiency 2%, photon flux 1%. These uncertainties are added in quadrature to obtain the estimated overall systematic uncertainty of 5%. For comparison with other data and with theoretical calculations the weighted means of the data shown in fig. 5 have been calculated and allowance has been made in calculating the errors for the degree of consistency achieved. The results are contained in table 1 .
P.A. Wallace et al. / 2H(y, p)n
627
TABLE 1
Angular differential cross sections for the 2H(y, p)n reaction . The cross sections in the centre-of-mass system are tabulated as a function of the c.m . proton emission angle ec.m . and the laboratory frame photon energy E;, ec.m.
(deg)
35 45 55 65 75 85 95 105 115 125 135 145
(dQ/dQ )c.m. (pb/sr)
Er = 133-145 MeV
E; = 145-158 MeV
4.91 ±0.09 4.76±0.09 4.86±0.09 5.09 ± 0.07 4.73±0.07 4.60 ± 0.07 4.30 ± 0.07 3.87±0.08 3.77 ± 0.09 3.72 ± 0.07 3.18±0.12 3.32±0.17
4.62±0.11 4.65±0.10 4 .76±0.10 4.87 ± 0.07 4.59±0.09 4.48 ± 0.07 4.33 ± 0.08 3.95±0.08 3.79 ± 0.09 3.61 ± 0.09 3.10±0.13 3.25±0.21
4.2. COMPARISON WITH PREVIOUS EXPERIMENTS The present results are compared in fig. 6 with the other recent experiments 5-7 ). The agreement is very much better than that achieved among earlier measurements of the 2H(y, p)n cross section in this energy region . Nonetheless discrepancies beyond the nominal errors are clear. To guide the eye fig. 6 shows separate smooth curves fitted to the present data and to the data points obtained at TRIUMF 5 ) and Frascati 5 ). These cross section shapes differ systematically from each other and from the present data by up to 10%. The angular distribution obtained at MIT by Matthews et al. 7 ) does, however, have a similar shape to the present results. (To facilitate this comparison in fig. 6 the MIT data are multiplied by 0.92. This normalisation is within the combined systematic errors of the two experiments.) It would appear that some of the recent measurements have been affected by undetected systematic errors. The techniques used were quite different in each case. Matthews et al. used a bremsstrahlung beam, which has clearly led to photon flux normalisation errors in the past . This difficulty was avoided by using a geometry in which the full bremsstrahlung cone passed through the deuterium target so that the flux could be calculated from the electron beam charge . A magnetic spectrometer was used for proton detection to reduce background problems. The Frascati measurements used a positron annihilation photon beam with its more favourable spectrum shape peaked at the high-energy end, which was monitored by a
P.A. Wallace et al. / ZH(y, p)n
628
v
bj e,
150 MeV
a
" PRESENT DATA O MIT9D ------
O TRIUMF 86 .
---- ®® FRASCATI 86,89-
0
9
20
1
-
40
'
60
1
1
80
100
1
120
1
140 160
180
()CM
Fig, 6. Differential cross sections for the'-H( , , p)n reaction at E,, = 140 and 150 Met' from this work and three other recent experiments. Solid circles - this work, open squares - TRIUMF 5 ), open and solid triangles - Frascati 6 ), open circles - MIT 7 ). In this figure the MIT data points have been renormalised by a factor of 0.92. The lines are fits to guide the eye. Only statistical errors are shown except in the case of the MIT results, for which the part of the systematic uncertainty which causes angle-to-angle variations was included. pair spectrometer. The experiments 6,' ) both used photon spectra with several different end point energies to provide some internal check on the consistency of the results. The TRIUMF experiment measured the inverse neutron capture reaction, 'H(n, d)y. The problem of neutron flux measurement was circumvented by normalising against the well known pn elastic-scattering cross section. Nonetheless, the experiment is a difficult one in which the determination of the efficiency of the gamma-ray and deuteron recoil detectors is crucial. it k not possible from the internal evidence of the results presented in fig. 6 or from the details given in refs. 5-7 ) to decide which of the recent experiments is most reliable . For this reason the older data 8-12 ) were also re-examined. Although these experiments are open to criticism in several respects, see for example the discussion in ref. 12), the main suspicion has fallen on the photon flux determination. It is worthwhile therefore to see if a consensus can be reached over
P.A. Wallace ei al. / 2H(y. p)n
629
the shape of the angular distribution. Unfortunately this is not the case. The angular distributions from refs . 8-10 ), which differ in magnitude by 35%, do have a similar shape to that obtained at Frascati 6 ) . However, the two other early experiments " .i2) both have a shape at the other extreme of those shown in fig. 6, in agreement with Matthews et al. 7 ) and the present experiment . One concludes that a further improvement in experimental techniques is required to obtain the consistency necessary to pin down the cross section in this energy region to better than 10%. However, the latest data do provide a much better test of the available theoretical calculations than hitherto possible. 5. Discussion There have been many theoretical treatments of the two-body photodisintegration of the deuteron. The most commonly followed theoretical approach to the problem is to perform the calculation in coordinate space using a multipole expansion of the electromagnetic transition operator. The transition matrix elements are calculated only for the lower multipoles, typically up to l = 4, but all partial waves are included in the final state. The treatment of meson exchange current (MEC) effects is facilitated by the use of the Siegert theorem by which the leading terms of the electric transition operators can be expressed '3) in terms of the one-body electric charge density instead of the total electric current operator . The advantage is that these so-called Siegert operators then contain implicitly a large part of the effects of the MEC contained within the `realistic' nuclear potential used to calculate the charge density. The magnetic transition operators and the higher order terms in the electric multipole operators still require MEC contributions to be added explicitly. Although the present photon energy of ti 140 MeV is well below the energy corresponding to the peak of the A-resonance it has become apparent that processes involving the photoproduction of a A in the intermediate state, with associated oneor two-pion exchange to restore the two-body np final state, are already important . The effects are predicted to be responsible for 15-20% of the cross section. There is at present no theoretical consensus as to the appropriate treatment of the propagation of the intermediate-state A in the nucleus. Finally there are effects of relativistic origin which produce significant modifications of the cross section . The most important is a spin-orbit term which must be included in the charge and current operators. This arises from a second order term in the non-relativistic reduction of the electromagnetic hamiltonian for a Dirac particle . In addition the deuteron wave function is modified by dynamical effects, which arise from a relativistic treatment of the NN bound state, and by kinematical corrections, e.g. Lorentz contraction and spin precession, which modify the intrinsic wave function when it is boosted to a moving reference frame 14). An alternative approach 15,16 ) uses a momentum space expansion of the amplitude into S-matrix diagrams representing the interaction of the photon with the nucleon, meson exchange and isobar currents followed by NN7c rescattering .
630
P.A. Wallace et al. / ZH(y, p)n
Both of the above techniques require the use of a realistic potential within which to calculate the initial deuteron wave function. The potentials most frequently used in modern calculations are the Bonn OBEP ") and Paris 18) models. Both give a good account of NN scattering data and of the static properties of the deuteron . However, these properties, such as the electric quadrupole moment, depend largely on the longrange part of the potential (i.e. > 1 .5 fm) which is mediated in both models by the well established one-pion-exchange mechanism . The transitions induced by photons in the present energy range are also sensitive to the shorter range parts of the potential where the two models have a rather different basis. The Siegert operator method is exemplified by the work of the Mainz theory group. Wilhelm et al 19 ) (WiL) present such a calculation performed using both the Bonn OBEP-R and Paris potentials. The calculation includes explicit a and p exchange mechanisms beyond those implicit in the Siegert operators. The impulse approximation is used to treat A currents and the calculation also takes into account the relativistic spin-orbit current . The results are shown in fig. 7a. The difference between the Bonn OBEPR and Paris results is 2-4 over most of the angular range . Only at forward angles is the Bonn prediction appreciably lower than the Paris curve. Also shown in fig. 7a are two more Bonn OBEP-R calculations performed by Schmitt and Arenh6Ve1 2° ) labelled `SchA' and `SchA+Rel' . This comparison gives an idea of the importance of the details of the calculation other than the potential . The SchA calculation differs from that of WiL in using a weaker p coupling constant and in omitting the A-MEC current. Both of these effects lead to a smaller cross section . The SchA -+- Rel calculation includes lowest-order relativistic effects beyond the spin-orbit term which again reduces the cross section over most of the angular range. It can be seen from fig. 7a that these changes produce effects which are at least as large as those produced by changing the potential . However the spread of the recent data is such that it cannot discriminate among the calculations. The calculation of Ying et a1 21) also uses the Bonn potential, but the treatment of the MEC additional to those contained in the Siegert operators uses an approximation which underestimates these contributions 22 ) and produces a result which is 30-50% below the data. Fig. 7b shows a series of calculations performed using the Paris potential . The results of Cambi et a!. 23 ) (CMR ), Jaus and Woolcock 14 ) (JaW) and Laget'6 ) are displayed together with the WiL-Paris calculation shown previously. The differences between WiL, JaW and CMR are essentially due to differences in the treatment of the isobar contributions 22 ) . The calculation of JaW differs from that of WiL in using a weaker yNA coupling and in employing a A-width even below the pion threshold where it should be absent. The CMR calculation employs a static treatment of the A-current which neglects its propagation in the nucleus. The resulting differences in their predictions are fairly large but again because of the spread of the data only the CMR result is clearly excluded . The calculation of Laget, on the other hand, is rather different being based on a Feynman diagram technique . The matrix elements are calculated directly with explicit
P.A. Wallace et al. / 2H(y, p)n
63 1
6 5 4 3 2 E u 5 4 3 2
Fig. 7. Comparison of recent data for the 2 H(7, p) n reaction at E; = 140 MeV with theoretical predictions using (a) the Bonn OBEP-R potential and (b) the Paris potential. References to the theoretical calculations are given in the text. The data are the same as those shown in fig. 6, except that the MIT results are not renormalised. expressions for the current densities. This is in contrast to the previous calculations which all used Siegert operators defined from the one-body charge density. The calculation uses a low-energy expansion of the nuclear electromagnetic currents which is Lorentz invariant to order (Prr/MN ) -2. The current density operators include the relativistic terms corresponding to the corrections introduced into the charge density by the other workers. The interaction is explicitly gauge invariant in the latest version of the calculation 16 ) and consistent wave functions derived from the Paris potential are used. All partial waves are implicitly included in the interaction and the final-state interactions have been calculated for S, P and D waves in the final state. The resultant cross section lies below the data over most of the angular range. Because of the different basis of the calculation it is not possible to say whether any specific feature of the calculation is responsible for the discrepancy.
632
P.A. Wallace et aL / 2N(y, p)n 6. Summary and conclusions
The angular differential cross section for the reaction 2My, p)n has been measured at photon energies between 133 and 158 MeV . The systematic uncertainty of the data is estimated to be 5°ßn and the statistical uncertainties are somewhat smaller. A detailed comparison of this data with that of other recent experiments indicates that our angular distribution shape agrees with that from MIT while the absolute normalisation differs by 8 which is within the combined systematic errors of the two experiments. On the other hand, if the data are compared with those from Frascati and TRIUMF one finds that the absolute magnitudes of the distributions are in reasonable agreement while the shapes differ significantly . We note that all the calculations tend more toward the flatter shape of this data and the MIT experiment rather than the Frascati or TRIUMF distributions which tend to be more sharply peaked around 90° . Taken together, however, the recent data define the shape and magnitude of the cross section to within a band of relative width 10°x. This represents a very considerable improvement upon the situation which existed previously but cannot be regarded as completely satisfactory. The data are good enough to permit criticism of some of the theoretical predictions on the grounds of their treatment of A-resonance and mediumrange MEC effects, but the experimental situation is not yet sufficiently well defined to allow a full evaluation of the theoretical calculations. The authors are grateful to the United Kingdom Science and Engineering Research Council and the Deutsche Forschungsgemeinschaft for supporting this work. The United Kingdom members of the collaboration also wish to thank the Institut fir Kernphysik, Maim University for the use of their facilities and for the assistance received during the course of the experiment . Three of us (P.A.W., S.N.D., and S.M.D.) 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. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)
J.D. Kellie et al., Nucl. Instr. Meth. A241 (1985) 153 I.J.D. MacGregor et al., Nucl. Instr. Meth. A262 (1987) 347 P.A. Wallace, Ph.D. thesis, University of Glasgow (1989), unpublished R.O. Owens, Nucl . Instr. Meth. A288 (1990) 574 J.M. Cameron et aL, Nucl. Phys. A453 (i986) 637 E. DeSanctis et al., Phys. Rev. C34 (1986) 413 P. Levl Sandri et al., Phys. Rev. C39 (1989) 1701 J.L. Matthews et al., to be published E.A. Whalin, B .D . Schriever and A.O. Hanson, Phys . Rev. 101 (1956) 377 R. Kose et al., Z. Phys . 202 (1967) 364 J. Buon et al., Phys . Lett. B26 (1968) 595 lu.A. Aleksandrov et al., Sov. Phys . JETP 6 (1958) 472 P. Dougan, V. Ramsay and W. Stiefler, Z. Phys. A276 (1976) 55 ; A280 (1977) 341 H. Arenh6vel, Z. Phys . A302 (1981) 25
P.A. Wallace et al. / 2H(y, p)n
14) 15) 16) 17) 18) 19) 20) 21) 22) 23)
633
W. Jaus and W.S. Woolcock, Nucl. i'hys. A473 (1987) 667; 685 J.M. Laget, Nucl . Phys. A312 (1978) 265 J.M. Laget, Can. J. Phys . 62 (1984) 1046 and private communication R. Machleidt, K. Holinde and Ch. Elster, Phys. Reports 149 (1987) 1 M. Lacombe et al., Phys . Rev. C21 (1980) 861 P. Wilhelm, W. Leidemann and H. Arenhövel, Few Body Systems 3 (1988) 111 and private communication K.-M. Schmitt and H. Arenhövel, Few-Body Systems 7 (1989) 95 S. Ying, E.M. Henley and G.A. Miller, Phys . Rev . C38 (1988) 1584 M. Sanzone and H. Arenhövel, Few-Body Systems Supplementum 3 (1991) A. Cambi, B. Mosconi and P. Ricci, Phys. Rev. Lett. G48 (1982) 462; J. of Phys. G10 (1984) L11 and private communication