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Analysing power for neutron-proton scattering at 14.1 MeV
Nuclear Ph,ysics A361 ( 198 1) 368 - 386 ; @ Not to be reproduced
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ANALYSING POWER FOR NEUTRON-PROTON SCATTERING AT 14.1MeV J. E. BROCK. A. CHISHOLM, Physics Departmenf,
J. C. DUDER ‘, R. GARREn
and J. L. POLETTI
Universiiy of Auckland, Private Bag, Auckland, New Zealand
Received I8 November 1980 Abstract: The analysing power A,(8) for neutron-proton
scattering has been measured at 14.1 MeV for cm. angles between 50° and 157°. A polarized neutron beam was produced by the reaction “H(&, n)4He at 110 keV, using polarized deuterons from an atomic beam polarized ion source. Liquid and plastic scintillators were used for proton targets and the scattered particles were detected in an array of plastic scintillators. Use of the associated alpha technique, multi-parameter recording ofevents and off-line computer treatment led to very low backgrounds. The results differ significantly from the predictions of the phase-shift analyses of Yale IV, Livermore X and Arndt et al. We find, however, excellent agreement with the predictions of the “Paris potential” of Lacombe et al. Existing n-p analysing power results up to 30 MeV are surveyed and found to be consistent. An attempt was made to look for an isospin splitting of the triplet P-wave phase shifts.
E
NUCLEAR
REACTIONS *H(fi, n), E = 14.1 MeV; measured .4,,(e); deduced spin-orbit phase-shift parameters and compared with proton-proton values.
1. Introduction Theories of the nucleon-nucleon interaction in terms of the exchange of bosom between the nucleons are now reaching the stage of being able to reproduce scattering observables to a good accuracy with only a small number OFfree parameters left to be adjusted. One such work is that of Lacombe et CZI.‘1, who have produced a potential which besides using one-pion exchange and o-exchange includes also two-pion exchange. These contributions are able to give a good description of the long- and medium-range forces without the need For any adjustable parameters. The short-range part is described phenomenologically using only five adjustable parameters, which were found by fitting 913 p-p scattering data points between 3 and 330 MeV and 2239 n-p scattering data points between 13 and 350 MeV. The x2 per degree of freedom for the p-p and the n-p scattering were 1.99 and 2.17, respectively. This model is referred to as the “Paris potential”. In spite of such impressive results the phase-shift analyses are still very important, not only as a way of summa~zing ex~rimenta~ results in a more or less model inde~ndent form, but also as an aid to the planning of future experiments. ’ Present address: Bell Laboratories, Holmdel, New Jersey. 368
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The nucleon-nucleon phase-shift analyses that have appeared over the last decade or so ‘- ‘) give in general a unique set of phases of quite good precision. However, even in the energy region below 30 MeV there are still some aspects that can benefit from further measurements of good accuracy. For example, there is the question of whether the usual expedience of assuming the isotopic spin triplet (T = 1) phase shifts obtained from proton-proton experiments to be accurate for the neutronproton system is justified. It is already well established 2-5) that the ‘S, phaseshift must be given different values for the p-p and n-p systems. At present, the triplet P-wave phase shifts 3P,, 1,2 are usually assumed in the analyses to be the same for both the p-p and n-p systems. However the analysis of Amdt et al. ‘) did use an approximate “charge splitting” although the data itself was not discriminating enough to distinguish between n-p and p-p phases. Thus, the predictions for the 3P phases for n-p scattering near 20 MeV depend essentially on an extrapolation downwards from higher energy p-p polarization experiments and the assumption of charge independence, an assumption already seen to be invalid for ‘S,. Since the analysing power in the 10 to 20 MeV region depends predominantly on a combination of the 3P phase shifts, measurements of this quantity are valuable. We present in this paper a measurement at 14.1 MeV of the neutron-proton analysing power A,(@. In the energy region below 30 MeV, a number of n-p A,, experiments of increasing accuracy have appeared 6- lg) over the last 20 years. These, together with the results of the present experiment are analysed in sects. 4 and 5. To a good approximation A,(O) has the form lo) A,(B) cc sin 8(d& + SA& cos fl), where AL and A& are combinations of the 3Po, 1,2 and 3D,,2,3 phase shifts, respectively. Thus we see that a measurement of A,(B) over a range of angles gives information on the 3D 1,2, 3 phases. This is important data, since the 3D phase shifts do not appear in proton-proton observables. Another parameter measurable only by n-p experiments and of some current interest, is cl, the coupling parameter between the 3S, and 3D, states. The major dependence of A,,(O) on a1 is given by an over-all factor 28)
multiplying the above equation for A,(B). Since .si is predicted by phase-shift analyses 3, ‘) and by a potential model r, z6) to be less than 19, this factor will differ from unity by less than 2 %. An over-all scale factor of this magnitude is not presently measurable (We give later an estimate of our scale factor error as 3 %.) The Coulomb splitting of A & between the p-p and n-p values near 25 MeV is estimated 4, as being about O.O8O,so if one is to look for this splitting an accuracy of about kO.02” is necessary, and it is this accuracy for which we aimed in the present experiment. (Incidentally, a challenge exists in the measurement of AIs for
370
J. E. Brock et al. 1 Analysing power
the p-p system. Even the very accurate p-p experiments at 6.14 MeV [ref. “)I and at 10 MeV [ref. “)I gave accuracies on AIs of only k0.031° and &O.ll”, respectively: the TUNL neutron-proton experiment 19) at 16.9 MeV gives ApLsto an accuracy of 5 0.012”.) These recent accurate n-p analysing power experiments from TUNL i9) gave an observable effect in the analysing power corresponding to the addition to the equation above of a term in cos’ 8 and this has been interpreted as suggesting that F-wave phase shifts are considerably larger than the predictions of phase-shift analyses. The various considerations in the above paragraphs imply that the 14 MeV n-p analysing power needs to be found, over as wide an angular range as possible, to an accuracy of at least 0.002, which with a typical beam polarization of about 0.5 means measuring asymmetries to 1 in 103. Apart from the problem of statistics, we have paid particular attention to the problem of reducing the background to which neutron experiments are particularly prone and to the elimination of spurious asymmetries arising from systematic errors. 2. Experimental method Some aspects of our method of the production of 14 MeV polarized neutrons and the scattering and detecting of them have been described fairly fully in an earlier publication “). Here, we summarize the main points and discuss some other points. 2.1. MEASUREMENT
OF VECTOR
ANALYSING
POWERS
The
differential cross section, o&0, 4) of the scattered particles in a reaction, with vector analysing power A,,(8), induced by particles with vector polarization P is given by: @I, 4) = o,(8) (1 + A,(W cos Q, where a,(B) is the cross section for an unpolarized beam and C$is the azimuthal angle. To find A,(8) one measures counting rates at Q, = 0 and 4 = 71(“left” and “right”). In practice, many problems in the determination of A,, particularly when neutrons are involved, are diminished very markedly if two detectors are used, placed symmetrically to left and right of the beam and if the beam polarization, P, is reversed periodically 23). One then measures relative rates L,, R, in the left and right counters with the spin “up” and rates L,, R, with the spin “down”. Then, independently of any beam monitor and of detector efficiencies, one has:
pqe) = where Y=
r-l r+l,
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There remains the problem of knowing the beam polarization. 2.2. THE POLARIZED
NEUTRON BEAM
We start with 150 keV vector polarized deuterons produced in a conventional atomic beam source “). Neutrons with energy 14.1 MeV are generated in the “H(d, Q4He reaction, in which the deuteron vector polarization is almost completely transferred to the neutron. The polarized deuteron source has three RF transition units, by means of which the polarization state of the deuterons can be selected. In particular, the deuteron vector polarization and hence the neutron polarization can be reversed by switching on or off the power to one or more of the RF cavities through which the deuterium atomic beam passes. This method of polarization reversal is preferable to that in which the magnetic field in the ioniser region is reversed. The latter method could cause changes in counting rate correlated with the beam polarization associated not with the nuclear scattering itself but rather with, for example, a change in the distribution of particles within the beam or a change in the gain of the photomultiplier detectors. We reverse the neutron polarization after a fixed number of n-p events, typically about every 5 min. While the RF oscillators are being switched, the data acquisition system is disabled and is not enabled again until it receives a signal from the RF cavities to indicate that the RF power has reached the required levels. The tritium target is in the form of a thin layer of tritiated titanium on a copper backing. The recoil a-particles from the 3H(d, n)4He reaction are detected in a thin rectangular sheet of the plastic scintillator NEl02A, whose size defines a cone or beam of neutrons for the scattering experiment. By measuring the tensor polarization P,, of the deuterons for certain sets of RF transitions we can estimate the neutron polarization to an accuracy of about 3 %, as we have previously argued 22). During the running of the analysing power experiments we monitor continuously the neutron polarization, using as polarimeter the neutron-carbon scattering 22). 2.3. SCATTERER AND DETECTOR SYSTEM
For most of the angular range (viz. 5 70” lab) the proton scatterers are those in the liquid scintillator NE213 and the scattered neutrons are detected in blocks of the plastic scintillator NE102A placed symmetrically to left and right of the neutron beam. In order to increase the effective counting rate, we usually use three or four pairs simultaneously at different angles. A triple coincidence is formed from the cc-particle from the 3H(d, n)4He reaction, the recoil proton in the scatterer and the neutron in the “left” and “right” detector. For each such triple coincidence we record event-by-event on magnetic tape a number
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J. E. Brock et al. J Analysing power
of parameters: polarization state (“up” or “down”) of the beam, detector number (giving angle and “left” or “right”), flight time from scatterer to side detector, pulse decay time in the scatterer (for pulse-shape discrimination), pulse height in the scatterer and pulse height in the side detector. Off-line computer treatment of these data enables us to obtain very clean pulse-height spectra in the scatterer, the background remaining all being attributable to multiple scattering 24). 2.4. BACKWARD
ANGLES MEASUREMENTS
For large scattering angles (> 70° lab) some problems appear with the above system. (i) The counting rate drops away steeply, due mainly to the cos 8 factor in the laboratory cross section. (ii) The scattered neutron energy becomes small and widely spread so that a broad time spectrum results. The broad energy spread of low-energy neutrons leads further to an uncertainty in the effective scattering angle for a given nominal position of the detectors. (iii) Multiple scattering contributes an appreciable fraction of the total events in the region of the recoil proton energy peak (about 16 y0 at 70° for the 50 mm diameter scatterer that we used for much of our work). This is in an angular region where we expect an asymmetry of the order of 10e3. Although our Monte Carlo simulation of the experiment 24) reproduces the shape of the spectrum quite well and leads us to believe that the multiple scattering background is essentially unpolarized here, we feel unhappy about subtracting such a large background. We are particularly concerned with getting believable data in this somewhat extreme angular region, because here the analysing power shows a sensitivity to a possible cos’ 8 term, which could suggest the influence of F-waves. A recent paper 19) has raised a certain amount of interest in this question. The use of a smaller diameter scintillator is not particularly helpful. The fraction of multiply scattered events would decrease linearly with the decreasing diameter, but the over-all rate of real events would decrease quadratically. Further, the proton recoil spectrum would become distorted because of the significant number of protons recoiling out of the scintillator volume. We solved these problems by using as scatterer a thin (2 mm) radiator of plastic scintillator (NE102A), detecting the protons recoiling out of this radiator at small angles to left and right in symmetrically placed pairs of similar pieces of scintillator. We again formed a fast triple coincidence (a-radiator-side detector). The amplitudes of the pulses from the radiator were added to those from each of the side detectors; the resulting spectra showed a well defined peak, with a background on the lowenergy side of less than 1 y0 of the peak height. Multiple scattering is now reduced to an insignificant level. Neutron-y discrimination on the radiator is now unnecessary since the probability of detecting the y-rays from the inelastic scattering of neutrons on carbon has become very small.
J. E. Brock et al. / Analysing power 2.5. NEUTRON
313
BEAM POLARIZATION
Measurement of the “left-right” asymmetry gives the product A,(@P,,, and the beam polarization P, has therefore to be determined independently. Our particular system allows this to be done simply. With the polarized ion source switched to produce tensor polarized deuterons, we measure Pz, by taking the ratio of neutrons counted in detectors near to 0” and 90”. The neutron polarization produced from vector polarized deuterons is simply related to P,,. As discussed more fully elsewhere 22), this technique gives P,, to an accuracy of about 3 %. Since the above measurement requires the switching of the deuteron polarization from the vector to the tensor mode, we made this measurement only occasionally, typically twice a day. In order to check that the neutron polarization was in fact remaining constant throughout the n-p analysing-power experiments we used a carbon polarization monitor 22) running simultaneously.
2.6. RUNNING
OF THE EXPERIMENT
- DETAILS OF SET-UP
The cylindrical scatterer scintillator was for most of the data collection 50 mm diameter and 75 mm high. For a few runs, particularly for the more forward angles, a 25 mm diameter, 100 mm high scintillator was used, to check that there were no gross size-dependent effects. In both cases the scatterer was at a distance of 1.2 m from the Ti-T target. The side detectors were usually 100 x 100 x 50 mm3 blocks of NE102 scintillator, with their 100 x 50 mm2 faces towards the scatterer, the 50 mm dimension being in the polar angle direction. The centre to centre distance between scatterer and side detector was usually 40 cm. Thus, the FWHM angle subtended was 7O. For some forward angle measurements, narrower side detectors were used. All scintillators were viewed by 56 AVP photomultipliers. The electronics and data handling are described in ref. 22). For the backwards angles (2 70“), the radiator was a 2 mm thick NE102 scintillator, with rectangular faces 50 x 25 mm’. This was at 60 cm from the Ti-T target. The side detectors for the recoiling protons were the same size as the radiator and at 20 cm from it. This gives essentially the same geometry as for the forwards angles. Radiator and side detectors were mounted in a light-tight box. Thin foils of aluminium prevented light from going from one scintillator to another. It was not necessary to evacuate the box. The electronics used for these back-angles measurements was similar to that used in the standard experiment and could be combined with it to give multi-parameter storage in the computer. (For some measurements we simply put windows on the time spectra and on the summed “radiator and side” pulse-height spectra and recorded the results on scalers. The four pulse-height spectra were sampled regularly to check for consistency and to look for background. We feel this procedure to be adequate in view of the - 1 % background.)
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3. Results
We present here the raw data, make any necessary corrections sources of error.
and examine
3.1. THE RAW DATA
As described fully elsewhere 22) the results are recorded event-by-event as sets of 3 matrices. After off-line computer treatment of these in which we separate neutrons from y-rays, provide a tight time of flight condition corrected for kinematic effects and set discrimination levels on the side detectors we obtain one-dimensional pulseheight spectra of the recoil protons in the scattering scintillator. A typical spectrum is shown in fig. 1. The background on either side of the peak is fully explained quantitatively by a Monte Carlo simulation of the experiment 24). The events accepted are those between the vertical arrows. The background under the peak is removed by using data obtained in the simulation: at small and at large angles a mere interpolation of the background between those measured on either side of the peak is not satisfactory. A spectrum from the backwards angle part of the experiment is shown in fig. 2. The abscissa is the sum of pulse heights from the target scintillator and a side (proton) detector.
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Fig. 2. Pulse-height spectrum for a large neutron scattering angle, where the recoil proton from a thin scintillator is detected in a second scintiliator, and the two pulses summed, to give the spectrum shown. This example is for 0 proton = 20°, corresponding to 0 neutron = 70°.
3.2. CORRECTIONS
AND ERRORS
(a) Inexact reversai o~~~tro~ spin: It is possible that the neutron spins will not be reversed exactly by the switching of the RF transition units in the polarized deuteron source. We estimated the difference in the analysing powers that would be measured with exact reversal (A) and inexact reversal (A’). For the case A = 0.02 (approp~ate to the present ex~riment) and for extreme cases of beam polar~ations with “spin up” of 0.6 and “spin down” of 0.4 we find A’-A N lo-‘, which is certainly a negligible effect. (b) Tensor-polarization in the vector polarized beam: For the production of polarized neutrons, we set the source to produce deuterons with pure vector polarization, P,. There is still, however, the possibility that there is some small amount of tensor ~larization Pz2 in the beam. The neutron polarization is then given by 22)
pn =
I-
P,
sin0
t_P2(cos 0) I?!)
where @is the angle between the deuteron spin and the direction in which the neutron is taken off (about 900 in our case). Measurements of P”) gave values of 5(0.02f0.01) at most. This gives a relative error of about k 1 % in the analysing power, in which the relative statistical error is already 10 % or greater. We therefore neglect this error. (c) ~ack@ro~d reactions: The possibilities for various reactions in the scatterer to contribute to the background have been discussed thoroughly already by, for example, Mutchler and Simmons lo). The only reaction that could be troublesome
J. E. Brock et al. / Analysing power
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at 14 MeV is the inelastic scattering of neutrons from carbon in the scatterer. As demonstrated earlier *‘), neutron-y discrimination on the scatterer removes these events. (d) Multiple scattering: The multiple scattering of neutrons on the carbon in the scatterer scintillator is potentially the most serious source of systematic error in our measurement. In an earlier paper 24) we have, however, shown that this effect is not too serious. In that work, we calculated an upper limit on the spurious asymmetry that would be induced by multiply-scattered events detected within the single-scattering n-p peak, and found that, except for very forward angles, the effect is at worst comparable with the statistical error that we are aiming for. We calculated also the asymmetries on backgrounds away from the peak. Since data on neutron-carbon polarizations did not exist in sufficient detail we did the calculations in a manner that would over-estimate all these asymmetries. From the experimental data we obtain a direct measurement of multiple-scattering asymmetries in the backgrounds and hence can express the extent of our overestimate of the effects in terms of the ratios r=
observed asymmetry in background simulated asymmetry in background’
We make the assumption that the overestimate is the a detector at a given scattering angle. We then calculate to the measured asymmetries in the single scattering times the spurious asymmetries from the simulation.
same at all pulse-heights for the corrections to be applied peaks as the products of r In fig. 3 we show the result,
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0.0
-O.ool-O.OOZ-0.003 -
-
-0.005 -
AUCKLAND
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-“.oo60 10
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20
30
40
50
60
70
80
90
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Fig. 3. The curve is our estimate of the spurious asymmetry induced by multiple scattering of neutrons on the carbon in the scatterer scintillator. Scatterer diameter is 50 mm. The points are from the calculation of ref. r9). These were for a scatterer diameter of 25 mm; we have doubled their results for comparison with our 50 mm result a4). The solid circles and crosses refer to the cases in which the analysing power of the 4.4 MeV level of carbon is taken to be non-zero or zero, respectively.
J. E. Brock et al. / Analysing power
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TABLE 1
Results of analysing power measurements dA( x 10’)
A( x 102)
e c.m.
K cs 50
50.6
61.8 68.6 81.1 90.8 102.6 121.1 141.0 138,9 156.6
cp 25
1.17& 1.43
2.11 rfi0.32 2.77kO.45 1.8720.25 2.073-0.36 l.SSf0.37 1.19kO.23 0.29kO.44 0.16+0.36 -0.07_10.36
2.47kO.64 1.87kO.47
1.52kO.45
4 50
4 25
0.22
0.11 0.07 0.06 0.04 0.02 0.01 0.00 0.00
0.14 0.11 0.07 0.04 0.02 0.01 0.00
0.0139~0.0145 0.02313_0.0032 0.0237rl: 0.0033 0.0194+0.0026 0.021 l&O.0036 0.0155;tO.O029 0.0120+0.0023 0.0029 jr 0.0044 0.~16~0.~36 -0.~7~0.~36
The values of A in columns 2 and 3 are for scatterer diameters of 50 mm and 25 mm respectively. The multiple scattering corrections, AA, of columns 4 and 5 are for these same scatterer sizes.
for our final estimate of the multiple scattering asymmetry, as a smoothed curve. The points represent the results of a recent calculation by the TUNL group r9) who had available a better approximation for the neutron carbon analysing power than we did. We conclude that the effect of multiple scattering is smalt, and quite well calculated. The curve of fig. 3 is used later (subsect. 3.4) to make small corrections for the multiple scattering effect. (e) Finite azimuthal angle: The experiment measures PA cos 4, where 4 is the angle between the polarization P and the normal to the scattering plane. The required average of cos 4 over the finite experimental geometry was found by dividing the scatterer and side detectors into a number of cells and calculating cos #J for pairs of cells. The values of A appearing in table 1 have been corrected for this effect. v> Mean scattering angh: The detectors were set at nominal scattering angles of 300, 40”, 50° etc. to an estimated accuracy of 0.2O. Finite geometry causes the effective average angles to differ appreciably from these nominal values. Data in the Monte Carlo simulation “3 were used to calculate the mean angles. 3.3. THE NEUTRON
BEAM ~~RIZA~ON
The neutron polarization from the “H(& Q4He reaction used here is found from measurements on the deuteron beam. With the RF transition units set to produce tensor polarized deuterons, the tensor component P,, is measured. Then for the n-p analysing power experiment with the transition units set to produce vector polarized deuterons, the resulting neutron polarization P, is given by P,, = jPZZ. We have already argued 22) that this procedure gives P, to a relative accuracy of 3 %.
378
J. E. Brock et al. i Andysing power
During the data collection, we normally attempt to run the experiment continuously for a number of weeks. The Pz, measurements, which require the interruption of the experiment, are usually taken twice daily. In order to be able to check the constancy of the neutron polarization during the actual data collection, we installed a neutron polarimeter downstream from the main scattering experiment and running simultaneously with it. This polarization monitor used neutron-carbon scattering at 45” (lab) as the analysing reaction. We used this monitor for two checks. First, for each “run”, we extracted an analysing power A,, from 1 r-1 A”, = --...-“_.E--$Pzzrn,+i ’ where rnc is the asymmetry for the polarization monitor, defined in a similar way to the asymmetry for the n-p scattering (see subsect. 2.1). This A,, gave consistent values for all the runs. The second test involved the actual magnitude of A,,. Since the flight path in our polarization monitor was too short for a time-of-flight separation of scattering from the ground state and the 4.4 MeV level of carbon, A,, corresponds to some average of the analysing power over these two levels. The analysing powers of these two levels have been measured at 14.2 MeV by a group at Base1 25). From their tabulated values, and from their time of flight spectra showing the relative numbers of elastic and inelastic events detected, we calculated a weighted average of the two anaiysing powers, which should be suitable for comparison with our A,, if we assume that our relative efgciencies for the detection of the two neutron groups is the same as it was at Basel. The A,, calculated from the Base1 experiment was -OSO+ 0.03 ; our measured value, averaged over all the runs was - 0.489 _+0.007. 3.4. RESULTS
The results of the n-p analysing power, A,(B). measurements are presented in table 1. The values quoted are averages of measurements taken over a span of five years. The angles given in column 1 are believed to be accurate to within 0.3O. They have been corrected for finite geometry effects. The values in colons 2 and 3 have been corrected for small geometrical effects. The multiple scattering corrections in columns 4 and 5 are taken from fig. 3. [That figure is for a 50 mm diameter scatterer; we take the correction for a 25 mm diameter one to be one-half of that for a 50 mm diameter one ‘“).I The values of A’ in column 6 are averages over the two sizes of scatterer, after the multiple scattering corrections have been applied. The final two measurements listed, at angles 138.9Oand 156.6O, were made using the “backwards angles” method with a thin radiator from which the recoil proton escaped and was detected in a separate scintillator. No multiple scattering corrections were made here, since they would be completely insignificant. The errors in columns 2 and 3 are purely statistical; those in column 6 include also
J. E. Brock et al. / Analysing power
319
a small contribution due to the multiple scattering correction. In addition, there is a 3 y0 relative error common to all points from the uncertainty in the polarization of the neutron beam ‘*). S’mce the maximum analysing power is 0.02, this scale error will contribute at most an extra standard deviation of 0.0006 to the essentially statistical errors listed in table 1; its effect is clearly not significant. Our measurements of the n-p analysing powers provide a further test on the magnitude of the multiple scattering effect. Although most of our measurements were made with a 50 mm diameter scatterer, giving A&e), we made also measurements at three angles with a 25 mm diameter scatterer, giving A25(0) (see table 1). For each of these three angles, Oi,we have calculated the difference A,Jf?J’- &(t$), using values corrected for multiple scattering, and then calculated the weighted average of these differences over the three angles. We find
40-A25 = + 0.0025 f 0.0037. (Incidently, if this quantity is calculated using values uncorrected for multiplescattering we find a value of +0.0021.) The major contribution to any multiplescattering induced asymmetry will arise from scattering from carbon in the scintillator, for which the analysing power is more than an order of magnitude greater than for n-p scattering. Since the n-C analysing power is negative in the angular region used here, the effect of the multiple scattering is to produce an asymmetry which is negative, as is shown both by our simulation 24) and by that of the TUNL
Ay re,
I
0.03
r. '\
---YALE
IY
*' /T
Fig. 4. The 14.1 MeV analysing power data, and a fit to the form A,(B) = (sin O/a(O)) (a,+a, cos 0). prediction of Yale and Livermore and from a meson model: the “Paris potential”.
The theoretical curves are from the phase-shift
380
3. E. Brock et al. / Anaiysing power
group 19). Further, the magnitude of the effect will be greater for a larger sized scatterer. Thus, if there were a multiple scattering asymmetry significantly larger than we estimate, the value of A,, - A,, would be negative. In fig. 4 we display our final results. The fit to the data has the form
A,(@= g
O),
(a+bcos
where a(6) is the n-p differential cross section. The curves from the phase-shift analyses are those of Yale-IV [ref. 2)] and of Livermore X [ref. ‘)I; the prediction from the analyses of Arndt et al. ‘) differs only slightly from that of Livermore X and is not plotted. The result of a calculation of the analysing power from the Paris potential 1,26) is also shown. 4. Analysis We have fitted our A,(B) results to the polynomial a(B
=
form
sin 6 c a, cos” S, n=O
where a(@) is the n-p differential cross section, for which we used values taken from the paper of Hopkins and Breit 27). The fit has been made for maxims n values, fi, of 1 and 2, giving polynomials terminating in cos B and in cos’ 8, the “two-term” and “three term” fits, respectively. The results are given in the upper part of table 2; xf is the chi-squared per degree of freedom. The “fit to the data” curve in fig. 4 uses the two -term fit. The data and the two fitted curves are displayed also in fig. 5 in the form of ~(0) A,(@ sin 0 against cos 8. We show atso the prediction of the Paris potential 26). Following the usual practice, the a, are interpreted in terms of the phase param-
Fits to a(B
TABLE2 = sin f&a,,+ a, cos 8 + a, cosz 0) and derived spin-orbit phase parameters Ais Zterm fit a0
a1
0.1055+0.0068 0.082 kO.017
a2
xf
0.50 0.340 * 0.022 0.052 +0.011
3-term fit 0.1114*0.0094 0.071 +0.021 -0.41 kO.45 0.45 0.333 +0.042 0.045 +0.013 -0.007 +0.008
J. E. Brock et al. /
Fig. 5. Fit of ~e)~~(~)~s~n B to ~~y~#rnin~s
~nalysing
power
in cos 8 and comparison with the p~diction potential.
381
of the Paris
eters AL representing combinations of triplet f-wave phase shifts arising from the spin-orbit part of the nucleon-nucleon interaction. Good approximations for the A& are 28):
where k2 is the c.m. wave alar of the nucleons. Using the LRL-K values 3>of the phase parameters 3S, and e1 we get the dis values shown in the lower part of table 2. We make a few remarks on the F-wave phase parameter, d&,. Firstly the inclusion of a third term, a2eos2 8 in the expression for ~(~)~~(~)leads to a greatly increased error in the P-wave parameter A Es. This arises partly because of the extra parameter, but also because of the large u~~~~~ty in a,, which appears in the expression for Ah. S~ondly~ if the pha~-s~~ analyses of Yale IV [ref. ‘)J Live~ore-X [ref. 3)] and Arndt et al, “) and the potential model prediction of Lacombe et al. ‘) give the correct order of magnitude for dz,, then the contributions to the cos2 6 term from A& and from the P- and D-wave combinations, are of similar magnitudes 28). Hence, it is not a good approximation to interpret the coeficient a2 in terms of dk only. In view of these remarks, and with the present accuracy of the data, we feel that the “two-term” form of the fit is the most realistic.
J. E. Brock et al. / Analysing power
382
^, al
E
c
1.0
a? a
1 2 3 L 5 6
(9117,
pq,-&
10 8 7 9 HAMBURG TUBINGEN TUNL ( DAVIS IlpBOl 19151 119781 I19771
I21 L
O10
HARWELL (1965, LOS AlAMCtS1l963~711 7.9.x) AUCKLANU 119721 HIROSHIMA119721 CAPE TOWN 119741 VIRGINIA(197LI
I
15
11 PRESENT WORK
I
25 ENERGY I MeV
30
20
I
35
1
Fig. 6. Spin-orbit phase parameters Ah and AD, deduced from existing n-p anatysing power experiments below 35 MeV. The curve for the P-wave case is a fit of the form & = nE”.
In order to compare the various n-p analysing-power experiments in the energy range up to about 30 MeV, we plot in fig. 6 the Als and A& values found from these experiments as a function of the neutron (laboratory) energy. [The Cape Town results 14) at energies of 16.4 MeV and 21.6 MeV have been reduced from the published values by factors of 0.76 and 0.84, respectively. This is because the magnitudes of the neutron beam polarizations should be modified by such factors in view of more recent work 29) on the source reaction polarization.] We have made a least squares fit of the A& points to a function of the form
where E is the neutron (laboratory) degrees ;
energy. We find, for E in MeV, and ApLsin
a = (2.5kO.4) x 10-3,
n = 1.86_+0.06,
with a x2 per degree of freedom of 1A. It is seen that there is quite good consistency among the results. The good agreement of the Cape Town results with the other measurements is significant since this experiment used techniques quite different from those used in all the others. In particular, the targets used as proton scatterers had dimensions of some millimetres instead of the more usual dimensions of some tens of miliimetres, implying that multiple scattering of the neutrons in the targets had no significant influence on the measured analysing powers. In fig. 7 we compare the experimental and phase-shift results for A& over the
J. E. Erock et al. / Analysing power
-
383
FIT TO EXRRIMENTS
Fig. 7. Comparison of phase-shift predictions for Ats with the experimentally determined curve of fig. 6.
ERLANGEN *’ 1 MADISON ?’ I ERLANGEN ” I PRESENT WORK
Fig. 8. Comparison of P-wave spin-orbit parameter A pLsdeduced from p-p and from n-p analysing power experiments. The points and broken curve iabelled “Paris” are from the Paris potential. The solid curve labelled “N-P Fit” is an extrapolation to lower energies of the curve fitted to n-p data in fig. 6. All the points marked with crosses are from p-p experiments and all those with solid dots are from n-p experiments.
TABLE 3 Isotopic spin splittings of P-waves in phase-shift analyses
Ref.
Energy
Amdt et al. ‘) Amdt et al. ‘) Bohannon et al. 4,
10 MeV 25 MeV 25 MeV
APls(np)- &(PP) O.OY 0.100 O.OfYJ
384
J. E. Brock et al. 1 Ana/ydng power
energy range 10 MeV to 30 MeV. The experimental result used is the curve fitted to the data points in fig. 6. The phase-shift results plotted are those of Yale-IV and Livermore-X; the results from Arndt et al. lie very close to those of Livermore-X and it is not practicable to plot them on the same graph. We have attempted to compare the values of Ats found from n-p and from p-p scattering, with the intention of looking for an isotopic spin dependence of the P-waves in the region below 20 MeV. In fig. 8 we show recent precise n-p results from TUNL iq) and from the present work at energies from 13.5 MeV to 16.9 MeV, and an older less precise result from Los Alamos ‘O) at I1 MeV. On the same figure are the only p-p results below 20 MeV. The p-p points labelled (1) and (2), of refs. 20,21), are those mentioned earlier in the introduction and use as input data differential cross sections and analysing powers. The point labelled (3) comes from a work very recently reported by Obermeyer et al. 31) of Erlangen. They have measured the p-p spin-correlation parameter A,, at 9.57 MeV and incorporated this in a phase-shift analysis near this energy. The analysing power used was that of the Madison group 21) but with a more recent measurement of the differential cross-section than was available to the Madison group for their phase-shift analysis. As a result, the error in the value of ALs for p-p scattering near 10 MeV is reduced by a factor of about 3. Unfortunately all of these p-p experiments are at energies lower than those of the n-p experiments, making a direct comparison impossible. However, we can make an indirect comparison by extrapoIating down to these energies our fit to the higher energy n-p data. The consistent difference between the n-p and p-p values of AIs shown in fig. 8 is not likely to be due to systematic experimental errors since the experiments come from different laboratories and use different techniques. The weakness in the comparison, of course, lies in the need to extrapolate the n-p data down to the region of the p-p data points, but we feel this procedure to be sufficiently accurate. For a comparison with theory, we show in table 3 the values of A~S(np)-A~s(pp) used in phase-shift analyses at two energies in this region. We see that although the experiments and phase-shift analyses find a similar magnitude of splitting, the sign of the effect is opposite. In fig. 8 we show also the predictions of the Paris potential 26*30) for AIS; these are seen to agree very well with the n-p measurements.
5. Conclusions As a result of Monte Carlo simulations of n-p analysing power experiments 1g*24) and of some measurements both in the present work and elsewhere ‘“) the effects of multiple scattering of the neutrons in the proton targets are quite well understood. It is clear that such effects present no serious problems to confidence in the results of n-p A,(@) me~urements, even at the high accuracies presently being achieved.
J. E. Brock et al.
385
/ Analysing power
A survey of all published n-p A,,(0) results over the energy range 10 MeV to 30 MeV shows that there is a remarkably good internal consistency among them. Our measurements at 14.1 MeV show small but definite disagreement with the phase-shift predictions (see figs. 4 and 7) for the P-waves and D-waves. We do, however, find excellent agreement with the predictions of the Paris potential, a model using only five adjustable parameters. The question of the possibility of the F-wave phase-shift combination AIs being much larger than all predictions r9, X* “) is not clearly resolved by our measurements. The analysis at the end of sect. 4 presents the first experimental evidence for an isotopic spin splitting of the triplet P-wave phase-shifts but in the opposite sense to that used in the phase-shift analyses of Bohannon et al. 4, and of Arndt et al. 5). The main requirement for investigating this question further is for accurate p-p analysing power measurements, preferably in the energy range 14 MeV to 17 MeV. This work was partially Committee of New Zealand.
supported
by funds from
the University
Grants
References I) M. Lacombe, B. Lo&au, J. M. Richard, R. Vinh Mau, J. C&e, P. Pires and R. de Tourreil, Phys. Rev. C21 (1980) 861 2) R. E. Seamon, K. A. Friedman, G. Breit, R. D. Haracz, J. M. Holt and A. Prakash, Phys. Rev. 165 (1968) 1579 3) M. H. MacGregor, R. A.Amdt and R. M. Wright, Phys. Rev. 182 (1969) 1714 4) G. E. Bohannon, T. Burt and P. Signell, Phys. Rev. Cl3 (1976) 1816 5) R. A. Amdt, R. H. Hackman and L. D. Roper, Phys. Rev. Cl5 (1977) 1002 6) W. Benenson, R. L. Walter and T. H. May, Phys. Rev. Lett. 8 (1962) 66 7) R. B. Perkins and J. E. Simmons, Phys. Rev. 130 (1963) 272 8) A. Langsford, P. H. Bowen, G. C. Cox and G. B. Huxtable, Nucl. Phys. 74 (1965) 241 9) J. J. Malanify, P. J. Bendt, J. R. Roberts and J. E. Simmons, Phys. Rev. Lett. 17 (1966) 481 10) G. S. Mutchler and J. E. Simmons, Phys. Rev. C4 (1971) 67 11) N. Ryu, J. Sanada, H. Hasai, D. C. Worth, M. Nishi, T. Hasegawa, H. Ueno, M. Seki, K. Iwatani, Y. Nojiri and K. Kondo, Nucl. Phys. A180 (1972) 657 12) R. Garrett, A. Chisholm, D. Brown, J. C. Duder and H. N. Btirgisser, Nucl. Phys. Al% (1972) 421 13) C. L. Morris, T. K. G’Malley, J. W. May and S. T. Thornton, Phys. Rev. C9 (1974) 924 14) D. T. L. Jones and F. D. Brooks, Nucl. Phys. A222 (1974) 79 15) R. A. Eldred, B. E. Bonner and T. A. Cahill, Phys. Rev. Cl2 (1975) 1717 16) B. T. L. Leemann, R. Casparis, M. Preiswerk, H. Rudin, R. Wagner and P. E. Zupranski, Proc. 4th Int. Symp. on polarization phenomena in nuclear reactions, Zurich 1975, p. 437 17) R. Fischer, F. Kienle, H. 0. Klages, R. Maschuw and B. Zeitnitz, Nucl. Phys. At8L (1977) 189 18) W. Steinkilberg, Dissertation, University of Ttibingen, 1978 19) W. Tomow, P. W. Lisowski, R. C. Byrd and R. L. Walter, Phys. Rev. Lett. 39 (1977) 915; Nucl. Phys. A340 (1980) 34 20) G. Bittner and W. Kretschmer, Phys. Rev. Lett. 43 (1979) 330 21) J. D. Hutton, W. Haeberli, L. D. Knutson and P. Signell, Phys. Rev. Lett. 35 (1975) 429 22) J. E. Brock, A. Chisholm, J. C. Duder and R. Garrett, Nucl. Instr. 164(1979) 311 23) R. C. Hanna, Proc. 2nd Int. Symp. on polarization phenomena in Nuclear Reactions, Karlsruhe 1965, p. 280 24) J. E. Brock, A. Chishohn, J. C. Duder and R. Garrett, Nucl. Instr. 138 (1976) 537
386
J. E. hock
et al. / Analysing power
25) R. Casparis, B. T. L. Leemann, M. Preiswerk, H. Rudin, R. Wagner and P. Zupranski, Nucl. Phys.
A263 (1976) 285 26) J. Cot& M. Lacombe, B. Loiseau, P. Pirts, R. de Tourreil and R. Vihn Mau, Proc. 5th Int. Symp. on polarization phenomena in Nuclear Physics, Santa Fe, 1980 (in press) 27) J. C. Hopkins and G. Breit, Nucl. Data Tables A9 (1971) 137 28) A. Chisholm, J. C. Duder, R. Garrett and J. L. Poletti, Phys. Rev. C21 (1980) 1653 29) J. R. Smith and S. T. Thornton, Nucl. Phys. A187 (1972) 433 30) J. CbtC, P. Pirts, R. de Tourreil, M. Lacombe, B. Loiseau and R. Vinh Mau, Phys. Rev. Lett. 44 (1980) 1031 31) H. Obermeyer, H. Kuiper, B. Seidler and K. Frank, Nucl. Phys. A344 (1980) 75
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ANALYSING POWER FOR NEUTRON-PROTON SCATTERING AT 14.1MeV J. E. BROCK. A. CHISHOLM, Physics Departmenf,
J. C. DUDER ‘, R. GARREn
and J. L. POLETTI
Universiiy of Auckland, Private Bag, Auckland, New Zealand
Received I8 November 1980 Abstract: The analysing power A,(8) for neutron-proton
scattering has been measured at 14.1 MeV for cm. angles between 50° and 157°. A polarized neutron beam was produced by the reaction “H(&, n)4He at 110 keV, using polarized deuterons from an atomic beam polarized ion source. Liquid and plastic scintillators were used for proton targets and the scattered particles were detected in an array of plastic scintillators. Use of the associated alpha technique, multi-parameter recording ofevents and off-line computer treatment led to very low backgrounds. The results differ significantly from the predictions of the phase-shift analyses of Yale IV, Livermore X and Arndt et al. We find, however, excellent agreement with the predictions of the “Paris potential” of Lacombe et al. Existing n-p analysing power results up to 30 MeV are surveyed and found to be consistent. An attempt was made to look for an isospin splitting of the triplet P-wave phase shifts.
E
NUCLEAR
REACTIONS *H(fi, n), E = 14.1 MeV; measured .4,,(e); deduced spin-orbit phase-shift parameters and compared with proton-proton values.
1. Introduction Theories of the nucleon-nucleon interaction in terms of the exchange of bosom between the nucleons are now reaching the stage of being able to reproduce scattering observables to a good accuracy with only a small number OFfree parameters left to be adjusted. One such work is that of Lacombe et CZI.‘1, who have produced a potential which besides using one-pion exchange and o-exchange includes also two-pion exchange. These contributions are able to give a good description of the long- and medium-range forces without the need For any adjustable parameters. The short-range part is described phenomenologically using only five adjustable parameters, which were found by fitting 913 p-p scattering data points between 3 and 330 MeV and 2239 n-p scattering data points between 13 and 350 MeV. The x2 per degree of freedom for the p-p and the n-p scattering were 1.99 and 2.17, respectively. This model is referred to as the “Paris potential”. In spite of such impressive results the phase-shift analyses are still very important, not only as a way of summa~zing ex~rimenta~ results in a more or less model inde~ndent form, but also as an aid to the planning of future experiments. ’ Present address: Bell Laboratories, Holmdel, New Jersey. 368
J. E. Brock et al. / Analysing power
369
The nucleon-nucleon phase-shift analyses that have appeared over the last decade or so ‘- ‘) give in general a unique set of phases of quite good precision. However, even in the energy region below 30 MeV there are still some aspects that can benefit from further measurements of good accuracy. For example, there is the question of whether the usual expedience of assuming the isotopic spin triplet (T = 1) phase shifts obtained from proton-proton experiments to be accurate for the neutronproton system is justified. It is already well established 2-5) that the ‘S, phaseshift must be given different values for the p-p and n-p systems. At present, the triplet P-wave phase shifts 3P,, 1,2 are usually assumed in the analyses to be the same for both the p-p and n-p systems. However the analysis of Amdt et al. ‘) did use an approximate “charge splitting” although the data itself was not discriminating enough to distinguish between n-p and p-p phases. Thus, the predictions for the 3P phases for n-p scattering near 20 MeV depend essentially on an extrapolation downwards from higher energy p-p polarization experiments and the assumption of charge independence, an assumption already seen to be invalid for ‘S,. Since the analysing power in the 10 to 20 MeV region depends predominantly on a combination of the 3P phase shifts, measurements of this quantity are valuable. We present in this paper a measurement at 14.1 MeV of the neutron-proton analysing power A,(@. In the energy region below 30 MeV, a number of n-p A,, experiments of increasing accuracy have appeared 6- lg) over the last 20 years. These, together with the results of the present experiment are analysed in sects. 4 and 5. To a good approximation A,(O) has the form lo) A,(B) cc sin 8(d& + SA& cos fl), where AL and A& are combinations of the 3Po, 1,2 and 3D,,2,3 phase shifts, respectively. Thus we see that a measurement of A,(B) over a range of angles gives information on the 3D 1,2, 3 phases. This is important data, since the 3D phase shifts do not appear in proton-proton observables. Another parameter measurable only by n-p experiments and of some current interest, is cl, the coupling parameter between the 3S, and 3D, states. The major dependence of A,,(O) on a1 is given by an over-all factor 28)
multiplying the above equation for A,(B). Since .si is predicted by phase-shift analyses 3, ‘) and by a potential model r, z6) to be less than 19, this factor will differ from unity by less than 2 %. An over-all scale factor of this magnitude is not presently measurable (We give later an estimate of our scale factor error as 3 %.) The Coulomb splitting of A & between the p-p and n-p values near 25 MeV is estimated 4, as being about O.O8O,so if one is to look for this splitting an accuracy of about kO.02” is necessary, and it is this accuracy for which we aimed in the present experiment. (Incidentally, a challenge exists in the measurement of AIs for
370
J. E. Brock et al. 1 Analysing power
the p-p system. Even the very accurate p-p experiments at 6.14 MeV [ref. “)I and at 10 MeV [ref. “)I gave accuracies on AIs of only k0.031° and &O.ll”, respectively: the TUNL neutron-proton experiment 19) at 16.9 MeV gives ApLsto an accuracy of 5 0.012”.) These recent accurate n-p analysing power experiments from TUNL i9) gave an observable effect in the analysing power corresponding to the addition to the equation above of a term in cos’ 8 and this has been interpreted as suggesting that F-wave phase shifts are considerably larger than the predictions of phase-shift analyses. The various considerations in the above paragraphs imply that the 14 MeV n-p analysing power needs to be found, over as wide an angular range as possible, to an accuracy of at least 0.002, which with a typical beam polarization of about 0.5 means measuring asymmetries to 1 in 103. Apart from the problem of statistics, we have paid particular attention to the problem of reducing the background to which neutron experiments are particularly prone and to the elimination of spurious asymmetries arising from systematic errors. 2. Experimental method Some aspects of our method of the production of 14 MeV polarized neutrons and the scattering and detecting of them have been described fairly fully in an earlier publication “). Here, we summarize the main points and discuss some other points. 2.1. MEASUREMENT
OF VECTOR
ANALYSING
POWERS
The
differential cross section, o&0, 4) of the scattered particles in a reaction, with vector analysing power A,,(8), induced by particles with vector polarization P is given by: @I, 4) = o,(8) (1 + A,(W cos Q, where a,(B) is the cross section for an unpolarized beam and C$is the azimuthal angle. To find A,(8) one measures counting rates at Q, = 0 and 4 = 71(“left” and “right”). In practice, many problems in the determination of A,, particularly when neutrons are involved, are diminished very markedly if two detectors are used, placed symmetrically to left and right of the beam and if the beam polarization, P, is reversed periodically 23). One then measures relative rates L,, R, in the left and right counters with the spin “up” and rates L,, R, with the spin “down”. Then, independently of any beam monitor and of detector efficiencies, one has:
pqe) = where Y=
r-l r+l,
J. E. Brock et al. / Analysing
power
371
There remains the problem of knowing the beam polarization. 2.2. THE POLARIZED
NEUTRON BEAM
We start with 150 keV vector polarized deuterons produced in a conventional atomic beam source “). Neutrons with energy 14.1 MeV are generated in the “H(d, Q4He reaction, in which the deuteron vector polarization is almost completely transferred to the neutron. The polarized deuteron source has three RF transition units, by means of which the polarization state of the deuterons can be selected. In particular, the deuteron vector polarization and hence the neutron polarization can be reversed by switching on or off the power to one or more of the RF cavities through which the deuterium atomic beam passes. This method of polarization reversal is preferable to that in which the magnetic field in the ioniser region is reversed. The latter method could cause changes in counting rate correlated with the beam polarization associated not with the nuclear scattering itself but rather with, for example, a change in the distribution of particles within the beam or a change in the gain of the photomultiplier detectors. We reverse the neutron polarization after a fixed number of n-p events, typically about every 5 min. While the RF oscillators are being switched, the data acquisition system is disabled and is not enabled again until it receives a signal from the RF cavities to indicate that the RF power has reached the required levels. The tritium target is in the form of a thin layer of tritiated titanium on a copper backing. The recoil a-particles from the 3H(d, n)4He reaction are detected in a thin rectangular sheet of the plastic scintillator NEl02A, whose size defines a cone or beam of neutrons for the scattering experiment. By measuring the tensor polarization P,, of the deuterons for certain sets of RF transitions we can estimate the neutron polarization to an accuracy of about 3 %, as we have previously argued 22). During the running of the analysing power experiments we monitor continuously the neutron polarization, using as polarimeter the neutron-carbon scattering 22). 2.3. SCATTERER AND DETECTOR SYSTEM
For most of the angular range (viz. 5 70” lab) the proton scatterers are those in the liquid scintillator NE213 and the scattered neutrons are detected in blocks of the plastic scintillator NE102A placed symmetrically to left and right of the neutron beam. In order to increase the effective counting rate, we usually use three or four pairs simultaneously at different angles. A triple coincidence is formed from the cc-particle from the 3H(d, n)4He reaction, the recoil proton in the scatterer and the neutron in the “left” and “right” detector. For each such triple coincidence we record event-by-event on magnetic tape a number
372
J. E. Brock et al. J Analysing power
of parameters: polarization state (“up” or “down”) of the beam, detector number (giving angle and “left” or “right”), flight time from scatterer to side detector, pulse decay time in the scatterer (for pulse-shape discrimination), pulse height in the scatterer and pulse height in the side detector. Off-line computer treatment of these data enables us to obtain very clean pulse-height spectra in the scatterer, the background remaining all being attributable to multiple scattering 24). 2.4. BACKWARD
ANGLES MEASUREMENTS
For large scattering angles (> 70° lab) some problems appear with the above system. (i) The counting rate drops away steeply, due mainly to the cos 8 factor in the laboratory cross section. (ii) The scattered neutron energy becomes small and widely spread so that a broad time spectrum results. The broad energy spread of low-energy neutrons leads further to an uncertainty in the effective scattering angle for a given nominal position of the detectors. (iii) Multiple scattering contributes an appreciable fraction of the total events in the region of the recoil proton energy peak (about 16 y0 at 70° for the 50 mm diameter scatterer that we used for much of our work). This is in an angular region where we expect an asymmetry of the order of 10e3. Although our Monte Carlo simulation of the experiment 24) reproduces the shape of the spectrum quite well and leads us to believe that the multiple scattering background is essentially unpolarized here, we feel unhappy about subtracting such a large background. We are particularly concerned with getting believable data in this somewhat extreme angular region, because here the analysing power shows a sensitivity to a possible cos’ 8 term, which could suggest the influence of F-waves. A recent paper 19) has raised a certain amount of interest in this question. The use of a smaller diameter scintillator is not particularly helpful. The fraction of multiply scattered events would decrease linearly with the decreasing diameter, but the over-all rate of real events would decrease quadratically. Further, the proton recoil spectrum would become distorted because of the significant number of protons recoiling out of the scintillator volume. We solved these problems by using as scatterer a thin (2 mm) radiator of plastic scintillator (NE102A), detecting the protons recoiling out of this radiator at small angles to left and right in symmetrically placed pairs of similar pieces of scintillator. We again formed a fast triple coincidence (a-radiator-side detector). The amplitudes of the pulses from the radiator were added to those from each of the side detectors; the resulting spectra showed a well defined peak, with a background on the lowenergy side of less than 1 y0 of the peak height. Multiple scattering is now reduced to an insignificant level. Neutron-y discrimination on the radiator is now unnecessary since the probability of detecting the y-rays from the inelastic scattering of neutrons on carbon has become very small.
J. E. Brock et al. / Analysing power 2.5. NEUTRON
313
BEAM POLARIZATION
Measurement of the “left-right” asymmetry gives the product A,(@P,,, and the beam polarization P, has therefore to be determined independently. Our particular system allows this to be done simply. With the polarized ion source switched to produce tensor polarized deuterons, we measure Pz, by taking the ratio of neutrons counted in detectors near to 0” and 90”. The neutron polarization produced from vector polarized deuterons is simply related to P,,. As discussed more fully elsewhere 22), this technique gives P,, to an accuracy of about 3 %. Since the above measurement requires the switching of the deuteron polarization from the vector to the tensor mode, we made this measurement only occasionally, typically twice a day. In order to check that the neutron polarization was in fact remaining constant throughout the n-p analysing-power experiments we used a carbon polarization monitor 22) running simultaneously.
2.6. RUNNING
OF THE EXPERIMENT
- DETAILS OF SET-UP
The cylindrical scatterer scintillator was for most of the data collection 50 mm diameter and 75 mm high. For a few runs, particularly for the more forward angles, a 25 mm diameter, 100 mm high scintillator was used, to check that there were no gross size-dependent effects. In both cases the scatterer was at a distance of 1.2 m from the Ti-T target. The side detectors were usually 100 x 100 x 50 mm3 blocks of NE102 scintillator, with their 100 x 50 mm2 faces towards the scatterer, the 50 mm dimension being in the polar angle direction. The centre to centre distance between scatterer and side detector was usually 40 cm. Thus, the FWHM angle subtended was 7O. For some forward angle measurements, narrower side detectors were used. All scintillators were viewed by 56 AVP photomultipliers. The electronics and data handling are described in ref. 22). For the backwards angles (2 70“), the radiator was a 2 mm thick NE102 scintillator, with rectangular faces 50 x 25 mm’. This was at 60 cm from the Ti-T target. The side detectors for the recoiling protons were the same size as the radiator and at 20 cm from it. This gives essentially the same geometry as for the forwards angles. Radiator and side detectors were mounted in a light-tight box. Thin foils of aluminium prevented light from going from one scintillator to another. It was not necessary to evacuate the box. The electronics used for these back-angles measurements was similar to that used in the standard experiment and could be combined with it to give multi-parameter storage in the computer. (For some measurements we simply put windows on the time spectra and on the summed “radiator and side” pulse-height spectra and recorded the results on scalers. The four pulse-height spectra were sampled regularly to check for consistency and to look for background. We feel this procedure to be adequate in view of the - 1 % background.)
314
J. E. Brock et al. / Analysing power
3. Results
We present here the raw data, make any necessary corrections sources of error.
and examine
3.1. THE RAW DATA
As described fully elsewhere 22) the results are recorded event-by-event as sets of 3 matrices. After off-line computer treatment of these in which we separate neutrons from y-rays, provide a tight time of flight condition corrected for kinematic effects and set discrimination levels on the side detectors we obtain one-dimensional pulseheight spectra of the recoil protons in the scattering scintillator. A typical spectrum is shown in fig. 1. The background on either side of the peak is fully explained quantitatively by a Monte Carlo simulation of the experiment 24). The events accepted are those between the vertical arrows. The background under the peak is removed by using data obtained in the simulation: at small and at large angles a mere interpolation of the background between those measured on either side of the peak is not satisfactory. A spectrum from the backwards angle part of the experiment is shown in fig. 2. The abscissa is the sum of pulse heights from the target scintillator and a side (proton) detector.
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J. E. hock 15000,
er at. / Andysing power
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Fig. 2. Pulse-height spectrum for a large neutron scattering angle, where the recoil proton from a thin scintillator is detected in a second scintiliator, and the two pulses summed, to give the spectrum shown. This example is for 0 proton = 20°, corresponding to 0 neutron = 70°.
3.2. CORRECTIONS
AND ERRORS
(a) Inexact reversai o~~~tro~ spin: It is possible that the neutron spins will not be reversed exactly by the switching of the RF transition units in the polarized deuteron source. We estimated the difference in the analysing powers that would be measured with exact reversal (A) and inexact reversal (A’). For the case A = 0.02 (approp~ate to the present ex~riment) and for extreme cases of beam polar~ations with “spin up” of 0.6 and “spin down” of 0.4 we find A’-A N lo-‘, which is certainly a negligible effect. (b) Tensor-polarization in the vector polarized beam: For the production of polarized neutrons, we set the source to produce deuterons with pure vector polarization, P,. There is still, however, the possibility that there is some small amount of tensor ~larization Pz2 in the beam. The neutron polarization is then given by 22)
pn =
I-
P,
sin0
t_P2(cos 0) I?!)
where @is the angle between the deuteron spin and the direction in which the neutron is taken off (about 900 in our case). Measurements of P”) gave values of 5(0.02f0.01) at most. This gives a relative error of about k 1 % in the analysing power, in which the relative statistical error is already 10 % or greater. We therefore neglect this error. (c) ~ack@ro~d reactions: The possibilities for various reactions in the scatterer to contribute to the background have been discussed thoroughly already by, for example, Mutchler and Simmons lo). The only reaction that could be troublesome
J. E. Brock et al. / Analysing power
376
at 14 MeV is the inelastic scattering of neutrons from carbon in the scatterer. As demonstrated earlier *‘), neutron-y discrimination on the scatterer removes these events. (d) Multiple scattering: The multiple scattering of neutrons on the carbon in the scatterer scintillator is potentially the most serious source of systematic error in our measurement. In an earlier paper 24) we have, however, shown that this effect is not too serious. In that work, we calculated an upper limit on the spurious asymmetry that would be induced by multiply-scattered events detected within the single-scattering n-p peak, and found that, except for very forward angles, the effect is at worst comparable with the statistical error that we are aiming for. We calculated also the asymmetries on backgrounds away from the peak. Since data on neutron-carbon polarizations did not exist in sufficient detail we did the calculations in a manner that would over-estimate all these asymmetries. From the experimental data we obtain a direct measurement of multiple-scattering asymmetries in the backgrounds and hence can express the extent of our overestimate of the effects in terms of the ratios r=
observed asymmetry in background simulated asymmetry in background’
We make the assumption that the overestimate is the a detector at a given scattering angle. We then calculate to the measured asymmetries in the single scattering times the spurious asymmetries from the simulation.
same at all pulse-heights for the corrections to be applied peaks as the products of r In fig. 3 we show the result,
I
O.OOl*MS
0.0
-O.ool-O.OOZ-0.003 -
-
-0.005 -
AUCKLAND
i I
-“.oo60 10
I
I
I
I
I
I
I
20
30
40
50
60
70
80
90
eLAB
Fig. 3. The curve is our estimate of the spurious asymmetry induced by multiple scattering of neutrons on the carbon in the scatterer scintillator. Scatterer diameter is 50 mm. The points are from the calculation of ref. r9). These were for a scatterer diameter of 25 mm; we have doubled their results for comparison with our 50 mm result a4). The solid circles and crosses refer to the cases in which the analysing power of the 4.4 MeV level of carbon is taken to be non-zero or zero, respectively.
J. E. Brock et al. / Analysing power
317
TABLE 1
Results of analysing power measurements dA( x 10’)
A( x 102)
e c.m.
K cs 50
50.6
61.8 68.6 81.1 90.8 102.6 121.1 141.0 138,9 156.6
cp 25
1.17& 1.43
2.11 rfi0.32 2.77kO.45 1.8720.25 2.073-0.36 l.SSf0.37 1.19kO.23 0.29kO.44 0.16+0.36 -0.07_10.36
2.47kO.64 1.87kO.47
1.52kO.45
4 50
4 25
0.22
0.11 0.07 0.06 0.04 0.02 0.01 0.00 0.00
0.14 0.11 0.07 0.04 0.02 0.01 0.00
0.0139~0.0145 0.02313_0.0032 0.0237rl: 0.0033 0.0194+0.0026 0.021 l&O.0036 0.0155;tO.O029 0.0120+0.0023 0.0029 jr 0.0044 0.~16~0.~36 -0.~7~0.~36
The values of A in columns 2 and 3 are for scatterer diameters of 50 mm and 25 mm respectively. The multiple scattering corrections, AA, of columns 4 and 5 are for these same scatterer sizes.
for our final estimate of the multiple scattering asymmetry, as a smoothed curve. The points represent the results of a recent calculation by the TUNL group r9) who had available a better approximation for the neutron carbon analysing power than we did. We conclude that the effect of multiple scattering is smalt, and quite well calculated. The curve of fig. 3 is used later (subsect. 3.4) to make small corrections for the multiple scattering effect. (e) Finite azimuthal angle: The experiment measures PA cos 4, where 4 is the angle between the polarization P and the normal to the scattering plane. The required average of cos 4 over the finite experimental geometry was found by dividing the scatterer and side detectors into a number of cells and calculating cos #J for pairs of cells. The values of A appearing in table 1 have been corrected for this effect. v> Mean scattering angh: The detectors were set at nominal scattering angles of 300, 40”, 50° etc. to an estimated accuracy of 0.2O. Finite geometry causes the effective average angles to differ appreciably from these nominal values. Data in the Monte Carlo simulation “3 were used to calculate the mean angles. 3.3. THE NEUTRON
BEAM ~~RIZA~ON
The neutron polarization from the “H(& Q4He reaction used here is found from measurements on the deuteron beam. With the RF transition units set to produce tensor polarized deuterons, the tensor component P,, is measured. Then for the n-p analysing power experiment with the transition units set to produce vector polarized deuterons, the resulting neutron polarization P, is given by P,, = jPZZ. We have already argued 22) that this procedure gives P, to a relative accuracy of 3 %.
378
J. E. Brock et al. i Andysing power
During the data collection, we normally attempt to run the experiment continuously for a number of weeks. The Pz, measurements, which require the interruption of the experiment, are usually taken twice daily. In order to be able to check the constancy of the neutron polarization during the actual data collection, we installed a neutron polarimeter downstream from the main scattering experiment and running simultaneously with it. This polarization monitor used neutron-carbon scattering at 45” (lab) as the analysing reaction. We used this monitor for two checks. First, for each “run”, we extracted an analysing power A,, from 1 r-1 A”, = --...-“_.E--$Pzzrn,+i ’ where rnc is the asymmetry for the polarization monitor, defined in a similar way to the asymmetry for the n-p scattering (see subsect. 2.1). This A,, gave consistent values for all the runs. The second test involved the actual magnitude of A,,. Since the flight path in our polarization monitor was too short for a time-of-flight separation of scattering from the ground state and the 4.4 MeV level of carbon, A,, corresponds to some average of the analysing power over these two levels. The analysing powers of these two levels have been measured at 14.2 MeV by a group at Base1 25). From their tabulated values, and from their time of flight spectra showing the relative numbers of elastic and inelastic events detected, we calculated a weighted average of the two anaiysing powers, which should be suitable for comparison with our A,, if we assume that our relative efgciencies for the detection of the two neutron groups is the same as it was at Basel. The A,, calculated from the Base1 experiment was -OSO+ 0.03 ; our measured value, averaged over all the runs was - 0.489 _+0.007. 3.4. RESULTS
The results of the n-p analysing power, A,(B). measurements are presented in table 1. The values quoted are averages of measurements taken over a span of five years. The angles given in column 1 are believed to be accurate to within 0.3O. They have been corrected for finite geometry effects. The values in colons 2 and 3 have been corrected for small geometrical effects. The multiple scattering corrections in columns 4 and 5 are taken from fig. 3. [That figure is for a 50 mm diameter scatterer; we take the correction for a 25 mm diameter one to be one-half of that for a 50 mm diameter one ‘“).I The values of A’ in column 6 are averages over the two sizes of scatterer, after the multiple scattering corrections have been applied. The final two measurements listed, at angles 138.9Oand 156.6O, were made using the “backwards angles” method with a thin radiator from which the recoil proton escaped and was detected in a separate scintillator. No multiple scattering corrections were made here, since they would be completely insignificant. The errors in columns 2 and 3 are purely statistical; those in column 6 include also
J. E. Brock et al. / Analysing power
319
a small contribution due to the multiple scattering correction. In addition, there is a 3 y0 relative error common to all points from the uncertainty in the polarization of the neutron beam ‘*). S’mce the maximum analysing power is 0.02, this scale error will contribute at most an extra standard deviation of 0.0006 to the essentially statistical errors listed in table 1; its effect is clearly not significant. Our measurements of the n-p analysing powers provide a further test on the magnitude of the multiple scattering effect. Although most of our measurements were made with a 50 mm diameter scatterer, giving A&e), we made also measurements at three angles with a 25 mm diameter scatterer, giving A25(0) (see table 1). For each of these three angles, Oi,we have calculated the difference A,Jf?J’- &(t$), using values corrected for multiple scattering, and then calculated the weighted average of these differences over the three angles. We find
40-A25 = + 0.0025 f 0.0037. (Incidently, if this quantity is calculated using values uncorrected for multiplescattering we find a value of +0.0021.) The major contribution to any multiplescattering induced asymmetry will arise from scattering from carbon in the scintillator, for which the analysing power is more than an order of magnitude greater than for n-p scattering. Since the n-C analysing power is negative in the angular region used here, the effect of the multiple scattering is to produce an asymmetry which is negative, as is shown both by our simulation 24) and by that of the TUNL
Ay re,
I
0.03
r. '\
---YALE
IY
*' /T
Fig. 4. The 14.1 MeV analysing power data, and a fit to the form A,(B) = (sin O/a(O)) (a,+a, cos 0). prediction of Yale and Livermore and from a meson model: the “Paris potential”.
The theoretical curves are from the phase-shift
380
3. E. Brock et al. / Anaiysing power
group 19). Further, the magnitude of the effect will be greater for a larger sized scatterer. Thus, if there were a multiple scattering asymmetry significantly larger than we estimate, the value of A,, - A,, would be negative. In fig. 4 we display our final results. The fit to the data has the form
A,(@= g
O),
(a+bcos
where a(6) is the n-p differential cross section. The curves from the phase-shift analyses are those of Yale-IV [ref. 2)] and of Livermore X [ref. ‘)I; the prediction from the analyses of Arndt et al. ‘) differs only slightly from that of Livermore X and is not plotted. The result of a calculation of the analysing power from the Paris potential 1,26) is also shown. 4. Analysis We have fitted our A,(B) results to the polynomial a(B
=
form
sin 6 c a, cos” S, n=O
where a(@) is the n-p differential cross section, for which we used values taken from the paper of Hopkins and Breit 27). The fit has been made for maxims n values, fi, of 1 and 2, giving polynomials terminating in cos B and in cos’ 8, the “two-term” and “three term” fits, respectively. The results are given in the upper part of table 2; xf is the chi-squared per degree of freedom. The “fit to the data” curve in fig. 4 uses the two -term fit. The data and the two fitted curves are displayed also in fig. 5 in the form of ~(0) A,(@ sin 0 against cos 8. We show atso the prediction of the Paris potential 26). Following the usual practice, the a, are interpreted in terms of the phase param-
Fits to a(B
TABLE2 = sin f&a,,+ a, cos 8 + a, cosz 0) and derived spin-orbit phase parameters Ais Zterm fit a0
a1
0.1055+0.0068 0.082 kO.017
a2
xf
0.50 0.340 * 0.022 0.052 +0.011
3-term fit 0.1114*0.0094 0.071 +0.021 -0.41 kO.45 0.45 0.333 +0.042 0.045 +0.013 -0.007 +0.008
J. E. Brock et al. /
Fig. 5. Fit of ~e)~~(~)~s~n B to ~~y~#rnin~s
~nalysing
power
in cos 8 and comparison with the p~diction potential.
381
of the Paris
eters AL representing combinations of triplet f-wave phase shifts arising from the spin-orbit part of the nucleon-nucleon interaction. Good approximations for the A& are 28):
where k2 is the c.m. wave alar of the nucleons. Using the LRL-K values 3>of the phase parameters 3S, and e1 we get the dis values shown in the lower part of table 2. We make a few remarks on the F-wave phase parameter, d&,. Firstly the inclusion of a third term, a2eos2 8 in the expression for ~(~)~~(~)leads to a greatly increased error in the P-wave parameter A Es. This arises partly because of the extra parameter, but also because of the large u~~~~~ty in a,, which appears in the expression for Ah. S~ondly~ if the pha~-s~~ analyses of Yale IV [ref. ‘)J Live~ore-X [ref. 3)] and Arndt et al, “) and the potential model prediction of Lacombe et al. ‘) give the correct order of magnitude for dz,, then the contributions to the cos2 6 term from A& and from the P- and D-wave combinations, are of similar magnitudes 28). Hence, it is not a good approximation to interpret the coeficient a2 in terms of dk only. In view of these remarks, and with the present accuracy of the data, we feel that the “two-term” form of the fit is the most realistic.
J. E. Brock et al. / Analysing power
382
^, al
E
c
1.0
a? a
1 2 3 L 5 6
(9117,
pq,-&
10 8 7 9 HAMBURG TUBINGEN TUNL ( DAVIS IlpBOl 19151 119781 I19771
I21 L
O10
HARWELL (1965, LOS AlAMCtS1l963~711 7.9.x) AUCKLANU 119721 HIROSHIMA119721 CAPE TOWN 119741 VIRGINIA(197LI
I
15
11 PRESENT WORK
I
25 ENERGY I MeV
30
20
I
35
1
Fig. 6. Spin-orbit phase parameters Ah and AD, deduced from existing n-p anatysing power experiments below 35 MeV. The curve for the P-wave case is a fit of the form & = nE”.
In order to compare the various n-p analysing-power experiments in the energy range up to about 30 MeV, we plot in fig. 6 the Als and A& values found from these experiments as a function of the neutron (laboratory) energy. [The Cape Town results 14) at energies of 16.4 MeV and 21.6 MeV have been reduced from the published values by factors of 0.76 and 0.84, respectively. This is because the magnitudes of the neutron beam polarizations should be modified by such factors in view of more recent work 29) on the source reaction polarization.] We have made a least squares fit of the A& points to a function of the form
where E is the neutron (laboratory) degrees ;
energy. We find, for E in MeV, and ApLsin
a = (2.5kO.4) x 10-3,
n = 1.86_+0.06,
with a x2 per degree of freedom of 1A. It is seen that there is quite good consistency among the results. The good agreement of the Cape Town results with the other measurements is significant since this experiment used techniques quite different from those used in all the others. In particular, the targets used as proton scatterers had dimensions of some millimetres instead of the more usual dimensions of some tens of miliimetres, implying that multiple scattering of the neutrons in the targets had no significant influence on the measured analysing powers. In fig. 7 we compare the experimental and phase-shift results for A& over the
J. E. Erock et al. / Analysing power
-
383
FIT TO EXRRIMENTS
Fig. 7. Comparison of phase-shift predictions for Ats with the experimentally determined curve of fig. 6.
ERLANGEN *’ 1 MADISON ?’ I ERLANGEN ” I PRESENT WORK
Fig. 8. Comparison of P-wave spin-orbit parameter A pLsdeduced from p-p and from n-p analysing power experiments. The points and broken curve iabelled “Paris” are from the Paris potential. The solid curve labelled “N-P Fit” is an extrapolation to lower energies of the curve fitted to n-p data in fig. 6. All the points marked with crosses are from p-p experiments and all those with solid dots are from n-p experiments.
TABLE 3 Isotopic spin splittings of P-waves in phase-shift analyses
Ref.
Energy
Amdt et al. ‘) Amdt et al. ‘) Bohannon et al. 4,
10 MeV 25 MeV 25 MeV
APls(np)- &(PP) O.OY 0.100 O.OfYJ
384
J. E. Brock et al. 1 Ana/ydng power
energy range 10 MeV to 30 MeV. The experimental result used is the curve fitted to the data points in fig. 6. The phase-shift results plotted are those of Yale-IV and Livermore-X; the results from Arndt et al. lie very close to those of Livermore-X and it is not practicable to plot them on the same graph. We have attempted to compare the values of Ats found from n-p and from p-p scattering, with the intention of looking for an isotopic spin dependence of the P-waves in the region below 20 MeV. In fig. 8 we show recent precise n-p results from TUNL iq) and from the present work at energies from 13.5 MeV to 16.9 MeV, and an older less precise result from Los Alamos ‘O) at I1 MeV. On the same figure are the only p-p results below 20 MeV. The p-p points labelled (1) and (2), of refs. 20,21), are those mentioned earlier in the introduction and use as input data differential cross sections and analysing powers. The point labelled (3) comes from a work very recently reported by Obermeyer et al. 31) of Erlangen. They have measured the p-p spin-correlation parameter A,, at 9.57 MeV and incorporated this in a phase-shift analysis near this energy. The analysing power used was that of the Madison group 21) but with a more recent measurement of the differential cross-section than was available to the Madison group for their phase-shift analysis. As a result, the error in the value of ALs for p-p scattering near 10 MeV is reduced by a factor of about 3. Unfortunately all of these p-p experiments are at energies lower than those of the n-p experiments, making a direct comparison impossible. However, we can make an indirect comparison by extrapoIating down to these energies our fit to the higher energy n-p data. The consistent difference between the n-p and p-p values of AIs shown in fig. 8 is not likely to be due to systematic experimental errors since the experiments come from different laboratories and use different techniques. The weakness in the comparison, of course, lies in the need to extrapolate the n-p data down to the region of the p-p data points, but we feel this procedure to be sufficiently accurate. For a comparison with theory, we show in table 3 the values of A~S(np)-A~s(pp) used in phase-shift analyses at two energies in this region. We see that although the experiments and phase-shift analyses find a similar magnitude of splitting, the sign of the effect is opposite. In fig. 8 we show also the predictions of the Paris potential 26*30) for AIS; these are seen to agree very well with the n-p measurements.
5. Conclusions As a result of Monte Carlo simulations of n-p analysing power experiments 1g*24) and of some measurements both in the present work and elsewhere ‘“) the effects of multiple scattering of the neutrons in the proton targets are quite well understood. It is clear that such effects present no serious problems to confidence in the results of n-p A,(@) me~urements, even at the high accuracies presently being achieved.
J. E. Brock et al.
385
/ Analysing power
A survey of all published n-p A,,(0) results over the energy range 10 MeV to 30 MeV shows that there is a remarkably good internal consistency among them. Our measurements at 14.1 MeV show small but definite disagreement with the phase-shift predictions (see figs. 4 and 7) for the P-waves and D-waves. We do, however, find excellent agreement with the predictions of the Paris potential, a model using only five adjustable parameters. The question of the possibility of the F-wave phase-shift combination AIs being much larger than all predictions r9, X* “) is not clearly resolved by our measurements. The analysis at the end of sect. 4 presents the first experimental evidence for an isotopic spin splitting of the triplet P-wave phase-shifts but in the opposite sense to that used in the phase-shift analyses of Bohannon et al. 4, and of Arndt et al. 5). The main requirement for investigating this question further is for accurate p-p analysing power measurements, preferably in the energy range 14 MeV to 17 MeV. This work was partially Committee of New Zealand.
supported
by funds from
the University
Grants
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A263 (1976) 285 26) J. Cot& M. Lacombe, B. Loiseau, P. Pirts, R. de Tourreil and R. Vihn Mau, Proc. 5th Int. Symp. on polarization phenomena in Nuclear Physics, Santa Fe, 1980 (in press) 27) J. C. Hopkins and G. Breit, Nucl. Data Tables A9 (1971) 137 28) A. Chisholm, J. C. Duder, R. Garrett and J. L. Poletti, Phys. Rev. C21 (1980) 1653 29) J. R. Smith and S. T. Thornton, Nucl. Phys. A187 (1972) 433 30) J. CbtC, P. Pirts, R. de Tourreil, M. Lacombe, B. Loiseau and R. Vinh Mau, Phys. Rev. Lett. 44 (1980) 1031 31) H. Obermeyer, H. Kuiper, B. Seidler and K. Frank, Nucl. Phys. A344 (1980) 75