Proton compton scattering at backward angles in the energy range from 400 MeV to 1050 MeV

Proton compton scattering at backward angles in the energy range from 400 MeV to 1050 MeV

Nuclear Physics B247 (1984) 313-338 © North-Holland Publishing Company PROTON COMPTON SCA'ITERING AT BACKWARD ANGLES IN!THE ENERGY RANGE FROM 40...

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Nuclear Physics B247 (1984) 313-338 © North-Holland Publishing Company

PROTON

COMPTON

SCA'ITERING

AT BACKWARD

ANGLES

IN!THE ENERGY RANGE FROM 400 MeV TO 1050 MeV Y. WADA*, K. EGAWA**, A. IMANISHI, T. ISHII, S. KATO and K. UKAI

Institute for Nuclear Study, Universityof Tokyo, Tokyo, Japan F. NAITO***, H. NARAt, T. NOGUCHI t t and K. TAKAHASHI

Tokyo University of Agriculture and Technology, Tokyo, Japan Received 6 June 1984

Differential cross sections of proton Compton scattering have been measured in the energy range between 400 MeV and 1050 MeV at C.M.S. angles of 150 ° and 160 °. The recoil proton was detected with a magnetic spectrometer using multi-wire proportional chambers and multi-wire spark chambers. The scattered photon was detected with a lead glass Cerenkov counter of the total absorptive type with two layers of multi-wire proportional chambers which measured the horizontal and vertical positions of the scattered photon. The proton Compton scattering was differentiated from the background of the ~r° photoproduction events with the use of angular correlations between the recoil proton and the scattered photon. The cross-section data show the clear second resonance peak at E v = 750 MeV and a bump around E r = 925 MeV at both angles. Also the angular distributions show the backward peak in the energy range between 700 MeV and 950 MeV. The data are compared with theoretical calculations based on an isobar model with some phases for the resonances. In this calculation, the proton Compton data were fitted varying the photocouplings of the nucleon resonances around the bump and the phases below the third resonances as free parameters. The calculation reproduced the angular distribution of differential cross sections well. However, it was inevitable that we use large photocouplings of P33(1600) in order to fit the bump.

1. Introduction The elastic scattering of a photon from a proton (proton Compton y+p~'r+p is a f u n d a m e n t a l

scattering): (1.1)

process in the study of the electromagnetic interaction of the

nucleon. * Visiting Scientist 1981-1982. Permanent address: Department of Physics, Meiji College of Pharmacy, Tokyo, Japan. ** Present address: National Laboratory for High Energy Physics, Ibaraki, Japan. *** Present address: Department of Applied Physics, Tokyo Institute of Technology, Tokyo, Japan. t Present address: Meidensha Electric Co. Ltd., Nagoya, Japan. t t Present address: Fuji FACOM Corporation, Tokyo, Japan. 313

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Y. Wada et al. / Proton Compton scattering

Proton Compton scattering changes its characteristics in the three energy regions. The first energy region is below the threshold of the pion photoproduction. In this energy region the reaction is explained well by the Klein-Nishina equation taking account of an anomalous magnetic moment of the proton. The second is the resonance region whose energy range is between the pion photoproduction threshold and E v = 2 GeV. In this region the proton Compton scattering reflects greatly the nucleon structure. The energy above E v = 2 GeV is the third region, where the data at the forward region show characteristics of a diffraction process similar to hadron-hadron scattering, which is explained by the vector meson dominance model. Studies on proton Compton scattering in the resonance region have been done by many authors both experimentally [1-21] and theoretically [17,18, 22-29]. In 1981, Jung et al. [20] reported angular distributions of the differential cross sections at E v = 700, 750, 800, 850, 900 and 950 MeV in the angular range from 40 ° to 130 ° by 10 ° steps, and discovered a sharp dip around t = - 0 . 6 (GeV) 2 and a backward peak for all measured energies. The structure is qualitatively explained by using the dual absorptive model [30, 31]. The model predicts the backward peak which results from the Regge term of the t-channel. Then it is important to see the behavior in the backward region beyond 130 ° . Two different types of calculations have been performed for proton Compton scattering in the resonance region. One is the calculation using dispersion relations, the disadvantage of which is the large ambiguity owing to the contribution from the unphysical region at high energies a n d / o r backward angles. Therefore most calculations using the dispersion relation have been concentrated upon small angles and low energies. Toshioka et al. [17] reproduced the data well up to the second resonance region at angles less than 90% The other type of calculation is a treatment based on an isobar model. The calculations by Ishii et al. [18] reproduced the data up to the second resonance region at angles less than 130 ° . These two calculations give very different values from each other at backward angles. Therefore, we have measured the excitations of the differential cross sections for proton Compton scattering at C.M.S. angles of 150 ° and 160 °, and analyzed the results using an isobar model. The present experiment has been performed at the 1.3 GeV electron synchrotron at the Institute for Nuclear Study (INS), University of Tokyo. In sect. 2 the experimental method and apparatus are described. The data reduction process is explained in sect. 3, and the theoretical treatments are given in sect. 4. Finally discussions and conclusions are given in sect. 5.

2. Experimental method and apparatus The experimental setup is illustrated in fig. 1. The recoil angles of the proton at the laboratory system are about 13 ° and 90 for C.M.S. photon scattering angles of 150 ° and 160 ° , respectively. The minimum angle at which the INS spectrometer

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Y. Wada et aL / Proton Compton scattering ~.

v

.LEAD GLASS CERENKOV COUNTER

T :TRIGGER COUNTER C-MAG:C-TYPE MAGNET A-MAG: ANALYZER MAGNET L i H : L I T H I U M HYDRIDE V : VETO COUNTER L : LEAD CONVERTER P : MWPC9-10

PROTON SPECTROMETER

H2BEAM MONITOR

C-MAG PHOTON DETECTOR

lm Fig. 1. Experimental layout.

system could be set was 21 ° with respect to the beam line. We made these forward protons be accepted by placing the target to the upper stream on the beam line and by setting an additional C-type magnet (C-mag) between the target and the spectrometer system. The bremsstrahlung beam illuminated a liquid hydrogen target. Photons scattered on the target were detected with a photon detector. The energy and the position of the photon were measured with the photon detector. The recoil protons were bent by the C-mag and analysed by the INS spectrometer system. In order to detect the process (1.1), the event signal was generated by the coincidence between the photon detector signal and the spectrometer signal. With this trigger condition, the single pion photoproduction process, 7+p~r°+p (2.1) ,,~2y, was also accepted. The process (2.1) was the main background against the process (1.1). In subsect. 3.2 we shall explain how to extract the Compton yield. The raw data were stored on a magnetic tape (MT) through a CAMAC system and a mini-computer, and were monitored on line with the central computer. 2.1. BEAM, BEAM MONITOR AND TARGET

A photon beam was produced by the bremsstrahlung process at a 50/~m thick platinum internal radiator. The beam was collimated by a lead block which had a

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rectangular hole of 3 mm x 9 mm (width x height). The beam had a rectangular shape of 12 m m × 36 mm (width × height) at the target position. During the data taking the spill time of the beam was kept about + 2 msec, which corresponded to a duty factor of 8%. The beam intensity was 109 equivalent quanta/sec. A thick-walled ionization chamber (thick chamber) was used to monitor the total energy of the photon beam. Ionization charges which were proportional to the total energy of the beam, were collected on the collector electrode. The coefficient for reducing the total energy from the collected charge had been calibrated as a function of the top energy of the bremsstrahiung beam [32]. A thin-walled ionization chamber was used as a subsidiary monitor, and was placed in front of the thick chamber. A liquid hydrogen target of a dosed gas system with a small refrigerator was used in this experiment [33]. The target container was made of 127/~m Mylar film. It had a cylindrical shape along the beam line, being 137 mm long and 50 mm in diameter, enough to cover the photon beam. To reduce heat inflow the target container was wrapped with aluminized Mylar films 20 ~tm thick and set in a vacuum chamber. 2.2. PHOTON DETECTOR

The photon detector system identified photons and measured their energies and their incident positions. The photon detector consisted of a lithium hydride (LiH) photon hardener, a veto counter, a lead plate converter, two multi-wire proportional chambers (MWPC's) which measured the position of the incident gamma-ray, and a lead glass Cerenkov counter. The photon detector was set on a rotatable platform. In order to reduce the background of'low-energy photons, lithium hydride was used as an absorber. The size of the LiH container box was 33 cm x 33 cm x 10 cm (width x height x length), which was made of soda glass 1 mm thick. The veto counter to reject charged particles consisted of two scintillation counters. The size of each counter was 153 mm × 302 mm x 5 mm (width × height × thickness). The lead plate converter of 1.00 radiation length was used to convert the scattered photons into e + e - pairs. The conversion efficiency was about 50%. T o detect the incident position of the photon which hits the lead converter, two MWPC's were set behind the converter. The dimension of the sensitive area was 30 cm x 30 cm (width x height) and the gap length between the electrodes was 6 mm. The anode plane consisted of gold-plated tungsten wires with a diameter of 20/~m, which were spaced 4 mm from each other. The MWPC's were filled with a mixed gas or argon 70% and isobutane 30%. In order to determine the two-dimensional position of the incident photon, two MWPC's were set orthogonal to each other. The last element of the photon detector was a flint glass SF-2 of 30 cm x 30 cm X 30 cm cube. We could measure the total energy of the photon. The Cerenkov lights were collected by nine R329 photomultipliers. The Cerenkov counter was tested with mono-energetic electrons. The detection efficiency of the Cerenkov counter was also investigated as a function of the shower

Y. Wada et al. / Proton Cornpton scattering

317

energy using the electron beam, and the threshold energy of the (~erenkov counter was set at 80 MeV. This was low enough because the lowest energy of a photon to be detected was 150 MeV in our experiment. The photons which hit the area within 1 cm from the edge of the lead glass were rejected at the stage of the off-line analysis, because the pulse height of the (~erenkov counter decreased. Therefore, the effective area of 28 cm X 28 cm (width x height) was used for the data reduction.

2.3. PROTON SPECTROMETER The proton spectrometer system identified protons and measured their momenta with a resolution of 0.5 - 1.0%. The proton spectrometer consisted of four trigger counters (T1, T2, T3 and T4), eight planes of multi-wire proportional chambers (MWPC's), an analyzing magnet (A-mag), an additional C-mag and five planes of multi-wire spark chambers (WSC's). It was set on a rotatable platform. In the measurement of the process (1.1) at backward angles, the angle of the proton in the laboratory system is very close to the beam line. Therefore, in this experiment, the forward protons were deflected by the C-mag to be accepted by the spectrometer. The gap, length, and width of the pole piece of the C-mag were 5 cm, 65 cm and 18.5 cm, respectively. The field strength at the medium plane of the C-mag were measured by a Rowson-type Gauss meter. The measurements were performed at two field points, that is, about 12 kG and 15 kG, where the experiments were carried out. As shown in fig. 1, the trigger counter T1 was placed just behind the C-mag, and T2 in front of the A-mag. T3 and T4 were placed behind the A-mag. Each trigger counter consisted of two scintillation counters. Eight planes of MWPC's were set between the T1 and T2 trigger counters, and were used to determine the trajectory of the incident particle to the A-mag. Among eight planes of the MWPC's, five planes were used to determine the horizontal trajectory and three planes for the vertical one. The frames of the MWPC's were made of G-10 epoxy glass. The anode plane consisted of gold-plated tungsten wires of 20/xm diameter and with a wire spacing of 2 mm. The cathode planes consisted of copper beryllium wires of 100 #m diameter and with a wire spacing of 1 ram. The gap length between the anode plane and the cathode plane was 6 mm. A magic gas mixture of argon, isobutane and a small amount of freon 13B1 was used to operate the chambers. A 20 ton sector-type magnet with a gap of 10 cm and a width of 52 cm analyzed the particle momentum. The field strength was measured by the nuclear magnetic resonance method (NMR). The floating wire measurement of the particle trajectory was also performed to determine the effective length of the magnetic field. Four planes of WSC-1 - 4 were placed between the trigger counter T3 and T4, and WSC 5 was placed behind T4. These five WSC's determined the trajectory of

Y. Wada et al. / Proton Compton scattering

318

the particle at the exit side of the A-mag. The frame of the WSC was made of bakelite 12 mm thick. The high-voltage plane and the ground plane consisted of copper-beryllium wires of 100/~m diameter and with a wire spacing of 1 mm. A magnetostrictive readout method was used in this system. Helium gas was used to operate the WSC's. 2.4. D A T A T A K I N G AND MONITORING SYSTEM

Signals from the scintillation counters and the Cerenkov counter were fed into NIM and CAMAC modules in an electronics hut. A signal from the ~erenkov counter(C) vetoed by the veto counter(V) was regarded as the detection of a photon (-f = C. V). A four-fold coincidence of T1, T2, T3 and T4 was regarded as the detection of a positive particle (P = T1 • T2- T3. T4). A coincidence signal between 7 and P generated a master signal. Though P might be contaminated by positive pions, the pion events were rejected kinematically by the coincidence with ~/. The data were stored and monitored by the on-line system of INS [34]. The system consisted of a CAMAC data taking system, a mini-computer of PANA FACOM U-400 (U-400) and a central computer of FACOM M-180 H A D (M-180). The informations from the MWPC's, WSC's, scintillation counters and lead glass Cerenkov counter were stored in CAMAC modules. The data were transferred to the M-180 through the U-400, and stored on a magnetic tape. On the central computer, a kinematical reconstruction of events was performed at every 10 transfers. The results (distributions of the proton momentum, the photon energy, the reaction point, the scattering angle, etc.) were also stored on the disk and printed out at every run end. The results were also monitored by a graphic display at any time during the run. The U-400 displayed firing points of the WSC's and MWPC's on a cathode ray tube (CRT). 3. Data reduction The differential cross sections were evaluated by using the following formula:

do~dO*= Y/[N, NTA~*(1--~?,)(1--~c)(1--~?p)(1--~?M)],

(3.1)

where Y, Ny, N T and AI2* denote the yield of the proton Compton scattering, the number of incident photons, the number of target protons and the solid angle acceptance at C.M.S., respectively. *Iv, */e, 71p and *IM are correction factors, which are described in subsect. 3.3. 3.1. RECONSTRUCTION

The momentum of the proton was calculated by using the effective edge approximation of the magnetic field. The trajectories before and behind the A-mag were reconstructed as follows.

Y. Wadaet al. / ProtonComptonscattering

319

(i) The horizontal and vertical coordinates of the particle trajectory in MWPC's or WSC's were treated independently. (ii) In principle, unless more than two chambers had firing points, the event was rejected. However, if there were only two chambers fired and each had only one firing point~ the line was determined uniquely. Then the line was accepted. (iii) If more than two chambers had firing points, firstly a pre-line was calculated from the firing points of the outermost chambers. If these two chambers recorded multiple firing points, the next chamber with one firing point was used to determine the pre-line of the trajectory. Finally the trajectory was determined by using all firing points which were located within 2 mm of the pre-line. The momentum of the proton at the interaction point in the target was evaluated by taking into account the energy loss in the material between the target and the A-mag. The incident photon energy and the scattering angle of the photon were also calculated using the proton momentum assuming proton Compton kinematics. 3.2. BACKGROUNDSUBTRACTION The expected position of the scattered photon on the y-MWPC's was calculated from the proton momentum. On the other hand the observed position of the scattered photon was known from the information of the 7-MWPC's. The hit rate of the y-MWPC's to the master signals was about 5 0 - 54%. This agrees with the conversion efficiency in the lead converter. The multi-hit events of y-MWPC's was about 60%. The multi-hit events were caused by the shower of the photon or the accidental hit of y-MWPC's. In order to exclude the accidental multi-hit events in the y-MWPC's, we rejected the event whose spatial spread was larger than two standard deviations of the expected shower spread. The distributions of the difference between the observed position of the photon and the one expected from the proton momentum were calculated for the vertical direction (YsuB) and for the horizontal direction (Xsua) , independently. A typical example is shown in fig. 2. The distribution shows a sharp peak of the Compton events over a broad background due to events of the process (2.1). The distribution of YsuB was fitted, assuming that the Compton peak 'was expressed by a gaussian form and the background by a polynomial, that is,

f ( y ) = A e x p [ - ( y - y o ) 2/2oy2] +Co+ Cly+ Czy2 + C3y3+ C4y 4,

(3.2)

where oe is the width of the Compton peak and A is the normalization factor of the Compton peak area. The number of events in the Compton peak, Nc, is given as follows:

Nc = 27~Ao~.

(3.3)

320

Y. Wada et al. / Proton Compton scattering EVENTS ETOP = 775 MeV E),

-

-

-j

= 700 ~ 12.5 MeV

0

Ysua Fig. 2. Distribution of the difference between the observed and expected positions of the photons for the vertical direction (YstJB). The solid line is the fitted curve (eq. (32)). The crosses represent the background part of the equation.

Since the Xsu B distribution showed a relatively broad peak for the Compton process, this information was used only for enhancing the Compton peak in the YsuB distribution. The background can be reduced by imposing a cut in the Xsu B space, where the Compton events were not reduced. For example, the fitted result of the Compton peak plus the background is shown with a solid line in fig. 2. 3.3. CORRECTIONS

The value of Nc needs to be corrected for the inhibit time at the trigger stage, for the reconstruction efficiency of the proton trajectory, for the conversion efficiency of the photon, and for the efficiency of the -/-MWPC's. Because the inhibit time, the reconstruction efficiency of the proton trajectory and the efficiency of the "pMWPC's do not depend on reactions, and the conversion efficiency of the photon is nearly constant for energies of one experimental set, the ratio of the Compton yield to the total yield remains correct among all the reconstructed events. Then, the Compton yield was normalized by using the count of the scaler, in the following way:

Y=Nc(Yrp/Ntot),

(3.4)

Y. IVada et al. / Proton Compton scattering

321

where the Yvp denote the count of (y. P - 3 " pal) at the experimental set. , / - p d means the accidental coincidence of the y and P signals. The Nc and Ntot are the number of the reconstructed Compton events in the data bin and reconstructed total events at the set, respectively. After this normalization several corrections were applied as follows. (i) The correction for the photon absorption */v, that is, the photon loss by e + e pair creation in the material between the interaction point and the veto counter, amounted to about 9%. (ii) Over-vetoing of the Cerenkov signals due to the high counting rates of the veto counter was estimated using the counting rate of the accidental coincidence between the veto (V) and the ~erenkov (C) counters. The over-vetoing rate was calculated by the formula

nc = ( C - C. V~)/C.

(3.5)

The values of ~/c varied between 3 and 8% depending on the experimental conditions. (iii) ~/p is the rate of proton loss due to the interaction with the materials in the path and was estimated to be 4 - 6%, using the data of the pp and the pn total cross section. (iv) */M is the rejection rate due to the multi-hit of the "t-MWPC's, which amounted to 13 - 20%. The yield from the empty target came mainly from Mylar walls of the target container. This contribution was measured by the empty target runs to be 2 - 6%. This background had been already subtracted together with the background from neutral pion photoproduction in the fitting procedure which was applied to extract the Compton yield. Therefore we did not correct for this empty yield.

3.4. ACCEPTANCE

The acceptance of the whole detection system was calculated by a Monte Carlo method. The following quantities were chosen randomly; the incident photon energy in the laboratory frame k whose spectrum was calculated by Schiff's formula [35], the polar and the azimuthal angles of scattered photons in the C.M.S. (8 and ~), and the reaction point (x, y, z). A track of the recoil proton, which meandered due to multiple Coulomb scattering and lost its energy in each material, was traced. A scattering angle in each material was generated randomly with a normal distribution. The horizontal and vertical projection angles were treated independently. The events which did not hit the trigger counters were rejected. The track of the scattered photon was also traced, and it was seen whether it hit the (~erenkov counter or not. The spatial resolutions of MWPC's, ~,-MWPC's and WSC's were taken into account in this track tracing.

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The solid angle acceptance AI2* is obtained from the number of trials NTR and the number of accepted events NOK, as AI2* = 41rNor./N.rR.

(3.6)

3.5. EXPERIMENTAL RESULTSAND UNCERTAINTIES The differential cross sections were calculated from eq. (3.1) for each experimental set. A photon energy bin was chosen to be 25 MeV for each data point. The final results are shown in fig. 3 and listed in table 1. Some angular distributions are shown in fig, 4. The error bars in the figures and tables denote statistical ones including uncertainties in the fitting procedure of the Compton events. Other possible sources of errors are described below. (i) The calibration constant of the thick-walled ionization chamber had been measured using a Faraday cup within an accuracy of 1.1%. (ii) The number of target protons has ambiguities due to the target length and the bubbles. The error of the target length is estimated to be 0.5%. Bubbles were roughly counted from the photograph of the liquid hydrogen target. The error due to the bubble was about 0.5%. (iii) The statistical error of the Monte Carlo simulation for the geometrical acceptance was less than 2%. (iv) The error in the estimation of the acceptance due to ambiguities in the setting of counters caused an error in the differential cross sections of less than 2.1%. (v) The error due to the energy dependence of the photon conversion efficiency was estimated to be less than 1%. (vi) The error due to the accidental firing points of the ?-MWPC's was estimated to be about 2%. (vii) The error in the over-vetoing in the photon detector system was about 0.6%. (viii) In the nuclear absorption of the proton, errors in the quantity of the materials in the path and in the cross section with nuclei were estimated to be about 0.7% in total. (ix) The error for the photon absorption between the target and the photon detector was estimated to be about 0.9%. (x) Inefficiency of the trigger and Cerenkov counters including the electronics was estimated to be less than 2%. In all the total systematical errors in the data amounted to 4.6%.

4. Theoretical treatments

4.1. GENERAL DESCRIPTION Two available analyses of the proton Compton scattering, which were given by Toshioka et al. [17] and by Ishii et al. [18], do not fit our data.

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Y. Wada et aL / Proton Compton scattering

Toshioka et al. analyzed the data using the unitarity and the fixed-t dispersion relation. An application of the dispersion theory for proton Compton scattering is restricted only to low-energy and/or forward angle regions. Their calculation reproduces the experimental data for scattering angles less than 90 ° , but does not for angles larger than 90 °. Ishii et al. used an isobar model for analyzing the proton Compton scattering. They decomposed the amplitudes by the following formula restricting to the non-diffractive region:

A = A R + ABe - c(1 - x),

(4.1)

where A R and A B are the resonant amplitude and the non-resonant amplitude calculated by the Born term, respectively. C is a damping parameter and x = cos 0". They took into account all nucleon resonances well known in the photoproduction process up to the third resonance region, and used the values of the photocouplings determined by the several analyses of the single pion photoproduction up to 1976. They determined the photocouplings of the three resonances Pl1(1470), Da3(1520) and $1x(1535) and the damping parameter C by fitting the proton Compton data. As is described in the next section, we tried to reproduce our data using this isobar model with small modifications.

4.2. FITTING PROCEDURE In 1982 the extensive analysis of the single pion photoproduction was reported by Fujii et al. [36]. Our data could not be reproduced by the calculation of the Ishii model using the new resonance parameters of Fujii et al., which are listed in table 2. Especially, the bump around Ev = 925 MeV could not be reproduced. Then we varied the photocouplings of PH(1440), D13(1504), 511(1550 ), $11(1650), $31(1620) and P33(1600) and C by a fit of the proton Compton data, but the calculation did not fit our data well. In general, the resonance formation amplitudes have the eigenphase e i2~r to the non-resonant amplitudes in the eigenchannel. The eigenphase is derived from time-reversal invariance and unitarity [37]. In the analysis of the single pion photoproduction, the eigenphases are not explicitly given for each nucleon resonance. It seems that the contribution of the eigenphases is attributed to the non-resonant amplitudes. Then, we tried to fit our data by Ishii's model, introducing phases to the resonances to make clear the interferences for the proton Compton process. The formalism of our calculation obeys the description by Ishii et al. [18]. The difference is that we introduced phases to the resonance terms. We used the

329

Y. Wada et aL / Proton Compton scattering

TABLE la Results of the differential cross sections at 0* = 150 ° Ey (MeV)

0* (degrees)

1050 ___12.5 1025 1000 975 950 925 900 875 850 825 800 775 750 725 700 675 650 625 600 575 550 525 500 475 450 425 400

151.6 151.7 152.0 152.3 151.9 151.4 151.7 152.1 151.5 151.0 151.3 151.7 151.2 150.4 150.8 150.3 150.0 149.8 150.5 150,4 149,5 150.1 151.2 151.0 149.7 150.4 151.7

d o'/d,Q* (nb/sr)

- t

da/dt

(GeV) 2

(nb/GeV 2)

1.279 1.241 1.203 1.165 1.124 1.082 1.044 1.007 0.966 0.925 0.888 0.852 0.812 0.772 0.737 0.696 0.662 0.624 0.592 0.554 0.517 0.486 0.455 0.420 0.384 0.354 0.327

204 _+47 371 ± 70 285 ± 60 376 ± 61 510 ± 50 607 ± 89 618 ± 97 789 ± 101 822 ± 73 878 ± 107 998 ± 112 1428 ± 129 1636 ± 100 1568 ± 122 1659 ± 121 1768 ± 86 1703 ± 92 1756 ± 111 1773 ± 115 1856 ± 97 1761 ± 113 2051 ± 126 2190 ± 158 1733 ± 143 2656 _+275 2749 + 285 4069 ± 731

22.1 ± 5.1 38.9 ± 7.3 29.0 ± 6.1 37.0 ± 6.0 48.4 ± 4.7 55.6 ± 8.2 54.6 ± 8.6 67.1 ± 8.6 67.2 ± 6.0 68.9 ± 8.4 75.1 ± 8.4 103.0 + 9.3 112.7 ± 6.9 103.1 ± 8.0 103.9 ± 7.6 104.9 ± 5.1 96.1 ± 5.2 93.6 ± 5.9 89.3 + 5.8 87.6 ± 4.6 77.9 ± 5.0 84.9 ± 5.2 84.6 ± 6.1 61.8 ± 5.1 87.0 ± 9.0 82.8 ± 8.6 112.5 ± 20.2

The angular acceptance is 1.2 ° to 1.5 ° with one standard deviation at Ey = 400 MeV to 1050 MeV, respectively.

following Breit-Wigner form with a phase factor for the resonant terms: A~,x(W ) = ko k

2yx-l," M 2 -

ei2~ r

W 2 - iWF

F = E ( - '- - - qo q ) 2°t ° + l ( q 2oq+2X+2X)

k

=

2

'

Jo ( k2+X

~

'

ko M

1

Mo 2 jo + 1

2]

A ~ oe ,

'

(4.2)

Y. Wada et al. / Proton Compton scattering

330

TABLE l b Results of the differential cross sections at 0* = 160 ° Ev (MeV)

O* (degrees)

1025 + 12.5 1000 975 950 925 900 875 850 825 800 775 750 725 700 675 650 625 600 575 550 525 500 475

161.3 .161.4 161.7 162.0 161.6 161.4 161.4 161.7 161.1 160.6 160.9 160.4 160.9 160.2 160.5 160.0 159.1 159.5 160.2 160.2 159.4 160.0 161.1

d o/d~2* (nb/sr) 27.4 41.5 48.3 64.0 68.5 66.7 55.6 65.4 72.8 88.5 126.3 119.6 125.3 117.6 112.7 96.4 100.1 100.0 80.5 80.5 87.9 91.0 87.0

+ 5.4 _ 5.4 + 6.2 + 6.9 + 5.1 + 8.1 + 8.2 +_ 9.9 _+ 7.8 _+ 16.3 + 16.3 + 6.7 + 7.7 + 8.1 _+ 7.8 + 4.8 + 5.8 +__6.0 + 6.2 + 5.0 + 5.5 + 6.3 + 11.5

- t (GeV) 2 1.283 1.245 1.204 1.164 1.123 1.081 1.041 1.002 0.962 0.920 0.882 0.836 0.802 0.764 0.727 0.685 0.647 0.612 0.578 0.541 0.503 0.470 0.439

do/dt ( n b / G e V 2) 261 407 491 674 749 755 654 800 927 1176 1751 1744 1907 1878 1894 1715 1880 1988 1699 1816 2128 2362 2427

_+ 70 +_ 53 _+ 63 + 72 + 56 _+ 92 + 96 + 121 + 99 + 217 + 226 +__98 + 117 + 129 +_ 131 _+ 85 + 109 + 119 + 131 + 113 + 133 + 163 + 321

The angular acceptance is 1.0 ° to 1.3 ° with one standard deviation of Ey = 475 MeV to 1025 MeV, respectively.

where 8r denotes the phase of the resonance. In this calculation we assumed that the phases do not depend on the helicities of the initial and final states. Phases of this kind were treated by Kanai et al. [38] who investigated dibaryon resonance in the pion-deuteron interaction, k and M are the incident photon energy in the C.M.S. and the mass of a proton, respectively. The parameters M 0 and Jo are the mass and the spin of the resonance, respectively. The parameters q and l 0 are the m o m e n t u m of the pion and the angular m o m e n t u m decaying into the ~rN state, respectively. A subscript 0 denotes the value at the peak position of the resonance. A~o*' is the so-called photocoupling and satisfies the following relation:

A ~ = P ( - 1)J°-l/2AJx°e. For X ' s we applied the values of Metcalf and Walker [39]. As a first step we fitted the data of the differential cross sections in the region of Er = 240 - 1150 MeV and 0* = 40 ° - 160 ° by varying C as a free parameter. We

Y. Wada et al. / Proton Compton scattering

331

TABLE 2 P h o t o c o u p l i n g s determined by the analysis of the single pion p h o t o p r o d u c t i o n [36], and the p h o t o c o u plings and the phases determined by our fit of proton C o m p t o n scattering (Ref. [36]) Resonance

O u r fit

Helicity

Coupling ( G e V - 1/2 x 1 0 - 3)

Coupling ( G e V - 1/2 x 1 0 - 3)

Phase (rad)

P11 (1440)

~

- 68

- 128.6

- 0.426

D13 (1504)

½

- 7

- 12.1

- 0.394

3

168

167.6

$11(1550 )

½

77

55.1

D15(1675)

2~ 32

34 24

(34.0) (24.0)

2.332

F15 (1680)

12 -3 2

- 9 115

( - 9.0) (115.0)

- 1.126 - 2.782

2

-0.371

$11(1650 )

½

50

90.5

D13 (1675)

12 3 2

- 2 29

( - 2.0) (29.0)

Pl1(1700)

~

28

(28.0)

(0.0)

P13 (1700)

~ 32

- 4 40

( - 4.0) (40.0)

(0.0)

P33 (1232)

12 -3 2

- 138 - 259

( - 138.0) ( - 259.0)

- 0.839

2.011

$31 (1620)

½

10

66.0

- 2.547

D33 (1710)

~ 32

89 60

(89.0) (60.0)

(0.0)

P33 (1600)

½ 32

- 46 25

- 200.2 23.2

- 1.898

~ 3

43 - 25

(43.0) ( - 25.0)

(0.0)

F35 (1910)

2

P31 (1910)

½

25

(25.0)

(0.0)

F37 (1950)

½ _3 2

- 68 - 94

( - 68.0) ( - 94.0)

(0.0)

The values in parentheses were not varied in the fit.

used the cross-section data of refs. [16-18,20] and ours i n the fit. The used photocouplings [36] are listed in table 2. The results are C = 0.482 + 0.006 and x 2 / n u m b e r of degrees of freedom--- 12.2. Next, fixing the value of C we fitted the differential cross sections in the incident photon energy regions from 400 MeV to 1050 MeV, by varying the photocouplings Pl1(1440), D13(1504), S 1 1 ( 1 5 5 0 ) , S 1 1 ( 1 6 5 0 ) , S 3 1 ( 1 6 2 0 ) a n d P33(1600), w h i c h are located around E v = 925 MeV, and the phases to each resonance which corresponds of

-1.0

-0.8

-0.6

-0.4

I

300

(a)

O * = 90 °

I

400

p

500

I

I

700

i

800

Incident P h o t o n E n e r g y ( M e V )

600

I

900

O TOKYO(1972)

I

1100

I

1000

Fig. 5. Recoil p r o t o n polarization. The solid line represents our analysis. (a) 0* = 90 °, (b) 8 = 100 °, (c) 0* = 130 °.

200

0.0

N .~

-0.2

0.2

c 0

0.4

0.6

0.8

1.0

"r+P--Y+P

Recoil Proton Polarization

1200

2.

P~

th

b~

-1.0

-0.8

-0.6

-0.4

200

0.0

N x..

o_ - 0 . 2

0.2

¢._o

0.4

0.6

0.8

1.0

(b)

3OO

I

O* = 100 °

_1 400 500

i

I

700

600

/

v TOKYO(19

Fig. 5 (continued).

Incident Photon Energy (MeV)

600

y+p-Y+p

Recoil Proton Polarization

I

1000

I

900

io)

I

1100

1200

c,q

9

0.0

N

200

-

-0.8

-1.0

-

-0.6

-0.4

-6 ~_ - 0 . 2

0.2

ro

0.4

0.6

0.8

1.0

(c)

3O0

I

O * = 130':'

400

t I

5OO

I

Photon

700 Energy

(MeV)

80O

I

i

900

~Z T O K Y O ( 1 9 8 0 )

Fig. 5 (continued).

Incident

6OO

Y+p--Y+p

Recoil Proton Polarization

I

1000

1100

I

i

1200

£

9

-1.0

-0.8

-0.6

-0.4

- -

200

0.0

<~ - 0 . 2

E

0.2

0.4

0.6

0.8

1.0

500

I

I

700

I L

r

800

I

I

_ _

incident Photon Energy (MeV)

600

I

I

900

I

× Frascati(1968)

I

__

1000

Fig. 6. Polarized photon asymmetry at 0* = 90 °. The solid line represents our analysis.

J

400

q

I

300

I

e * = 90 °

y+p--¥+p

Beam Asymmetry

I

1100

1200

9

e~

336

Y. Wada et al, / Proton Compton scattering

to the incident photon energies below 1050 MeV, that is, Pl1(1440), D13(1504), SH(1550), D15(1675), F15(1680), $11(1650), D13(1675 ), P33(1232), $31(1620) and P33(1600). The other photocouplings were fixed to those of Fujii et al. The resultant x 2 / n u m b e r of degrees of freedom was 3.7. The results of the photocouplings and phases are shown in table 2. The signs of photocouplings cannot be determined from proton Compton scattering only, because a photocoupling contributes quadratically. Therefore we adopted the sign which was determined from the single pion photoproduction. The resultant differential cross sections agree very well with the data. The resultant curves are shown in figs. 3 and 4. The recoil proton polarizations and the target asymmetries are shown with the experimental data in figs. 5 and 6, respectively. Though the polarization data were not used in the fit, the agreement is good. 5. Discussions and conclusions

We have measured energy excitations of the differential cross sections of proton Compton scattering in the incident photon energy range from 400 MeV to 1050 MeV at 0* = 150 °, and from 475 MeV to 1025 MeV at 0* = 160 °. This was the first measurement at such backward angles. The data are plotted in fig. 3, and listed in table 1. Our data show clearly the second resonance peak at ET = 750 MeV, and a large tail of the first resonance at both angles. At 0* = 150 ° the data show a broad bump around ET = 900 MeV. At 0*= 160 ° the data also show a clear bump around E~ = 925 MeV and decrease rapidly with the increase of the incident photon energy. In the angular distribution of the differential cross section our data show a clear backward peak in the energy range between 700 MeV and 950 MeV. This aspect has been already suggested by the data up to 0* = 130 ° presented by the Bonn group [20]. Near the second resonance the data show a behavior like cos20 *, as shown in fig. 4. This behavior shows that the D13(1504 ) is enhanced. The data were reproduced by introducing some phases to the isobar model. In this calculation we determined the photocouplings of resonances Pl1(1440), D13(1504), $11(1550 ), $x1(1650), $31(1620) and P33(1600), and phases of resonances Pl1(1440), D13(1504), $11(1550), D15(1675), F15(1680), $11(1650), D13(1675), P33(1232), $31(1620 ) and P~3(1600), below the mass of 1700 MeV. The data were well reproduced with the fit by varying the photocouplings and the phases together. The resultant x 2 / n u m b e r of degrees of freedom was 3.7. The photocouplings of the resonances, $11(1650 ), $31(1620) and P33(1600), must be somewhat larger than accepted values tO reproduce the bump around Ey = 925 MeV. Pl1(1440) contributes to the cross section around Ev -- 635 MeV and makes the first resonance tail large. The phases of Pl1(1440), Dx3(1504), Sn(1550 ) and P33(1232) are small, but those of D15(1675 ), 1=15(1680), $11(1650), D13(1675 ), $31(1620) and P33(1600) are large. This result means that the non-resonant amplitudes of this calculation are good at low energies below the second resonances, but get worse at higher energies. There might be other contributions to the non-resonant amplitudes from the t or u channels (or °,

Y. Wada et a L / Proton Compton scattering

337

~, etc. exchanges in the t c h a n n e l a n d A or N* exchanges in the u channel) or more h i g h - e n e r g y resonances. I n this calculation the recoil p r o t o n polarization agrees well with the m e a s u r e d data [13,19] except at Ev = 400 MeV a n d 800 MeV at #* = 130 ° as s h o w n i n fig. 5. The value of the polarized p h o t o n a s y m m e t r y is two times larger t h a n the e x p e r i m e n t a l data from the Frascati group [10], which is shown i n fig. 6. T h e overall consistency between this calculation a n d the data is good. T h e a u t h o r s express their gratitude to the staff of the I N S electron synchrotron, to the staff of the c o m p u t e r center a n d to the m a c h i n e workshop group for their c o n t i n u i n g assistance. Also they t h a n k Messrs. M. Ikeda a n d M. Saito for their assistance i n the data taking in this experiment. The d a t a analyses were d o n e using FACOM M-180//AD

of the I N S c o m p u t e r center, This work was partly supported

b y a G r a n t - i n A i d from the Japanese M i n i s t r y of Education, Science a n d Culture,

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Y. Wada et aL / Proton Compton scattering

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