Measurements of ΔσL and ΔσT in pp scattering between 200 and 520 MeV

Nuclear Physics A403 (1983) 525-552 @ North-Holland Publishing Company

MEASUREMENTS

AaT IN pp SCATTERING 520 MeV

OF AaL AND

BETWEEN

200

J.P. STANLEY

AND

and N.M.

STEWART

Bedford College, London, England D.V.

BUGG,

J.A.

EDGINGTON

and

N.R.

STEVENSON

Queen Mary College, London, England A.S.

CLOUGH

University of Surrey, Guildford, England D.A.

AXEN

and

R. SHYPIT

University of British Columbia, Vancouver, Canada and M. COMYN,

D. HEALEY

and

G.A.

LUDGATE

TRIUMF, Vancouver, Canada Received 20 October (Revised 9 Februrary

1982 1983)

Abstract: The differences AgL (Au=) between proton-proton total cross sections for parallel and antiparallel longitudinal (transverse) spin states have been measured at six (seven) energies between 200 and 520 MeV. Point-to-point uncertainties vary from kO.41 mb to 51.21 mb for AuL; for AaT they vary from ~kO.33 mb to kO.73 mb. Both are subject to additional normalisation uncertainties of about +6.7%. Differences from data obtained by other groups are discussed.

E

NUCLEAR REACTIONS ‘H (polarized p, p), E = 200,520 MeV; measured spin-dependent (T differences. Longitudinal, transverse beam polarization, polarized target.

1. Introduction Until recently, the general features of the nucleon-nucleon interaction below 1 GeV were thought to be understood purely in terms of t- and u-channel exchanges plus strong coupling to the inelastic channel ZVA. Interest in the possible existence of s-channel dibaryon resonances ‘) was stimulated in the late 1970s when groups 2*3) working at the Argonne laboratory found structure in spin-dependent total crosssection differences AaL and ACTS in the l-2 GeV/c range. For longitudinally 525

526

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polarised beam and target drr_ = (r(d) -a(~)

= (47r/p) Im F3,

(14

-t477/p)ImF1,

(lb)

and for transverse polarisations Aw=c(?J)-cr(tf)=

where F; and F3 are spin-dependent forward scattering amplitudes 4), and p is the laboratory momentum. Extensive pp elastic scattering measurements have allowed partiaf wave analyses? with unique solutions up to 800 MeV. The precise values of AuL and AC= play an important role. Elastic data alone determine phase shifts 6 accurately. However, elasticities n are rather poorly determined, except in the dominant inelastic channels ‘Dz and 3F~, which make large contributions to the shape of the elastic diffraction peak. Because Im F2.3 depends on sums of partial wave amplitudes through terms of the form (1 -n cos S ), and since most S are rather small, AaL and AaT give delicate information on the spin dependence of n-parameters. This is because inelastic channels contribute directly to ACTSand AaT. Early attempts 6,7) to calculate the opening of the strong inelastic channels failed to reproduce the structure observed in Aqr_ and AuT above 1 GeV/c ; phase-shift solutions using elasticities from ref. ‘) were shown 8, to disagree substantialIy with Im F3, and hence Apt., from 800 to 1200 MeV/c. A further problem was that dispersion relation calculations 4, using smooth curves through Im F 2.3 determined from experiment gave values for Re F2.3 at variance with phase-shift analyses. Since then, Grein and Kroll “) have repeated their pp analysis and have concluded that small adjustments bring F2 into agreement with phase shifts of Dubois et al. “1 and Arndt and Verwest il); however, in the case of F3, discrepancies with the former persist. Since then, it has gradually become clear that the dominant inelasticities emerging from phase-shift analyses (in ID?, 3F3 and 3Pt) are 12), after all, in qualitative accord with the Mandelstam model, where inelasticity is dominated by the NA channel. If dibaryon resonances exist, they are certainly weakly coupled to the NN channel; there has been considerable debate as to whether the phase-shift solutions demand resonance poles or not. Kloet and Silbar “) have developed a unitary mode1 of NN-NA coupling where resonances are not required, and Kloet and Tjon 14) assert that half-loops in the Argand diagrams of 3F3 and ‘Dz can be understood within an exactly soluble coupled-channel model with conventional dynamics. On the other hand, there have been claims that polarisation data in yd -, pn seem to favour NN resonances 15); also, vector polarisation data of Bolger et al. 16) in v’d elastic scattering exhibit remarkable angular dependence suggestive of a 3F3 or lG4 resonance. If dibaryon resonances exist, there would be important implications for quark models, Because of the difficulties described in ref. *) in reconciling AC,_ data quantitatively with phase-shift analysis and dispersion relations, we felt it desirable to remeasure

527

J.P. Stanley et al. / pp scattering

both AaL and AUT within with

careful

attention

the energy

to systematic

range available errors.

at TRIUMF

In particular,

(200-520

measurements

MeV), up to

325 MeV are in the energy range where inelasticity is zero or very small, with the result that elastic data and phase-shift analysis make precise predictions of ACT,_ and AuT; this is a valuable check on experimental results. As will become clear in sect. 4, our results satisfy this check well, but differ systematically from results of other groups from 400 to 515 MeV by a few mb; this amount is important for details of the phase-shift analysis, since it is comparable cross section. Results given here supersede our preliminary lier 17) small changes arise from (i) improved evaluations to zero solid angle. and (ii a superior extrapolation

with the total inelastic results published earof target polarisations,

2. Experimental details measurements were made by the conventional transThe total cross-section mission method using the experimental layout shown in fig. 1. Six circular scintillation counters Ti, subtending solid angles L?, recorded the fractions t’ of the beam transmitted by the target when its polarisation PT and that of the beam PB were parallel (+) or antiparallel (--). The attentuation is a product of three factors, which all depend on L&. The largest in the target, air and counters. dent scattering

on hydrogen

term, exp (-a) = 0.97, is due to unpolarised nuclei Secondly, there is attentuation due to spin-indepen-

in the target. Thirdly,

there is the term of direct interest

Fig. 1. The beamline and experimental layout in the AuT and ACQ configurations: P, monitor of beam polarisation; Ql, Q2, quadrupole magnets; S, solenoid; C, collimator; M, bending magnet; PC, wire chamber monitor; S1,2.3, beam-defining counters; PT, polarised target; W, wire chamber monitors with trigger scintillators; T1_6, transmission counters; E1,2, efficiency counters.

528

J.P.Sfunit-y

et al. / pp scafferiffg

in this experiment, namely the spin-dependent in the target. Thus

attentuation

due to polarised protons

-$Ps * PTAv,)] ,

t’ = exp (-LX)exp [-NJY-“pul((~)i

(2)

where No is Avogadro’s constant, f is the length of the polarised target, pH the density of hydrogen in it, and H is the atomic weight of hydrogen; also (3) where (TV)is the unpolarised total cross section and the sum is over all reactions producing charged particles within lab solid angle Qi. In the approximation tanh x = x, which is numerically very accurate here, Agi = 2H(t7 -tT)/‘[(t:

+ r;)NopuIP,

’ PT] e

(4)

Then AaL or AcrT is obtained by extrapolating Aci to zero solid angle. A technical complication is that, if the transmission counters are misaligned left or right of the beam, the large values of P and dcr/df2 for scattering at small angles from nuclei (mostly carbon) give rise to a further spin-dependent correction to eq. (2) in AaT measurements. The right-hand side of eq. (2) is multiplied by a term

depending on PB but not on PT. Here Ai2i represents the left-right asymmetry in solid angle subtended by the counters. The sum over j is over all materials of atomic number A, density pi, and thickness I/ in the target, air and counters. This term may be eliminated by averaging ArT data over beam polarisation. For a given configuration of beam and target polarisation, eq. (4) is modified by the addition of an extra term al = K(L$)P,’

)

(61

where K(Ri) depends on the ratio of unpoIarised nuclei to polarised hydrogen. We find evidence for such an instrumental asymmetry, of small but non-negligible magnitude, in our measurments of Au=.

2.1.THE

BEAM

For a polarised target of length 2.5 cm, a value Aa = 0.2 mb corresponds to a difference in the transmitted fractions t+ and t- of about 1 part in 105. The corrections for accidental coincidences (see subsect. 2.3) must be made to this precision, so the beam intensity was restricted to 63 x lo5 ssr. The minimum stable intensity of the internal poIarised H- beam in the TRIUMF cyclotron is -1Or’ s-‘; the required reduction in intensity was achieved in two stages. Firstly, a thin wire

J.P. SImtiey et al. / pp scaftekg

529

foil intercepted and stripped about 0.1% of the circutating beam, giving an extracted beam of about lo8 protons - s-l, This beam intensity and the magnitude of the polarisation were recorded continuously by the monitor P. Secondly, the quadrupoles Ql defocussed the beam on to a copper collimator C, of length 20 cm with a bore of 1 mm, giving a further reduction of order 103, The magnet M after the collimator deflected the beam through 35” with a lever arm of 9.6 m to a momentumdispersed spot at the target. Focussing after the collimator was used only at the Iowest energy, thus avoiding the possibility of beam grazing the beam pipe and being steered on to the target by the quadrupoles Q2. The shape and position of the beam spot were monitored by a wire chamber PC of 1 mm resolution followed by three scintillators SI, SZ, S3 positioned in an air gap between the end of the beam pipe and the vacuum chamber containing the target. The beam spot was elongated vertically by the optics of the beamline and also by vertical oscillations in the cyclotron. Both S1 and SZ were 1 mm thick, 2.5 cm square and split horizontally or vertically into two halves, allowing vertical or horizontal beam movements of 0.01 mm to be detected. The final counter SS, I mm thick and 1 cm diameter, had an air light guide and was 42 cm from the target centre. It counted typically 90% of the protons in SL * Sz, the small loss being due to the vertical image size. The horizontal dispersion was calculated to be about I MeV/cm. At energies where the tune of the cyclotron and beamline were particularIy favourable, two distinct images 150 keV apart were visible, due to the stripping of adjacent and partially separated turns within the cyclotron. At no energy was the horizontal width of the beam greater than 5 mm at the base, so the energy resolution was <*300 keV. Hence we are confident that the collimator did not degrade the beam quality. Indeed, the horizontal image was better than has generally been observed without the collimator. The energy of the beam was determined within an uncertainty less than 1 MeV from the position of the stripping foil and the accurately known field of the cycfotron. For AcF~, the ~oIa~sation of both beam and target were vertical. For AcrL, the 1 m long solenoid S precessed the vertical beam ~lar~sation into the horizontal transverse direction and the dragnet M then precessed it about the vertical to give a beam whose poIarisation was aligned at a small angle (90” - $1 to the momentum vector. Vaiues of 4 varied between 76” and 98” from the Iowest to the highest energy, as shown in table 1. The beam polarisation Ps was monitored continuously by the polarimeter P, detecting pp elastic scattering at 26” lab from a (CH& foil 1.6 mm thick. Two counters in each of the forward and recoil arms made a fourfold coincidence, reducing carbon background to ~5.6%. ‘The performance of P was well-known from our previous extensive polarisation measurements, and its absolute calibration to an accuracy of *LttS% has been reported previously ‘*I_ As the cohimator transmits only about one thousandth of the protons sampled by the polarimeter, it is necessary to consider whether there could be systematic

530

J.P. Stanley et al. / pp scaitering TABLET Spin precession angle i,h for angle of bend of 35” in magnet Energy

at M

an M

ti

Ideg)

(MeV) --208.2 329.6 423.3 459.4 500.7 519.9

16.7 84.8 91.1 93.5 96.2 97.5

differences in polarisation between the central paraxial particles and the remainder. Such differences might arise from correlations between regions of phase space in the extracted beam and processes in the cyclotron which might lead to depolarisation, e.g. betatron oscillations. This requires a discussion of the beam optics. One can think of the beamline as a simple two-stage telescope, with the intermediate focus close to the polarimeter P and with the collimator nearly midway down the second stage (fig. 1). The coIlimator acts only as a simpIe geometrical stop, since its aperture limits beam divergence only at ~t2.5 mrad, which is much larger than the natural beam divergence close to the axis (~0.85 mrad at 465 MeV, due to multiple scattering in the polarimeter foil). Since the collimator does not limit beam divergence, the final image receives rays from all origins on the stripping foil. There is ample experimental evidence for this: (i) movements of the stripping foil vertically or azimuthally round the cyclotron are reflected directly in corresponding vertical or horizontal movements of the image at S3, and (ii) steering magnets near P have no effect on the image size. Hence the only depolarisation correlations of concern are with beam coordinates at the collimator, i.e. with the divergence with which particles leave the stripping foil. Craddock et aE. *‘) have made a detailed study of depolarisation resonances in the cyclotron. They observed two (expected) resonances, one at 298 MeV associated with the fifth harmonic of imperfections in horizontal field components, and the second at 466 MeV associated with the sixth harmonic of imperfections coupled to the first harmonic of vertical betatron oscillations. The former affects the whole beam, and is therefore uncorrefated with beam direction at the stripping foil. The second resonance is responsible for a drop of up to 5% in polarisation over a few MeV. However, at this energy, multiple scattering in the stripping foil (25 p,rn C) increases the vertical divergence of the beam by a factor of 2, and multiple scattering in the polarimeter foil (1.5 mm CH2) is responsible for a further factor of 5 in divergence, i.e. the latter foil is responsible for most of the dispersion of the beam across the face of the collimator (3~5mm with quadrupoles Ql off, more with them defocussing). Consequently, any intrinsic correlation between depolarisation of the internal beam and vertical beam direction

J.P. Stanley et al. / pp scazze~i~g

531

is washed out by a factor -10 by multiple scattering before the beam reaches the collimator. One can therefore safely conclude that any difference dPB between polarisation monitored by the polarimeter and that of the beam going through the collimator is sl%, and probably
2.2. THE

TARGET

The polarised target 20), obtained from Liverpool University, used a target material frozen into small beads maintained at an operating temperature of 0.5 K by a 3He evaporation refrigerator. The composition by weight of the material in the target was 92.2% 1-butanol (C4Hi00), 4.9% HZ0 and 2.9% Cr”-EHBA dopant in the form of sodium bi-(2-ethyl-2-hydroxybutyrato)-oxochromate-V (NaCrC~~O,H~“). The density of free hydrogen in the target was 13.25% of the whole, and was found to be 0.0717 g, cme3, with an uncertainty of +5.3%. The majority of this error represents uncertainty in the filling, or packing, factor, which varied by a surprisingly large amount with the uniformity of the target beads and with the dispersal of static charges during the filling process. We draw attention to the facts that (i) our value of target density is about 7% lower than that reported by most other groups, and might be partially responsible for our values of AcL and drT being higher than those found elsewhere, and (ii) the uncertainty in target density is unfortunately the largest source of error in the normalisation of our data. We attribute the lower density to a considerable variation in bead size (1.0 to 1.7 mm diameter), giving rise to poor packing. Subsequent to this experiment, we have found that improved techniques producing beads of uniform size have led to densities very close to those of other groups. Different target cells were used for daL and daT. Each was a perforated cylinder of hydrogen-free polymer (FEP), of diameter 15 mm and lengths 23.68 * 0.10 mm for ACT=and 20.79 f 0.10 mm for AaL. The target was polarised by irradiation with microwaves of 71 GHz at the centre of a 2.5 T magnetic field supplied by two superconducing Helmholz coils. The magnetic field was vertical for AcT measurements; for Aa,_ the field, but not the target cell, was offset horizontally by 12” from the longitudinal, to allow scattered particles detected by the polarisation monitors to emerge between the coils. Routinely, we obtained an average target polarisation PT of 0.65, falling to 0.60 over a period of days, owing to a slow drift in the field.

5.72

J.P. Stanley

et al. / pp scattering

Microwave

,

3cm

\

,

Perforated Perforked

Fig. 2. Target

The

polarisation

was monitored

fep

target

cell within the microwave

continuously

fep former

for

NMR

cavity

coil

holder

cavity.

by a microprocessor-based

NMR

system employing sampling NMR coils wound round the two target cells as in fig. 2. The absolute accuracy of this method was limited by the measurement of the small thermal equilibrium signal to *2.1% for AaT and to *6.4% for Am. However, the NMR system could follow the variation of PT with time to a precision of better than 0.1% . An independent normalisation of PT was obtained by measuring the asymmetries of protons scattered elastically from hydrogen in the target. This was done by the monitor W which, in the case of AuT, consisted of two pairs of arms, each with a single wire chamber and trigger scintillator, detecting forward (26” lab) and recoil protons. Each MWPC was 25 cm square with 1 mm wire spacing in both the horizontal and vertical planes; the distance to the target was about 37 cm, giving an angular resolution of *0.15”. The ArL experiment had only a single pair of conjugate arms because of geometrical restrictions, but two chambers were used in each arm, instead of one, to improve reliability. Full details of the extraction of PT for each experiment will be given in sect. 3, along with the treatment of other systematic spin effects. The sensitivity of the NMR coil was greatest for hydrogen near the coil, and less for the material at the centre of the target, while the beam was more intense at the centre. Hence we trust the absolute magnitude of the scattering calibration of

J.P. Stanley

533

et al. / pp scattering

PT more than the NMR calibration, and attach *6.4% error to the scale of the latter for both AcrL and AaT. The scattering monitors did not resolve different parts of the target,

and there was insufficient

beam time to allow extensive

checks of the

variation of PT over the target. However, deliberate movements of the beam horizontally and vertically by +2 mm at 516 MeV had no effect on the scattering calibration

of PT at the *2%

2.3. TRANSMISSION

level.

ARRAY

The intensity transmitted through the target was measured with six closely spaced circular scintillation counters Tr-T6. Their radii varied from 9.0 cm to 29.5 cm and covered the angular range 4” to 13” lab in roughly equal steps of solid angle. The distances from the centre of the target to the first scintillator were 118.3 cm and 130.1 cm for AaT and Au= respectively; further details are given in table 2. The complete assembly was contained in an aluminium frame with each scintillator viewed externally by a phototube through an air light guide. Two 5 cm square counters Ei, E2 mounted on the frame downstream of the array were used to monitor efficiency continuously. The frame was mounted on a teflon-coated table which allowed easy movement and alignment.

TABLE 2 Dimensions

Scintillator

1 2 3 4 5 6

Radius (cm)

9.01 12.00 16.50 19.99 25.46 29.50

of transmission

counters

Thickness

(cm) 0.91 0.92 0.94 0.97 0.99 1.23

Distance from scintillator 1 (cm) 0 1.24 10.00 11.28 20.01 21.44

In order to eliminate noise, pairwise coincidences were formed and transmissions ti were measured by the ratio of coincidences B . Ti. Tit1 and B = Si * S2 * S3. Efficiencies (>99.95%) were monitored from E = B . El . E2 and B * Ti * Ti+i * E. Accidental coincidences ri were monitored continuously by recording D . Ti . Ti+r, where D is the beam signal B delayed by 86 ns, twice the r.f. period of the beam. The corrected transmission is ti - ri(l - ti), the correction term being typically 0.05% of ti ; since beam intensities were similar for both beam polarities, the correction to AaT or AgL was much smaller, 2.5 mb in the worst run and generally much less.

534

J.P. Stanley

2.4. SETTING

UP AND

At every energy the left-right profile

DATA

TAKING

the beam was centred

asymmetry

was checked

et al. / pp scattering

measured

on monitor

with unpolarised

on the MWPC

monitor

P and a check was made that beam

was ~0.01.

The beam

PC, and it was also required

that not

more than 10% of the beam in Sr . SZ missed S3. At every energy, the beam was aligned on the target by removing S3 from the B coincidence, steering the beam in both planes, and minimising the transmission in T5T6. Consistent results were obtained at all energies *l mm, and the mean vertical location of the cold target was consistent within kO.5 mm with its warm surveyed location and the calculated 3 mm contraction of the supports at low temperature. taking Polaroid photographs of the beam at the target at the front and back of the transmission array. These SZ and !$ were aligned to within 0.5 mm, and that the ments was offset by 1.4 mm from this line. Across the a circular region, which at its closest approached to

A final check was made by entrance and exit, and also beam scans showed that S1, target for the AaT measureface of the target, S3 defined within 1.2 mm of the edge.

Neither beam divergence nor multiple scattering was enough to cause protons traversing S1.3 to miss the target. Horizontal alignment was more precise (+0.5 mm) for the AaL measurements, as the magnetic field of the target was nearly longitudinal, and we are confident that in both experiments all beam particles travelled the full length of the target. The alignment of the transmission array was likewise better for AaL, since the field used for Am bent the beam by up to 10.6”; the alignment accuracy was determined mainly by the precision with which the Polaroid film could be referred to the cross-wires marking the axis of the array. The polarisation of the beam was cycled through an eleven minute sequence of spin up (5 min), spin off (1 min) and spin typically aO.7. The ion source was operated the same

intensity

as polarised

runs.

down (5 min). The polarisation was so that spin-off runs were at roughly

Left/right

and up/down

ratios

in the split

counters Si, SZ monitored beam movements continuously. Shifts of 0.05 mm were seen between the two spin orientations, but these were not serious as tests with deliberate movements of *2 mm horizontally or vertically were needed to produce significant changes in measured cross sections. Several additional systematic checks were made. (i) The measured accidentals in the transmission array were compared with calculation and checked against changes in transmission as the beam intensity was varied between lo5 and lo6 s-i. (ii) At every energy, data were taken using both target polarisations, and on three occasions (twice for ArT and once for AuL) the target was also run unpolarised. In the ACT,_measurements, data were taken with both solenoid polarities, and also with it de-energised. (iii) At 497 MeV the solenoid current was varied so as to precess the beam polarisation from 0 to 180” in 30” steps; the expected sine curve of (t + - t-) versus precession angle was obtained. At all energies, several runs were made, each with -10’ incident particles. Every run allowed about 40 000 scatters into the target polarisation monitors W, and all

J.P. Stanley et al. / pp scattering

data were recorded recorded

on magnetic

every 15 s and averaged

tape for off-line

535

analysis.

The NMR integral

was

over the run.

3. Data analysis 3.1. BEAM

POLARISATION

The polarimeter scattered elastically

monitored continuously the left-right asymmetry E for protons by the (CH*),, target; checks on instrumental effects were made

by measuring the asymmetry e. (in almost all runs ]E~I< 0.018) with unpolarised beam. A small factor f was appied to the pp analysing power P&26’) to correct for the background of quasi-free scattering from carbon. The factor f’ has been measured to kO.005, and we also regard our claimed absolute accuracy of &1.5% for P&24”) [ref. ‘“)I to be reliable, in view of the agreement found **) between many independent measurements. Phase-shift analysis relates P&24”) to P&26’), with an uncertainty less than 0.001. The values of f” and P&26’) are given in table 3 for beam energies at the polarimeter, and the beam polarisation was calculated from PB = (E - Eo)f/P,,(26”)

TABLE The pp analysing correction factor

3.2. TARGET

I

3

power P,, (26”) and the carbon f as a function of proton lab energy T

T (MeV)

P&26’)

f

209.0 330.1 379.2 423.7 459.8 501.0 520.3

0.268 0.331 0.342 0.353 0.367

1.031 1.050 1.054 1.056 1.056 1.056 1.056

0.397 0.400

POLARISATION

The NMR measurement allowed the polarisation PT of the target to be followed with high statistical precision. However, the absolute calibration of this method has an uncertainty up to about *6.4%. Hence the absolute value of PT was also determined by measuring the asymmetry of elastic pp scattering from the target. The chambers monitoring PT were described in subsect. 2.2. For every event the angles of the forward and recoil particles were evaluated, allowing for the effect

536

J.P. Stanley et al. / pp scattering

of the magnetic field of the target. Opening angle 19and an angle Qi measuring the coplanarity were calculated. As no data were taken with a hydrogen-free target, the background (mainly from carbon) was estimated in a two-step approach. Firstly, the events used were weighted by exp {-b (8 - e)‘} , where g is the mean opening angle and b is a constant related to the experimental resolution. The back~ound was reduced by about 50% in this way. The distributions in Q, were well represented by f(G) = NH exp {-yH(@ - 6)2}+NB exp (-~n(@ - 6)2},

18)

where subscripts II and B refer to hydrogen and background events. The five parameters NH, NB, YH, yu and (;iswere fitted separately for every run, but were highly reproducible at one energy and smoothly varying with energy. Values of 6 and yI_rwere consistent with the geometry and calculated resolution respectively, and yn was consistent with the calculated acceptance folded with Fermi motion in carbon. An example of the fit to one run is shown in fig. 3. The signal was determined by subtracting the fitted background from the counts in a range of &2 x full width about the centre of the hydrogen peak. Where necessary, this count was corrected for chamber efficiencies. Typically, the background subtraction was 5-10%. From alternative background fits with a quadratic form, we assess the maximum possible systematic error in Pr arising from the form chosen for the background to be *2.5%, and include this in our overall normalisation uncertainty. The resulting elastic events yielded broad distributions in c.m. scattering angle 0 (maximum extent *20”), which were used to evaluate weighted mean values of analysing power and spin-correlation parameters for each polarisation combination. Values of these parameters as a function of angle and energy were taken from predictions of our current phase-shift analysis. The target polarisations were evaluated separately for the two experiments as explained in the following sections, which describe how the monitor chambers were used to calibrate the NMR signal, 3.2.1. litle lungit~~~~a~~~l~ri~at~on. The count rate in a monitor at angle 6 is R =&[I

+PBPT(LYA,..~.(~)+PAL~(~)-YA,,(B)}I t

(9)

where R0 is the unpolarised count rate. The coefficients CX,/3 and y arise from three effects: (i) the spin precession angle II, in the 35” magnet, although close to 90”, varies with energy, (ii) the target field is offset from the longitudinal by an angle C$= 12”, and (iii) the magnet of the polarised target precesses the polarisation. This last effect is a perturbation of only O-l-0.5% in the analysing power of the monitor. Values of CY,/3 and y are given in table 4, and the algebra of effects fi) and (ii) is contained in the appendix. It is convenient to work with the ratio r = R/R0 defined so that r = 1 +&P&(S)

)

(10)

537

(a)

0.8

t-

oa0.6-

$8Meg) Fig. 3. Fitted distributions in Q, for the same sense of PT: (a) beam-spin positive, (b) beam-spin negative. Coplanar scattering is given by @ = 90”. The range over which the fitted background was subtracted from the hydrogen peak is shown between the arrows.

where M(B) contains all the terms involving the pp spin-correlation For a given target po~arisation~ and beam polarisati~n + or -,

r- = &I&M+

r+ r++r-

,

-P&c)

=P&Ql4++P&vf-)+2.

(111

TABLET Energy T (MeV) 208.2 323.6 42x3 459-4 500.7 519.9

variation

of the angular

(Y= sin JI cos 4 0.9518 0.9741 0.9780 0.9764 0.9724 0.9697

coefficients

parameters.

a, 0 and y of eq. (9)

P=cos(~+~) 0.023 1 -0.1183 -0.2260 -0.2668 -0.3129 -0.3341

r=cosJ,sinQ 0.0473 0.0189 -0.0038 -0.0216 -0.0226 -0.0272

538

J.P. Stanley cl al. / pp scatrering

If we define an asymmetry l= (r+--r-)/(r++r-1, the value of target polarisation solenoid polarity is

(12)

for each run under given conditions of target and

PT= 2~[(P+&+-P-&-)-~(P;M++P,M-)]-*.

(13)

The ratio of this measure of Pr to the NMR integral yields a calibration factor C for every run: C = Pr/(NMR

integral) .

(14)

Simple averages of C are taken over solenoid polarity and both target spin directions, to eliminate possible systematic effects discussed below. Results for C at individual energies are given in table 5. The majority of the uncertainty in each value of C arises from generous errors attached to values of M derived from phaseshift predictions. These predictions incorporate and smooth all world NN data; uncertainties were estimated by calculating predictions for a large variety of data bases. The error on M was assessed as the maximum change these variations produced, plus statistical errors from the phase-shift minimisation. In addition, we allow for the uncertainty in 8, the effect of which is generally less than 20% of the total error. TABLES

The NMR calibration factor C as determined at every energy. f? = 1.0701kO.028 Energy

Calibration factor

WeV)

c

202.7 325.4 419.5 455.8 497.1 516.5

1.104*0.039 0.995 f 0.053 1.142*0.108 1.184*0.125 1.026*0.115 0.998i 0.121

The overall weighted mean value c was calculated and combined with the NMR value, which was assigned an error of *6.4%. Finally, PT was found for every run by multiplying c by the value of the NMR integral for the run. At 325 MeV, there was evidence for unwanted components of beam polarisation. This evidence came from two sources: (a) a change in transmission through the polarised target was observed when PB was reversed with the solenoid unpowered; (b) the monitor asymmetry 6, which should change sign but not magnitude when PT is reversed, in fact altered considerably, and also there was a significant change

J.P. Stanley et al. / pp scattering

in 5 on reversal found

of PT when the solenoid

to be all quantitatively

539

was unpowered.

consistent

These observations

with the existence

of a horizontal

were spin

component in the extracted beam of 0.16*0.02 at this energy, but ~0.06 at all other energies. It is shown in the appendix that its effect is eliminated by averaging C over both target spins and both solenoid

polarities.

Data taken with the solenoid unpowered give a measurement of P,,(B)PB, hence providing an important check on the results from the polarisation monitor. The calculated and measured values are in excellent agreement (their ratio is 0.992* 0.041), giving an absolute check on PB at the polarised target to *4.1%. 3.2.2. The transverse polarisation. The count rate in a monitor at an angle 6 is R = &[I Since

+P,P,,(B)

a large part of the monitor

+P&‘p,(0) asymmetry

+P,A,,(~)II . now comes

(14)

from the uninteresting

term PBP,,(0), we grouped the runs into pairs with opposite senses of target polarisation and determined the magnitude of PT from the asymmetry when PT changed sign but PB remained unchanged in sign. For the left monitor, we formed the asymmetry

(16) where

+P;+A,,(Bl ,

cl = P&e) and the first superscript

refers

~2

=

Ppp(@)

+P;-ANN(B)

to the beam polarisation,

Since Pi+ = Pi-, and cl =c2, the first term compared with that containing PT. Finally,

,

the second

in the numerator

(17) to the target.

of (16) is small

(18) For this left monitor,

Ppp and PBANN add constructively

spin +, giving an enhanced sensitivity. likewise add constructively for beam-spin cl = P,,(8)+

PB+ANN(O) ,

in cl and c2 for beam-

For the right monitor, -, so we used c2 = P&O) + PB-Am(e)

Ppp and PBANN

.

The other two combinations of monitor and beam-spin give low sensitivity, because of destructive interference between P,, and PBANN, and were discarded. As before, a calibration factor C was found for the NMR signal at every energy and then averaged over energies to give a mean value C = 0.944*0.031, which is used in the evaluation of PT for every run.

540

J.P. Stanley

3.3. COULOMB

et al. / pp scattering

CORRECTIONS

The full scattering

amplitude

is a sum of Coulomb

and nuclear

parts:

f =fc+fb!. For one partial

wave, the contribution

(19)

to the Coulomb

amplitude

fc

is

(e 2’t - 1)/2i ; spin-orbit and magnetic moment terms are included in the Coulomb phase shift 6, with dipole form factors for each proton. The contribution, including Coulomb distortion,

to the nuclear

amplitude e2”[n

where

fN is

exp {2i(S + A + i@)} - 1]/2i,

8, n are the true nuclear

phase

shift and elasticity

parameter

respectively,

and A, @ are the Coulomb barrier corrections, due to the distortion of the incident plane wave by the long-range Coulomb potential. Values of A and @ are taken from the prescription 23) of the Graz group. The elastic scattering contributions to ArL and Acv are A~:L(&)=-4~~~~Al,(~)ELsinBdf3, EL

where These (CNI) integrals

(20)

sin 8 d0,

AcFL (di) = -2~

19, is the maximum c.m. scattering angle for the ith transmission counter. integrals were evaluated numerically. The Coulomb nuclear interference from the differences in the corrections to ArEL and AuFL were obtained between

(a) Coulomb

the two cases: amplitudes

present,

(b) all 5 = 0 and hence fc = 0. The Coulomb barrier (CB) corrections were obtained, using the optical theorem, from differences between (a) Graz values for A and 0, (b) A = @ = 0; by this means, the

corrections

to AuL

and

ACT= were

obtained

for both

elastic

components of the Coulomb barrier. Errors were estimated by varying the nuclear phase shifts S and generous amounts, reflecting possible systematic errors in the NN probably overestimate the true errors of the Coulomb corrections. given in table 6 are those calculated by Arndt 24), and are in very with our own evaluations.

3.4.

EXTRAPOLATION

TO ZERO

SOLID

and

inelastic

elasticities n by data base. They The corrections close agreement

ANGLE

The transmission ratio for the ith counter using eq. (4), and CNI and CB corrections

was converted were applied.

into a cross section Aui At the higher energies,

er al. / pp scattering

J.P. Stanley

TABLE

541

6

Coulomb corrections: the Coulomb-nuclear interference correction (CNI) at 8” c.m. near the first transmission counter (all values kO.06 mb) and the Coulombbarrier correction (CB) applied at zero solid angle CNI (mb)

Energy (MeV)

202.7 325.2 374.8 419.5 455.8 497.1 516.3

AUl_

ANT

2.26 1.06

0.74 0.47 0.44 0.43 0.40 0.35 0.33

0.74 0.63 0.51 0.46

CB (mb) h_

-0.83 f 0.22 -0.35~tO.25 -0.lO~kO.23 -0.06 * 0.25 -0.06kO.25 -0.04+0.25

AW

-0.09* 0.01 0.03 f 0.05 0.08+0.13 0.14~tO.20 0.16ZtO.18 0.09~tO.16 0.10+0.16

values of Aai did not vary linearly with solid angle L!i. This was expected for counters recording a significant number of deuterons from the strongly anisotropic reaction pp+dr’. Therefore a quadratic fit was made as a function of L& for every run. The quadratic coefficients were averaged over all runs at every energy, and examined for energy dependence. As expected at 202 MeV, below the pp+dr’ threshold, this coefficient for AvL did not depart significantly from zero. The statistical variation of the quadratic coefficients with energy was eliminated by drawing a smooth curve through the fitted values, and the extrapolation was repeated using the smoothed quadratic coefficients to give the intercept at zero solid angle (figs. 4 and 5). In our previous publication I’) of preliminary results, only a linear extrapolation was used. Finally, the results for AmL were corrected for the small contribution (~0.32 mb) from ACT=,arising from the transverse components of beam and target polarisation. Phase-shift analysis gives predictions for the slopes of the elastic contributions to the extrapolations to zero solid angle, and the data of the Geneva group *‘) give the slopes of the d7r+ contributions. The contributions from pnr+ and pp7r” final states is small because the cross sections are low and particles can appear kinematitally over a wide angular range. The predicted slopes agree well with our ACT,_data at all energies; for ACT=,the predicted slopes are slightly lower than observed experimentally at 202, 497 and 516 MeV, but using the predicted slopes would change values of Au= by only about one standard deviation, and reliance on direct experimental data seems preferable. Notice on fig. 4 that the slope of the extrapolation at 325 MeV for AuL is marginally negative. This is not surprising, since the elastic contribution, which is positive at 202 MeV, falls close to zero for energies of 325 MeV and above. The contribution to the slope from the dr+ channel is positive above 350 MeV, because of dominance of ‘Dz inelasiticity, but at 325 MeV 3P1 inelasticity is greater than ‘D2 and the d7rf contribution to AaL is predicted to be small and negative. Thus at 325 MeV, a zero or slightly negative slope is predicted, in accord with observation.

542

J.P. Stanley

et al. / pp scattering

419.5 MeV

j 20

40

60

80

loo

A(msrl Fig. 4. Lto~ as a function of solid angle R. The points represent the values from the first five transmission counters, and the solid lines the fitted quadratic curves. Statistical errors are given for the first counter. Similar (but correlated) errors occur for the remaining points. The arrows correspond to t = -0.01 IGeV/c?.

4. Results and discussion The results obtained at TRIUMF for both AaL and AcT are given in table 7. As mentioned in sect. 2, the measurement of AaT is sensitive to small horizontal misalignments of the transmission counters. Results given in table 7 have been obtained by averaging over PB to eliminate the instrumental asymmetry ai. Values of crl (eq. 6) corresponding to a misalignment of 10 mm have been calculated from known values 26) of the cross section and polarisation in proton-carbon scattering at small angles, and are listed for illustration in table 8. Instrumental asymmetries of about this magnitude were observed at several energies in dcT data taken with opposite senses of PT. Data taken at two energies with PT = 0 lay midway between data with positive and negative P T, as expected. From Polaroid film exposed to the beam passing through the transmission array, we conclude that misalignments of several mm were definitely present at some energies, and hence that the observed instrumental asymmetries are accounted for. In our earlier publication I’), we inflated errors on AaT results to cover these instrumental effects, which at that time were not fully understood.

543

f.P. Srunky et al. / pp scattering

Fig. 5. AaT as a function

of solid angle R. Legend

as for fig. 4.

TABLE 7 Values of dcr,_ and 3uT.

Parameter

JUT

Energy

Value

(MeV)

(mb)

252.8 325.1 374.8 419.4 455.7 497.5 516.6

0.29 zk0.38 0.16icO.37 2.68 zk0.33 4.21 kO.37 6.76 ZIZ 0.50 10.84 zk0.73 11.17zkO.64

202.7 325.4 419.5 455.8 497.1 516.5

-30.27 i 0.66 -25.99* 1.21 -21.25 f 0.96 -16.90~0.97 -14.69kO.41 -12.77 f 0.45

There is an additional normalisatian all energies, and an independent *6.9%

Phase-shift prediction tmb) 0.16*0.30 0.51 *OS9

-30.88zt0.32 -2.5.78kO.63

error of +6.6% in AcrL common to error in il~r~common to all energies.

544

J.P. Stanley

et al. / pp scattering

TABLE 8 An estimate of (T’ arising from the instrumental asymmetry present in the i-1~~ experiment (a linear extrapolation to zero solid angle was used) Energy

(MeV)

203 325 375 419 456 497 517

c’ (mb) -0.84 -0.72 -0.63 -0.63 -0.57 -0.51 -0.51

Our results are compared in figs. 6 and 7 with those of other groups. The published dcL data of the LAMPF and ZGS groups used Coulomb-interference corrections of Watanabe *‘), ignoring the angular dependence of nuclear amplitudes. This is a poor approximation, since some amplitudes (notably the OPE contribution to AuL) have a strong angular dependence, and even change sign. Phase-shift analysis now predicts this angular dependence accurately up to 800 MeV, and both we and

10

Lab EnergyfMeV) 400

600

Fig. 6. Results for 3~~ compared with those of other groups. Our points are denoted by full circles, LAMPF result ‘a) by triangles, ZGS *) results by squares, and preliminary SIN *‘) results by open circles. Results of the LAMPF and ZGS groups have been amended according to table 9 to the latest Coulomb-nuclear corrections of Arndt, and results of all groups have the Coulomb-barrier correction of table 6 included. The ZGS point at 561 MeV has been withdrawn. Phase-shift fits of Dubois et al. ‘“) are shown by the full line. The dashed line indicates the upper limit allowed by phase-shift analysis if elasticities for J 24 are taken from OPE and remaining inelasticity is all in ‘Da.

JJ? Stanley et al.

/ pp

545

scattering

Lab GIergyW) &oa

300

500

1

I

HI0

I

I

,

10 z E -ii s 5-

Ok

Fig. 7. Results for AaT compared with those of other groups. Our points are denoted by full circles, Saclay results 31) by open circles, and a ZGS result 3, by a triangle. All results have the Coulomb-barrier correction of table 6 included. Dashed and full lines are as in fig. 6.

Arndt 24) have re-evaluated the Coulomb-nuclear interference corrections over this energy range. The amendments required to published LAMPF and ZGS data are shown in table 9, and have been applied in fig. 6. Also, all results shown in figs. 6 and 7 have been

amended

by the Coulomb-barrier

TABLE

corrections

9

Amendments required to published AuL data for Arndt’s Coulomb-nuclear interference corrections Ref.

Energy (MeV)

28

302.9 384.6 434.4 485.0 518.4 535.4 569.6 586.3 619.8 638.8

-0.53 -0.46 -0.44 -0.42 -0.37 -0.36 -0.30 -0.27 -0.22 -0.19

433.0 507.5

-0.51 -0.33

1

*I

Amendment

(mb)

of table 6.

546

J.P. Stanley

et al. / pp scattering

(This correction is necessary before comparing data with the strictly nuclear amplitudes used in forward dispersion relations.) Our itut results are consistently about 3 mb more negative than ZGS *) and LAMPF 28) or preliminary SIN 29)data at nearby eneriges. Also AaT is up to 1.5 mb larger than the results from LAMPF 30) and Saclay 31). Exhaustive discussions with the Argonne, Lampf and SIN groups have not exposed reasons accounting quantitatively for the AcL discrepancies, which are beyond error limits. They have significant consequences for ~-parameters in the phase-shift analysis. There are two points of experimental technique in which our measurements are superior to Argonne and LAMPF. Deuterons from the reaction pp-+dm+ are confined kinematically within a narrow cone (half-angle 12” at 500 MeV) comparable with that covered by the transmission array. In our experiment, the thicknesses of transmission counters and the target were chosen to allow even the slowest deuterons to pass through the entire system; the smallest transmission counter, which is the most critical in the extrapolation to zero solid angle, came first. In both ZGS *f and LAMPF *‘) experiments, the transmission array was the other way round, i.e. the smallest counter came last; since ten counters were used, backward deuterons stopped in their transmission array, before reaching their smallest counter. The effect on both the slope and curvature of the extrapolation to zero solid angle is a maximum in the energy range 400 to 600 MeV, where the discrepancy in AcL is largest. It is noteworthy that our extrapolation to zero solid angle is curved above the pp -+ drr+ threshold, as expected, while ZGS and LAMPF data require straight line extrapolations; this suggests that they have not detected some or all of the products of this reaction. However, the LAMPF group claims that this effect changes their results by ~0.2 mb. We believe that under the worst circumstances it could have an effect of 0.5 mb. However, the product ALL dc/dR, which contributes to AQ, is sufficiently small for pp + dr+ that there is no possibility of accounting for all of the 3 mb discrepancy this way. Secondly, in measuring Au-,-, the LAMPF group 30) used a veto counter 9 cm upstream of the polarised target. This vetoes some backward pions and reduces the measured value of AaT by an amount we cannot quantify. Again the LAMPF extrapolation to zero solid angle is surprisingiy flat. We now address the question whether the discrepancies in ACT,_and AvT could be attributed to overall normalisation errors in our data, which appear to need renormalising downwards in order to agree with other data. Firstly, we recapitulate normalisation errors in table 10. There are independent errors of +6.6% and *6.9% respectively for AuL and Aa=, data; since the major uncertainty in target density is in the filling factor, and this could be different for AcT and AaL runs, we feel that this source of normalisation error is best treated as independent for the two sets of data. The following internal cross checks have been made: (i) The attenuation of unpolarised beam through the AcrT and AcrL targets checks that the product pf is consistent for the two targets within *7%; this error arises

J.P. Stun/ey

et al. / pp scattering

547

TABLE 10 A summary of normalisation errors (percent) Source target density target length & (statistical) shape of C-background in PT monitors total

from uncertainties in the attentuation due to air and transmission counters themselves. (ii) The calibrations of PT by elastic scattering and by the NMR system are consistent within the *6.4% error of the latter. (iii) The magnitude of PB is checked with an accuracy of +4.1% by the asymmetry in ACF~ monitor data with PT= 0. However, normafisation uncertainties in PB contribute very little to those in AaL or AaT. The reason is that the spin-dependent part of the transmission I depends on FgPTA~p white the monitor asymmetry, which is used to find fT, depends on P& also; hence, to the extent that Ir, is determined more accurately by monitor asymmetry ~t2.4 to *X2% than by the NMR +6.4%, Fn cancels out in the evahtation of An Next we relate our data to phase-shift analysis. Our ACT,_results at 202 and 325 MeV, where inelasticity is zero or very small, agree closely with phase-shift predictions at these energies (see table ‘7). These predictions are very secure, since the large contributions to AQ. arise from ‘PI, 3P2 and ‘D2, and these partial waves are accurately fixed by extensive and precise elastic data. If one tries renormalising all our AuL data by 20%, so as to agree with other groups above 400 MeV, x2 in the phase-shift fit increases by unreasonably large amounts at 202 and 325 MeV (-67 and -22 respectively), The Arndt-Verwest phase-shift fit also displays the same behaviour 24)a Our conclusion is that the norma~isation of our Arr, data is unlikely to be wrong by more than about one standard deviation (6.6%), which would increase x2 at 202 and 325 MeV together by about 10, Expressions for the forward scattering amplitudes F2 and FZ (eq. (1)) in terms of the singlet amplitude R,, the triplet amplitudes RL,., and the mixing amplitude RS are -i.++z = C i2J + lIR_r-JR,_I,J J

- (J J- l)RJ+l,_r -2(.T(.T + l)}‘/“R’]

Above the inelastic threshold, very firm positive bounds on both An

)

and Am

(21)

are

548

J.P. Stanley er al. / pp scattering

obtained by putting all inelasticity into ‘D:! and setting all other n = 1. A slightly more restrictive set of bounds (displayed on figs. 6 and 7) is found by fixing 77 for J 34 to OPE values; up to 700 MeV, there is excellent agreement amongst theoretical groups for those high partial waves. This leaves seven v-parameters for ‘So, 3P0, 3P1, 3P2, rDZ, 3F2 and 3F3. Of these, q(‘Dz) and 77(3F3) are large and quite well determined by the shape of the elastic diffraction peak and the spin-averaged total inelastic cross section, which is known with an accuracy of *lo%. Clearly An and ACTScannot fix the remaining five q-parameters uniquely. The result is that alternative phase shift solutions can be found fitting either ZGS-LAMPFSaclay-SIN data or our Au,_ and AC, data. The Arndt-Verwest solution I’) omits our data. The solution of Dubois et al. lo), shown in figs 6 and 7, incorporates all data, with due allowance for quoted normalisation errors. Fig. 7 illustrates the fact that our Aa, data lie uncomfortably close to the positive bound allowed by phase-shift analysis, and so do ZGS-LAMPF-SIN 4~~ data. The implication of our Aa,_ data, which lie well away from the positive bound, is that RJ.,, which contributes negatively to eq. (22), are significant (for either or both of 3P1 and 3F3). Qualitatively, the latter conclusion agrees with the limited amount of inelastic data up to 515 MeV. In this energy range, the dominant inelastic channel is pp+dw+, and from data on da/da and P it is clear 32) that inelasticity starts in 3P1 at threshold, is overtaken at 345 MeV by ‘DZ, and in the energy range 400 to 500 MeV 3F3 and 3P2 inelasticities become significant. The 3P2 inelasticity poses some problem in fitting our ACT=data, which imply that the imaginary parts of amplitudes RJ, R.,_l,J and R I+l,f in eq. (21) are small up to 515 MeV. The best fit to our AcrT data alone requires v(~P~) = 1 up to 515 MeV. However, at 580 MeV and above, there is clear evidence for rapidly rising inelasticity in 3P2. The inelastic amplitude in this partial wave should rise from threshold as q5”, where q is the c.m. pion momentum in pp + dr+; all theoretical predictions exhibit this momentum dependence up to at least 580 MeV. Hence, the solution of Dubois et al. lo) imposes this momentum dependence, with the result that the fit to AcT lies slightly below the data reported here. If one likewise imposes the threshold dependence q3’2 on the lDz inelastic amplitude up to 515 MeV and q”’ for 3F3 up to 580 MeV, (a) pp+drr’ data may be fitted quantitatively with small and reasonable phase variations, and (bf the optimum overall x2 in the phase-shift fit to elastic data is obtained by renormalising both our AaL and AaT data down by about one standard deviation, i.e. 6.8%. The most likely origin of such a normalisation error would be the target density; in subsect. 2.2 we remarked that our measured density is 7% below that quoted by other groups. A fit to ZGS-LAMPF-SIN values of AQ demands either (a) Im R,,, = 0, i.e. v(~P,) = q (3F3) = 1, in contradiction to pp + drr+ data, or (b) T(~F~) = OPE and large inelasticity in 3Pa; the latter is the solution favoured by Arndt and Verwest ‘*), but the large inelasticity in 3Po is surprising, since this wave is forbidden in pp + dv +.

J.P. Stanley

et al. / pp scattering

549

Our AU,_ and ACT=data have little to say directly about whether dibaryon resonances exist or not. Clearly there are peaks in both at -550 MeV. If one draws by eye a smooth background under these peaks, the surviving peaks are equal in magnitude, width and energy with one another and with the peak in the pp + dT+ overall cross section, within experimental errors (*15%). This suggests strongly that all are due to ‘D2 inelasticity, which has the same Clebsch-Gordan coefficient for Au,_ and Au=. The rd total cross section has a 230 mb peak just above this energy, due to the A(1230) resonance plus a spectator nucleon. A final-state interaction between the A and the spectator nucleon will couple to the pp channel in the ID2 state. Thus it is possible to account for all three peaks as a pseudoresonance, or doorway state. It is possible that this is associated with a resonance in the dibaryon system, but confirmation would require detailed phase information. Lastly, we comment on forward dispersion relations for F2 and F3. The most recent calculations of Grein and Kroll 9, report satisfactory agreement for F2 (ACT=) with both the Arndt-Verwest phase-shift solution and ours lo). However, in the case of F3 (ACT,_),they find discrepancies with our phase shifts. Our own calculations are displayed in our previous publication “), and are very little altered by the small changes to AuL reported here; satisfactory agreement can be obtained between this forward dispersion relation and our phase shifts by a small change in the contribution to F3 from the unphysical cut. We wish to thank the staff at TRIUMF for their support, and we are especially indebted to Mr A. Bishop for his invaluable assistance in maintaining our experimental equipment at a high state of readiness. We thank Dr. G. Court, Mr D. Gifford and Mr K. Arbuthnot for their help with the polarised target, and also Dr C. Waltham for assistance during a run. We are grateful to the Argonne, Geneva and Saclay groups for extensive and helpful discussions on their data and ours, and to Dr R. Arndt for calculating Coulomb-nuclear interference corrections. We are grateful to Dr H. Zankel for advice on Coulomb-barrier corrections to the parameters E and q. D.V.B. thanks the SERC for a Fellowship; J.P.S. and N.R.S thank the SERC for Studentships. R.S. thanks NSERC for a Postgraduate Scholarship. This experimental work was partially funded by a grant from NSERC.

Appendix

We discuss the presence of non-vertical components of polarisation in the beam at the entrance to the solenoid S, and show how their effects can be eliminated, both from the measurements of transmission and from the monitor measurements of PT. We define orthogonal axes by unit vectors n, r and 1, where n is vertically upwards, I is parallel to the momentum of the beam, and r = I An, i.e. to the right as seen by the beam. Let the components of the beam polarisation PB before S be

J.P. Stanley ei al. j pp scattering

550

(Pa, T, L), the angle of precession of the polarisation by S be 8, the angle of precession of the polarisation by the magnet be 41/,and the angle which the magnetic field of the target makes with the axis of the beam be 93, Hence, before S PB=PBn+Tr-+L1,

(A.11

and after S Pa=fPBcos6-Tsin3)n~(PasinB+TeosBfr+LE.

(A.2)

After M Pa = (Pa cos B - T sin 6)~ + [(Pa sin 6 + T cos 6) cos Jr -L sin &Jr +[(Pas~~$+Tcos~)sin~+Lcos~]~.

iA.3)

If 6, is positive for a rotation to the left (as here, see fig. l), the difference 4t in the transmission fraction t on reversal of PB becomes, using eq. (A.3) and eq. (2): 4t = ktPT(Aq_ cos 4, [(PB sin 0 + 7” cos 8) sin .$ + L cos $1 + day sin #J[L sin +?I- iPB sin B + T cos B1cos 41) ,

(A.4)

where fc is a constant depending on the target composition and length, If the current in the solenoid is adjusted so that B is +f-f90” for +(-f polarity, then At(*) = iktPd4q

cos cf,(PR sin 4 iL cos 4)

+ Awr sin 4, (+L sin ~5- PB cos 4)) .

(A.3

We note that (a) T has no effect on the transmission, (b) the effect of L can be eiiminated by averaging At(+) and At(-), (c) there remains a small term containing LLCTT, which is directly calculable. A general expression for the asymmetry 5, monitored by the chambers W, can be obtained from eq. (A.3), noting that the forward scattering arm is to the right of the incident beam. Thus

For B = *90”,

J.P.

Stanley

et al. / pp scattering

551

Apart from the main term depending on PTP~ there is (a) a term of modulus ITP,,\ independent of PT, which changes sign with the polarity of S, (b) a term involving L which changes sign on reversal of PT, but is independent of the polarity of S. Hence, the effect of L and T can be eliminated by averaging [ over both target and solenoid polarities. These arguments can be extended straightfo~ardly to include precession of beam polarisation by the field of the polarised target. In this case, small teams survive in the transmission t and in the monitor asymmetry 5 depending on T and which do not entirely drop out upon averaging over target and solenoid polarity. These have been taken into account explicitly in our analysis.

References 1) K.

2) 3) 4) 5)

6)

7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 2.5) 26)

Hidaka et al., Phys. Lett. 70B (1977) 479, N. Hoshizaki, Prog. Theor. Phys. 58 (1977) 716; 60 (1978) 1796; 61(1979) 129; A. Yokosawa, in Nucleon-nucleon interactions, ed. D.F. Measday, H.W. Fearing and A. Strathdee (AIP, New York, 1978) p. 59 I.P. Auer er al., Phys. Lett. 67B (1977) 113; 708 (1977) 475 W. de Boer et al., Phys. Rev. Lett. 34 (1975) 558; E.K. Biegert er al., Phys. Lett. 73B (1978) 235 W. Grein and P. Kroll, Nucl. Phys. B137 (1978) 173 R.A. Arndt, R.H. Hackman and L.D. Roper, Phys. Rev. Cl5 (1977) 1002; D.V. Bugg eta/., J. of Phys. 64 (1978) 1025; L21 (1980) 1004; J. Bystricky et al., Saclay preprint D.Ph.P.E. 82-09 (1982) EL. Berger, P. Pirila and G.H. Thomas, Argonne preprint ANL-HEP-PR-75-72 (1975); W.M. Kloet ef al., Phys. Rev. Lett. 39 (1977) 1643; M. Arik and P.G. Williams, Nucl. Phys. B136 (1978) 425 A.M. Green and M.E. Sainio, J. of Phys. GS (1979) 503 D.V. Bugg, J. of Phys. G5 (1979) 1349 W. Grein and P. Kroll, Nucl. Phys. A377 (1982) 505 R. Dubois ef al., Nuct. Phys. A377 (1982) 554 R.A. Arndt and B.J. Verwest, Texas A & M preprint DOE/ER/O5223-29 (1980) CL. Hollas, Phys. Rev. Lett. 44 (1980) 1186 W.M. Kloet and R.R. Silbar, Nucl. Phys. A338 (1980) 281; A338 (1980) 317 W.M. Kloet and J.A. Tjon, Phys. Lett. 1068 (1981) 24 T. Kamae et al., Phys. Rev. Lett. 38 (1977) 468; Nucl. Phys. B139 (1978) 394; T. Kamae and T. Fujita, Phys. Rev. Lett. 38 (1977) 471 .I. Bolger et al., Phys. Rev. Lett. 46 (1981) 167; 48 (1982) 1667 D. Axen et al., J. of Phys. 67 (1981) L225 C. Amsler et al., J. of Phys. G4 (1978) 1047 M. Craddock et al., TRIUMF preprint TRI-PP-81-37 (1981) P.S.L. Booth et al., Nucl. Phys. B121 (1977) 45 M. Comyn and R.I.D. Riches, in High energy physics with polarised beams and polarised targets, ed. C. Joseph and J. Soffer, Experientia Supplementum 38 (Birkhauser, Base], 1981), 466 M.W. McNaughton et al., Phys. Rev. C23 (1981) 1128 J. Frohlich and H. Zankel, Phys. Lett. 82B (1979) 173 R. Arndt, private communication E. Aprile et nl., Nucl. Phys. A335 (1980) 245, and private communication. D. Besset er al., Nucl. Instr. 166 (1979) 379

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