c

Nuclear Physics B96 (1975) 54-66 © North-Holland Publishing Company

MEASUREMENT OF K - p ELASTIC DIFFERENTIAL CROSS SECTIONS BETWEEN 610 AND 943 MeV/c C.J. ADAMS *, J.D. DAVIES, J.D. DOWELL, G.H. GRAYER**, P.M. HATTERSLEY, R.J. HOMER, R.J. HOWELLS ***, C. McLEOD, T.J. McMAHON, H.B. VAN DER RAAY and L. ROB****

Physics Department, University of Birmingham, Birmingham, England C.J.S. DAMERELL and M.J. HOTCHKISS

Rutherford Laboratory, Chilton, Oxon, England Received 1 April 1975 Measurements of K-p elastic scattering have been carried out at 14 momenta between 610 MeV/c and 943 MeV/c over the angular range -0.9 < cos 0 < 0.9. The results agree well with the best existing data and have significantly smaller errors.

1. Introduction We have already reported measurements of K*p elastic differential cross sections at lab momenta below 1 GeV/c [1]. The present K-p data at 14 momenta were obtained using the same apparatus. The experiment approximately doubles the statistics in the c.m. energy range 1 6 1 0 - 1 7 6 5 MeV. In sect. 2 we briefly recall the methods used in obtaining and analysing the data, which have been fully discussed in ref. [1]. Sect. 3 describes the corrections particular to the K-p experiment and the absolute normalization. The results are presented and discussed in sect. 4 and summarized in sect. 5.

2. Method The experiment was carried out in an enriched beam having a m o m e n t u m spread of 3.5% (FWHM). The K - flux at the 60 cm long hydrogen target ranged from 60 at 610 MeV/¢ to 500 at 943 MeV/c, for 3 X 1011 protons incident on a copper target * Present address: Rutherford High Energy Laboratory, Chilton, Berkshire, England. ** Present address: CERN, Geneva, Switzerland. *** Present address: Brighton Polytechnic, Brighton, Sussex, England. **** Visitor from Physics Department, University of Prague, Czechoslovakia.

CJ. Adams et aL / K - p elastic cross sections

55

and the corresponding n - / K - ratios were 90 and 35. The direction of the incident kaon was measured using sonic spark chambers. Over the c.m. angular regiqn - 0 . 6 < cos 0 < 0.7 a correlation method was used in which the directions of the scattered K- and the recoil proton were measured with sonic spark chambers. For the forward and backward angles a magnetic spectrometer with sonic chambers was used to measure either the forward K- or the forward proton. The effective overlap if the two sets of data was about 0.1 in cos 0 at each end of the angular range. Full details of the beam line and detection equipment are given in ref. [ 1]. The reconstructed events were required to have a good vertex in the hydrogen and to satisfy the kinematics for elastic scattering within the experimental errors. The spectrometer data have angular regions at each momentum where a forward Kfrom elastic scattering cannot be resolved from a/l- or n- from a Ku2 o r KTr 2 decay. Data from these regions have not been used. The acceptance for protons (or kaons) scattered close to the forward direction was limited by a beam veto counter after the hydrogen target. A correction was made for the loss of proton events caused by the decay products of scattered kaons but this became large and unreliable for very slow kaons from forward scattered protons. Consequently data for cos 0 < - 0 . 9 have not been used. There is furthermore a random loss of events due to accidental tracks in the sonic chambers from background particles not in the beam. The absolute differential cross sections have therefore been obtained by normalization to Ku2 decays as in ref. [1]. The acceptance of the apparatus was calculated by a Monte-Carlo program which used as input the measured beam momentum and angular distributions obtained in special runs. The calculation was checked for Ku2 decays in the spectrometer data and gave excellent agreement with the shapes of the observed decay angular distributions [ 1].

3. Corrections and normalization The data have been corrected for spark chamber efficiency, kaon decay, energy loss, absorption and geometrical acceptance as described in ref. [ 1]. The main source of background for the correlation data is the reaction K-p ~ 2;+7rwhere the ~+ decays to pg0. The contribution lying within the selection criteria f o r elastic events is calculated to be <1% of the elastic scattering in the worst case and no correction has been applied. For the spectrometer data where the forward proton was detected there is a significant contribution of background protons from hyperon decays (A 0, 2;0 and 1~÷) at all momenta. In each angular interval the momenta of the background protons range from well below the elastic proton momentum to a value about 30% above it. Consequently the peak of elastic protons is superimposed on a flat background of protons from hyperon decays. Momentum cuts have been applied for each angular interval so as to include all the elastic events and include a

56

CJ. Adams et al. / K - p elastic cross sections

background contribution which varies between 10% and 20% of the total. The background has been estimated by interpolation of the events outside the elastic peak and checked both in shape and magnitude by Monte-Carlo calculations using the bubble chamber data of Armenteros et al. [2,3] as input. We have included an additional systematic uncertainty on the background subtraction of + 30% at each momentum. As mentioned in sect. 2 there was a loss of events due to accidental tracks in the sonic chambers caused by charged and neutral background particles. This has been discussed in ref. [ 1] for K*p scattering. In that case we established that the losses in the correlation and spectrometer data were the same within statistics at all momenta This check has been repeated for the K- data using a similar method. We have fitted Legendre polynomials to the two parts of the angular distribution and allowed the relative normalization between them to vary. On average the lowest ×2 is obtained for unit relative normalization in agreement with the result for the K+p experiment. To determine the overall normalization we have compared the observed number of K~2 decays at each momentum with that expected from the incident number of beam particles allowing for the acceptance of the apparatus. The extraction of K~,2 decay events is very straightforward for empty target data but, unlike the K÷p experiment, we ran with an empty target only at the highest and lowest momenta. The extraction of K,2 events from the full target data is more difficult than in the K÷p case, because the forward differential cross section is several times larger and one can use reliably only angular regions where the kinematic separation between decays and scatters is adequate. This reduces the statistics relative to the empty target case. As a consequence we have taken an average value for the renormalization factor of 1.17 + 0.06 where the error represents the possible fluctuations between different momenta. The corresponding average value for the K÷p experiment was 1.15. We cannot exclude that there might be reasons for the normalization deficiency in addition to those mentioned but they are catered for by the K,2 factor.

4. Results and discussion 4.1. T h e d i f f e r e n t i a l cross sections

The differential cross sections, normalized as described in sect. 3, are presented in fig. 1 and table 1. In table 1 the angles measured with both techniques are marked with an asterisk. The weighted average of the two measurements is quoted. Also shown in fig. 1 are values of the 0 ° and 180 ° differential cross sections which are listed in table 2. The forward points were calculated using the latest dispersion relation calculation (and measurement) of the forward real parts by Baillon et al. [4] and the latest measurements of the total cross section by the Brookhaven group [5]. The errors are derived from an estimated systematic uncertainty of the real parts. The backward points are interpolated at our momenta from the published

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58

CJ. A d a m s et al. / K - p

elastic cross sections

Table 1 Differential cross sections measured in this e x p e r i m e n t cos 0

610 MeV/c

642 MeV/c

672 MeV/c

-0.875 -0.825 -0.775 -0.725 -0.675 -0.625 -0.575 -0.525 -0.475 -0.425 -0.375 -0.325 -0.275 -0.225 -0.175 -0.125 -0.075 -0.025 0.025 0.075 0.125 0.175 0.225 0.275 0.325 0.375 0.425 0.475 0.525 0.575 0.625 0.675 0.725 0.775

0.634 0.666 0.501 0.579 0.695 0.757 *0.524 *0.640 0.870 0.666 0.875 0.596 0.830 0.799 0.897 0.805 1.080 1.137 1.042 1.009 1.110 1.002 1.281 1.417 1.472 L1.505 1.639 1.685 1.876 2.149 *2.384 2.205 3.308

0.679 0.387 0.442 0.380 0.468 0.525 *0.523 "0.615 0.751 0.577 0,698 0.766 0.696 0.779 0.736 0.635 0.872 0.934 0.854 1.140 1.140 1.140 1.405 1.128 1.226 1.403 1.542 1.667 1.981 2.060 2.592 2.362 2.520 3.254

0.530 0.591 0.459 0.495 0.463 *0.496 *0.406 0.483 0.441 0.537 0.610 0.684 0.690 0.746 0.824 0.856 0.805 0.930 0.923 0.930 1.026 1.250 1.321 1.128 1.509 1.388 1.673 1.764 2.091 2.047 2.480 2.021 2.523

cos 0

703 MeV/c

730 MeV/c

758 MeV/c

-0.875 -0.825 -0.775 -0.725 -0.675 -0.625 -0.575 -0.525 -0.475 -0.425

0.417 0.469 0.331 0.241 0.329 0.252 *0.349 0.564 0.366 0.392

0.453 0.392 0.234 0.343 0.267 *0.282 0.183 0.232 0.267

0.808 0.794 0.508 0.638 0.377 0.344 "0.291 0.304 0.266 0.262

± 0.114 -+ 0.124 ± 0.121 ± 0.097 -+ 0.124 ± 0.143 ± 0.071 ± 0.083 ± 0.094 ± 0.078 ± 0.087 +, 0.069 -+ 0.081 +, 0.077 ± 0.081 -+ 0.076 -+ 0.087 ± 0.089 -+ 0.084 ± 0.083 ± 0.087 ± 0~083 ± 0.094 ± 0.098 ± 0.101 ± 0.103 ± 0.108 -+ 0.111 ± 0.119 ± 0.133 -+ 0.146 ± 0.491 ± 0.503

-+ 0.091 ± 0.103 ± 0.107 + 0.081 ± 0.082 -+ 0.084 ± 0.055 ± 0.077 -+ 0.058 ± 0.057

-+ 0.104 -+ 0.108 +, 0.077 ± 0.092 ± 0.104 ± 0.130 -+ 0.068 +- 0.070 ± 0.082 ± 0.068 ± 0.071 -+ 0.073 ± 0.068 ± 0.070 ± 0.068 ± 0.063 ± 0.073 ± 0.075 ± 0.073 ± 0.083 ± 0.083 +, 0.083 +, 0.092 +- 0.082 ± 0.087 -+ 0.092 -+ 0.097 -+ 0.103 +, 0.115 ± 0.122 ± 0.140 ± 0.482 +, 0.426 +- 0.442

+- 0.120 + 0.094 ± 0.074 ± 0.112 ± 0.100 ± 0.057 ± 0.047 +, 0.049 ± 0.050

+ 0.097 ± 0.080 ± 0.074 ± 0.097 ± 0.090 ± 0.061 ± 0.062 -+ 0.063 ± 0.058 ± 0.063 ± 0.067 +, 0.069 -+ 0.069 -+ 0.070 -+ 0.074 +, 0.075 +, 0.073 -+ 0.077 -+ 0.077 +- 0.077 ± 0.081 ± 0.090 -+ 0.092 +- 0.085 ± 0.099 +, 0.096 +- 0.106 -+ 0.112 -+ 0.124 +- 0.128 ± 0.398 +- 0.316 ± 0.328

+- 0.121 +- 0.130 +, 0.105 -+ 0.114 ± 0.092 ± 0.096 -+ 0.058 ± 0.062 ± 0.053 ± 0.049

CJ. A d a m s et al. / K - p elastic cross sections

59

Table 1 (continued) cos 0 -0.375 -0.325 --0.275 -0.225 -0.175 -0.125 -0.075 -0.025 0.025 0.075 0.125 0.175 0.225 0.275 0.325 0.375 0.425 0.475 0.525 0.575 0.625 0.675 0.725 0.775 0.825

703 MeV/c 0.426 0.398 0.401 0.438 0.516 0.484 0.606 0.665 0.670 0.690 0.787 0.865 0.942 0.971 0.964 1.047 1.305 1.388 1.629 2.224 1.994 2.191 2.457 3.804 3.253

± 0.058 ± 0.055 ± 0.054 ± 0.055 -+ 0.060 ± 0.057 -+ 0.063 ± 0.066 ± 0.066 ± 0.067 ± 0.071 ± 0.075 ± 0.078 ± 0.080 ± 0.080 ± 0.083 ± 0.094 -+ 0.097 ± 0.108 ± 0.131 ± 0.131 ± 0.429 ± 0.399 ± 0.464 ± 0.304

730 MeV/c 0.170 ± 0.039 0.167 ± 0.037 0.186 ± 0.039 0.257 ± 0.044 0.252 ± 0.043 0.247 +- 0.043 0.234 ± 0.041 0 . 4 4 i ± 0.056 0.445 -+ 0.056 0.525 +- 0.061 0.624 ± 0.067 0 . 6 3 1 ; ± 0.067 0.660 ± 0.068 0.766 ± 0.074 0.831 ± 0.077 0.847 ± 0.078 1.109 ± 0.090 1.329 ± 0.101 1.438 -+ 0.108 1.755 ± 0.122 2.257 ± 0.146 2.083 ± 0.374 2.457 -+ 0.363 3.526 ± 0.409 3.323 ± 0.374

758 MeV/c 0.259 0.232 0.282 0.233 0.274 0.302 0.296 0.360 0.413 0.439 0.565 0.610 0.922 0.848 0.879 1.154 1.342 1.286 1.767 2.070 *2.463 2.087 3.986 3.525 4.662

± 0.048 -+ 0~044 -+ 0.048 ± 0.043 ± 0.047 ± 0.048 ± 0.048 ± 0.051 ± 0.056 +- 0.057 ± 0.064 ± 0.068 ± 0.083 ± 0.080 -+ 0.081 ± 0.094 - 0.102 ± 0.101 ± 0.119 ± 0.132 ± 0.150 ± 0.421 ± 0.526 ± 0.427 -+ 0.367

cos 0

785 MeV/c

810 MeV/c

833 MeV/c

-0.875 -0.825 -0.775 -0.725 -0.675 -0.625 -0.575 -0.525 -0.475 -0.425 -0.375 -0.325 -0.275 -0.225 -0.175 -0.125 -0.075 -0.025

1.073 0.830 0.909 0.665 0.393 0.535 *0.356 *0.395 *0.323 0.408 0.328 0.370 0.350 0.364 0.374 0.328 0.303 0.393

1.053 1.t44 1.013 0.855 0.569 0.693 *0.689 *0.383 0.394 0.490 0.363 0.397 0.365 0.446 0.370 0.457 0.526 0.386

0.917 1.192 0.840 0.643 0.749 0.445 *0.528 *0.476 0.510 0.393 0.413 0.590 0.339 0.409 0.298 0.442 0.303 0.378

± 0.150 +- 0.137 -+ 0.121 -+ 0.105 ± 0.101 -+ 0.124 ± 0.067 ± 0.068 ± 0.061 ± 0.073 ± 0.063 -+ 0.066 ± 0.063 ± 0.063 -+ 0.063 ± 0.058 ± 0.056 ± 0.064

± 0.158 ± 0.170 -+ 0.176 +-0.130 ± 0.101 +- 0.141 ± 0.090 +-0.069 ± 0.074 +-0.078 ± 0.067 ± 0.068 ± 0.064 ± 0.070 ± 0.063 ± 0.070 ± 0.075 -+ 0.063

± 0.152 ± 0.178 -+ 0.194 ± 0.114 ± 0.149 ± 0.129 ± 0.085 +- 0.078 ± 0.089 -+ 0.074 ± 0.074 +- 0.085 ± 0.064 ± 0.069 ± 0.058 ± 0.071 ± 0.058 ± 0.064

60

CJ. Adams et a L / K - p elastic cross sections

Table 1 (continued) cos 0 0.025 0.075 0.125 0.175 0.225 0.275 0.325 0.375 0.425 0.475 0.525 0.575 0.625 0.675 0.725 0.775 0.825 0.875

785 MeV/c

810 M e V / c

833 MeV/c

0.441 0.646 0.649 0.710 0.862 1.004 1.168 1.243 1.381 1.543 2.119 2.216 *2.978 2.925 3.767 3.756 4.867

0.626 0.887 0.702 0.876 0.908 0.949 1.155 1.434 1.647 1.865 1.894 2.298 *2.762 2.457 4.621 4.072 5.019 5.616

0.511 0.703 0.703 0.714 0.858 1.088 1.296 1.321 1.496 1.888 2.059 2.483 *2.335 3.112 2.918 3.506 4.451 5.777

_+ 0 . 0 6 7 _+ 0 . 0 8 2 -+ 0.081 -+ 0 . 0 8 5 _+ 0 . 0 9 4 _+ 0.101 +- 0 . 1 1 0 -+ 0 . 1 1 3 -+ 0.121 +- 0 . 1 2 8 -+ 0 . 1 5 2 _+ 0 . 1 5 9 -+ 0 . 1 8 6 +- 0 . 4 8 0 _+ 0.503 -+ 0 . 4 6 8 -+ 0.386

:t 0.081 ± 0.096 ~ 0.085 -+ 0.095 _+ 0 . 0 9 7 ± 0.099 -+ 0 . 1 0 9 -+ 0 . 1 2 2 -+ 0.131 ± 0.140 -+ 0 . 1 4 4 +- 0 . 1 6 4 -+ 0.181 _+ 0 . 4 6 8 +- 0 . 5 8 5 _+ 0 . 5 0 3 -+ 0 . 4 0 9 -+ 0.363

_+ 0 . 0 7 5 +- 0 . 0 8 8 -+ 0 . 0 8 8 -+ 0.089 _+ 0 . 0 9 7 +- 0 . 1 0 9 -+ 0 . 1 1 9 -+ 0 . 1 2 2 -+ 0 . 1 3 0 -+ 0 . 1 4 7 -+ 0 . 1 5 8 _+ 0 . 1 8 0 -+ 0 . 1 7 2 +- 0 . 5 5 0 _+ 0.501 _+ 0 . 4 8 6 -+ 0 . 4 1 2 -+ 0.381

cos 0

856 MeV/c

876 MeV/c

899 MeV/c

-0.875 -0.825 -0.775 -0.725 -0.675 -0.625 -0.575 -0.525 -0.475 --0.425 -0.375 -0.325 -0.275 -0.225 -0.175 -0.125 -0.075 -0.025 0.025 0.075 0.125 0.175 0.225 0.275 0.325

1.019 0.931 1.006 0.924 0.735 0.586 *0.557 *0.548 0.628 0.429 0.432 0.365 0.300 0.399 0.429 0.380 0.343 0.432 0.515 0.656 0.427 0.920 1.106 0.874 1.039

1.192 1.093 1.115 0.924 1.172 0.903 "0.501 *0.624 *0.488 0.491 0.532 0.428 0.402 0.400 0.522 0.353 0.550 0.551 0.436 0.432 0.452 0.748 0.842 1.127 1.186

1.590 1.395 1.424 1.052 0.951 0.694 "0.701 '0.717 *0.723 0.407 0.442 0.388 0.439 0.386 0.441 0.424 0.464 0.563 0.448 0.484 0.557 0.641 0.895 0.931 0.990

+_ 0 . 1 6 6 -+ 0 . 1 7 2 +- 0 . 1 5 0 -+ 0.176 -+ 0.161 -+ 0 . 1 4 5 -+ 0.085 _+ 0 . 0 8 5 -+ 0 . 0 9 8 _+ 0 . 0 7 6 -+ 0 . 0 7 3 +- 0 . 0 6 6 -+ 0 . 0 5 8 +- 0 . 0 6 8 _+ 0 . 0 6 9 _+ 0 . 0 6 6 +_ 0 . 0 6 2 +_ 0 . 0 6 9 _+ 0 . 0 7 5 -+ 0 . 0 8 4 +- 0 . 0 6 8 _+ 0.101 ± 0.110 +_ 0 . 0 9 8 _+ 0 . 1 0 8

_+ 0.165 _+ 0 . 1 7 4 +_ 0 . 1 5 2 +_ 0 . 1 8 2 -+ 0.193 -+ 0 . 1 6 9 _+ 0.085 +_ 0.091 -+ 0 . 0 7 8 -+ 0 . 0 8 7 _+ 0.089 +_ 0 . 0 7 8 _+ 0 . 0 7 4 +_ 0 . 0 7 3 +_ 0 . 0 8 2 +_ 0.067 _+ 0 . 0 8 3 _+ 0 . 0 8 2 +_ 0 . 0 7 3 -+ 0.071 _+ 0 . 0 7 4 +_ 0 . 0 9 5 _+ 0 . 0 9 9 -+ 0 . 1 1 6 _+ 0 . 1 1 9

_+ 0 . 2 0 0 -+ 0.203 +_ 0 . 1 7 6 _+ 0.145 _+ 0 . 1 5 8 -!-_0 . 1 3 2 _+ 0 . 0 9 9 _+ 0 . 0 9 9 _+ 0 . 0 9 9 +_. 0 . 0 8 0 +_ 0.081 +_ 0 . 0 7 4 -+ 0 . 0 7 6 _ 0.070 -+ 0.075 +_ 0 . 0 7 3 _+ 0 . 0 7 5 _+0.083 -+ 0 . 0 7 4 -+ 0.076 +_ 0 . 0 8 2 -+ 0 . 0 8 8 _+ 0 . 1 0 4 -+ 0.106 _ 0.110

C.J. A d a m s et al. / K - p

elastic cross sections

61

Table 1 (continued) cos 0 0.375 0.425 0.475 0.525 0.575 0.625 0.675 0.725 0.775 0.825 0.875

856 MeV/c

876 M e V / c

899 MeV/c

1.253 1.438 1.833 1.756 2.157 "2.512 2.621 2.597 4.458 5.452 5.113

0.991 -!-- 0 . 1 1 0 1.448'-+ 0 . 1 3 5 1.684 ± 0 . 1 4 6 1.911 -+ 0 . 1 5 9 2 . 1 5 9 -+ 0 . 1 7 4 * 2 . 4 8 0 -+ 0.191 2.761 ± 0.515 3.147 ± 0 . 5 0 3 4 . 0 6 0 +- 0 . 5 5 0 5 . 2 7 7 -+ 0 . 4 4 5 6 . 0 9 6 +- 0 . 3 8 6

1.123 1.434 1.557 1.775 2.114 "2.751 2.281 3.583 3.752 5.579 6.252

-+ 0 . 1 1 9 ~+ 0 . 1 2 8 -* 0.145 -* 0 . 1 4 4 ~+ 0 . 1 6 4 ~* 0 . 1 8 3 ~ 0.526 -* 0.491 +_ 0 . 5 5 0 ~ 0.480 :~ 0 . 3 7 4

cos 0

922 M e V / c

943 M e V / c

-0.875 -0.825 -0.775 -0.725 -0.675 -0.625 -0.575 -0.525 0.475 0.425 -0.375 -0.325 -0.275 -0.225 -0.175 -0.125 -0.075 -0.025 0.025 0.075 0.125 0.175 0.225 0.275 0.325 0.375 0.425 0.475 0.525 0.575 0.625 0.675

1.547 1.517 1.478 1.181 0.984 0.977 *0.735 *0.750 0.480 0.523 0.627 0.557 0.578 0.353 0.398 0.393 0.384 0.569 0.329 0.475 0.638 0.587 0.738 1.025 0.886 0.883 1.307 1.328 1.823 2.334 *2.675 2.644

1.578 1.365 1.253 0.998 0.922 0.906 *0.827 *0.536 "0.441 *0.450 0.508 0.508 0.391 0.424 0.310 0.261 0.408 0.390 0.494 0.464 0.532 0.666 0.666 0.718 0.808 0.954 1.287 1.523 1.468 1.957 "2.149 1.977

-+ 0 . 2 1 7 _+ 0 . 2 2 7 _+ 0 . 3 0 6 ~ 0.168 _+ 0 . 1 8 4 +_ 0 . 1 8 8 ~ 0.109 _+ 0 . 1 0 8 _+ 0 . 0 9 6 _+ 0 . 0 9 4 _+ 0 . 0 9 9 ± 0.090 _* 0 . 0 9 0 _+ 0 . 0 6 9 -+ 0 . 0 7 3 _+ 0.071 _+ 0 . 0 7 0 _+ 0 . 0 8 5 _+ 0 . 0 6 4 :__- 0 . 0 7 7 +_ 0 . 0 8 9 +_ 0 . 0 8 5 -+ 0 . 0 9 6 _+ 0 . 1 1 3 --- 0 . 1 0 5 ± 0.106 ± 0.130 ± 0.133 _+ 0 . 1 5 9 + 0.190 _+ 0 . 2 1 9 _+ 0 . 5 3 8

+ 0.130 _+ 0 . 1 2 3 _+ 0.125 ± 0.142 _+ 0 . 0 9 4 _+ 0 . 0 9 8 +_ 0 . 0 8 2 _+ 0 . 0 7 0 ± 0.070 ± 0.082 +_ 0 . 0 9 6 _+ 0 . 0 9 2 _+ 0 . 0 8 0 _+ 0 . 0 8 2 ± 0.069 _+ 0 . 0 6 3 _+ 0 . 0 7 8 _+ 0 . 0 7 6 _+ 0.085 _+ 0 . 0 8 3 _+ 0 . 0 8 9 _+ 0 . 0 6 8 _+ 0 . 0 9 9 ± 0.104 ± 0.110 ± 0.121 _+ 0 . 1 3 9 ± 0.154 +_ 0 . 1 5 6 ± 0.186 ± 0.156 +_ 0.201

-+ 0 . 1 1 8 - 0.133 -+ 0 . 1 4 2 -+ 0 . 1 5 3 -+ 0 . 1 7 4 +- 0 . 2 0 2 -+ 0 . 4 4 5 -+ 0 . 5 2 6 ± 0.515 ± 0.526 ± 0.372

CJ. Adams et al. / K p elastic cross sections

62 Table 1 (continued) cos 0

922 MeV/c

0.725 0.775 0.825 0.875

3.253 4.540 4.796 6.716

943 MeV/c

--- 0.550 -+ 0.620 -+ 0.445 _+ 0.702

2.847 3.634 5.460 6.090

-+ 0.218 -+ 0.228 +- 0.212 +- 0.186

The units are mb/sr and the values listed are at the centre of each bin of 0.05 in cos 0.

Table 2 Differential cross section at 0 ° calculated from dispersion relations and at 180 ° interpolated from bubble chamber measurements Lab momentum (MeV/c)

d o (0 o) (mb/sr) d~2

d o (180 o) (rob/st) d~2

610 642 672 703 730 758 785 810 833 856 876 899 922 943

3.70 4.15 4.62 5.13 5.66 6.42 7.40 7.74 7.59 8.10 8.77 9.39 10.16 10.71

0.38 0.31 0.27 0.31 0.45 0.75 0.94 1.08 1.17 1.27 1.37 1.48 1.60 1.70

+- 0.37 _+0.41 +_0.46 _+0.51 -+ 0.56 ± 0.64 +- 0.60 _+0.60 + 0.60 + 0.60 + 0.60 + 0.60 +- 0.60 _+0.60

+- 0.15 +- 0.15 +- 0.15 -+ 0.15 -+ 0.15 +- 0.18 -+ 0.20 + 0.20 + 0.20 + 0.20 -+ 0.20 + 0.20 + 0.20 + 0.20

b u b b l e c h a m b e r e x t r a p o l a t i o n s to 180 ° [6]. We have s m o o t h e d t h e b u b b l e c h a m b e r d a t a a n d applied an error c o r r i d o r b a s e d o n t h e i r q u o t e d errors. I n all cases o u r data s h o w good c o n s i s t e n c y w i t h t h e f o r w a r d a n d b a c k w a r d p o i n t s .

4.2. Legendre p o l y n o m i a l coefficients To obtain better estimates of Legendre polynomial coefficients than would be o b t a i n e d f r o m o u r d a t a a l o n e we have i n c l u d e d t h e f o r w a r d a n d b a c k w a r d p o i n t s . B e l o w 7 3 0 M e V / c c o e f f i c i e n t s u p t o A 4 are sufficient b u t at this m o m e n t u m a n d above A 5 a n d A 6 are n e e d e d . F o r ease o f c o m p a r i s o n w i t h t h e c o e f f i c i e n t s p u b l i s h e d b y A r m e n t e r o s et al. [2] a n d C o n f o r t o et al. [6[ we q u o t e c o e f f i c i e n t s u p t o A 6 at all m o m e n t a . T h e s e are t a b u l a t e d in t a b l e 3 t o g e t h e r w i t h t h e ×2 p r o b a b i l i t i e s o f t h e fits, a n d are p l o t t e d in fig. 2. T h e elastic cross s e c t i o n is o b t a i n e d f r o m t h e A 0 coefficient. T h e errors o n t h e values given for Oel in t a b l e 4 a n d p l o t t e d in fig. 3 include t h e e r r o r o n t h e n o r m a l i z a t i o n discussed in sect. 3.

CJ. Adams et aL / K - p elastic cross sections

63

Table 3 Fitted Legendre polynomial coefficients and x 2 probabilities Momentum (MeV/c)

A1/A 0

A2/A 0

A3/A 0

A4/A 0

AsIA 0

A6/A 0

x 2 prob.

610

1.060 -+ 0.062

0.620 -+ 0.075

0.215 +- 0.067

-0.029 -+ 0.060

-0.093 _+ 0.061

-0.125 +_0.060

0.16

642

1.186 ± 0.062

0.729 ± 0.076

0.300 ± 0.072

0.024 ± 0.065

-0.081 ± 0.060

-0.066 _+0.054

0.02

672

1.195 ± 0.066

0.775 -+ 0.085

0.319 ± 0.083

0.132 _+0.073

0.039 -+ 0.064

0.109 ± 0.056

0.57

703

1.443 ± 0.069

1.133 -+ 0.088

0.533 -+ 0.089

0.194 -+ 0.082

0.016 ± 0.069

-0.059 ± 0.059

0.32

730

1.622 ± 0.082

1.545 ± 0.105

0.664 +- 0.106

0.280 -+ 0.095

0.124 -+ 0.075

-O.039 +- 0.062

0.5O

758

1.523 ± 0.074

1.630 ± 0.096

0.613 ± 0.098

0.240 ± 0.089

0.052 _+0.068

0.064 -+ 0.057

0.66

785

1.450 ± 0.066

1.591 -+ 0.084

0.563 ± 0.085

0.204 -+ 0.079

0.018 -+ 0.066

-0.058 +- 0.056

0.73

810

1.354 ± 0.054

1.534 ± 0.069

0.570 ± 0.072

0.241 ± 0.071

0.113 -+ 0.063

-0.066 +- 0.056

0.42

833

1.368 ± 0.057

1.534 -+ 0.073

0.577 -+ 0.077

0.268 ± 0.076

0.150 -+ 0.067

0.106 -+ 0.059

0.39

856

1.335 ± 0.058

1.612 ± 0.074

0.666 ± 0.076

0.316 -+ 0.075

0.182 +- 0.066

0.060 _+0.060

0.16

876

1.323 ± 0.055

1.695 -+ 0.069

0.750 ± 0.072

0.354 -+ 0.071

0.143 -+ 0.064

0.006 -+ 0.060

0.22

899

1.252 ± 0.053

1.759 ± 0.067

0.774 -+ 0.070

0.392 -+ 0.068

0.202 _+ 0.061

-0.040 ± 0.057

0.92

922

1.253 -+ 0.059

1.832 -+ 0.075

0.876 -+ 0.074

0.441 +- 0.070

0.207 ± 0.062

-0,002 ± 0.059

0.40

943

1.266 ± 0.037

1.956 +- 0.049

1.006 ± 0.059

0.718 -+ 0.063

0.425 -+ 0.056

0.017 _+0.050

0.11

4. 3. Comparison with other data I n fig. 2 w e p l o t f o r c o m p a r i s o n w i t h o u r r e s u l t s t h e v a l u e s o f t h e L e g e n d r e p o l y n o m i a l c o e f f i c i e n t s A 1 - A 6 d i v i d e d b y A 0 as a f u n c t i o n o f m o m e n t u m

obtained by

A r m e n t e r o s et al. [2] a n d C o n f o r t o et al. [ 6 ] . T h e s e h a v e t h e s m a l l e s t e r r o r s a n d a r e t h e m o s t c o n t i n u o u s in m o m e n t u m o f t h e p u b l i s h e d d a t a . T h e a g r e e m e n t w i t h o u r d a t a is v e r y s a t i s f a c t o r y e x c e p t f o r a s m a l l s y s t e m a t i c d i s c r e p a n c y in t h e r e g i o n 8 0 0 t o 8 5 0 M e V / c w h i c h is m o s t n o t i c e a b l e in t h e c o e f f i c i e n t s A 3 , A 4 a n d A 5.

CJ. A d a m s et aL / K - p elastic cross sections

64 1.7 1.6

A~/Ao

1C

1.5 1.z,

Az,/Ao

0~

tF{t

1.3 14 1.1 1.£

06

07

A2/Ao

0.~ 0; 0 o Conic, rio el at • This exoer, ment

08

-0-; 09

10

06

t~f~tIt~tt~tlIt~tt~t't 0z

07

08

09

10

A5/Ao

{ {,{~tt,f,{t{t,t!,tI I ~'~'{'{

0.; 0 - 0; .0.z 0!6

017

0'.8

o!9

• o!s

~Io

0'.7

0'8

o19

;'o

0.8

09

10

A3/Ao

o

~ti t~tIt~ttt~tt~ o!6

0'7

o.~

Laboratory Momentum GeV/¢

o19

~io

J ;)J 0.6

I

0,7

Laboratory

Momentum GeVlc

Fig. 2. Normalized Legendre polynomial coefficients plotted as a function of momentum from this and two bubble chamber experiments. There is nothing very obviously different when the differential cross sections are compared directly and one must await the outcome of a phase-shift analysis to know whether the difference is physically significant. For the central two-thirds of the angular distribution our errors are typically a factor o f two smaller than theirs.

C.J. Adams et a L / K - p elastic cross sections

65

25

u

l

t

HolIeyel al. a Bertcanzca et(157) ca[ (69) x Armenteros et al (70) o Conforlo et cal. (71)

• This Experimen~

lO

o!6

0!7

olo

o19

Lcaborcatory Momentum (GeV/c)

~.'o

Fig. 3. Elastic cross sections from this and other experiments. The values shown for this experimerit were obtained from the A o Legendre polynomial coefficients. The errors include the overall normalization uncertainty. Table 4 Elastic cross sections derived from the A0 coefficients of the 6th-order fit including the 0 ° and 180 ° points Momentum (MeV/c)

Elastic cross section (rob)

610 642 672 703 730 758 785 810 833 856 876 899 922 943

17.66 17.23 16.22 15.22 14.07 16.93 19.37 20.67 19.63 19.78 21.07 22.02 22.34 21.01

± 1.00 ± 0.96 ± 0.92 ± 0.86 +_ 0.70 -+ 0.98 ± 1.09 +_ 1.13 ± 1.08 -+ 1.09 ± 1.16 _+ 1.20 +_ 1.25 _+ 1.10

I n fig. 3 w e c o m p a r e t h e e l a s t i c c r o s s s e c t i o n s o b t a i n e d f r o m t h e A 0 c o e f f i c i e n t s w i t h all p r e v i o u s l y p u b l i s h e d d a t a [ 2 , 6 , 7 ] . W h e r e t h e r e are d i s a g r e e m e n t s a m o n g t h e p u b l i s h e d d a t a o u r s g e n e r a l l y f a v o u r t h o s e o f A r m e n t e r o s e t al. a n d C o n f o r t o et al. This comment applies also to the shapes of the differential cross sections.

66

cJ. Adams et al. / K - p elastic cross sections

5. Summary and conclusion We have measured K - p elastic differentail cross sections at 14 momenta between 610 MeV/c and 943 MeV/c over the angular range - 0 . 9 < cos 0 < 0.9. The data show good consistency with the 0 ° differential cross sections calculated with the help of dispersion relations and the 180 ° differential cross sections obtained b y interpolating bubble chamber data. The Legendre polynomial coefficients A 1/Ao to A 6 / A 0 agree well with those of Armenteros et al. [2] and Conforto et al. [6] apart from a small discrepancy between 0.80 and 0.85 GeV/c in the coefficients A3, A 4 and A 5. No obvious differences are noticeable in the differential cross sections. The elastic cross sections deduced from the A 0 coefficients also agree well with the results o f these authors. This experiment approximately doubles the statistics in this m o m e n t u m interval. We gratefully acknowledge the assistance of S. Alwyn, J. Hall, J. Kilner, M. Sproul and E.J.N. Wilson in the early stages of this work. We thank Mrs. G. Blakely for her help in the data processing. The work could not have been accomplished without the support and services provided by the Science Research Council at the Rutherford Laboratory and the University of Birmingham for which we are grateful.

References [1] [2] [3] [4] [5] [6] [7]

C.J. Adams et al., Nucl. Phys. B66 (1973) 36. R. Armenteros et al., Nucl. Phys. B21 (1970) 15. R. Armenteros et al., Nucl. Phys. B8 (1968) 216. P. Baillon et al., Phys. Letters 50B (1974) 383. K.K. Li et al., Purdue Conf. on baryon resonances (1973) p. 283. B. Conforto et al., Nucl. Phys. B34 (1971)41. P. Bastien et al., Phys. Rev. Letters 10 (1963) 188; L. Sodickson et al., Phys. Rev. 133 (1974) B 757; W.R. Holley et al., Phys. Rev. 154 (1967) 1273; L. Bertanza et al., Phys. Rev. 177 (1969) 2036.