Elastic pion-deuteron scattering near the 3-3 resonance

NuclearPhysics

A350 (1980) 253-264 @North-Holland

Not to be reproduced

Publishing Co., Amsterdam

by pbotoprint or microfilm without written permission from the publisher

ELASTIC PION-DEUTERON SCATTERING NEAR THE 3-3 RESONANCE K. GABATHULER,

J. DOMINGO,

P. GRAM*, W. HIRT, J. ZICHY

G. JONES**,

Swiss Institute for Nuclear Research, CH-5234 J. BOLGER

and

Vi&en,

P. SCHWALLER

and

Switzerland

Q. INGRAM***

Znstitutfiir Experimentelle Kemphysik, Kemforschungszentrum und Universitiit Karlsruhe, Postfach 3640, D-7500 Karlsruhe, Germany and J.P.

ALBANESE****

and J. ARVIEUX*****

Institut des Sciences Nucleaires, Waiversite de Grenoble, BP 257, F-38044 Grenoble-Cedex, France Received

7 July 1980

Abstract: The elastic scattering of positive pions by deuterium has been studied at seven energies between 82 MeV and 292 MeV laboratory kinetic energy in the angular range between 30” and 130” (lab). The results are compared to recent relativistic three-body calculations.

I

NUCLEAR

REACTION

*H(rr+, n+), E = 82-292

MeV; measured

o(e).

I

1. Introduction Theoretical

calculations

of rd elastic scattering

in the neighbourhood

of the 3-3

resonance have now reached a high level of sophistication ‘*‘). Based on a “fully relativistic” three-body theory they now include not only the dominant Ps3 pionnucleon partial wave, but also the small S rr, S3r, PI3 and P3r partial wavest, as well as realistic deuteron wave functions. Giraud et al. I) were able to include the small TN partial waves exactly and to improve on the deuteron wave functions by requiring the correct quadrupole moment of the deuteron. The latter constraint has the effect that the differential cross sections are quite insensitive to the deuteron D-state. The * On leave from LAMPF, Los Alamos Scientific Laboratory, Los Alamos, NM 87545, USA (present address). ** On leave from University of British Columbia, Vancouver, B.C. V6T lW5, Canada (present address). *** Present address: SIN, CH-5234 Villigen, Switzerland. **** Present address: CERN, CH-1211 Geneve 23, Switzerland. ***** Present address: Laboratoire National Saturne, F-91190 Gif-sur-Yvette, France. t The inclusion three-body model.

of Pii,

which

contains

the nucleon 253

pole part,

cannot

be incorporated

into a strict

254

K. Gabathuler

et al. / Pion-deuteron

scattering

sensitivity to the D-state obtained by Rinat er al. 2, may thus be simply a manifestation of the less sophisticated deuteron wave functions employed by them. Rinat et al. 2, included the small ?rN partial waves by perturbatively estimating their interference effects; however, this may not be sufficient at energies where the P33 partial wave is not overwhelmingly dominant. Nucleon-nucleon rescattering by other than the 3S1-3D1 partial waves, and p-exchange in the multiple scattering series (rrN + A + pN + A + rN) are shown to have very little effect. As a further improvement Rinat et al. 2, have included pion absorption and re-emission through the nucleon pole part in the PI1 pion-nucleon interaction, although this task could not be solved strictly within the three-body model used so far. Including p-exchange and pion rescattering effects for this absorption correction to all orders, they find that up to 180 MeV the differential cross sections are not greatly affected whereas the large-angle differential cross sections above the resonance are changed quite drastically. The p-exchange is found to play an important role in this absorption correction. The non-pole part of the Prr pionnucleon partial wave has been omitted. Fayard et al. 3, have taken into account the pole and the non-pole parts of the Plr channel, but neglected p-exchange. They arrive at similar absorption corrections, but this must be considered as accidental. The high level of sophistication being achieved in these theoretical efforts requires more abundant and precise data in order to provide the stringent tests necessary for these calculations. The data published before 1979 are too crude and imprecise to serve this purpose. In addition, large discrepancies which exist between these theories and the published data have raised questions regarding the overall reliability of the data sets themselves. In order to resolve these questions we have measured the rr+-d differential cross sections at seven energies between 82 and 292 MeV in the angular range from 30” to 130”. In sect. 2 the experimental method is described and in sect. 3 we present the data. Finally, sect. 4 contains the comparison of our results with other data and with theory. 2. Experimental method and data analysis The experiment was carried out on the high-resolution pion beam and pion spectrometer facility of the Swiss Institute for Nuclear Research (SIN). The positive pions were momentum analysed both before and after scattering on a liquid DZ target. The experimental equipment is described in detail in ref. 4). The standard detector system was supplemented by an additional wire chamber placed immediately in front of the target. With pairs of wire chambers before and after the scattering target it was possible to measure the scattering angle to rt:0.5” (FWHM), thus minimising the con~ibution of the kinematical broadening to the energy resolution (up to 1 MeV/deg). The introduction of the additional wire chamber at a

K. Gabat~uler et al. / Fion-~euteronscu~e~ng

255

point where the beam spot was very small did however reduce the total detector efficiency and limit the useful incoming pion flux to less than 5 x lo6 pious/s. The 15 mm thick liquid Dz target had a gas ballast window system? in order to guarantee a very uniform target thickness over the beam spot. A feedback control system kept the temperature of the liquid at a preset value to within ztO.02 K. The target density was determined from the measured vapour pressure of the liquid using cryogenic tables 6). Data were recorded in steps of 10”. Where the cross section varied rapidly with scattering angle the angular acceptance of the spectrometer (10”) was divided into three bins, each 3” wide. At each spectrometer setting the magnetic field was adjusted so that the elastic peak fell onto the same portion of the focal plane detector of the spectrometer. The overall normalisation was determined by comparing the rr+p scattering, measured with liquid hydrogen in the same target cell, to the known cross sections determined from phase shifts ‘). The calibration runs were performed for each angle and energy in such a manner that the momentum of the scattered pions was identical for the data run on deuterium and the calibration run on hydrogen. This procedure required considerably higher incoming pion energies for the calibration runs. Calibrations for pion energies greater than 300 MeV could not be obtained, however, because of the large discrepancies which characterize the different sets of phase shifts for this energy region. Such a calibration procedure has the following advantages: (i) The influence of any momentum dependence of the spectrometer’s acceptance and solid angle is eliminated. (ii) The correction for the decay of the scattered pions cancels out in the final cross sections. (iii) The elastically scattered pions from hydrogen and deuterium intercept the large wire chambers at the focal plane of the spectrometer in the same area. Thus using the simple spectrum obtained from hydrogen scattering the efficiencies of the chambers were determined in the region relevant for the elastic events from deuterium. For low incident pion energies the beam spot on the scattering target became quite large due to the multiple scattering from the materials in the beam line. This simulated a drop in the spectrometer acceptance since the wings of the beam distribution were no longer seen by the spectrometer. This effect was different for the data runs and calibration runs due to the fact that they were taken at different incident pion energies. Corrections for this effect were found to be negligible for beam energies at 142 MeV and higher; for lower energies they remained less than 10%. i For a description of such a target see for example Axen et al. ‘).

256

I(: ~abat~u~er et al. / Pion-deuteron

scattering

Due to the different densities of liquid hydrogen and deuterium the thin inner windows of the target cell deflected by a slightly different amount under the different hydrostatic pressures of the two liquids. Measurements at room temperature under conditions that reproduced this pressure difference indicated a ratio of the target thicknesses of 1.02 Dz/H2. This value can be considered an upper limit to the values for liquid hydrogen temperatures (due to the increasing strength of mylar with decreasing temperature), and the ratio of the target thicknesses was taken to be 1.01*0.01. The data were collected as energy loss spectra. These spectra exhibit a prominent elastic peak and a continuous distribution from the deuteron break-up. For energy losses less than that of the elastic peak a small flat back~ound was present due to the windows of the target cell and to muons resulting from the pions which decay near the end of the spectrometer. For angles below 40” a second peak due to the elastic scattering on carbon and oxygen in the mylar window was also present; this second peak limited the forward angular range which could be reached at the lower pion energies. The energy loss spectra were fitted with an idealised shape which was then smeared out by the finite energy resolution determined from the width of the elastic peak. This idealised spectrum contained three parts: A &function representing the elastic peak, a flat continuous background present on both sides of the elastic peak and a break-up spectrum of quadratic shape starting at a point 2.225 MeV from the elastic peak. The break-up spectrum was permitted to contain a positive pedestal in order to include the possibility of an enhancement due to the final-state interaction of the two nucleons. The elastic peak was allowed a tail characteristic of energy straggling. The fitted background under the elastic peak amounted to 13% in the worst cases, more typically to 5 % . The data were further corrected for the inefficiencies of the wire chambers, the computer dead time, the possibility of having more than one pion in the 1 ns wide beam burst, the muon contamination of the incident pion beam which was different for the data and calibration runs, and for pion decay in the spectrometer for those cases where the calibrations were not performed with the same scattered pion momentum.

3. The results Our results are presented in table 1 and in figs. l-3. The data points at 0” are calculated from the results of ref. a). The angle given is that appropriate to the center of the angular bin used (either 3” or 10” width in the laboratory frame). We also give those momenta at which the calibrations were made with r+p elastic scattering and the calibration cross section as calculated from phase shifts ‘>_These calibration cross sections contain Coulomb effects.

K. Gabathuler et al. / Pion-deuteron scattering TABLE

257

1

r+d elastic scattering cross sections c.m. system

Lab system

Calibration (lab)

T lab angle

da/d0

angle

(mb/sr)

duJdf2 (mb/sr)

82 MeV

50 60 70 80 90 100 110 120 130

1.82*0.10 l.lSztO.08 0.930*0.054 0.831 ztO.049 0.933 f 0.059 0.989 f 0.058 1.07 f 0.07 1.24kO.07 1.34+0.08

55.0 65.6 76.0 86.3 96.4 106.2 115.9 125.4 134.8

1.59*0.09 1.04*0.07 0.870*0.051 0.807 f 0.048 0.942 f 0.060 1.04ztO.06 1.16iO.08 1.40~0.08 1.56 + 0.09

116 MeV

27 30 33 37 40 43 47 50 53 57 60 63 70 80 90 100 110 120 130

12.33k0.76 10.5OzkO.64 f3.99*0.59 7.44 l 0.44 6.8OkO.40 5.74*0.35 4.61 zt0.31 3.78kO.26 3.18~~0.22 2.56zt0.15 2.26kO.13 1.93k0.12 1.61 f 0.09 1.241tO.09 1.23kO.07 1.30*0.07 1.39*0.07 1.46ztO.08 1.55 f 0.08

30.4 33.7 37.0 41.5 44.8 48.0 52.4 55.6 58.9 63.2 66.3 69.5 76.8 87.1 97.2 107.0 116.6 126.1 135.4

9.93 i 0.61 8.51 rt0.52 7.34 f 0.48 6.14zkO.36 5.66zkO.33 4.82 f 0.29 3.92kO.26 3.25 f 0.22 2.76zt0.19 2.26*0.13 2.02zko.12 1.74*0.11 1.50*0.08 1.2OztO.09 1.25kO.07 1.37*0.07 1.53*0.08 1.67 kO.09 1.84zkO.09

17 20 23 27 30 33 37 40 43 47 50 53 57 60 63 67

29.56* 1.44 26.82* 1.28 23.7Ozt 1.16 19.83 f 0.94 17.43 f 0.92 14.70*0.80 11.06*0.54 9.59zkO.48 7.68*0.51 5.94zto.30 4.93zt0.25 4.36zt 0.23 3.08ztO.17 2.55ztO.15 2.24hO.13 1.97ztO.12

19.4 22.8 26.2 30.7 34.1 37.4 41.9 45.2 48.5 52.9 56.2 59.4 63.7 66.9 70.1 74.3

22.93~1~1.12 20.91 f 1.00 18.58*0.91 15.68 f 0.74 13.88 f 0.73 11.80*0.64 8.98 f 0.44 7.86 f 0.39 6.36zt0.42 4.99zt0.25 4.19zkO.21 3.75 f 0.20 2.69kO.15 2.26kO.13 2.01 kO.12 1.80*0.11

142 MeV

dcr/dn (Me&c) 180 183 186 190 195 199 204 208 212

218

221

225

230 235 241 248 254 261 268 274

247

250

253

258

264

(mb/sr) 2.23 2.20 2.40 2.94 3.70 4.69 5.85 7.08 8.32 11.62 11.03 10.37 10.29 9.59 8.79 8.71 8.02 7.41 7.47 6.99 6.62 6.76 7.31 8.58 10.34 12.26 14.00 15.33 28.28 27.53 26.39 25.95 24.25 22.49 21.60 19.74 17.96 16.93 15.31 13.87 13.03 11.90 10.97 10.42

K. Gubffth~~eret af. / P~5n~eu~er~n sca~e~~g

258

TABLE

1 (continued) c.m. system

Lab system

Calibration (lab)

TIaLl angle

dVJldR

angle

(mb/sr)

181 MeV

217 MeV

dVJdt2

da/d0

(mb/sr)

bbhr)

70 73 80 90 100 110 120 130

1.61r0.10 1.47*0.10 1.275 0.06 1.18*oo.06 1.18*0.06 1.20*0.06 1.17ztOo.06 1.19kO.06

77.4 80.5 87.7 97.8 107.6 117.2 126.6 135.8

1.49kO.09 1.38zkO.09 1.23*0.06 1.2OkO.06 1.261tO.06 1.3410.07 1.36kO.07 1.44*0.07

17 20 23 27 30 33 37 40 43 47 SO 53 57 60 63 67 70 73 80 90 100 110 120 130

47.40*2.22 41.30* 1.93 35.04* 1.69 26.06* 1.29 21.59+ 1.07 18.40+ 1.00 13.75 *0.67 10,46ztOSl 8.17*0.43 5.91 zto.32 4.90 f 0.26 3.77zt0.24 2.51~0.14 1.96kO.10 1.53*0.10 1.15~0.08 1.05*0.07 0.930*0.066 0.697 f 0.035 0.589* 0.029 0.540* 0.028 0.510~0.027 0.472* 0.025 0.428rtO.021

19.7 23.1 26.6 31.2 34.6 38.0 42.5 45.8 49.2 53.6 56.9 60.2 64.5 67.7 70.9 75.2 78.3 81.4 88.6 98.7 108.5 118.0 127.3 136.4

35.70 f 1.67 31.28zt 1.46 26.71 f. 1.30 20.06 f 0.99 16.76 zt 0.83 14.41 tt0.78 10.91 *to.53 8.39rt0.41 6.63 f 0.35 4.87 f 0.26 4.09kO.22 3.19~~0.20 2.16ziO.12 1.71~0.09 1.36~0.09 1.04*0.07 0.961 f 0.060 0.868 f 0.062 0.675 ztO.034 0.601 iO.030 O.S80*0.030 0.576rtO.030 0.558ztO.030 O.S33*0.026

17 20 23 27 30 33 31 40 43 47 50 53 57

44.93k2.15 35.32+ 1.71 28.74* 1.48 20.80* 1.01 18.03 k0.87 14.41 *to.80 10.40*0.49 7.66 f 0.38 6.16ztO.33 4.15zt0.23 3.06*0.18 2.20*0.14 1.62*0.09

20.0 23.5 27.0 31.6 35.0 38.5 43.0 46.4 49.8 54.3 57.6 60.9 65.2

32.95k 1.58 26.06 f 1.26 21.36* 1.10 15.621tO.76 13.67rt 0.66 11.04zk0.61 7.81 f 0.38 6.03 f 0.30 4.90rt0.26 3.372to.19 2.51kO.15 1.83i0.12 1.39~tO.08

271 279 287 296 305 314 323

292

295

301

307

316

325 336 348 361 373 387 400

332

337

344

352

9.85 9.45 9.14 9.26 9.73 10.11 10.20 9.99 50.31 47.60 44.72 40.87 37.71 34.55 30.28 27.30 24.47 20.46 18.14 16.06 12.98 11.50 10.25 8.12 7.37 6.81 5.26 4.31 3.85 3.60 3.3s 3.09 45.95 42.95 39.97 34.94 32.01 29.11 24.10 21.53 19.10 15.03 13.12 11.41 8.53

K. Gabathuler et al. / Pion-deuteron scattering

259

TABLE 1 (continued) Lab system

c.m. system

Calibration (lab)

Tlab angle

daJdf2

angle

(mb/sr)

254 MeV

292 MeV

duJdf2 (MepV/c)

(mb/sr)

363

7.35 6.36 8.12 7.37 6.81 5.27 4.31 3.85 3.60 3.35 3.09

60 63 67 70 73 80 90 100 110 120 130

1.11*0.07 0.866 f 0.068 0.531 f 0.038 0.391 f 0.025 0.323 * 0.029 0.280 f 0.014 0.215*0.011 0.196*0.011 0.179*0.011 0.173*0.009 0.162*0.010

68.5 71.7 75.9 79.1 82.2 89.4 99.5 109.2 118.7 127.9 137.0

0.960 f 0.058 0.761 f 0.060 0.477 l 0.034 0.358kO.023 0.300*0.027 0.271 ztO.014 0.220*0.011 0.213~kO.012 0.205ztO.013 0.208+0.011 0.204*0.013

17 20 23 27 30 33 37 40 43 47 50 53 57 60 63 67 70 73 80 90 100 110 120 130

32.33k1.64 25.30*1.29 21.09+1.15 15.42zkO.82 12.25 f 0.65 9.26k0.56 6.72 f 0.34 5.01 ztO.26 3.64ztO.22 2.48kO.14 1.78*0.10 1.25rtO.09 0.812hO.049 0.550*0.034 0.415*0.033 0.29%~ 0.018 0.194*0.013 0.150*0.013 0.0940 f 0.0056

20.2 23.8 27.3 32.0 35.5 39.0 43.6 47.0 50.4 54.9 58.3 61.9 66.0 69.2 72.5 76.7 79.9 83.0 90.2 100.3 110.0 119.4 128.6 137.5

23.09* 1.17 18.19hO.93 15.34k0.84 11.31ztO.60 9.08 f 0.48 6.94 f 0.42 5.12kO.26 3.86~kO.20 2.85k0.17 1.97zto.11 1.45 f 0.08 1.03*0.07 0.683 ztO.041 0.470 f 0.029 0.360+ 0.029 0.263 kO.016 0.176+0.012 0.14OkO.012 0.0910*0.0054 0.0804 f 0.0045 0.0731 zkO.0042 0.084OkO.0055 0.0842 f 0.0045 0.104*0.006

17 20 23 27 30 33 37 40 43 47

0.0780*0.0044 0.0667 f 0.0038 0.0710* 0.0047 0.0688 * 0.0037 0.0810~0.0047 25.16,. 1.22 19.87 f 0.97 15.20*0.79 ll.llzkO.56 8.48 f 0.47 6.69k0.37 4.47+0.25 3.36hO.20 2.37zt0.14 1.55kO.08

20.5 24.1 27.7 32.4 36.0 39.5 44.1 47.6 51.0 55.6

dujdR

(mb/sr)

17.51 zkO.85 13.93rtO.68 10.75 f 0.56 7.96+0.40 6.15ztO.34 4.91+0.27 3.34*0.19 2.54kO.15 1.82ztO.11 1.22kO.06

325 336 348 361 374 387 400

373

379

388

398

412

325 336 369 361 374 369 369

323

337

344

35.59 33.03 30.56 26.21 23.87 21.58 17.40 15.42 13.54 10.33 8.89 7.61 5.44 4.58 3.85 8.12 7.37 6.81 5.27 3.06 3.85 3.60 4.48 4.97 45.95 42.95 39.97 30.94 32.01 29.11 24.10 21.53 19.10 15.03

IC. Gabathuier et ai. / Pion-deuteron scattering

260

TABLE 1 (continued) Lab system

c.m. system

Calibration (lab)

Tlab angle

dcr/dl2

angle

Cmblsr) 50

53 57 60 63 67 70 73 80 90 100 110 120 130

1.07rtO.06 0.717zko.044 0.453 * 0.028 0.308 ..k0.020 0.223 rfr0.017 0.139rto.013 0.0942 rt 0.0072 0.0721 rt 0.0087 0.0404 f 0.0024 0.0263 j: 0.0016 0.0308 f. 0.0019 0.035 1 f 0.0022 0.0433 rt 0.0022 0.0489 f 0.0031

58.9 62.3 66.7 70.0 73.2 77.5 80.7 83.8 91.0 101.0 110.7 120.1 129.2 138.1

du/dfI

du/dD

imblsr)

imblsr)

0.852iO.045 0.582 * 0.036 0.377kO.023 0.261zkO.017 0.192~0.015 0.123ztO.012 0.0852 f 0.0065 0.0665*0.0080 0.0391*0.0023 0.0272+0.0017 0.0341*0.0021 0.0414 f 0.0026 0.0540& 0.0027 0.0642 f 0.0040

352

363

325 336 343 361 374 387 400

13.12 11.41 8.52 7.35 6.36 8.12 7.37 6.81 5.27 4.31 3.85 3.60 3.35 3.09

The statistical error was typically *3%. The other sources are: *2% for the calibration cross sections, f 1% for the local chamber efficiencies at the focal plane of the spectrometer, f I% for estimating the probability of having more than one particle in a beam burst, it 1% for the muon correction in the incident beam and, where necessary, in the spectrometer, f 1% for the target thickness ratio, rt 3% for the peak fitting procedure and (at low energies) f 2.5% for the correction due to the larger beam spot on the target. All errors were added quadratically. 4. Discussion of the results So far our results represent

the most complete set of pion-deuteron elastic differential cross sections available. Comparing them with other data we can make the following remarks: (i) At 142 MeV and 181 MeV there is consistency with old bubble chamber data 9,10). (ii) The deep minimum previously observed in the angular distribution at 256 MeV [ref. “)I could not be reproduced. Whereas the forward angle points of ref. 11) are in agreement with the new data, all backward angle points are too low. (iii) The data at 231 MeV [ref. ‘“)I confirm the trend of our results. This can be seen by comparing them with the theoretical curves in fig. 2. However, it is conceivable that the two most forward points at 23 1 MeV are too low compared to our data since at these angles there is much better agreement between theory and experiment at 217 and 254 MeV.

K. Gabathuler et al. / Pion-deuteron scattering

261

8 mtdegrees)

Fig. 1. z-+d differential cross sections in the c.m.s. for laboratory kinetic energies of 82,116 and 142 MeV. The data points marked with crosses of Stanovnik et al. 13)were measured at 141 MeV, those at 180“ of Holt et al. 14) at 80, 120 and 140 MeV. The data points at 0” were calculated from total cross sections *). The theoretical curves are from the Lyon group ls3). The full lines include ail the S and P pion-nucleon partial waves (with the exception of Pll) and a realistic deuteron wave function with 6.7% D-state. The dashed line contains in addition the full PII pion-nucleon channel which brings about the inclusion of pion absorption and re-emission.

(iv) The recent backward angle data from CERN 13) are in good agreement at 142 MeV and 254 MeV (figs. 1 and 3), whereas at 181 MeV there is a discrepancy of about 20% (fig. 2). (v) The data points of Holt et al. 14) at 80, 120 and 140 MeV and 180” are consistent with our data (fig. 1). We choose to compare our data with the theoretical calculations of the Lyon group 1*3).The full lines in figs. l-3 represent cross sections without corrections for pion absorption and re-emission ‘). They include all the S and P pion-nucleon partial waves (except PI%), and a realistic deuteron wave function (D-state probability 6.7%). At low energies (fig. 1) the theoretical calculations reproduce the shape of the angular distributions almost perfectly. As energy increases, starting at 181 MeV, deviations between theory and experiment increase beyond about 70” whereas the

262

K, Gubathuler et al. / Pion-deute~~ scattering

ecm Idegrees)

Fig. 2. Ir+d differential cross sections in the c.m.s. for laboratory kinetic energies of 181 and 217 MeV. The data points marked with crosses of Stanovnik et al. 13) were measured at 177 MeV. The data at 231 MeV (open circles) are from ref. 12). For the theoretical curves see fig. 1.

forward-angle data remain in agreement up to 217 MeV. Above 217 MeV the small-angle data tend to lie about 10% below the theory. The full inclusion of the so far neglected Pli pion-nucleon channel, which through its nucleon pole part brings about pion absorption and reemission, does not change significantly the cross sections up to 181 MeV [ref. 3)] (dashed lines in figs, 1 and 2). The large discrepancies at large angles above the resonance are greatly enhanced by the absorption correction, whereas at small angles agreement is improved (dashed line in fig. 3). It is doubtful whether the effects of p-exchange in the absorption correction which have been neglected in the present calculation and are claimed to be important ‘), could sufficiently reduce the large discrepancies in the backward hemisphere. At high energies, inelasticities of the WN partial waves and higher-order partial waves may become important. An alternative and highly speculative interpretation of the lack of agreement concerns dibaryon resonances Is). However, extraction of dibaryon parameters from vd data must await the results from experiments involving polarised deuterons. This would allow a phase shift analysis for pion-deuteron scattering.

263

K. Gabathuler et al. / Pion-deuteron scattering

:a. 00

300

60*

90"

1200

1500

1800

Fig. 3. rr+d differential cross sections in the c.m.s. for laboratory kinetic energies of 254 and 292 MeV. The data points marked with crosses of Stanovnik et&. r3) were measured at 260 MeV. For the theoretical curves see fig. 1.

We are grateful to J.B. Walter and G.A. Rebka for providing us with their computer code for the calculation of rr+p differential cross sections. We also wish to thank C, Fayard and the Lyon group for their theoretical calculations.

References 1) 2) 3) 4) 5) 6)

N. Giraud, C. Fayard and G.H. Lamot, Phys. Rev. CZl(1980) 1959 AS. Rinat et al., Nucf. Phys. A329 (1979) 285 C. Fayard, G.H. Lamot and T. Mizutani, Phys. Rev. Lett. 45 (1980) 524 J.P. Albanese et al., NIM 158 (1979) 363; Phys. Lett. 73B (1978) 119 D. Axen et al., Nucl. Phys. A256 (1976) 396 Selected Cryogenic Data Notebook, BubbIe Chamber Group, Brookhaven National Laboratory, ed. J.E. Jensen et ai. 7) J.B. Walter and G.A. Rebka, Los Alamos Informal Report LA-7731-MS 8) E. Pedroni et al., Nucl. Phys. A300 (1978) 321 9) E.G. Pewitt et al., Phys. Rev. 131(1963) 1826

264 10) 11) 12) 13) 14) 15)

K. ~abathul~r et al. f Pio~~e~tero~ scattering J. Norem, Nucl. Phys. B33 (1971) 512 K. Gabathuler et aZ.,Nud. Phys. B55 (1973) 397 R.H. Cole et al., Phys. Rev. Cl7 (1978) 681 A. Stanovnik et al., Phys. Lett. 94B (1980) 323 R.J. Holt et al., Phys. Rev. Lett. 43 (1979) 1229 K. Kanai et al., Prog. Theor. Phys. 62 (1979) 1.53; see also: K. Kubodera et al., J. Phys. 66 (1980) 171