The continuous energy dependence of pp differential elastic cross sections between 500 and 1200 MeV

Nuclear Physics @ North-Holland

A445 (1985) 669-684 Publishing Company

THE CONTINUOUS ELASTIC

ENERGY

CROSS

M. GARCON,

Service de Physique NucKaire

DEPENDENCE

SECTIONS

BETWEEN

OF pp DIFFERENTIAL 500 AND

D. LEGRAND, R.M. LOMBARD, M. ROUGER and Y. TERRIEN

1200 MeV

B. MAYER,

- Moyenne Energie, CEN Saclay, 91191 Gif-sur-Yvette

Cedex, France

A. NAKACH Laboratoire

National

Saturne, CEN Saclay, 91191 Gif-sur-Yvette Received (Revised

Cedex, France

30 May 1985 10 July 1985)

Abstract: Using an internal jet target in the Satume synchrotron, we have measured the proton-proton differential elastic cross section at 90” c.m. as a continuous function of energy (from 500 to 1200 MeV) during the acceleration of the beam. The energy resolution is about 2 MeV. The results are compared to predictions of phase-shift analyses and discussed in connection with amplitude analyses at 90” c.m. No resonant structure was observed and no evidence for narrow dibaryons was found.

E

NUCLEAR

REACTIONS ‘H(p, p), E = 0.5-1.2 GeV, measured (O(E), no dibaryon evidence. Internal hydrogen jet target.

6 =90”;

deduced

1. Introduction

Extensive work on the nucleon-nucleon system, both theoretical and experimental, has been done during the last few years in order to settle the question of dibaryonic resonances [see the review articles of ref. ‘) and references therein]. Structures have been seen in spin-dependent proton-proton elastic scattering observables which most phase-shift analyses 2-6) attribute to a resonant behaviour of the ‘Dz partial wave, and some also to the 3F3 or 3P0 waves. These structures are broad and might be accounted for by the opening of the NN+ NA channels, although definite conclusions have not been reached on this issue. The precise measurement of the excitation function of any observable is, in this respect, a useful constraint on the various phase-shift analyses, especially those which are energy dependent 2S3). On the other hand, the discovery of narrow structures would have far-reaching consequences: narrow resonances (F s 20 MeV) would be unlikely to be explained solely in terms of nucleons and pion-nucleon resonances. Then one would have to consider the formation of a new object. Considered as a six-quark bag, such a state, given its mass, would set a scale of the quark colour excitation and constrain the 669

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M. Gaqon et aL / pp cross sections

phenomenological models derived from quantum chromodynamics [see e.g. ref. ‘) and references therein]. From the assumed quark dynamics, nothing forbids such an object to exist. However its width is not predicted in the framework of the existing models. We note that, in the framework of a chiral model, one does not expect a particle-like non-strange dibaryon to exist ‘). The search for narrow dibaryons has developed following different experimental approaches. In ad elastic scattering, a narrow structure around & = 2136 MeV was reported from a measurement of the tensor polarization fZOat backward angles at SIN 9). This is in contradiction with another measurement of the same observable at LAMPF lo). Missing-mass and effective-mass measurement experiments in few-nucleon systems are one way of searching for narrow states in NN or NNrr systems. In the past two years, claims have been made of the observation of such states. There are convincing agreements on the masses of observed structures between Dubna (study of dp [ref. “)I and ‘up [ref. “)I reactions) and Saturne 13) experiments, and in the latter between measurements for the same reaction (p + 3He + d + X) when projectile and target particles are interchanged. It still remains to be explained why the same structures are not seen in all measured spectra and in two other experiments on the proton-deuteron interactions carried on at KEK 14) and at LAMPF “). Possible low-lying states of the diproton have also been reported from yd-+ppr[ref. ‘“)I and rr-C + ppX [ref. “)I experiments. This class of experiments offer a wide range of dynamical possibilities that may make it more probable to produce dibaryons, if they exist. The interpretation of spectra is however not straightforward. The existing nucleon-nucleon scattering data are generally not measured in small enough energy steps to address the issue of narrow dibaryons. Furthermore, systematic errors and normalization uncertainties often make it hard to extract excitation functions from sets of different measurements, particularly for partial or total cross sections. Exceptions to this are the measurements of the energy dependence of np total cross section below 800 MeV [ref. ‘*)I, which did not show any narrow structure, and preliminary studies of the wd + pp reaction ‘5), also reported as fig. 3 of ref. 19), and its inverse pp + drr [ref. “) J. In order to determine unambiguously the energy dependence of some nucleonnucleon observables and to carry on a systematic search for narrow dibaryons, we developed an original experimental method which allows us to measure excitation functions at intermediate energies very precisely. We are reporting here on the first high-resolution study of the proton-proton elastic channel. The differential cross section has been measured continuously between 500 and 1200 MeV incident kinetic energy at a fixed laboratory angle (40.44”) inside the Saturne synchrotron. The kinematics correspond to a scattering angle in the center of mass reference system of nearly 90” and thus to the maximum momentum transfer between the nucleons. Classically speaking, this is the condition for the most central collision and thus the optimal condition for studying effects due to the internal structure of the nucleons.

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et al. / pp cross sections

671

In sect. 2, we give a description of the experimental method. Sect. 3 will be concerned with the results, while sect. 4 will contain a discussion oftheir interpretation and significance. 2. Experimental

method

An internal target was installed in the Saturne ring, as shown in fig. 1, and measurements were performed during the acceleration of the proton beam. In the other experiments using the same technique [see e.g. ref. 2’)], the measurements were generally made at one energy at a time and averaged over a wide energy span. This being to our knowledge the first continuous measurement of an excitation function carried out inside an accelerator, we shall dwell on some details concerning the description of the experimental method, and show the various factors which vary with energy.

I - ---!

-internal

jet

i ’

target

Jet dump *

Fig. 1. (a) The third quadrant of the Satume ring and the location view of the target system, with its Roots (R), turbomolecular

i

Jet formation A

\

of the internal jet target. (b) Schematic (T) and cryogenic (C) pumps.

672

M. Gargm et al. / pp crms sections

2.1. THE TARGET

Hydrogen molecular clusters with a very homogeneous thermal velocity distribution form a continuously operating jet that crosses the proton beam within the accelerator vacuum chamber. Its design, operation and calibration have been fully described elsewhere 22,23 ). During the experiment the target density at the point of intersection with the beam was about 2 x 1014protons/cm3 (*30%), the diameter 0.9 cm. Of special interest for our purpose is the fact that the target is a pure and windowless hydrogen target.

2.2. THE BEAM

Special care was taken in tuning the Saturne beam: First, the focusing was adjusted so that, during the 128 ms corresponding to the acquisition time within the accelerating ramp, betatron wave numbers were kept fixed and far from any intrinsic resonance. This ensures a constant intensity of the proton beam and the optimal decoupling of horizontal and vertical motions of the beam trajectories. As a check, we showed that the crossing of a high-order resonance, though resulting in no measurable beam loss, produced a peak in the count rate of our detectors at the corresponding energy. Second, the mean trajectory was always kept on the theoretical closed orbit in order to keep a known relationship between the velocity and the accelerating frequency. At any time the velocity of the proton beam is thus known with a relative uncertainty of 2 x 10P4. This means an absolute error of the beam energy varying from 0.5 to 1.5 MeV when the energy rises from 500 to 1200 MeV. Third, the extraction of the beam on external target areas is only 80% efficient: the high level of radiation which then prevails inside the accelerator would damage the optical fibers used in the detection (see below). For this reason, we had to run the synchrotron in an unusual mode: after acceleration, the beam was decelerated (without extraction) and lost at a low energy, about 60 MeV, where the induced radiation was harmless. The energy resolution is given by the momentum spread of the beam and evolves according to the synchrotron laws of motion from 1.5 to 2.5 MeV (half-width at the base of the distribution). During the experiment, the intensity of the beam was typically 5 x 10” protons per cycle.

2.3. THE TARGET-BEAM

INTERSECTION

At the intersection with the target, the beam is about 4 cm high and 1 cm wide. The luminosity (I,) of the target-beam intersection is calculated knowing the geometry of the crossing volume (- 1 cm3) and the evolution of emittances, taking

M. Garcon

et al. / pp cross sections

into account both betatron and synchrotron

673

movements. We have

L = A&n,fs/22 co5 a, where Nb is the number of circulating beam particles (-5 x lo”), n, the target particle density (-2 x 1Or4p/cm3), f the revolution frequency (2 to 2.5 MHz), s the target section (-0.65 cm2), (Y the angle of the hydrogen jet with respect to the horizontal (ZOO),and 22 the vertical extension of the beam at the intersection with the target. z is inversely proportional to the square root of the momentum p ; it varies from 2.3 cm at 500 MeV to 1.7 cm at 1200 MeV. The above expression is valid for any horizontal distribution of the beam particles, but it assumes that the vertical distribution is uniform. The luminosity increases with beam energy from 30 to 45 mb-’ * ms-’ on account of the rise in the revolution frequency and of the shrinkage of the beam size, the fraction intercepted by the target increasing commensurately. This property partially compensates for decreasing cross sections in the counting rates. With the beam tuning described before, the energy variation of the luminosity may only be monotonic. Furthermore, in the most unlikely occurrence of a sudden jerk in the beam position at the target spot, the geomery of the detection, as described below, is such that there would be a dip in the count rates as a function of energy. The absolute error in the luminosity is *40%, mostly due to the poor knowledge of the target density. 2.4. THE DETECTION

Small scintillation detectors (B, Hr, . . . , HJ, placed as shown in fig. 2, were used to detect pp elastic events. Being close to the target, they were shaped to minimize edge effects. The angular acceptance is given by the sizes of the beam target intersection volume and of the detector B: it has an approximately trapezoidal shape, with widths of 4.5” at the base and 0.5” at maximum height. The absolute error on the mean laboratory scattering angle is rtrO.33”. In order for the photomultipliers to escape the magnetic field of the Saturne magnets, 1 m long sets of optical fibers were used as light guides. Each scintillator of the H-hodoscope was viewed by two of those sets coupled to the same photomultiplier. A pair of larger scintillators (G,, G2) added in coincidence reduced the level of random coincidences. 2.5. ELECTRONICS

AND ACQUISITION

An event was registered provided it satisfied the coincidence G1 *GZ *(CT=, Hi>. The electronic processing of the information was purely logical. The configuration of detected signals (H, B * Hi, Hi * Hi, etc.) was read through a Camac unit. A scaler linked to the ramp of the Saturne magnetic field was read synchronously. Events were binned in energy intervals ranging from 5 to 6 MeV wide.

674

M. Garqon et a[. / pp cross sections

Fig. 2. Schematic view of the detectors, the target and the beam.

The acquisition dead-time was 14.5 ks. It lead to corrections (C) to the counting rates varying from 1.35 to 1.14. These corrections were measured by counting the event rates with scalers before and after the dead-time inhibit at different times during the acceleration; they are accounted therefore well understood.

for by a simple calculation

“) and are

3. Results 3.1. DATA ANALYSIS

For each elementary energy bin, the elastic scattering events, because of the kinematical angular correlation, show as a peak in the histogram of coincidences B 9Hi (fig. 3). The background is the result of scattering off the residual vacuum (-8 x lop7 Torr), inelastic processes and uniformly distributed random coincidences. Its subtraction is straightforward below 900 MeV when H, and H6, and at most energies H5 as well, are out of the angular correlation. Above 900 MeV, the amount of background in H, is determined assuming a known shape of the counting-rate distribution which is calculated through a Monte Carlo simulation and checked at lower energies: the elastic event distribution is very well reproduced by this simulation which takes into account the spatial distribution of beam particles, the loss of

M. Gargon et at. / pp cross sections

1 Tz598

7 He’4

T&01

5 MeV

675

1

I T-1002.6

MeV

2000

1000

I lb

-_ Y

Y

In H1

‘

Fig. 3. Histograms of coincidences between detectors B and H, as a function of i. The peaks correspond to elastic pp events. The estimated background is shown as the dashed lines.

scattered protons by nuclear reactions in the vacuum chamber walls (-l%), and edge effects in the scintillators. A slope for the elastic differential cross section around 90” (p) has also been put in the simulation to account for the finite angular bin, without leading to significant changes in the results. Because the scintillators Hi are not edge to edge, some events are lost in the angular correlation. As the beam energy increases, the elastic peak moves down on the hodoscope and the ratio R of registered counts to all possible elastic scattering events between the target and the detector B oscillates between two extreme values (0.61-0.65). R is computed at each energy by the Monte Carlo simulation. The anaiysed data (-750000 events) were obtained in less than two hours of running time.

3.2. NUMERICAL

RESULTS

The differential cross section is given by u(e)=

NC.I/LdtR&,

where all factors but the solid angle fins depend on the energy: N is the integrated count in the elastic peak after background subtraction, J a jacobian, dt (-1 ms) the time interval corresponding to the elementary energy bin; L is the above-defined luminosity multiplied by the number of machine cycles, C and R the corrections due to the dead-time and to the geometry. The center-of-mass angle varies from 87.7” to 95’ as the kinetic energy increases from 500 to 1200 MeV. Apart from the energy-independent errors in L and J&, the error in u originates from the statistical uncertainty in N, and from systematic errors in R (AR = 0.004) and in the background-subtraction procedure (0.25% at 500 MeV, 0.7% at 850 MeV, 3% at 1200 MeV), added in quadrature.

676

For

M. Garqon et al. / pp cross sections

a better

differential

comparison

cross section

with

other

data

at 90”, a,, through

or calculations,

we computed

the

the relation

CT(e)=a,(l+pcos2e). The slope parameter p is taken from a phase-shift analysis 2), and somewhat arbitrarily set to a constant value of 5 above 1 GeV, this value being compatible with the existing data of differential cross section 24). Strikingly large differences (50-100%) on this parameter have been found between the predictions of the phase-shift analyses of Arndt et al. ‘) and of Bystricky et al. ‘). However the term p cos2 8 is very small, less than 0.01 below 930 MeV and rising to 0.04 at 1200 MeV. We include in the error on a, a contribution coming from an error on this term. The results appear in table 1. They are normalized using the Saclay-Geneva phase-shift analysis 2) at 708 MeV and 90”. TABLET

Measured

elastic

pp differential

Energy

Angle

NV1

Ided

507.8 513.1 518.3 523.6 528.9 534.2 539.5 544.8 550.1 555.5 560.9 566.3 571.6 577.0 582.4 587.9 593.3 598.7 604.2 609.7 615.2 620.7 626.2 631.7 637.2 642.7 648.3 653.8 659.4

87.71 87.77 87.84 87.90 87.96 88.03 88.09 88.15 88.21 88.28 88.34 88.40 88.47 88.53 88.59 88.66 88.72 88.78 88.85 88.91 88.97 89.04 89.10 89.16 89.22 89.29 89.35 89.41 89.48

cross sections (a), as a function mass angle is given) C7

AU

[mb/srl 3.578 3.472 3.430 3.327 3.335 3.286 3.261 3.213 3.126 3.074 3.094 2.977 2.965 2.918 2.875 2.845 2.720 2.686 2.707 2.553 2.524 2.425 2.354 2.364 2.305 2.195 2.172 2.091 2.087

of energy

(the center-of-

all “1

AC, “1

[mb/srl 0.038 0.037 0.036 0.035 0.035 0.034 0.034 0.034 0.033 0.033 0.033 0.032 0.032 0.032 0.032 0.031 0.031 0.031 0.030 0.030 0.029 0.029 0.028 0.028 0.028 0.027 0.027 0.026 0.026

3.574 3.469 3.427 3.324 3.333 3.283 3.259 3.211 3.124 3.072 3.092 2.975 2.963 2.916 2.874 2.843 2.719 2.685 2.706 2.552 2.523 2.424 2.353 2.363 2.305 2.195 2.172 2.091 2.087

0.038 0.037 0.036 0.035 0.035 0.035 0.034 0.034 0.033 0.033 0.033 0.032 0.032 0.032 0.032 0.031 0.03 1 0.03 1 0.030 0.030 0.029 0.029 0.028 0.028 0.028 0.027 0.027 0.026 0.026

M. Gavon et al. / pp moss sections

677

TABLE 1 (cant)

Energy

Angle

[MeVl

[deal

664.9 670.5 676.1 681.8 687.4 692.9 698.6 704.2 709.9 715.6 721.2 726.9 732.6 738.3 744.0 749.7 755.5 761.1 766.9 772.6 778.4 784.2 789.9 795.7 801.5 807.3 813.1 818.9 824.7 830.5 836.4 842.2 848.0 853.9 859.8 865.6 871.5 877.4 883.3 889.2 895.1 901.0 907.0 912.9 918.8 924.7 930.7 936.7 942.6

89.54 89.60 89.66 89.73 89.79 89.85 89.92 89.98 90.04 90.10 90.17 90.23 90.29 90.35 90.42 90.48 90.54 90.60 90.67 90.73 90.79 90.85 90.91 90.98 91.04 91.10 91.16 92.22 91.28 91.35 81.41 91.47 91.53 91.59 91.65 91.72 91.78 91.84 91.90 91.96 92.02 92.08 92.14 92.20 92.27 92.33 92.39 92.45 92.51

0‘

AU

bb/srl 2.028 1.945 1.905 1.819 1.775 1.729 1.640 1.672 1.623 1.596 1.510 1.478 1.419 1.441 1.382 1.345 1.256 1.262 1.219 1.194 1.145 1.120 1.069 1.069 1.019 1.027 1.009 0.960 0.952 0.936 0.919 0.914 0.882 0.848 0.842 0.799 0.783 0.785 0.769 0.764 0.731 0.712 0.717 0.711 0.679 0.689 0.676 0.648 0.655

flo “1

Aa, “)

[mb/srl 0.026 0.025 0.025 0.024 0.024 0.024 0.023 0.023 0.022 0.022 0.022 0.021 0.021 0.021 0.020 0.020 0.020 0.019 0.019 0.019 0.018 0.018 0.018 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.016 0.015 0.016 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015

2.027 1.944 1.905 1.819 1.775 1.729 1.640 1.672 1.623 1.596 1.510 1.478 1.418 1.441 1.382 1.344 1.256 1.262 1.218 1.193 1.144 1.118 1.067 1.067 1.018 1.025 1.007 0.958 0.950 0.933 0.916 0.911 0.878 0.844 0.838 0.794 0.779 0.780 0.764 0.759 0.725 0.707 0.712 0.704 0.673 0.682 0.669 0.642 0.648

0.026 0.025 0.025 0.024 0.024 0.024 0.023 0.023 0.022 0.022 0.022 0.021 0.021 0.021 0.020 0.020 0.020 0.020 0.019 0.019 0.018 0.018 0.018 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016

678

hf. Garfon

et at. / pp cross sections

TABLE 1 (conr) Energy

Angle

l’MeV1

[deal

948.5

92.57 92.63 92.69 92.75 92.81 92.87 92.93 92.99 93.05 93.11 93.17 93.23 93.29 93.35 93.41 93.47 93.53 93.59 93.65 93.71 93.76 93.82 93.88 93.94 94.00 94.06 94.12 94.17 94.23 94.29 94.35 94.41 94.46 94.52 94.58 94.64 94.69 94.75 94.81 94.86 94.92 94.98 95.03

954.5 960.5 966.5 912.5 978.5 984.5 990.5 996.5 1002.6 1008.5 1014.6 1020.6 1026.7 1032.8 1038.8 1044.9 1050.9 1057.0 1063.1 1069.2 1075.3 1081.3 1087.4 1093.5 1099.6 1105.7 1111.7 1117.8 1123.9 1130.0 1136.1 1142.1 1148.2 1154.3 1160.4 1166.5 1172.6 1178.7 1184.7 1190.8 1196.9 1202.9

f.7

AU

[mb/srl 0.649 0.621 0.626 0.603 0.594 0.611 0.618 0.582 0.555 0.562 0.589 0.553 0.557 0.530 0.552 0.538 0.556 0.523 0.510 0.530 0.518 0.516 0.474 0.487 0.483 0.498 0.498 0.482 0.468 0.483 0.465 0.456 0.437 0.444 0.418 0.441 0.436 0.438 0.432 0.416 0.427 0.412 0.406

_, a, is our extrapolation to Oc.m,= 90”.

obal

A@, “)

[mbisrl 0.015 0.015 0.015 0.015 0.015 0.016 0.015 0.016 0.015 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016

0.641 0.614 0.619 0.596 0.587 0.603 0.610 0.573 0.547 0.553 0.580 0.544 0.548 0.521 0.542 0.528 0.545 0.513 0.500 0.519 0.507 0.505 0.463 0.476 0.471 0.486 0.485 0.470 0.456 0.470 0.452 0.443 0.424 0.430 0.405 0.427 0.422 0.423 0.417 0.401 0.412 0.397 0.391

0.016 0.016 0.106 0.016 0.016 0.016 0.016 0.017 0.016 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.018 0.017 0.017 0.018 0.018 0.018 0.018 0.017 0.018 0.017 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018

M. Gorpn 3.3. SYSTEMATIC

et al. /

pp crosssections

679

ERRORS

We shall discuss here the factors which could affect the determination of the energy variation of a,. As a quantitative reference, we shall use the ratio r= ~~(1 GeV)/a,(600 MeV), which we measured to be 0.216. Energy calibration: a maximal systematic error of 0.5 MeV at 600 MeV and of 1.3 MeV at 1 GeV yields an uncertainty in r of *OS%. Labor~to~ ~cQftering angle: it is determined within *0.33”. Through the jacobian and the term 1 +p cos*B, this gives an error on r of *0.5%. Dead-time correction uncertai~rie~: the effect on r is *0.5%. Luminosity: the choice of the beam-particle vertical distribution which enters the calculation is somewhat arbitrary. Since the beam was largely cut by slits at the injection into the synchrotron, we used a uniform distribution. Any enhancement in the central part of the distribution will increase the luminosity, but the effect on its energy dependence will be small. We have tried various distributions (in the shape of a cosine function, a triangle, etc.), even some unlikely ones with a small dense core at the center of the beam, showing that r cannot be raised by more than 3%. We also assumed (and measured within a few percent) that the intensities of the beam and of the hydrogen jet remained constant during a cycle of the machine. A decrease of these quantities would lead to an increase of r in the same proportion which we estimate as not more than 1%. Detection eficiency: all scintillators were assumed to have the same energy independent efficiency. During the experiment, voltage adjustments of the photomultipliers were made at the highest energies in order to provide a maximal efficiency for the less-ionizing detected particles. We think that the detection efficiency is indeed constant, but do not have the quantitative information that would set a limit on its possible variation as a function of energy. If we omit the last factor, the combined uncertainty on r ranges from -1.5% to i-5.5%.

4. Discussion of the results 4.1. COMPARISON

WITH

PREVIOUS

DATA

Fig. 4 shows the proton-proton differential elastic cross section at 90”, from our experiment and from a compilation 24,25), Our results are in very good agreement with the recent and precise measurements from SIN “) between 500 and 600 MeV (although with a slight but statistically significant difference of slope) and from LAMPF 2”) at 800 MeV. The existing data in the 1 GeV region are very much scattered; our measurements go through the lowest ones, among them the most precise “) at 991 MeV. On both sides of our energy span, the continuity is perfect with two recent sets of measurements: one

680

M. Gayon

et al. / pp cross sections 6

(MeV) 2300

2200

I

1.6-

0.6-

700

600

800

900

1100

1000

1200

T (MeV) Fig. 4. Elastic

pp differential

from TRIUMF

cross

28) between

section

at 90” (u,,): l, this work; interval [88”, 92”].

X,

compilation

300 and 500 MeV and the other from Argonne

of data

in the

2g) between

1200 and 2000 MeV. We emphasize that this overall excellent agreement is an a posteriori proof of the validity of the experimental method, and in particular of the calculation of the luminosity. This being established, the advantage of the method is clear; compared with different sets of data coming from different laboratories, each with its normalization uncertainty, only our measurements give a direct determination of the excitation function.

4.2. COMPARISON

WITH

PHASE-SHIFT

ANALYSES

There exist two energy-dependent phase-shift analyses with which we can compare our results (fig. 5): Arndt et al. 3), from 0 to 1000 MeV, and Bystricky et al. ‘) (Saclay-Geneva) in the interval 514-832 MeV with in addition a fixed energy analysis at 1 GeV. The two analyses fail to describe exactly the elastic cross section between 500 and 600 MeV, because they do not include the data of Chatelain et al. 25). They also predict a somewhat less steep overall slope than we have measured. This is

M. Cat-goonet al. / pp cross sections

681

l,,,,l,~,~l,~~~l~~~~l~~~~l~~~~l~~~~~~~~~l~~~~l~~~ 500

800

700

600

900

1000

T (MeV) Fig. 5. Elastic pp differential cross section analyses: X, this work: - - -, ref. 3); - - -

at 90” (~~0) and predictions of energy-dependent and 0, ref. I); and 0, ref. *) after inserting

phase-shift our results.

especially the case for the prediction of Arndt et al. above 800 MeV: we note that their analysis underestimates the total reaction cross section by as much as 10% at 1 GeV; this leads to an overestimation of the elastic cross section when a given total cross section is used. Our data [together with some new polarization measurements ‘“)I have been included in the Saclay-Geneva phase shift analysis which accommodates them without any change in the chi-square per degree of freedom: 1.20 in the interval 514-832 MeV, 1.30 for the H-solution at 1 GeV. The effect on the small and distributed among all partial waves. Only the imaginary wave rises somewhat more sharply after threshold at 575 MeV. This a change of slope in our data around 600 MeV and above 600 MeV than previously predicted.

4.3. AMPLITUDE

ANALYSIS

phase shifts is part of the 3Po may be due to a steeper slope

AT 90”

Due to symmetry relations occurring from the Pauli principle, only three independent amplitudes, out of five, describe the elastic proton-proton scattering at 90”

682

M. Garpn

et al. / pp cross sections

[ref. “)I. In the past few years, several authors 23*32-36)have used this fact to give a direct reconstruction of the amplitudes, or only of their moduli, from a limited set of observables. spin-dependent

The main issue is to determine whether the structures seen in some observables, e.g. AOOnnand AOOkk,are due to resonances in the

scattering process [we use the notations of ref. 3’)]. Because of the monotonic behaviour of the differential cross section, as shown by our measurements, the hypothesis of Svarc et al. 32) concerning the possibility of a strongly resonant behaviour of the triplet cross section around 700 MeV is to be discarded. As the conclusions of the other authors depend mostly on the spin correlation coefficients or on Wolfenstein parameters, our data will not affect them qualitatively. However we have two comments in that respect: (i) The overall slope of the amplitudes depends on the cross section, which is now measured. (ii) Very small changes in the assumed behaviour of the spin-dependent observables, often compatible with the systematic uncertainties of the measurements, are sufficient to make a structure appear or disappear in some of the amplitudes. ‘The sensitivity is such that, in our opinion, a definitive conclusion concerning the true energy dependence of the amplitudes has not yet been reached.

4.4. THE

QUESTION

OF NARROW

DIBARYONS

Our data bear no evidence for narrow structures. Out of 121 points, only one is more than three standard deviations away from an average polynomial behaviour. We note however a small enhancement of the cross section with 2.5 standard deviations, between 820 and 860 MeV (invariant pp mass -2258 MeV). The invariant proton-proton mass domain covered by our measurements is 21152406 MeV. Within this range, eight observations of narrow structures, 16 to 59 MeV wide, have been reported from missing-mass or effective-mass measurements 11-13). Signals might not have been seen in pp elastic scattering because of their smallness; it is however unlikely that much better precision can be obtained with our experiment, especially in the low-energy part of the data where the errors are of the order of 1% . are negative, we feel the issue to be too Although our result and others 14315*18*30) consequential to give up the search. If narrow dibaryons exist, no decisive argument can be given that they could be observed in few-nucleon systems and not in NN observables.

5. Conclusion We have reported on the first measurement of an excitation function of protonproton elastic cross section as a continuous function of energy. For this purpose, we made use of an internal hydrogen-jet target installed in the Satume synchrotron.

M. Gargon et al, / pp cross sections

683

Between 500 and 1200 MeV, 121 points of the differential elastic cross section at 90” were measured in the same running time during the accelerating cycle of the machine. The results give a direct determination of the energy variation of this observable. Systematic errors due to the experimental method have been discussed; they are small compared to the precision needed to extract the nucleon-nucleon amplitudes and to the dispersion among the previous data. Our results are a significant constraint in a phase-shift analysis, but they do not affect the qualitative behaviour of the partial waves as it is known today, No eviderice is found for narrow structures in the excitation function. Nevertheless, we think that this kind of experiment should be pursued, in order to establish a necessary link between the narrow structures seen in some missing-mass experiments and the nucleon-nucleon observables. This work arose from an idea of R. Beurtey, who always kept a stimulating interest in the project. The support of the Saturne Scientific Committee, and especially M. Jean, was very gratifying through the long and trying period of setup and tests. We thank R. Maillard and M. Grand for their help in the operation of the target and the whole accelerator operating crew for their efficiency during the runs. References 1) T. Kamae, 2) 3) 4) 5) 6) 7) 8) 9) 10) I!) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)

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