* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Physics Research A
Survey
Document related concepts
Mössbauer spectroscopy wikipedia , lookup
Dispersion staining wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Optical aberration wikipedia , lookup
Two-dimensional nuclear magnetic resonance spectroscopy wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Photomultiplier wikipedia , lookup
Harold Hopkins (physicist) wikipedia , lookup
Cross section (physics) wikipedia , lookup
Optical coherence tomography wikipedia , lookup
Gaseous detection device wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Transcript
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 596 (2008) 311–316 Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima A threshold Cherenkov detector for Kþ =pþ separation using silica aerogel R. Siudak a,b, A. Budzanowski b, A. Chatterjee f, H. Clement j, E. Dorochkevitsch j, J. Ernst a, P. Hawranek d, F. Hinterberger a,, R. Jahn a, L. Jarczyk d, R. Joosten a, K. Kilian c, Di. Kirillov e, S. Kliczewski b, D. Kolev i, M. Kravcikova g, H. Machner c, A. Magiera d, G. Martinska h, F. Massmann a, J. Munkel a, N. Piskunov e, D. Protic c, J. Ritman c, P. von Rossen c, B. Roy f, I. Sitnik e, I. Slepnev e, J. Smyrski d, R. Tsenov i, K. Ulbrich a, J. Urban h, G. Vankova i, G.J. Wagner j, R. Ziegler a a Helmholtz-Inst. f. Strahlen- u. Kernphysik, Universität Bonn, Germany Institute of Nuclear Physics, PAN, Cracow, Poland c Institut für Kernphysik, Forschungszentrum Jülich, Jülich, Germany d Institute of Physics, Jagellonian University, Cracow, Poland e Laboratory for High Energies, Joint Institute for Nuclear Research, Dubna f Nuclear Physics Division, BARC, Bombay, India g Technical University Kosice, Kosice, Slovakia h University Kosice, Kosice, Slovakia i Physics Faculty, University of Sofia, Sofia, Bulgaria j Physikalisches Institut, Universität Tübingen, Germany b a r t i c l e in fo abstract Article history: Received 29 May 2008 Received in revised form 31 July 2008 Accepted 13 August 2008 Available online 28 August 2008 A new threshold Cherenkov detector has been built for the detection of charged pions in the focal plane of a magnetic spectrograph. Silica aerogel with refractive index of n ¼ 1:05 is applied as a radiator. The detector exhibits a very high detection efficiency for pions with momenta X900 MeV=c. Using two Cherenkov detectors in series a very high pion suppression factor of 105 was achieved. & 2008 Elsevier B.V. All rights reserved. Keywords: Threshold Cherenkov detector Silica aerogel Reaction pp ! Kþ ðLpÞ Kþ =pþ separation 1. Introduction We describe a threshold Cherenkov detector which was developed for a high resolution measurement of the reaction pp ! Kþ ðLpÞ near the Lp threshold [1]. In order to achieve a high missing mass resolution the kaons are detected in the focal plane of the magnetic spectrograph BIG KARL [2–4] at the Cooler Synchrotron COSY [5]. The momenta of the kaons are in the range of 900–1070 MeV=c. For the particle identification of the kaons a threshold Cherenkov detector was necessary in order to suppress the huge background of pions. Using silica aerogel with an index of refraction n ¼ 1:05 only pions emit Cherenkov light, whereas the velocities of protons and kaons are below the threshold velocity. The Cherenkov detector was designed using the experience from a previous experiment [6,7] performed at SATURNE II with the spectrometer SPES4. Concerning the radiator material and the Corresponding author. Fax: +49 228 73 2505. E-mail address: [email protected] (F. Hinterberger). 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.08.129 reflecting foil of the light collection box we refer to the threshold Cherenkov detector developed for the BELLE experiment [8–10] and the HERMES experiment [11]. The threshold Cherenkov detector was designed with the aim to achieve a very high detection efficiency for pions and a good homogeneity of the detection efficiency over the focal plane of the magnetic spectrograph. In Section 2 the design of the Cherenkov detector is sketched. The Monte Carlo simulations of the detector are described in Section 3. Experimental results are presented and discussed in Section 4. 2. The Cherenkov detector design In order to identify the Kþ particles the huge background of scattered pions can be suppressed using aerogel threshold Cherenkov detectors. The scheme of the Cherenkov detector is shown in Fig. 1. The light collection box has 820 mm 117 mm cross-section and 266 mm depth. A 80 mm thick wall of silica aerogel tiles with an index of refraction n ¼ 1:05 is used as a Author's personal copy ARTICLE IN PRESS 312 R. Siudak et al. / Nuclear Instruments and Methods in Physics Research A 596 (2008) 311–316 Cherenkov threshold based on the simulation framework GEANT4 [14]. The program yields the number of photons produced by a charged particle traversing the silica aerogel and measured by photomultipliers. The optical properties of the silica aerogel and reflector foil as well as the quantum efficiency of photomultipliers used in the simulations are described in this section. The simulations help to find the most effective and simple detector geometry and the necessary aerogel thickness. 3.1. Optical properties of silica aerogel Fig. 1. Scheme of a Cherenkov detector unit. The 8 cm thick radiator consists of eight layers of silica aerogel tiles (n ¼ 1:05). The inner surfaces of the light collection box are covered by a Whitestar reflector foil R. The Cherenkov light is detected using seven 5 in. photomultiplier tubes (PMT) which are arranged vertically above and below the detector midplane. radiator. Seven photomultiplier tubes (PMT) with a diameter of 5 in. are arranged vertically above and below the detector midplane. In total, two Cherenkov detectors have been built using seven RCA 8854 (now BURLE 8854) and seven Philips XP2041Q phototubes, respectively, for the light collection. The effective diameter of the photocathode amounts to 114 mm (BURLE 8854) and 110 mm (Philips XP2041Q), respectively. The inner surfaces of the light collection box are completely covered with a highly reflecting Whitestar reflector foil R (Gore-tex) [12]. The side walls of the light collection box are made from 12 mm thick aluminum. The front and rear windows are thin and made of 0.5 mm thick Whitestar reflector foil, 0.025 mm thick aluminized mylar foil and 0.1 mm thick carbon foil. The silica aerogel tiles were produced by the advanced technology research laboratory of Matsushita Electric Works [13]. The silica aerogel is hydrophobic. Therefore, the optical quality of the radiator is not affected by the ambient humidity. The refractive index amounts to n ¼ 1:05; the density is 0:18 g=cm3 . The details of the optical properties of our silica aerogel are discussed in Section 3.1. The radiator wall of silica aerogel consists of 56 silica aerogel tiles. The tile size is characterized by 113 mm 113 mm cross-section with 10 mm depth. In x-direction seven aerogel tiles are arranged to form a layer with 791 mm 113 mm cross-section. There are in total eight aerogel layers in z-direction which are staggered in x-direction by about 3 mm in order to minimize the inhomogeneity which is caused by the gaps. The stack of aerogel tiles is fixed using Al retainers which are covered by a soft foam and the reflecting foil. The effective area of the Cherenkov detector is sufficiently large to cover the focal plane size of the magnetic spectrograph BIG KARL. 3. Monte Carlo simulations of the threshold Cherenkov detector Monte Carlo simulations were performed in order to estimate the detection efficiency for particles above and below the The optical properties of silica aerogel are characterized by the refractive index nðlÞ, the Rayleigh scattering length Lsc ðlÞ and the absorption length Labs ðlÞ. The refractive index nðlÞ and the scattering length Lsc ðlÞ are rather well known. However, the absorption length is not so well known. In order to determine the Rayleigh scattering length Lsc ðlÞ and the absorption length Labs ðlÞ the manufacturer measured the transmittance TðlÞ of a 10.33 mm thick silica aerogel tile. The transmittance TðlÞ accounts for the residual light from aerogel in the forward direction. The transmittance data are listed in Table 1. From these measurements the Rayleigh scattering length Lsc ðlÞ, the absorption length Labs ðlÞ and the attenuation length Ltot ðlÞ have been deduced assuming the following equations [8]: Labs ¼ Lsc ¼ l2 (1) a l4 1 Ltot ðlÞ (2) b ¼ 1 Lsc ðlÞ TðlÞ ¼ exp þ s 1 Labs ðlÞ Ltot ðlÞ . (3) (4) Here, s is the thickness of the aerogel tile (s ¼ 10:33 mm). The program Minuit of the CERN program library [15] is used in order to determine the parameters a and b in a nonlinear leastsquare fit. Since the uncertainties of the transmittance data measured by the manufacturer are not known, we estimate the uncertainties using a method described by Bevington [16]. We assume a constant error s for each data point. The value of s is deduced from the sample variance s2 of the nonlinear least-square fit P s2 s2 ¼ Ni¼1 ½T meas ðli Þ T fit ðli Þ2 =ðN nÞ. Here, N is the number of data points, n the number of fit parameters and N n denotes the number of degrees of freedom. The resulting error s amounts to 0.0087. Taking this estimated error into account the nonlinear least-square fit yields the parameters a and b and the estimated uncertainties of the parameters a and b, a ¼ ð9:18 1:69Þ 1013 m b ¼ ð7:54 0:24Þ 1025 m3 . (5) (6) 2 red This method yields automatically a reduced chi-square w ¼ w2 =ðN nÞ ¼ 1:0. The resulting fit values are denoted by T fit;1 ; Labs;1 and Lsc;1 in Table 1. However, in view of more recent direct measurements of the absorption length Labs ðlÞ and scattering length Lsc ðlÞ of n ¼ 1:03 silica aerogel by the HERMES collaboration [11] the l-dependence 2 of the ansatz Labs ðlÞ ¼ l =a of Eq. (1) is questionable. According to Ref. [11], the absorption length Labs is nearly constant between about 320 and 900 nm and it drops down on a logarithmic scale between 320 and 200 nm. It should be mentioned that the silica aerogel investigated by HERMES was from the same producer as Author's personal copy ARTICLE IN PRESS R. Siudak et al. / Nuclear Instruments and Methods in Physics Research A 596 (2008) 311–316 Table 1 Transmittance T, absorption length Labs and scattering length Lsc of n ¼ 1:05 silica aerogel l (nm) T meas T fit;1 Labs;1 Lsc;1 (cm) T fit;2 (cm) 250 300 350 400 450 500 550 600 650 700 750 800 0.1359 0.3436 0.5408 0.6849 0.7850 0.8522 0.8935 0.9247 0.9417 0.9544 0.9651 0.9701 0.1170 0.3441 0.5508 0.6952 0.7892 0.8500 0.8901 0.9172 0.9361 0.9495 0.9594 0.9667 6.8 9.8 13.3 17.4 22.1 27.2 33.0 39.2 46.0 53.4 61.3 69.7 Labs;2 0.5 1.1 2.0 3.4 5.4 8.3 12.1 17.2 23.7 31.8 42.0 54.3 0.0987 0.3501 0.5721 0.7093 0.7850 0.8374 0.8703 0.8908 0.9047 0.9146 0.9231 0.9282 2.8 9.2 19.6 22.0 18.1 18.4 18.4 18.1 17.9 17.9 18.4 18.4 0.5 1.1 2.0 3.5 5.6 8.5 12.4 17.6 24.3 32.7 43.0 55.7 used in our detector and it has very similar transmittance although it has different refractive index. In order to test the effect of a nearly constant absorption length Labs ðlÞ as measured by HERMES we perform a second fit taking directly Labs ðlÞ from HERMES (Fig. 7 of the HERMES paper [11]) and fitting only the free parameter b of Eq. (2). The fit yields b ¼ ð7:35 0:43Þ 1025 m3 . Table 2 Quantum efficiency q:e: of BURLE 8854 and Philips XP2041Q PMT E (eV) l (nm) BURLE q:e: Philips q:e: 4.96 4.13 3.54 3.10 2.76 2.48 2.25 2.07 250 300 350 400 450 500 550 600 0.13 0.19 0.23 0.22 0.17 0.11 0.04 0.01 0.13 0.22 0.26 0.26 0.21 0.13 0.05 0.01 Lsc;2 (cm) (cm) (7) The absorption lengths from HERMES, denoted by Labs;2, and the fit values T fit;2 and Lsc;2 from the second fit are listed in Table 1. 3.2. Optical properties of the reflector foil The reflector foil is a 0.5 mm thick Whitestar Gore-Tex membrane. The reflectivity R of this diffusely reflecting foil is very high. It is given by the manufacturer as Rðl ¼ 400 nmÞ ¼ 0:987 and Rðl ¼ 700 nmÞ ¼ 0:981. We assume a linear dependence on the wave length l in the range 250–800 nm. The diffuse reflection of photons is described by the cosine Lambert’s law. The amount of specular reflection is negligibly small. 3.3. Quantum efficiency of the photomultiplier The photocathodes of the RCA 8854 (now BURLE 8854) and Philips XP2041Q phototubes are bialkali cathodes yielding a rather high quantum efficiency q:e: in the wavelength range 250–500 nm. The quantum efficiencies are taken from the PMTs data sheets. They are listed in Table 2. 313 and the application of mirrors was tested in the simulations as shown in Fig. 2(a)–(c). In Fig. 2(a) the simplest configuration with the PMTs placed just above and below the aerogel stack is presented. Increasing the number of detected photons was obtained by moving the PMTs in the forward direction of the incoming pions as is shown in Fig. 2(b). An application of mirrors (Fig. 2(c)) improves again somewhat the detected photon number but increases also the costs and causes additional complexity. Therefore, the detector geometry from Fig. 2(b), described in Section 2, was decided to be optimal for our purpose. An example of the simulated distribution of the total number of photoelectrons (sum over photoelectrons detected by seven photomultipliers) at pion momenta of 960 MeV=c for the detector geometry described in Section 2 is shown in Fig. 3. For comparison, the results for two sets of the aerogel absorption length Labs ðlÞ and scattering length Lsc ðlÞ as presented in Table 1 and discussed in Section 3.1 are shown. Both sets yield very similar photoelectron distributions. This is due to the fact that the quantum efficiency of PMTs with bialkali photocathodes is high only in the range of 250–500 nm where the differences between those two descriptions of aerogel optical properties are small. A mean photoelectron number of about 20 is predicted for the detector geometry described in Section 2 with 8 cm thick aerogel. The radiator thickness plays a crucial role with respect to the detected number of photoelectrons. The simulated dependence of the mean photoelectron number on the aerogel thickness for pions at 960 MeV=c is shown in Fig. 4. An aerogel thickness of 8 cm was chosen for our detector (see Fig. 1) to get a required detector efficiency and a pion suppression factor larger than 104 . 4. Experimental results 3.4. Simulation results The detector geometry considered in the simulations is described in Section 2. Modifications of this detector geometry as shown in Fig. 2 were also studied. The response of the detector for pions with momenta larger than 900 MeV=c, incoming perpendicularly to the surface of entrance foil and homogeneously distributed over the full detector area was investigated. The simulated pion distribution corresponds to the real situation in the focal plane of the spectrograph BIG KARL, which is characterized by a small angle dispersion in the horizontal plane and a nearly point-to-parallel imaging in vertical direction. Silica aerogel with refractive index of n ¼ 1:05 and optical properties discussed in Section 3.1 was used in the simulations. The optical properties of reflecting foil and quantum efficiency of photomultipliers are described in Sections 3.2 and 3.3, respectively. In order to find the optimum geometry of the light collection box the position of aerogel with respect to the photomultipliers The reaction of interest pp ! Kþ ðLpÞ is measured at forward direction using the magnetic spectrograph BIG KARL [2–4]. The momentum of the incoming proton beam amounts to about 2:735 GeV=c. The scattered particles are detected in the momentum range 900–1070 MeV=c. Two threshold Cherenkov detectors are located in the focal plane of the magnetic spectrograph. The layout of the magnetic spectrograph BIG KARL is shown in Fig. 5. The charged particle tracks are measured by two stacks of multiwire drift chambers (MWDC). The DE signals of the scintillator hodoscopes and the time-of-flight (TOF) information of a 5 m long TOF setup made from the scintillator hodoscopes are used for the particle identification. An example of the TOF spectrum of particles detected at 960 MeV=c is shown in Fig. 6. Very pronounced peaks for pions and protons can be identified in the spectrum. The measured kaons are expected to appear at the right side of the pion peak in the TOF spectrum. The 5 m path is not long enough for the separation of kaons and pions using the Author's personal copy ARTICLE IN PRESS 314 R. Siudak et al. / Nuclear Instruments and Methods in Physics Research A 596 (2008) 311–316 PMT PMT Aerogel Mirror PMT π+ Fig. 2. Scheme of possible geometries of the threshold Cherenkov detector. Focal plane detectors MWDC D2 Q3 Scintillator Hodoscope 50000 40000 Counts Cherenkov 30000 D1 Q2a Q2 20000 TARGET 10000 Q1 3m e ret ll wa nc co 0 10 0 20 30 40 50 Npe Fig. 3. Simulated distribution of total number of photoelectrons N pe from Cherenkov detector for pions at 960 MeV=c with two different sets of aerogel absorption lengths and scattering lengths presented in Table 1. Solid line represents simulation results with parameters Lsc;1 and Labs;1 and dashed line with Lsc;2 and Labs;2 (see Table 1). 20 mean Npe 16 12 8 4 0 0 2 4 6 8 10 aerogel thickness (cm) Fig. 4. Simulated mean number of photoelectrons as a function of aerogel thickness for 960 MeV=c pions. Fig. 5. Layout of the magnetic spectrograph BIG KARL. The charged particles are measured in the focal plane using two stacks of multiwire drift chambers, two threshold Cherenkov detectors and two scintillator hodoscopes. TOF information. In order to identify the Kþ particles, the huge background of scattered pions is suppressed using the signal from the threshold Cherenkov detector. Pions with TOF signals smaller than the peak maximum ( 17 ns) do not contaminate any other particles and they can be used to determine the pion suppression factor for the tested Cherenkov detector. Signals from seven PMTs of the Cherenkov detector were read through charge ADC’s, triggered by coincidences between two layers of the scintillator hodoscopes. Each single ADC spectrum was normalized to photoelectron number using the location of single photoelectron peak. Next for every event, the sum over all seven ADC readouts was performed and total number of photoelectrons N pe was deduced. The events with track position jxjp380 mm and jyjp40 mm from the Cherenkov box center, corresponding to the size of the magnetic spectrograph focal plane, were included in the efficiency determination. An example of the distribution of total number of photoelectrons N pe for pions at 960 MeV=c is shown in Fig. 7. An average experimental value of Npe 20 is found to be very close to the value predicted by the simulations (see Fig. 3). Author's personal copy ARTICLE IN PRESS R. Siudak et al. / Nuclear Instruments and Methods in Physics Research A 596 (2008) 311–316 315 106 x103 400 pions protons pions 104 Counts F (Npe) protons 300 102 200 1 0 100 10 20 30 Npe (photoelectrons) 40 50 Fig. 8. Spectrum of N pe for protons and pions at 960 MeV=c. First large peak at N pe ¼ 0 corresponds to ADC pedestal. 0 15 10 20 TOF (ns) 25 30 1 Fig. 6. TOF spectrum from pp ! X reaction measured at 960 MeV=c momentum. pions Misidentification M 10−1 20000 Counts 15000 10−2 10−3 protons 10−4 10000 10−5 5000 0 10 20 30 Nth pe (photoelectrons) 40 50 Fig. 9. Misidentification of pions (solid line) and protons (dashed line) from the Cherenkov detector. 0 0 20 40 60 Npe (photoelectrons) 80 Fig. 7. Measured distribution of total number of photoelectrons N pe from Cherenkov detector for pions at 960 MeV=c. Although protons are below Cherenkov threshold, a small fraction of them produced a Cherenkov signal with total number of photoelectrons larger than zero as is shown in Fig. 8. It could be due to proton induced d-electrons with velocity above the Cherenkov threshold, random coincidences of photomultiplier noises with the trigger or light produced in some other than aerogel components of the light collection box. Analysis of the photoelectron distributions for pions and protons (as in Fig. 8) allows one to deduce the Cherenkov detector efficiency for particles above and below Cherenkov threshold. All particles with Npe larger than the threshold value Nth pe can be treated as pions. The pion efficiency Ep can be deduced from the photoelectron spectrum for pions, F p ðN pe Þ, R1 p F ðN pe Þ dNpe Nth pe p . (8) E ¼ R1 p F ðNpe Þ dNpe 0 th For given Nth pe some protons will have N pe 4N pe so they will be treated as pions. In case of protons we call it proton misidentification Mp . Proton misidentification can be calculated from photoelectron distribution for protons, F p ðNpe Þ, R1 p F ðN pe Þ dNpe Nth pe p . (9) M ¼ R1 p F ðNpe Þ dN pe 0 The misidentification of pions, M p , can be defined as Mp ¼ 1 Ep . (10) Author's personal copy ARTICLE IN PRESS 316 R. Siudak et al. / Nuclear Instruments and Methods in Physics Research A 596 (2008) 311–316 1 pions protons 105 pions 10−1 10−2 Counts Misidentification M 104 103 10−3 102 10−4 protons kaons 10 10−5 1 10 0 10 20 40 total (photoelectrons) Nth, pe 60 80 Fig. 10. Misidentification of pions (solid line) and protons (dashed line) from two Cherenkov detectors. The pion misidentification M p is connected with the pion suppression factor S through the relation Mp ¼ 1 . S (11) The misidentification distributions for pions and protons at 960 MeV=c are shown in Fig. 9. We assume that the misidentifications of kaons and protons are of the same order of magnitude. Proper choice of threshold N th pe , for which the high number of pions is properly identified, and low number of protons misidentified as pions, provides a high pion suppression factor. However, as can be seen in Fig. 9, to get necessary pion suppression factor S 105 one should use Nth pe 1. To improve the situation a second Cherenkov detector was built with the same design as the first one. The sum of photoelectron numbers from both detectors (N th;total ) is used in the final pion pe identification th;2 Nth;total ¼ N th;1 pe pe þ N pe . 20 TOF (ns) 30 Fig. 11. TOF spectrum from pp ! X reaction measured at 960 MeV=c momentum. Solid line—full spectrum, dotted line—TOF spectrum in coincidence with Cherenkov, dashed line—TOF distribution vetoed with Cherenkov. The searched kaon peak is indicated. cooler synchrotron COSY (Jülich, Germany). Silica aerogel with refractive index n ¼ 1:05 and thickness of 8 cm was used as a radiator in each detector. The inner surface of the light collection box was covered by high reflectivity Whitestar Gore-Tex foil. The Cherenkov detectors were applied in kaon/pion separation measured in the momentum range of 90021070 MeV=c. A very high pion suppression factor of 105 was achieved. At the same time, the misidentification of the particles with velocity below Cherenkov threshold was found to be less than 1%. Acknowledgments We thank the operating team of COSY for excellent beam support. This work was supported by the Bundesministerium für Bildung und Forschung, BMBF (06BN108I), and Forschungszentrum Jülich GmbH, COSY FFE (41520742). (12) Misidentification distributions for pions and protons at 960 MeV=c for two Cherenkov detectors are shown in Fig. 10. As can be seen, a very high pion suppression factor of about 105 and a low (below 1%) misidentification of protons with velocity below the Cherenkov threshold was achieved with Nth;total 5 for two pe Cherenkov detectors. In Fig. 11 the decomposition of the TOF spectrum with and without coincidences with two Cherenkov detectors is presented. The Nth;total ¼ 5 threshold is used in pion pe identification with the Cherenkov detector. The clearly visible kaon peak after pion suppression is indicated in the figure. 5. Summary Two new threshold Cherenkov detectors were built and used in the focal plane of the magnetic spectrograph BIG KARL at the References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] R. Siudak, et al., Eur. Phys. J. A, to be published. S. Martin, et al., Nucl. Instr. and Meth. 214 (1983) 281. M. Drochner, et al., Nucl. Phys. A 643 (1998) 55. J. Bojowald, et al., Nucl. Instr. and Meth. A 487 (2002) 314. R. Maier, Nucl. Instr. and Meth. A 390 (1997) 1. C. Lippert, et al., Nucl. Instr. and Meth. A 333 (1993) 413. R. Siebert, et al., Nucl. Phys. A 567 (1994) 819. R. Suda, et al., Nucl. Instr. and Meth. A 406 (1998) 213. T. Sumiyoshi, et al., Nucl. Instr. and Meth. A 433 (1999) 385. A. Abashian, et al., Nucl. Instr. and Meth. A 479 (2002) 117. E. Aschenauer, et al., Nucl. Instr. and Meth. A 440 (2000) 338. W.L. Gore & Associate GMBH, P.O. Box 1152, D-85636 Putzbrunn, Germany. Matsushita Electric Works 1048 Kadoma, Kadoma-shi, Osaka 571-8686, Japan. [14] The Geant4 Collaboration, Nucl. Instr. and Meth. A 506 (2003) 250. [15] F. James, M. Roos, Comput. Phys. Commun. 10 (1975) 343. [16] P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969.