- Email: [email protected]
High-efficiency polarimeter for a secondary proton beam of 16–22MeV
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
High-efficiency polarimeter for a secondary proton beam of 16–22 MeV M. Yamaguchi*, K. Sawada, T. Katabuchi1, N. Kawachi, N. Yoshimaru, K. Shiga, Y. Tagishi Institute of Physics and Tandem Accelerator Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan Received 11 November 2002; received in revised form 27 March 2003; accepted 28 March 2003
Abstract A high-efficiency (B2 104 ; Ay ¼ 0:5) polarimeter that is used for a secondary proton beam with energy of 16–22 MeV is described. The Polarimeter is based on the elastic scattering of protons from liquid helium. It allows a measurement of the vertical polarization component of the incident protons. The measured effective analyzing powers were compared with these values obtained from a computer simulation by using a Monte Carlo method. The results of the simulation reproduced the measured values within the statistical uncertainty. r 2003 Elsevier Science B.V. All rights reserved. PACS: 07.60.F Keywords: Polarimeters; Proton polarization; Liquid helium
1. Introduction We have been studying nuclear reaction mechanisms by using polarized proton beams or polarized deuteron beams at Tandem Accelerator Center, University of Tsukuba (UTTAC). Especially, we have measured differential cross-sections and analyzing powers for (d,p) reactions for several target nuclei and have studied the direct *Corresponding author. Tel.: +81-298-53-2569; fax: +81298-53-2563. E-mail address: [email protected] (M. Yamaguchi). 1 Present address: Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA.
nuclear reaction mechanisms [1,2]. For understanding of the nuclear reaction mechanisms, we needed to measure new observables, such as the polarization of emitted protons or spin transfer coefficients. In order to obtain such observables, we developed a polarimeter for double scattering experiments. Here we report on the design and the performance of this polarimeter. The target of the polarimeter is 4 He: We use this polarimeter for proton energies between 16 and 22 MeV: For this energy range, the p-4 He scattering has a high figure of merit, sA2 ; where s is the differential cross-section and A is the analyzing power, and its analyzing power varies only slightly with energy and with angle in this energy range [3].
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-9002(03)01390-1
ARTICLE IN PRESS 36
M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
Generally, double scattering experiments take much more time than single scattering experiments. Therefore, a thick target is needed to obtain a high efficiency, and one of the ways to obtain a thick target is to use a high-pressure gas. Proton polarimeters using high-pressure 4 He gas have been reported by several authors [4–8], however, gaseous 4 He targets have thickness limitations. So we have used liquid helium as the target of our polarimeter because liquid helium has the advantage of making the target compact. The target thickness of our polarimeter is about 1 cm; equivalent to a gaseous 4 He target having a thickness of about 40 cm and having a pressure of about 20 atm at room temperature. By using liquid helium with large solid angles, a high efficiency, about 2:0 104 ; was obtained with an effective analyzing power of about 0:5 at proton energies around 20 MeV: In developing the present liquid helium polarimeter, we referred to one developed by Sagara et al. [9]. Their polarimeter is based on the scattering of protons from liquid helium, and the usable energy range is between 14 and 18 MeV: There polarimeter have a different target cell geometry and a placement of detectors. They used silicon solid-state detectors to measure the elastically scattered protons from liquid helium. These detectors were placed near the liquid helium target to obtain large solid angles. In our polarimeter, scintillation counters having large surface areas are used and are arranged at large distance from the liquid helium target to reduce the asymmetry of the solid angle of each counter and the uncertainty of the scattering angles. As a consistency check, we compared the measured analyzing powers of the polarimeter with those obtained from a computer simulation. The results of the simulation reproduced the measured effective analyzing powers within the statistical uncertainties.
2. Liquid helium cryostat The vertical cross-section of the polarimeter is shown in Fig. 1. Liquid helium is held in a reservoir tank having a volume of about 6 l that is
Fig. 1. Vertical section of the polarimeter.
placed at the center of the polarimeter. A target cell is fixed at the bottom of the reservoir tank. One of the causes of heat input to the reservoir tank and to the target cell is radiation from the outside wall of the polarimeter. In order to reduce the heat input, the reservoir tank and the target cell are surrounded by a liquid nitrogen reservoir tank and by copper walls which are cooled to the liquid nitrogen temperature. Moreover, radiation shields of thin aluminum-coated mylar foils are inserted between the helium tank and the nitrogen tank. Another cause of heat input is heat conduction. The liquid helium reservoir tank is supported by four stainless-steel pipes with diameters of 15 mm and thicknesses of 0:5 mm and fixed to an upper flange of the polarimeter. Generally, heat conduction depends on both the temperatures of the hightemperature edge and of the low-temperature one. In the case of our polarimeter, the heat input is reduced by cooling the upper parts of the pipes, so the upper parts of the pipes are connected to the liquid nitrogen tank with bundled copper wires.
ARTICLE IN PRESS M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
The total heat input is estimated to be about 300 mW from the consumption of liquid helium. There is enough liquid helium in the 6 l reservoir tank to last about 24 h:
3. Detectors and target cell The horizontal cross-section of the polarimeter at the target position is shown in Fig. 2. Protons scattered from the helium target are detected by two scintillation counters placed symmetrically to the incident proton axis at scattering angles of 60711 in the horizontal plane. The scintillation counters consist of plastic scintillaters and photo-multipliers. The diameter of the plastic scintillaters is 5 cm and the thickness is 7 mm: Each of the solid angles is 116 msr: A transmission-type surface barrier silicon detector ð200 mmÞ is placed in front of the liquid helium target together with an entrance slit. This silicon detector counts the number of the protons coming into the target and gates the scintillation counters. The diameter of the aperture of the slit is 8 mm: The distance between this detector and the helium target is about 8 cm: Protons passing through the helium target are detected by an one-dimensional position sensitive
37
silicon detector having an aperture slot 45 mm wide and 6 mm high. This detector is placed to monitor the horizontal distribution of the protons. In order to facilitate to identify which channel in the position spectrum corresponds to the geometrical center, we attached a copper absorber having thickness of 1:5 mm and width of 1 mm across the center of the aperture slot. This absorber interrupt a part of the proton beam and the position spectrum of the position-sensitive silicon detector has a hollow and we can easily recognize the center of the detector by this hollow. The horizontal cross-section of the target cell is a semi-circle having a radius of about 10 mm: The windows of the target cell are made of mylar foil having the thickness of 25 mm: The position of the target cell can be observed from outside of the polarimeter through two observation windows and can be adjusted by moving the upper flange. After liquid helium is added, such an adjustment is necessary to place the target cell in right position.
4. Calibration The effective analyzing powers of the polarimeter were measured by using polarized protons Position Sensitive Silicon Detector
Scintillation Counter
Scintillation Counter
Target Cell
Transmission Type Silicon Detector
Slit
10cm Proton Beam
Fig. 2. Liquid helium target and proton detectors (horizontal section of the polarimeter).
ARTICLE IN PRESS 38
M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
Fig. 3. Schematic layout of the experiment, showing the polarimeter, the QDQ magnetic analyzer system, and the scattering chamber. 100000 normal spectrum 10000 coincidenced spectrum 1000
100
10
1 0
10
20
30
40
50
60
70
80
90
100
110
Fig. 4. A typical energy spectrum of the protons scattered from liquid helium target. The incident energy of the protons was 22 MeV: The background at low energy can be rejected by making coincidence with the transmission-type silicon detector.
with known polarization at proton energies from 16 to 22 MeV: The effective analyzing powers Aeff are expressed by the following equation: Aeff ¼
1 NL NR ; Py NL þ NR
ð1Þ
where Py is the polarization of the proton beams, and NL and NR are the number of protons counted with the left detector and right one, respectively. Fig. 3 shows the schematic layout of the calibration experiment. Vertically polarized proton beams were produced by a Lamb-shift polarized ion source [10] and were accelerated up to 16–22 MeV: The beams were introduced on the
first target of gold foil having the thickness of 1 mm: Elastically scattered protons from the gold target with a scattering angle of 2270:5 were momentum analyzed by a QDQ magnetic spectrograph [11] and focused on the polarimeter target. The polarization of the proton beam was measured by the quench-ratio method [15]. The typical value of the polarization was about 0.07. Uncertainty of the polarization was estimated to be correct within 0.02 [16]. The degree of polarization of the scattered protons is estimated to be the same as that of the incident proton beam. The reasons of this are the following. Firstly, according to the optical model calculation using a set of optical potential
ARTICLE IN PRESS M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
parameters [12], the absolute value of the analyzing power for the elastic scattering of 197 Auðp; pÞ is estimated to be smaller than 0.003 at the scattering angle of 2270:5 at proton energies from 16 to 22 MeV: Secondly, spin-flip provability is negligible because nucleon–nucleus spin–spin interaction is abundantly smaller than Coulomb force at this scattering angle [13,14]. A typical energy spectrum of the protons scattered from the liquid helium target is shown in Fig. 4. The background signals lying in the lowenergy region can be rejected by making a coincidence with the transmission-type silicon detector placed at the entrance of the helium target. Table 1 shows the measured effective analyzing powers and efficiencies. The error of each effective analyzing power includes the uncertainty of the beam polarization and the statistical uncertainty. Each efficiency is defined by the ratio of the number of protons detected by the scintillation counters to the number of protons incident on the liquid helium target.
5. Simulation We compared the measured analyzing powers of the polarimeter with the values obtained from a Table 1 Measured values of effective analyzing powers Energy (MeV)
Effective analyzing power
Efficiency
16 17 18 20 22
0:5970:02 0:5170:02 0:4970:02 0:4470:02 0:4370:02
2:6 104 2:4 104 2:4 104 2:0 104 1:9 104
39
computer simulation. In order to treat the straggling of the proton track in the helium target easily and correctly, we used the Monte Carlo method. Each track of protons in the helium target is represented by a sequence of step-points. Each step-point has a position vector and a momentum vector. Every interval of these step-points is 0:5 mm: The position vector and the momentum vector of a step-point are calculated from those of the previous step-point. The Molie" re scattering process [18] and the scattering process caused by nuclear force were considered in the simulation. The former caused small angle scatterings and the latter caused large angle scatterings. We used the sub-routine which calculates the former process and which is already in the CERN program library ‘‘GEANT’’ [19]. Phase shift data of p þ 4 He elastic scattering given in Refs. [3,17] were used to calculate the latter process. Table 2 shows the simulated values of the analyzing powers and those of the measured values. The statistical uncertainties of calculated values are about 0.01. The measured analyzing powers are reproduced by the present calculations quite well within the statistical uncertainty.
6. Summary A proton polarimeter, based on the elastic scattering from liquid helium, for double scattering experiments has been described. Effective analyzing powers were obtained at proton energies between 16 and 22 MeV: We compared the measured effective analyzing powers of the 4 He-polarimeter with the values obtained from a computer simulation by using a Monte Carlo method. The results of the
Table 2 Calculated analyzing powers and the measured values Proton energies
Calculated values Measured values
16 MeV
17 MeV
18 MeV
20 MeV
22 MeV
0:59 0:59
0:51 0:51
0:50 0:49
0:45 0:44
0:44 0:43
ARTICLE IN PRESS 40
M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
simulation reproduced the measured values with uncertainty of about 0.01. Acknowledgements The authors would like to deeply thank Prof. K. Sagara and Prof. H. Ikeda for useful suggestions in designing the present polarimeter.
References [1] M. Masaki, Ph.D. Thesis, University of Tsukuba, 1994, unpublished. [2] K. Hirota, Ph.D. Thesis, University of Tsukuba, 1998, unpublished. [3] P. Schwandt, T.B. Clegg, W. Haeberli, Nucl. Phys. A 163 (1971) 432. [4] F. Sperisen, W. Gruebler, V. Konig, P.A. Schmelzbach, K. Elsener, B. Jenny, C. Schweizer, Nucl. Instr. and Meth. 190 (1981) 301. [5] R.A. Hardecopf, D.D. Armstrong, P.W. Keaton Jr., Nucl. Instr. and Meth. 114 (1974) 17. [6] J.F. Clare, Nucl. Instr. and Meth. 116 (1974) 525. [7] W.G. Weitkamp, I. Halpern, T.A. Trainer, S.K. Lamoreeaux, Nucl. Phys. A 417 (1984) 405.
[8] K.A. Fletcher, W.H. Geist, C.R. Brune, B.M. Fisher, R.P. Fitzgerald, H.J. Karwowski, D.E. Kruse, D.S. Leonard, E.J. Ludwig, R.C. Runkle, K.D. Veal, M.H. Wood, Nucl. Instr. and Meth. A 455 (2000) 620. [9] K. Sagara, K. Maeda, H. Nakamura, K. Aita, M. Izumi, M. Nakashima, T. Nakashima, A. Isoya, Nucl. Instr. and Meth. A 270 (1988) 450. [10] Y. Tagishi, J. Sawada, Nucl. Instr. and Meth. 164 (1979) 411. [11] Y. Aoki, S. Hiroki, M. Tomizawa, Y. Tagishi, K. Yagi, UTTAC Ann. Rep. 54 (1987) 5. [12] R.L. Verner, Phys. Rep. C 201 (N2) (1991) 57. [13] T. Nakano, M. Nakamura, H. Sakaguchi, M. Yosoi, M. Iseri, H. Togawa, S. Hirata, O. Kamigaito, H.M. Shimizu, M. Iwaki, Y. Nakai, S. Kobayashi, T. Noro, H. Ikegami, Phys. Lett. B 240 (1990) 301. [14] B.V. Przewoski, P.D. Eversheim, F. Hinterberger, U. . M. Hammans, R. Henneck, G. Lahr, J. Campbell, J. Gotz, Masson, I. Sick, W. Bauhoff, Phys. Rev. Lett. 64 (1967) 93. [15] G.G. Ohlsen, J.L. McKibben, G.P. Lawrence, P.W. Keaton Jr., D.D. Armstrong, Phys. Rev. Lett. 27 (1971) 599. [16] Y. Tagishi, et al., Phys. Rev. C 46 (1992) R1155. [17] R.A. Arndt, L.D. Roper, R.L. Shotwell, Phys. Rev. C 3 (1971) 2100. [18] J.B. Marion, B.A. Zimmerman, Nucl. Instr. and Meth. 51 (1967) 93. [19] GEANT—Detector Description and Simulation Tool, CERN Program Library.
Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
High-efficiency polarimeter for a secondary proton beam of 16–22 MeV M. Yamaguchi*, K. Sawada, T. Katabuchi1, N. Kawachi, N. Yoshimaru, K. Shiga, Y. Tagishi Institute of Physics and Tandem Accelerator Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan Received 11 November 2002; received in revised form 27 March 2003; accepted 28 March 2003
Abstract A high-efficiency (B2 104 ; Ay ¼ 0:5) polarimeter that is used for a secondary proton beam with energy of 16–22 MeV is described. The Polarimeter is based on the elastic scattering of protons from liquid helium. It allows a measurement of the vertical polarization component of the incident protons. The measured effective analyzing powers were compared with these values obtained from a computer simulation by using a Monte Carlo method. The results of the simulation reproduced the measured values within the statistical uncertainty. r 2003 Elsevier Science B.V. All rights reserved. PACS: 07.60.F Keywords: Polarimeters; Proton polarization; Liquid helium
1. Introduction We have been studying nuclear reaction mechanisms by using polarized proton beams or polarized deuteron beams at Tandem Accelerator Center, University of Tsukuba (UTTAC). Especially, we have measured differential cross-sections and analyzing powers for (d,p) reactions for several target nuclei and have studied the direct *Corresponding author. Tel.: +81-298-53-2569; fax: +81298-53-2563. E-mail address: [email protected] (M. Yamaguchi). 1 Present address: Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA.
nuclear reaction mechanisms [1,2]. For understanding of the nuclear reaction mechanisms, we needed to measure new observables, such as the polarization of emitted protons or spin transfer coefficients. In order to obtain such observables, we developed a polarimeter for double scattering experiments. Here we report on the design and the performance of this polarimeter. The target of the polarimeter is 4 He: We use this polarimeter for proton energies between 16 and 22 MeV: For this energy range, the p-4 He scattering has a high figure of merit, sA2 ; where s is the differential cross-section and A is the analyzing power, and its analyzing power varies only slightly with energy and with angle in this energy range [3].
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-9002(03)01390-1
ARTICLE IN PRESS 36
M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
Generally, double scattering experiments take much more time than single scattering experiments. Therefore, a thick target is needed to obtain a high efficiency, and one of the ways to obtain a thick target is to use a high-pressure gas. Proton polarimeters using high-pressure 4 He gas have been reported by several authors [4–8], however, gaseous 4 He targets have thickness limitations. So we have used liquid helium as the target of our polarimeter because liquid helium has the advantage of making the target compact. The target thickness of our polarimeter is about 1 cm; equivalent to a gaseous 4 He target having a thickness of about 40 cm and having a pressure of about 20 atm at room temperature. By using liquid helium with large solid angles, a high efficiency, about 2:0 104 ; was obtained with an effective analyzing power of about 0:5 at proton energies around 20 MeV: In developing the present liquid helium polarimeter, we referred to one developed by Sagara et al. [9]. Their polarimeter is based on the scattering of protons from liquid helium, and the usable energy range is between 14 and 18 MeV: There polarimeter have a different target cell geometry and a placement of detectors. They used silicon solid-state detectors to measure the elastically scattered protons from liquid helium. These detectors were placed near the liquid helium target to obtain large solid angles. In our polarimeter, scintillation counters having large surface areas are used and are arranged at large distance from the liquid helium target to reduce the asymmetry of the solid angle of each counter and the uncertainty of the scattering angles. As a consistency check, we compared the measured analyzing powers of the polarimeter with those obtained from a computer simulation. The results of the simulation reproduced the measured effective analyzing powers within the statistical uncertainties.
2. Liquid helium cryostat The vertical cross-section of the polarimeter is shown in Fig. 1. Liquid helium is held in a reservoir tank having a volume of about 6 l that is
Fig. 1. Vertical section of the polarimeter.
placed at the center of the polarimeter. A target cell is fixed at the bottom of the reservoir tank. One of the causes of heat input to the reservoir tank and to the target cell is radiation from the outside wall of the polarimeter. In order to reduce the heat input, the reservoir tank and the target cell are surrounded by a liquid nitrogen reservoir tank and by copper walls which are cooled to the liquid nitrogen temperature. Moreover, radiation shields of thin aluminum-coated mylar foils are inserted between the helium tank and the nitrogen tank. Another cause of heat input is heat conduction. The liquid helium reservoir tank is supported by four stainless-steel pipes with diameters of 15 mm and thicknesses of 0:5 mm and fixed to an upper flange of the polarimeter. Generally, heat conduction depends on both the temperatures of the hightemperature edge and of the low-temperature one. In the case of our polarimeter, the heat input is reduced by cooling the upper parts of the pipes, so the upper parts of the pipes are connected to the liquid nitrogen tank with bundled copper wires.
ARTICLE IN PRESS M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
The total heat input is estimated to be about 300 mW from the consumption of liquid helium. There is enough liquid helium in the 6 l reservoir tank to last about 24 h:
3. Detectors and target cell The horizontal cross-section of the polarimeter at the target position is shown in Fig. 2. Protons scattered from the helium target are detected by two scintillation counters placed symmetrically to the incident proton axis at scattering angles of 60711 in the horizontal plane. The scintillation counters consist of plastic scintillaters and photo-multipliers. The diameter of the plastic scintillaters is 5 cm and the thickness is 7 mm: Each of the solid angles is 116 msr: A transmission-type surface barrier silicon detector ð200 mmÞ is placed in front of the liquid helium target together with an entrance slit. This silicon detector counts the number of the protons coming into the target and gates the scintillation counters. The diameter of the aperture of the slit is 8 mm: The distance between this detector and the helium target is about 8 cm: Protons passing through the helium target are detected by an one-dimensional position sensitive
37
silicon detector having an aperture slot 45 mm wide and 6 mm high. This detector is placed to monitor the horizontal distribution of the protons. In order to facilitate to identify which channel in the position spectrum corresponds to the geometrical center, we attached a copper absorber having thickness of 1:5 mm and width of 1 mm across the center of the aperture slot. This absorber interrupt a part of the proton beam and the position spectrum of the position-sensitive silicon detector has a hollow and we can easily recognize the center of the detector by this hollow. The horizontal cross-section of the target cell is a semi-circle having a radius of about 10 mm: The windows of the target cell are made of mylar foil having the thickness of 25 mm: The position of the target cell can be observed from outside of the polarimeter through two observation windows and can be adjusted by moving the upper flange. After liquid helium is added, such an adjustment is necessary to place the target cell in right position.
4. Calibration The effective analyzing powers of the polarimeter were measured by using polarized protons Position Sensitive Silicon Detector
Scintillation Counter
Scintillation Counter
Target Cell
Transmission Type Silicon Detector
Slit
10cm Proton Beam
Fig. 2. Liquid helium target and proton detectors (horizontal section of the polarimeter).
ARTICLE IN PRESS 38
M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
Fig. 3. Schematic layout of the experiment, showing the polarimeter, the QDQ magnetic analyzer system, and the scattering chamber. 100000 normal spectrum 10000 coincidenced spectrum 1000
100
10
1 0
10
20
30
40
50
60
70
80
90
100
110
Fig. 4. A typical energy spectrum of the protons scattered from liquid helium target. The incident energy of the protons was 22 MeV: The background at low energy can be rejected by making coincidence with the transmission-type silicon detector.
with known polarization at proton energies from 16 to 22 MeV: The effective analyzing powers Aeff are expressed by the following equation: Aeff ¼
1 NL NR ; Py NL þ NR
ð1Þ
where Py is the polarization of the proton beams, and NL and NR are the number of protons counted with the left detector and right one, respectively. Fig. 3 shows the schematic layout of the calibration experiment. Vertically polarized proton beams were produced by a Lamb-shift polarized ion source [10] and were accelerated up to 16–22 MeV: The beams were introduced on the
first target of gold foil having the thickness of 1 mm: Elastically scattered protons from the gold target with a scattering angle of 2270:5 were momentum analyzed by a QDQ magnetic spectrograph [11] and focused on the polarimeter target. The polarization of the proton beam was measured by the quench-ratio method [15]. The typical value of the polarization was about 0.07. Uncertainty of the polarization was estimated to be correct within 0.02 [16]. The degree of polarization of the scattered protons is estimated to be the same as that of the incident proton beam. The reasons of this are the following. Firstly, according to the optical model calculation using a set of optical potential
ARTICLE IN PRESS M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
parameters [12], the absolute value of the analyzing power for the elastic scattering of 197 Auðp; pÞ is estimated to be smaller than 0.003 at the scattering angle of 2270:5 at proton energies from 16 to 22 MeV: Secondly, spin-flip provability is negligible because nucleon–nucleus spin–spin interaction is abundantly smaller than Coulomb force at this scattering angle [13,14]. A typical energy spectrum of the protons scattered from the liquid helium target is shown in Fig. 4. The background signals lying in the lowenergy region can be rejected by making a coincidence with the transmission-type silicon detector placed at the entrance of the helium target. Table 1 shows the measured effective analyzing powers and efficiencies. The error of each effective analyzing power includes the uncertainty of the beam polarization and the statistical uncertainty. Each efficiency is defined by the ratio of the number of protons detected by the scintillation counters to the number of protons incident on the liquid helium target.
5. Simulation We compared the measured analyzing powers of the polarimeter with the values obtained from a Table 1 Measured values of effective analyzing powers Energy (MeV)
Effective analyzing power
Efficiency
16 17 18 20 22
0:5970:02 0:5170:02 0:4970:02 0:4470:02 0:4370:02
2:6 104 2:4 104 2:4 104 2:0 104 1:9 104
39
computer simulation. In order to treat the straggling of the proton track in the helium target easily and correctly, we used the Monte Carlo method. Each track of protons in the helium target is represented by a sequence of step-points. Each step-point has a position vector and a momentum vector. Every interval of these step-points is 0:5 mm: The position vector and the momentum vector of a step-point are calculated from those of the previous step-point. The Molie" re scattering process [18] and the scattering process caused by nuclear force were considered in the simulation. The former caused small angle scatterings and the latter caused large angle scatterings. We used the sub-routine which calculates the former process and which is already in the CERN program library ‘‘GEANT’’ [19]. Phase shift data of p þ 4 He elastic scattering given in Refs. [3,17] were used to calculate the latter process. Table 2 shows the simulated values of the analyzing powers and those of the measured values. The statistical uncertainties of calculated values are about 0.01. The measured analyzing powers are reproduced by the present calculations quite well within the statistical uncertainty.
6. Summary A proton polarimeter, based on the elastic scattering from liquid helium, for double scattering experiments has been described. Effective analyzing powers were obtained at proton energies between 16 and 22 MeV: We compared the measured effective analyzing powers of the 4 He-polarimeter with the values obtained from a computer simulation by using a Monte Carlo method. The results of the
Table 2 Calculated analyzing powers and the measured values Proton energies
Calculated values Measured values
16 MeV
17 MeV
18 MeV
20 MeV
22 MeV
0:59 0:59
0:51 0:51
0:50 0:49
0:45 0:44
0:44 0:43
ARTICLE IN PRESS 40
M. Yamaguchi et al. / Nuclear Instruments and Methods in Physics Research A 506 (2003) 35–40
simulation reproduced the measured values with uncertainty of about 0.01. Acknowledgements The authors would like to deeply thank Prof. K. Sagara and Prof. H. Ikeda for useful suggestions in designing the present polarimeter.
References [1] M. Masaki, Ph.D. Thesis, University of Tsukuba, 1994, unpublished. [2] K. Hirota, Ph.D. Thesis, University of Tsukuba, 1998, unpublished. [3] P. Schwandt, T.B. Clegg, W. Haeberli, Nucl. Phys. A 163 (1971) 432. [4] F. Sperisen, W. Gruebler, V. Konig, P.A. Schmelzbach, K. Elsener, B. Jenny, C. Schweizer, Nucl. Instr. and Meth. 190 (1981) 301. [5] R.A. Hardecopf, D.D. Armstrong, P.W. Keaton Jr., Nucl. Instr. and Meth. 114 (1974) 17. [6] J.F. Clare, Nucl. Instr. and Meth. 116 (1974) 525. [7] W.G. Weitkamp, I. Halpern, T.A. Trainer, S.K. Lamoreeaux, Nucl. Phys. A 417 (1984) 405.
[8] K.A. Fletcher, W.H. Geist, C.R. Brune, B.M. Fisher, R.P. Fitzgerald, H.J. Karwowski, D.E. Kruse, D.S. Leonard, E.J. Ludwig, R.C. Runkle, K.D. Veal, M.H. Wood, Nucl. Instr. and Meth. A 455 (2000) 620. [9] K. Sagara, K. Maeda, H. Nakamura, K. Aita, M. Izumi, M. Nakashima, T. Nakashima, A. Isoya, Nucl. Instr. and Meth. A 270 (1988) 450. [10] Y. Tagishi, J. Sawada, Nucl. Instr. and Meth. 164 (1979) 411. [11] Y. Aoki, S. Hiroki, M. Tomizawa, Y. Tagishi, K. Yagi, UTTAC Ann. Rep. 54 (1987) 5. [12] R.L. Verner, Phys. Rep. C 201 (N2) (1991) 57. [13] T. Nakano, M. Nakamura, H. Sakaguchi, M. Yosoi, M. Iseri, H. Togawa, S. Hirata, O. Kamigaito, H.M. Shimizu, M. Iwaki, Y. Nakai, S. Kobayashi, T. Noro, H. Ikegami, Phys. Lett. B 240 (1990) 301. [14] B.V. Przewoski, P.D. Eversheim, F. Hinterberger, U. . M. Hammans, R. Henneck, G. Lahr, J. Campbell, J. Gotz, Masson, I. Sick, W. Bauhoff, Phys. Rev. Lett. 64 (1967) 93. [15] G.G. Ohlsen, J.L. McKibben, G.P. Lawrence, P.W. Keaton Jr., D.D. Armstrong, Phys. Rev. Lett. 27 (1971) 599. [16] Y. Tagishi, et al., Phys. Rev. C 46 (1992) R1155. [17] R.A. Arndt, L.D. Roper, R.L. Shotwell, Phys. Rev. C 3 (1971) 2100. [18] J.B. Marion, B.A. Zimmerman, Nucl. Instr. and Meth. 51 (1967) 93. [19] GEANT—Detector Description and Simulation Tool, CERN Program Library.