polarimeter for photoreactions below 1 GeV

NUCLEAR

INSTRUMENTS

AND METHODS

166 (1979)

171-186; ~

NORTH-HOLLAND

PUBLISHING

CO.

A PROTON SPECTROMETER/POLARIMETER FOR PHOTOREACTIONS BELOW 1 Ge¥* I. ARAI, T. FUJII, H. IKEDA**, N. KAJIURA ~**, T. KAMAE, S. KAWABATA +, T. KOBAYASHI + +, K. NAKAMURA, K. OGAWA** find H. TAKEDA + +

Department of Physics, Universityof Tokyo, Tokyo, Japan Received 24 April 1979 We describe the construction and performance of an apparatus to measure the polarization of protons in the kinetic energy range 1 0 0 - 4 0 0 MeV, operated with an extracted electron beam and a high-intensity bremsstrahlung photon beam. It consists of four multiwire proportional chambers, a spectrometer magnet, ten wire spark chambers with magnetostrictive readout, a carbon scatterer of variable thickness and a range counter hodoscope. The multiwire proportional chambers are placed before the magnet and are directly exposed to intense electromagnetic background coming from a target. For this reason, special care is taken of the readout electronics. A method of polarization analysis is also described in detail.

1. Introduction Polarization measurements of recoil protons in various reactions provide powerful information to resolve ambiguities in amplitude analysis. For protons having kinetic energies of 100-400MeV, 0~ Work supported in part by the Grant-in-Aid from the Japanese Ministry of Education, Science and Culture. ** Present address: National Laboratory for High Energy Physics (KEK), Tsukuba, lbaraki, Japan. + Present address: DESY, Hamburg, Germany. ++ Present address: Lab. of Int. Coll. on Elementary Particle Physics, University of Tokyo, Tokyo, Japan.

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carbon is extensively used as a polarization analyzer. We have constructed a spectrometer and carbon polarimeter using multiwire proportional chambers (MWPCs) and wire spark chambers (WSCs) to determine the proton track before and after scattering in the carbon analyzer. A schematic drawing of the apparatus is shown in fig. 1. It has been used in polarization measurements of the proton in the deuteron photodisintegration ?d--+pn between Ey = 350 and 700 MeV ~,2), and in the single pion photoproduction 7n--+ n p between E~,= 700 and

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1200 MeV 3) performed by using a bremsstrahlung photon beam from a 1.3 GeV electron synchrotron at the Institute for Nuclear Study, University of Tokyo. Calibration for zero polarization has been done by using either protons from the elastic electron-proton scattering whose polarization is known to be negligible4), or negative pions which have spin zero.

A special feature involved in the use of an electron beam or a bremsstrahlung photon beam is a huge amount of low-energy background photons and electrons to which MWPCs are sensitive. Since MWPCs are placed in front of a magnet, they must withstand a high counting rate due to this background. To cope with this high background rate, special care is taken in the design of the readout electronics of the MWPCs. The apparatus has been successfully operated over three years of the experiments. In the course of the experiments, however, the apparatus and analysis software have been improved in many respects, and here the latest version will be reported, unless otherwise stated.

2. Apparatus 2.1. MULTIWIRE PROPORTIONAL CHAMBERS

2.1.1. Construction The construction parameters of the chambers are: sensitive area: 224×150 mm 2 and 2 8 8 × 2 0 0 m m 2 ; sense wires: gold-plated tungsten, 20/.tm in diameter, 2 mm spacing, 50 g tension;

cathode wires: gold-plated molybdenum, 100 ~m in diameter, 2 mm spacing, 250 g tension; chamber gap: 6.2 ram. 2.1.2. Electronics Amplifiers and discriminators used are basically the same as the ones designed by Cunitz et al.5). Eight-channel amplifier-discriminator cards are plugged into connectors mounted on the chamber frame. The discriminator outputs are transmitted to gated register modules at a remote counting room by twisted pair cables. One gated register module has eight channels corresponding to an amplifier-discriminator card. Thirty-two gated register modules and a readout controller module are accommodated in a specially-designed crate. The data stored in the gated registers are read out under the control of the readout controller module, and are sent to a TRACK ENCODER which is designed according to the CAMAC specifications. A maximum of eight crates is connected to one TRACK ENCODER. Fig. 2 shows a schematic diagram of the electronics for MWPC readout. Important features of the present MWPC readout system are: (a) Use of differential-type line drivers and line receivers together with transmission cables renders a high degree of tolerance against common-mode spark-chamber noises. (b) Dual-in-line type lumped delay lines* are * Manufactured by Showa Electric Wire Tokyo, Japan.

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used to adjust the timing of the data signal with the gate signal. They are superior to univibrators in many respects, e.g., no deadtime, smaller time jitter, smaller temperature dependence (_+ 100 ppm/ °C), and negligible long-term variation of the characteristics, although they increase the cost problem of the electronics. (c) After every 200 ns of transmission through each lumped delay line, an inverter is inserted to shape the pulse. This cuts down the time jitter caused by the deterioration in the rise time. In addition, a lumped 30 ns delay line with taps in 3 ns steps is used for finer timing adjustment. (d) Each gated register module is provided with a light-emitting-diode indicator showing an OR (normal mode) or N A N D (inverse mode) of the eight registers in the module. Using the inverse mode and manually or externally produced test pulses which are capacitively coupled to all sense wires, one can easily find faulty electronics. (e) As can be seen from fig. 2 an,d fig. 3 (timing chart), the readout logic is simple and its operation is fast. (In fig. 3, the repeat mode operation is shown as an example.) A " S C A N " signal senses a first non-zero eight-bit OR of gated register modules starting with the one having the lowest module address, with a propagation delay through an IC gate per module (N 10 ns). The contents of a nonzero eight-bit register are cleared after the completion of the data transmission to the CAMAC system, and the readout cycle continues until all data are transferred. The module address is provided by a printed circuit board in the backplane of the specially-designed crate. (£) The T R A C K E N C O D E R has three modes (normal, group and average) of data encoding. In

the normal mode, the position of a non-zero bit in the register is binary coded and transferred with the corresponding module address. In the group mode, a group of consecutive non-zero bits (irrespective of whether they are in one module or not) are so encoded as to give the number of consecutive nonzero bits and the binary-coded address of the first non-zero bit within the group, while in the average mode the address of the center of consecutive nonzero bits is directly encoded. 2.1.3. Performance We used a mixture of argon and isobutane for the chamber gas. The gas flow rate was kept to be about 50 cc/min per chamber. The thresholds of the amplifier-discriminators were adjusted to about 200 # V according to the data of ref. 5. Test were performed using a 9°Sr/J-source to find out stable operating conditions for a high efficiency with a narrow gate signal. Fig. 4 shows the efficiency of the chamber as a function of the applied high voltage for gas mixtures of 60% argon + 40% isobutane and 50% argon + 50% isobutane, and for gate widths of 30 ns and 50 ns. Fig. 5 shows the v

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tors are connected to the largest chamber, while one 4000 pF capacitor is connected to each of the other chambers. The CX1154 thyratron pulser is basically the same as the one employed by Foley et al. 6) except that capacitors are used instead of strip discharge lines.

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resolving time of the chamber determined from the measurements of the rise of the delay curves. The minimum resolving time obtained is 30 ns. Based on these test results, we have operated the chambers at a high voltage of around 5.1 kV with a gas mixture of 50% argon + 5 0 % isobutane and with a gate width of 50 ns for most of the time. The efficiencies have always been better than 99%. 2.2. WIRE SPARK CHAMBERS

2.2.1. Construction and high voltage pulsing Wire spark chambers of four different sizes have been constructed, whose sensitive area varies from 5 0 0 × 4 0 0 r a m 2 to l l 0 0 x 5 0 0 m m 2. Each chamber frame is made of a single Bakelite board 12 m m thick. On one side of the frame 100/~m diameter BeCu wires are stretched parallel to the shorter edge with 200g tension and at 1 m m spacing, and are used as the high voltage plane. On the other side wires are streched at +15 ° (or - 1 5 °) inclination with respect to the high voltage wires and are used as the ground plane. Chambers are made gas-tight by gluing Mylar sheets onto the two sides. Some chambers suffered from outgassing from uncured epoxy resin. To prevent this, silicone oil* was introduced into chambers to cover the entire inner surface with a thin layer of oil. This operation not only improved the efficiency greatly, but also suppressed edge sparking and prevented corrosion of wires. High voltage pulses are produced by discharging capacitors through an English Electric Valve EXl154 thyratron and are fed to the chambers through 50-(-2 coaxial cables. Two 4000 pF capaci* Toshiba silicone TSF451, 100 centistokes, manufactured by Toshiba, Tokyo, Japan.

2.2.2. Electronics Spark positions are read out from the high voltage plane and from the ground plane by means of magnetrostrictive readout wires (Remendur P, 4 x 20 rail 2) with pickup coils. The magnetostrictive wire is threaded through Teflon tubing and placed in a straight groove machined on an aluminum wand. This wand is slid into or out of the proper position, allowing easy servicing of the magnetostrictive wire. Although the magnetostrictive wire is surrounded by air in the Teflon tubing, we have observed no reported deterioration due to corrosion 6) during many months of operation. Sound signals produced in the magnetostrictive wires are detected and amplified in the preamplifiers and sent to TIME DIGITIZER modules placed in a remote counting room. A TIME DIGITIZER module is a double-width CAMAC module, and digitizes the spark positions. A schematic diagram of the time-to-digital logic is shown in fig. 6. About 40/~s after the spark chamber trigger, an externally supplied ENABLE G A T E enables the integrating discriminator to accept the preamplifier outputs and clears all the registers in the module. The first output logic pulse from the integrating discriminator (corresponding to the first fiducial signal) makes a 16-bit scaler start counting a 20 MHz external clock. Each subsequent pulse from the integrating discriminator causes the contents of the scaler to be stored in a 16-bit × 16-bit memory. The maximum allowed number of signals accepted is fifteen since the first 16 bits of the memory is reserved for a data-status word which includes the number of accepted signals and the error-status information. The data-status word is indicated by light-emitting diodes for visual monitoring of the operation of the chambers. Data are transferred to the computer by the block transfer mode. 2.2.3. Performance A gas mixture of helium and argon has been used throughout the experiments, owing to the cost problem. Fig. 7 shows the result of a study on the

PROTON SPECTROMETER/POLARI METER

the trigger delay and clearing field. Uniformity of the sparking efficiency over the active area was found satisfactory. The average efficiency of the chambers for a proton track has been better than 96% during the experiments. Most of the inefficiency has not been due to the chambers themselves, but rather due to the deterioration of the magnetostrictive wires. In this case remagnetization of the magnetostrictive wires has greatly improved the efficiency.

relation between the sparking efficiency and the gas mixing ratio. A high voltage giving 95% efficiency for minimum-ionizing particles is plotted against the amount of argon added to helium. A minimum was observed at 3% of argon, which is interpreted as due to the Penning effect. Typical operational conditions were a gas mixture of 95% helium +5% argon, - 1 2 . 5 k V high voltage, + 1 0 0 V d c clearing field and 800ns trigger delay. Fig. 8 shows the sparking efficiency as a function of

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The trajectory of the proton is measured with four M W P C s (MWPC 1 and M W P C 3 for x coordinate, and M W P C 2 and M W P C 4 for y coordinate) in front of the magnet and three or four WSCs (WSC 1 - W S C 4) behind the magnet. The magnet and trigger counters limit the m o m e n t u m acceptance to Ap/p = 9 % - 1 7 % (fwhm) depending on the central orbit m o m e n t u m . The angular acceptance is defined by the counter CI to be 3 msr.

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2.3. MAGNETIC SPECTROMETER

A sector-focussing magnet with a gap distance of 10 cm is used. This magnet was designed to analyze the m o m e n t u m up to 700 M e V / c with a central orbit 120 cm in radius and a bending angle of 50 °. In order to measure the proton m o m e n t u m up to 1000 MeV/c, we have chosen the central orbit tilted by 1.6 ° at the entrance and by 13.9 ° at the exit with respect to the normal of the pole-piece edges, with a bending angle of 34.5 ° and a radius of 170.7 cm. The magnetic fields have been measured by using a Rawson-type fluxmeter.

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In the 7d--+ pn reaction, the reaction rate rapidly decreases as the photon energy increases beyond 300 MeV. In the 7n ~ n -- p reaction the trigger rate is limited owing to the coincidence between the pion and proton arms and to the Fermi motion of the neutron in the deuteron. Therefore the present polarimeter was designed to have a wide acceptance together with a high scattering efficiency. These requirements are met by the use of a reasonably thick carbon scatterer and large track detectors. However, if the scatterer is one thick carbon plate, the multiple Coulomb scattering dominates at small scattering angles and the hadronic scattering at these angles has to be discarded from the data sample. Moreover, with one thick scatterer, one cannot distinguish double scattering in the scatterer, which should be removed from the data as much as possible, from single scattering. Our solution was subdivision of the scatterer. Thus the polarimeter consists of the seven wire spark chambers ( W S C 4 - W S C 10) interspersed with one to five layers of carbon, and the range counter hodoscope. This configuration helps make unambiguous recognition of the scattering point, scattering angle and the kinetic energy of the proton in the p r o t o n - c a r b o n scattering. The thickness of each carbon layer is determined such that the r.m.s, multiple Coulomb scattering angle in each layer should be less than 1.5 ° . The total thickness of the carbon scatterer is so chosen that the kinetic energy of the proton after the scatterer is greater than 95 MeV, below which no reliable data exist for the analyzing power. The maxim u m thickness of the carbon scatterer used is 68.5 g / c m 2 for proton kinetic energy Tp >_ 360 MeV, and the m i n i m u m is 2.5 g / c m 2 for ~ = 110 MeV. The range counter hodoscope serves to distinguish highly inelastic p r o t o n - c a r b o n scattering events for which the polarization analyzability is poor and not well known. It consists of five layers of 1 m × 0 . 5 m scintillation counter planes. Each

178

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to know the position of the wire spark chambers as precisely as possible. Prior to the experiment the position of each chamber had been measured to within a few millimeters. In order to align the chambers more precisely, we used those events that suffer only small multiple C o u l o m b scattering in the carbon scatterer. Then unscattered proton tracks behind the magnet were fitted to straight lines by the least-squares method. With W S C 1 and WSC 10 fixed to the measured positions, the other chamber positions were adjusted so as to minimize the sum of the square of deviations from the fitted tracks. The chamber position thus determined was, in the worst case, different from the measured one by as m u c h as 5 ram. This was understood as due to the weight of the carbon plates which deformed the supporting structure for the chambers. Thus we readjusted the chamber positions each time the setting of the carbon plates was changed, by the method described before. As the result, the relative alignment of the chambers was always known to an accuracy of _+0.15 m m for horizontal coordinates and _+0.3 m m for vertical coordinates. Possible systematic biases due to the chamber misalignment are discussed in subsection 5.2.2. 4.2. SPACE RESOLUTION OF THE WIRE SPARK CHAMBERS With a 20 MHz clock for digitizing spark signals, the absolute limit of accuracy in determining the spark position along the magnetostrictive wire is 0.25 ram. The actual space resolution for proton tracks ( T p = 4 2 5 M e V ) was measured during the recent 7 d - , p n experimenff) by taking out the carbon scatterer. Fig. 10 shows the deviation histograms for the case in which four chambers (WSC 3 - W S C 6) were used for the straight-line fit, Assuming that the space resolution is the same for all the chambers, we obtain Ax =

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select only those events that have IARI < 5 cm for further processing. The m o m e n t u m re~olution Ap/p is calculated by taking into account the space resolution of the MWPCs ( + 1 ram) and WSCs, and the multiple Coulomb scattering. It is 1.3% (fwhm) at 940 M e V / c and 2% at 540 MeV/c. 4.4. SCATTERINGIN THE POLARIMETER Since the carbon scatterer is in most cases quite thick, it is necessary to remove the effect of the multiple Coulomb scattering before and after the hadronic scattering of interest. Only then are the scattering angle and the scattering position of the proton determined accurately. The configuration of alternating layers of the wire spark chambers and the carbon plates partly allows this with the following three-step reconstruction procedure. (i) Determine the straight trajectory before and behind the polarimeter using three or four consecu1600 E 1400 E ,.,r 1200 hi Q.

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rive wire spark chambers with no carbon plates in between. From this, a first approximation for the scattering point and scattering angle is calculated. (ii) In order to increase the accuracy, remove the nearest chambers before and behind the scattering point determined in step (i), and use the remaining three or four consecutive chambers for a straightline fit. (Unless we remove the nearest chambers, we miss the correct scattering point if the true point is not in the presumed carbon plate.) (iii) Use the nearest three or four consecutive chambers before (behind) the scattering point determined in step (ii) for the final straight-line fit before (after) the scattering. Fig. 13 shows the scattering-point and the scattering-angle distributions obtained in each step. The positions of the carbon plates are shown at the bottom of the figure. The scattering-point distributions are shown for all scattering angles and for 0 >_ 6 °. A progressive improvement of the scattering-point resolution is evident. As seen from this figure, most of events have small scattering angles (0<4°), due mostly to the multiple Coulomb scattering. Although the above procedure does not guarantee to give an actual multiple scattering angle, especially for very small angles, ln(N(O)/ sin 0) vs. 02 plots shown in fig. 14 exhibit a linear part expected for the Gaussian form of the angular distribution of the multiple Coulomb scattering

N(O)dO w_ exp(-02/02) sin0d0, where 6 is a constant. The deviation from linearity at relatively larger angles is predominantly due to hadronic scattering. The resolution (fwhm) for the scattering angles 0 and 0 around 0 ~ 0 ° and 180 ° is estimated to be zI0 = 3 ° and /1~ = 12.5 ° by a Monte Carlo program in which the space resolution of the wire spark chambers and the multiple Coulomb scattering are taken into account. In order to know the analyzing power event by event, the exictation energy of the carbon nucleus after the scattering (which in good approximation is equivalent to the energy loss of the proton) must be known. This is done by comparing the information from the range counter hodoscope with the proton m o m e n t u m measured by the magnetic spectrometer (ionization loss of the proton is corrected). Fig. 15 shows the distribution in the excitation energy AE of the carbon nucleus. A prominent elastic peak with resolution less than 2 0 M e V (fwhm) is clearly seen.

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ulO

7 hi h 0

ation

z12 8

% O

'" 6 ~Z ~:

500

w

O©

eo

..

4 2 i

i

i

.~ loo

Z

-4(

-20

0 /iE

20

40 (MeV)

60

U U')

80

(MeV)

Fig. 16. Scattering efficiency of the polarimeter. The solid curve shows the result of the simulation. The open circles are the corresponding data taken from the latest 7d ~ pn experiment (ref. 2). The filled circles are the scattering efficiency after the cut is applied on reflected tracks.

Fig. 15. An example of the energy loss distribution in the proton-carbon scattering, taken from the latest 7d--,pn experiment (Tel'. 2). Central orbit momentum = 943 MeV/c. Thickness of carbon = 66.3 g/cm 2.

that the lower cut on 0 for these data is 5 ° - 7 ° , depending on the data points. The filled circles show the efficiency after the cut on reflected tracks to remove a geometrical bias (see subsection 5.1 for details), given by N s / N 4 in table 1.

4.5. SYSTEM EFFICIENCY 4.5.1. Scattering efficiency T h e e f f i c i e n c y o f t h e p o l a r i m e t e r is r e p r e s e n t e d b y t h e s c a t t e r i n g e f f i c i e n c y d e f i n e d as t h e p e r c e n tage of the triggered events usable for the polarization analysis. A simulation program, which takes into account the geometry of the apparatus and the differential cross section of the proton-carbon scatt e r i n g , h a s b e e n w r i t t e n to e s t i m a t e t h i s e f f i c i e n c y . U s a b l e e v e n t s a r e d e f i n e d as t h o s e t h a t h a v e a scattering angle 5 °_< 0 ~ 30 ° , a n energy loss A E < 30 M e V a n d a k i n e t i c e n e r g y at t h e s c a t t e r i n g p o i n t g r e a t e r t h a n 100 M e V . T h e r e s u l t i n g s c a t t e r i n g e f f i c i e n c y as a f u n c t i o n o f t h e k i n e t i c e n e r g y o f t h e p r o t o n i n c i d e n t o n t h e p o l a r i m e t e r is s h o w n b y t h e s o l i d c u r v e in fig. 16. A l s o in t h i s f i g u r e , t h e a c t u a l l y o b s e r v e d e f f i c i e n c y in t h e l a t e s t 7d ~ p n e x p e r i m e n t : ) is s h o w n b y t h e o p e n circles. N o t e TABLE

Tp

4.5.2. Reconstruction efficiency To discuss the reconstruction efficiency, statistics of the data analysis in the latest 7 d ~ p n experiment 2) are listed in table 1. In this table, N O is the number of triggers. We cut out those events without any reasonable MWPC and/or WSC information due to chamber inefficiencies or chance coincidences of the trigger counters, and retain N~ events. Subsequently, reaction points are required to lie around the target cell and also a cut is applied on the geometrical Z 2 of the straight-track fit behind the magnet (N 2 events retained). A cut on the

1

Statistics of the data analysis taken from the latest 7d ~ pn experiment (ref. 2). Eend is the bremsstrahlung end-point energy, 0 Lab and correspond to the spectrometer central orbit, N o is the number of triggers, and N 5 is the number of events used for the maximum likelihood analysis of the polarization. For the meaning of N~, N 2, N 3 and N 4, see text. The ratio N3/N 2 represents the reconstruction efficiency. The ratio N5/N 4 represents the scattering efficiency after the cut on the reflected tracks, and is plotted in fig. 16 (filled circles) as a function of Tp. Eend (MeV) 500 500 550 600 600 600 650 650 650 700 700

01~"ab

Tp (MeV)

33.5 ° 54.3 ° 33.0 ° 32.5 ° 52.7 ° 99.6 ° 32.1 ° 51.3 ° 69.0 ° 97.6 ° 114.9 °

314 236 353 392 353 176 400 363 274 206 167

N0 29 800 81 012 23 089 17 050 37 752 58 319 18 200 19 441 70 097 172 763 104 999

N1 29 222 80 412 22 808 16 448 36 758 57 822 16 515 19 145 68 957 171 889 104 780

N2 26 734 74 152 21 337 14 625 34 271 54 424 13 575 18 052 65 054 163 096 98 767

N3 25 440 71 000 20 676 13 654 32 461 52 010 11 865 17 282 62 363 157 840 93 581

N4 16 973 45 624 14 579 9 441 21 238 28 148 7 800 10 615 35 792 82 004 51 949

N5

N3/N 2

N5/N 4

1006 1 812 835 790 1022 624 556 594 1691 2 091 756

0.952 0.957 0.969 0.934 0.947 0.956 0.874 0.957 0.959 0.968 0.947

0.059 0.040 0.057 0.084 0.048 0.022 0.071 0.056 0.047 0.025 0.015

182

I. A R A I et al.

geometrical Z 2 of the proton tracks inside the polarimeter further reduces the n u m b e r of events to N 3. We have checked that the variation of the strength of the cut on the geometrical Z 2 has no appreciable effects on the polarization results. The actual cut strength depends on the thickness of the carbon scatterer. Then, a tight fiducial cut on the reaction points in the target (to ensure that the reaction took place in the liquid hydrogen) and a cut on the m o m e n t u m mismatch AR are applied (N4 events retained). Finally, after the cuts on the energy loss 3E, the scattering angle 0 and the reflected tracks, N5 events are retained for the m a x i m u m likelihood analysis of the polarization. The loss of events due to the cut on the geometrical Z 2 is caused partly by poor straight-line fits due to the multiple scattering and chamber resolution, and partly by the difficulties in the reconstruction due to inefficiencies of the wire spark chambers. In addition, chance coincidences of the trigger logic cause the loss of events on going from N~ to N 2. Thus the ratio N3/N 2 roughly gives a measure of the reconstruction efficiency. For most cases it is more than 95%. The deterioration of the ratio N3/ N 2 for highest proton kinetic energies is caused by increased multiple scattering in accordance with the increased thickness of the carbon scatterer.

5.2.

5. Polarization analysis 5.].

(ii) If the p r o t o n - c a r b o n interaction point lies outside the polarimeter, the event is discarded ~. (iii) Events with highly inelastic p r o t o n - c a r b o n scattering ( A E > 3 0 MeV) are excluded, because the analyzing power is not well known. (iv) Protons suffering only the multiple Coulomb scattering in the carbon plates must be removed from the sample. To determine the cut-off angle 0,~, the polarization is calculated by varying 0~, and we d e m a n d that the polarization should level off for 0 >_ 0~.. The value of 0~ depends on the thickness of the carbon scatterer and the kinetic energy of the proton, and is determined each time the run conditions are changed. Fig. 18 shows two examples corresponding to the data shown in fig. 14, The upper limit of 0 is taken to be 30 °, i.e. those events with 0~ _< 0_< 30 ° are used for the final polarization analysis. (v) In order to remove possible systematic biases clue to the finite size of the polarimeter, the scattered proton trajectory is rotated around its incident direction by 180 ° . W e d e m a n d that the reversed trajectory should also satisfy the trigger condition and survive all the fiducial cuts *~. Examples of the 0 distribution of the events surviving the cuts (i)-(v) and the corresponding likelihood function are shown in fig. 19.

SELECTION OF EVENTS

The proton polarization is determined as a value of P which maximizes the likelihood function

SYSTEMATIC BIASES, BACKGROUND AND ERRORS

5.2.1. Spin precession by the spectrometer magnet The precession angle 6o of the proton spin in the h o m o g e n e o u s magnetic field is given by o~ = ~oo(g/2-1)y,

L(P)=

i=tl~dQ~Q)o(l +A(T~,AE;,Oi)Pc°s4);)'

(1)

where (da/dO)0 is the differential cross section for the unpolarized p r o t o n - c a r b o n scattering, A is the analyzing power which is a function of the kinetic energy T of the proton, the exictation energy zIE of the carbon and the scattering angle 0, and 0 is the azimuthal scattering angle with respect to the plane normal to the proton polarization vector. The definition of the coordinate system is shown in fig, 17. To select bias-free events useful for the polarization analysis, we apply the following cuts on the reconstructed events. (i) A cut is applied on the coordinate of the reconstructed reaction point in the target so that the background contribution from the target cell and the v a c u u m jacket be removed.

where coo is the total bending angle of the proton (~34.5°), g/2 = 2.79 and y is the ratio of the total energy of the proton to its rest mass. The apparent depolarization due to the spin precession is approximately estimated as sin 2 ~(1 - cos co), Even inside the polarimeter, a small fraction of protons interact with the air or the wire spark chambers, since in the worst case their total collision length amounts to 0.4% of that of the carbon. To see this effect, we applied a cut on the scatteringpoint distribution (for example, see fig. 13) at the boundaries of the carbon plates, and compared the proton polarization calculated for the cut and uncut samples of events. We always found that both samples gave consistent results. Therelbre we do not apply this cut for the final polarization analysis. ~'*A mathematical basis for this operation in conncection with the maximum likelihood method is described in ref. 1.

PROTON

SPECTROMETER/POLAR1

pn

Y d -~

METER

183

~'p

Yn-~

I~x~ J tlrget

~y

~target

photon beam

photon beam

O.,0

,/,

\,

carDon

\ ~ o t o n ~ .~ ~,

Z

Z

Y Fig. 17. Definition of the coordinate s y s t e m relevant to the polarization analysis. In the 7d ~ pn reaction, the positive direction of the proton polarization is defined to be parallel to the vector product k×p, where k and p are the m o m e n t u m vectors of the photon and proton, respectively. However, in the yn ~ rc p reaction, the positive direction of the proton polarization is defined, by convention, to be parallel to the vector product k × q , where q is the m o m e n t u m vector of the Non. T h u s the positive direction of the proton polarization in the ?d --, pn reaction is opposite to the one in the ?n ~ ~ - p reaction.

-1.0

-1.0

z

i

(a)

Yd 4" pn Ey = 600MeV 0" = 1 2 0 =

i

i

i

i

i

Yd .-.. pn Ey = 550

MeV

e * = 4 5"

z

O

i

(b)

o

I'--

F--

N nr - 0.5 .,(

,2_ -0.5

O CL

oQ.

(1: .J

0

I

4

I

[

5 8¢

I

6

I

I

7

[

I

B

0

i

4

5

(DEGREES)

ec

6

I

i

7

I

8

(DEGREES)

Fig. 18. Examples of the P vs. 0 c plot. T h e data samples used are the same as those used to obtain fig. 14.

where q/ is the angle between the directions of the proton spin and the magnetic field, and is less than __2 °. With our run conditions (Tr -- 100 - 4 0 0 MeV), co is 70 ° - 85 °, and therefore the apparent depolarization due to the magnetic field is negligibly small (less than 0.1%). 5.2.2. Systematic bias due to misalignment of the wire spark chambers Even though the wire spark chambers are aligned with each other so that the reconstruction program

recognizes a straight track as really straight, there remains possible ambiguity in the translation and rotation with respect to the true track. So long as the relative positioning of the trigger counters and wire spark chambers is correctly preserved, a small a m o u n t of overall translation and rotation does not cause significant systematic biases. However, if the axis (central orbit) of the wire spark chambers recognized by the reconstruction program does not coincide with the real central orbit (which is the axis of the trigger counters), a serious systematic

184

I. ARAI et al.

bias arises. By artificially inclining the spark chamber axis with respect to that of the trigger counters, we have found that the bias in the left-right asymmetry amounts to 2% per milliradian. For typical analyzing power A = 0.4, this corresponds to a 5% bias in the polarization per milliradian. The relative alignment of the wire spark chambers and trigger counters has been checked by carefully comparing the profile of the counters given by the reconstructed events with the measured counter positions. In practice, however, the profile of C4 is smeared out owing to the multiple scattering and the spread of incident angles, and it is not easy to compare with a precision within a few millimeters. The best way to check these kinds of bias is provided by a calibration of the zero polarization using unpolarized protons or spin-zero particles. As described in subsection 5.3, no indication of biases has been found within the sensitivity of the calibrations. 5.2.3. Double-scattering in the carbon analyzer Although an appreciable percentage of protons suffer double-scattering in the carbon scatterer, only those double-scattering events satisfying the following conditions would be misidentified by the reconstruction program as single-scattering events. (i) The total energy loss is less than 30 MeV. (ii) The two scattering points lie in the same carbon plate, or at least one of the two scattering angles is small. However, the small-angle elastic or nearly-elastic scatter is almost harmless for the polarization analysis because (a) if it is preceded by a large-angle scatter, the scattering angle recognized by the reconstruction program is practically determined by the first scatter; (b)even if it is the first scatter, the analyzing power is very small for 0_< 3 ° , which means that the polarization is almost preserved. Removing such cases, the remaining contribution from double-scattering events is estimated to be not more than 2%, even in the worst case. 5.2.4. Background contamination* For the deuteron photodisintegration 7 d ~ p n , possible background processes are 7d ~ ~ - pp, 7d ~ 7~°np and 7d ~ ~ + nn with one positively charged particle entering the spectrometer system. The last process can easily be identified and * For more detailed discussions, see refs. 1-3.

i

1.0

"I'd -~ p n Q.

E¥ = 600 MeV

40

,

,

i

,

(a)

08

Z

>~ 30

0,6

2o

0.4

} ,0

0 2

I

a

1

-180 -120 - 6 0

I

0

60

¢

i

120

180

0 -09

-07

-05

0.3

(DEGREES)

Fig. 19. (a) An example of the 0 distribution. The data sample used is the same as that used for fig. 14(a) and fig. 18 (a). (b) The corresponding likelihood function.

rejected by the pulse-height and time-of-flight information from the trigger counters, while the first two processes are suppressed by setting the bremsstrahlung end-point energy no more than 100 MeV above the proper value corresponding to the central orbit of the spectrometer. The amount of possible background contamination is estimated to be less than a few per cent by reconstructing the photon energy spectrum from all triggered events based on the yd--, pn kinematics. In the experiment of the photoproduction of negative pions yn--, ~z- p, a double-arm spectrometer was used. Possible background processes are the double-pion photoproduction 7n --, rr° 7r- p and 7P---" rr-Tr p. To estimate the contribution from these two processes, the double-arm spectrometer was set to detect two positively charged particles in coincidence. Only two triggers of the + + combination occured during the time corresponding to 200 triggers of the - + combination. However, the positively charged particles detected by the proton arm turned out to be pions from the time-of-flight and range information, and could be rejected in the off-line analysis. Therefore the contamination from the double-pion photoproduction process is also less than a few per cent. In the 7 d ~ p n experiments, an appreciable a m o u n t of background protons from Mylar walls of the target container was observed. As already described in subsection 5.1, this background was suppressed by the cut on the reaction points in the target. By reconstructing proton tracks back to the target, the reaction-point distribution along the beam direction was obtained. From target-empty runs, then, the position of Mylar walls was known and a cut was applied so as to remove the contribution from the Mylar walls. The same procedure was

PROTON S P E C T R O M E T E R / P O L A R I M E T E R

applied to the yn--, n - p experiment, although the contribution from this background was negligibly small (less than 0.4%) at the trigger level by virtue of double-arm coincidence. 5.2.5. Errors For the polarization P which maximizes the likelihood function (1), the statistical errors AP' (one standard deviation) is determined such that P+_ AP' gives e -~/2 times the m a x i m u m of the likelihood function. The uncertainties in the analyzing power (typically A A / A - 5 %) cannot be taken into account by this method. The polarization is alternatively determined from the left-right asymmetry e of the p r o t o n - c a r b o n scattering as P = e / A . Then the uncertainty of the proton polarization due to the uncertainty of A is P A A / A . The total uncertainty of the polarization AP may be given by (AP) 2 = (AP') 2 + p 2 ( A A / A F . In our experiments, AP' is typically 0 . 1 - 0 . 1 5 , and therefore the statistical uncertainty dominates. The effects of the background contamination and the misidentification of the double-scattering events are difficult to evaluate precisely. If the nature of these processes (percentage of the contamination, differential cross section and proton polarization) is known, a Monte Carlo program may be written for this purpose. Instead, an easy estimate of the upper bound of the polarization error due to the background contamination can be made in the following way, using the left-right asymmetry. The polarization P is given as p_

1 NL-N R A N '

where N L and NR are the number of events with the proton scattered to the left and right, respectively, and N = N L+ N R. Assuming that there are N ' = N~ +N~ background events (including the double-scattering events), and that the protons from these events are completely polarized, we have the relation +1

-

For example, taking P = 0 . 5 , A =0.4 N ' = 0.02N (2% background contamination), P+-P

= -0.01,

P--P

= +0.03.

185

and

Therefore 2% contamination of the background is tolerable compared with the statistical uncertainty. 5,3. CALIBRATION OF ZERO POLARIZATION There are a number of possible sources for systematic asymmetry of the polar±meter other than the misalignment of the wire spark chambers discussed in subsection 5.2.2. For example, inhomogeneous efficiency of the detectors, imperfect functioning of some electronics, and inefficiency of the reconstruction program are also dangerous. Calibration of zero polarization is quite helpful to gain confidence in the operation of the entire system. In the course of the experiments, we have tried the following two methods for this purpose. Before the first 7d ~ pn experiment~), an electron beam was extracted from the synchrotron and the polarization of the protons from the elastic electron-proton scattering was measured at E~ = 695 MeV and 808 MeV. It is a well-known fact that the proton polarization is only few per cent, if at all, in this reaction4). Our results were P=0.1-4-0.1 at 6 9 5 M e V and P - - - 0 . 1 + _ 0 . 1 at 808 MeV. Although the statistical accuracy was a bit poor, no indication of the systematic asymmetry was found. The other calibration method employed was to use negative pions which scatter on the carbon isotropically. We measured the left-right asymmetry of the negative pion-carbon scattering and found no indication of significant systematic asymmetry either. For example, at p~ = 497 MeV/c (the thickness of the carbon was 6 1 . 6 g / c m 2) the left-right asymmetry observed was (N L - N R)] ( N L + N R ) = O . O 0 5 + O . 0 3 4 for 3 0 ° _ > 0 _ > 0 c = 7 ° and [OI, I n - O l - ~ 6 0 °.

N' From this, we obtain A

N,L± _ 1 ! A N' -

T

6. C o n c l u s i o n

1 -T-A N' '

N~

-

2

"

The upper and lower bounds of the polarization are given by p±

l (NL--NL±) - - ( N ~ - N ' R ±) A

N-N'

We have constructed a spectrometer and carbon polarimeter for protons with kinetic energies between 100 and 400 MeV. It has been successfully operated over three years to measure the proton polarization in the reactions yd --, pn and yn --, 7r p.

186

I. ARAI et al.

T h e s a n d w i c h s t r u c t u r e o f the a l t e r n a t i n g layers o f wire spark c h a m b e r s and carbon plates a d o p t e d for the p o l a r i m e t e r allows a high scattering efficiency and wide a c c e p t a n c e to be o b t a i n e d , c o m p a t i b l e with g o o d r e s o l u t i o n for the scattering points a n d scattering angles. T h e s e f e a t u r e s are essential to o b t a i n good statistical accuracy a n d to m i n i m i z e v a r i o u s biases. W e wish to t h a n k Drs. Y. W a t a s e , H. Fujii a n d Messrs. H. Iwasaki and T. S u m i y o s h i for their c o o p e r a t i o n at v a r i o u s stages in c o n s t r u c t i n g a n d i m p r o v i n g the apparatus. T h a n k s are also d u e to the staff o f the INS high e n e r g y d i v i s i o n for help and s u p p o r t d u r i n g the experiments. References J) T. Kamae, 1. Arai, T. Fujii, H. lkeda, N. Kajiura, S. Kawaba-

ta, K. Nakamura, K. Ogawa, H. Takeda and Y. Watase, Phys. Rev. Lett. 38 (1977) 468; and Nucl. Phys. B139 (1978) 394. 2) H. lkeda, 1. Arai, H. Fujii, T. Fujii, H. lwasaki, N. Kajiura, T. Kamae, K. Nakamura, T. Sumiyoshi, H. Takeda, K. Ogawa and M. Kanazawa, Phys. Rev. Lett. 42 (1979) 1321. 3) H. Takeda, 1. Arai, H. Fujii, T. Fujii, H. Ikeda, H. Iwasaki, N. Kajiura, T. Kamae, S. Kawabata, T. Sumiyoshi, S. Homma, M. Kanazawa, N. Yamashita and K. Ogawa, University of Tokyo report UTPN-116 (1978), to be published. 4) T. Powell, M. Borghini, O. Chamberlain, R. Z. Fuzesy, C. G. Morehouse, S. Rock, G. Shapiro, H. Weisberg, P. L. A. Cottrell, J. Litt, L. W. Mo and R. E. Taylor, Phys. Rev. Lett. 24 (1970) 753. 5) H. Cunitz, W. Sippach and J. Dieperink, Nucl. Instr. and Meth. 91 (1971) 211. 6) K. J. Foley, W. A. Lowe, S. Ozaki, E. D. Platner, A. C. Saulys, E. H. Willen and S. J. Lindenbaum, Nucl. Instr. and Meth. 108 (1973) 33. 7) N. Kajiura, 1. Arai, H. lkeda and H. Takeda, to be published. 8) N. Kajiura, I. Arai, T. Fujii, H. Ikeda, T. Kamae, S. Kawabata, K. Nakumara, K. Ogawa and H. Takeda, Nucl. Instr. and Meth. 138 (1976) 681.