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A high pressure 4He polarimeter for double scattering experiments
438
Nuclear Instruments and Methods in Physics Research A245 (1986) 438-442 North-Holland, Amsterdam
A HIGH PRESSURE 4He POLARIMETER FOR DOUBLE SCATI'ERING EXPERIMENTS W. K R E T S C H M E R , H. L O H **, A. R A U S C H E R , a n d N. S T A M M I N G E R
R. S C H M I T T ,
W. S C H U S T E R ,
*
W. S T A C H t
Physikalisches lnstitut der Universitiit Erlangen - N~rnbergo D-8520 Erlangen, FRG
Received 16 December 1985
We describe the performance of a high pressure (up to 50 bar) 4He polarimeter designed as the second scatterer in nuclear double-scattering experiments for protons and deuterons at energies up to 12 MeV. The main characteristics are an efficiency of - 3 x 10-5 and an effective analyzing power of 0.7-0.8 for protons (measured at a pressure of 20 bar). For deuterons the efficiency is estimated to be of the same order of magnitude whereas the effective analyzing power is about half the magnitude. The polarimeter is equipped with several beam monitoring devices and can be moved along its symmetry axis as well as rotated around it.
I. Introduction Measuring the depolarization, i.e. the spin transfer coefficient K y', is a way to investigate the spin dependence of the nuclear forces. For this purpose one has to carry out a double-scattering experiment which determines the polarization of the incoming beam as well as that of the scattered particles. The Erlangen double* Work supported by the Deutsche Forschungsgemeinschaft. ** Now at AOA Apparatebau Gauting, GmbH, FRG. t Now at Kraftwerk Union, Erlangen, FRG.
Double
scattering arrangement (see fig. 1) consists of three main parts: the sliding seal chamber [1], the magnetic spectrometer [2] and the 4He polarimeter to be described. The sliding seal chamber contains the target T1 as the first scatterer. Furthermore, T1, together with symmetrically arranged surface barrier detectors, serves as the polarimeter for the incoming beam. The chamber is designed very compact (diameter 14 cm) to obtain a large solid angle (20 msr) accepted by the following spectrometer. The exit to the first quadrupole can be turned around - 1 0 ° up to - 1 2 0 ° without loss of vacuum.
Scattering Arrangement
•t I n c i d e n t
o
/
Fig. 1. Principle of double-scattering arrangement in Erlangen. 0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Polcrimeter
ilOCml
W Kretschmer et aim / A high pressure
The magnetic spectrometer consists of a first quadrupole, a bending magnet and a second quadrupole. This m o m e n t u m analysis (dispersion A x ( A p / p ) -1 = 1.3 m) separates the desired particles from those scattered inelastically or by T1 contaminants. This is necessary because the expected low counting rates in a double-scattering experiment require thick targets and large accepted solid angles which leads to considerable energy straggling due to energy loss and reaction kinematics. The quadrupoles are installed to enlarge the accepted solid angle, to improve the image, and to obtain a narrow and parallel beam in the polarimeter region.
2. Requirements The polarimeter has been designed for protons and deuterons with energies less than 12 MeV. Of course a polarimeter should have a high analyzing power but moreover this polarimeter should have a high efficiency too, since it is used as a second scatterer causing the problem of low counting rates. Thus the scattering medium should have a large target thickness and the detectors should accept a large solid angle. This requires a scatterer with a high analyzing power over a wide energy and angle range. In this polarimeter 4He under high pressure is used. The polarimeter is mounted at the end of a spectrometer and hence it has to provide beam monitoring devices to adjust the proper fields of the magnets. Furthermore it should be movable along the beam axis
l/ Icintillator I
Iightgalde
4He polarimeter
439
to achieve a double focus of the spectrometer at the polarimeter entrance. To avoid systematic errors due to instrumental asymmetries, it is common practice to measure with two symmetrically arranged detectors once with the polarization vector being parallel to ki, × kou t and then being antiparallel. Since after the first scattering the polarization vector cannot be flipped easily, the polarimeter has to be turned around its symmetry axis by 180 ° .
3. Performance For the following description see figs. 2 and 3. The polarimeter tube is fixed at the end of a rod which contains two pipes for gas inlet and outlet. The rod passes through the slide mechanism holder and the plastic sleeve, where it can move along its axis but not rotate around it. The sleeve is running in needle bearings and can be turned around the symmetry axis together with the rod, the mechanism holder and the slide motion motor. The rotary motion is managed by another motor that is fixed at the cover plate of the polarimeter housing. The sleeve and a few electrical plugs pass vacuum-sealed through this plate. Each motion motor simultaneously turns a potentiometer to determine the actual position. The slide motion covers a length of 86 mm and can be stopped at an arbitrary position. The rotary motion has three stops at 0 ° ( " N O R M " ) , 90 ° ( " V E R T I C A L " ) and 180 ° ( " R E V E R S E " ) respectively. The positions of both motors can be set via remote control from the Tandem
cover plate of pol~rlmeter housing
mu-metal eh)eld containing photomultlpJler
needle hearing toothed wheel for rotlr~ motion
gt=
L
~oeabl~ I=mella holder
etoo[ foil
i
1
lntor=edltte piece
etHp
dotector tlot
Fig. 2. Vertical section through the polarimeter.
holder
turn-elide ro6
"
tdth ftrtdt¥ CUp end guide rill for po*ition oeneltive detector
slide mechanlem
pipe
T~ovldur =loevo
tooth rack for elide motion
)
5 Om
I
440
I~ Kretschmer et al. / A high pressure 4He polarimeter
Fig. 3. Photographs of the polarimeter. The mu-metal shield and additionally, in the right photograph, the position sensitive detector have been removed.
Fig. 4. Photograph of the polarimeter insert. The four detectors have been removed.
W. Kretschmeret al. / A highpressure 4He polarimeter
441
control room. Furthermore, the rotation can be operated by a P D P l l computer to turn the polarimeter periodically during a measurement. The polarimeter tube itself has an oval entrance window of 6 x 20 m m 2 which is vacuum-sealed by a 25 # m high grade steel foil. The maximum pressure in the tube is 50 bar. The insert in the tube (see fig. 4) consists of an intermediate piece and the lamella and detector holder. The intermediate piece contains the Faraday cup and a slot to move in two vertical strip detectors side by side. This allows the determination of a possible disalignment of the beam in the polarimeter. The lamella holder may be exchanged depending on the particles to be analyzed, protons or deuterons. Essentially it is built of four L-shaped profiles with 10 (for deuterons, 5) slots to hold the lamellae (see next section. The lamellae are 0.3 mm thick, nonmagnetic VA-steel sheets with a depth of 6 (for deuterons, 10) mm and a height of 16 mm for the top and bottom and of 22 mm for the left and right detectors. These surface barrier detectors are mounted directly behind the lamellae whereby the top and bottom detectors have been installed additionally to determine a t o p - b o t t o m asymmetry. The active target zone has a length of 50 m m and the effective surface of the left-right detectors is 459 mm 2.
axis and rotate around it together with the whole tube, it is possible to determine the beam position and spread in the polarimeter region, both in the horizontal and in the vertical direction. This ensures the optimal settings of the spectrometer magnets and a narrow and nearly parallel beam in the polarimeter region.
In front of the tube is a 200 # m thick scintillator which covers the whole entrance window. The light of this scintillator is guided to a photomultiplier on top of the polarimeter. The multiplier is surrounded by a mumetal shield to protect it against the fringe field of the second quadrupole. A fast coincidence of the polarimeter detector signals with the pulses from the photomultiplier drastically reduces the background (see fig. 5) and thus any subsequent subtraction becomes superfluous. The position-sensitive detector is guided in a rail which is fixed on the surface of the scintillator flange. By means of an electric motor which can be operated from outside, the detector can be slid into the beam line. Since the detector can move along the polarimeter
A eff = ( oA )eff/Oeff
,
i
r
r
:ts
oo
4. Calculations and measurements
The three parameters O0, b and l decisive in designing the lamellae are shown in fig. 6. For a scattered particle, the probability W(O) to reach the detector is zero for a scattering angle smaller than a, it then rises linearly up to 1 at an angle of O 0 and then falls linearly to zero for a scattering angle of B or larger. Using measurements of the analyzing power A(O, E) and the differential cross section o(O, E) of 4He(p, p)4He [3] and 4He(d, d)4He [4] the efficiency e, the effective analyzing power Aeff and the figure of merit f can be approximated at a given energy assuming an ideal linear beam: e = number of particles, detected in both the left and right d e t e c t o r / n u m b e r of incoming particles
= C~#o(O, E)W(O) d~2,
c2 fBo( O, E)W( O )A( @, E) dFg ~Bo( O, E)W( O) d~2 f = a2effe, with C1, C 2 being constant for a given pressure, temperature and azimuthal accepted angle. The parameters O0, b and I were varied to give a maximum figure of merit [5]. This leads to the following values for protons, b : l = 7 : 10, O o = 135 °, 90 ° ~< Op 153 ° . The values for deuterons are b: l = 6 : 1 0 and O0 = 126°, 89° ~< @d ~ 146°. Here a larger counting rate due to reaction kinematics can be obtained by detecting the recoil 4He nuclei instead of the deuterons. The effective analyzing power Aerf for protons was
.'4.. .'.:.
./--- detector .- /
\
,\.
lO z ~ , ' ~ ~ ~ ~ - ' - -
I00
200
300
400 500 chin
I00
200
300
400 500 chart
Fig. 5. Spectra of polarimeter detector after the scattering 27Al(p, p)27A1 at 11 MeV. Left: with coincidence to the entrance ZlE scintillator, right: without coincidence.
.
.
.
.
lame I la
.
beam line
~
b
J
Fig. 6. Definition of the geometrical parameters for the lamellae.
442
W. Kretschrner et al, / A high pressure
4He polarirneter
the scattered particles in the polarimeter detectors. Since we are mostly interested in protons the effective analyzing power for deuterons has only been estimated with the above mentioned formula to range from 0.23 at 10 MeV to 0.35 at 4 MeV and the efficiency should give values of about 3 and 10 × 10 -6 p bar -1, respectively.
A.. .8-
.6-
5. Applications .4
I
I
L
10.5
11
11.5
F:. ,~,2
Fig. 7. Aeff of the polarimeter reaction 4He(p, p)4He vs the energy of the protons in front of the scintillator. Measured points and least-squares fit of a quadratic polynominal with error band.
With the polarimeter described above we succcessfully measured the depolarization in the elastic scattering of polarized protons on 27A1 at 10.35 MeV [6], on 27A1 and 89y at 11 MeV and on 1H at 12 MeV [7].
Acknowledgments measured in a double-scattering experiment. A proton beam with known polarization was scattered in the sliding seal chamber from a 2°8pb target. Since Pb at forward angles has a very small analyzing power and since the depolarization is 1, the outgoing scattered particles have the same polarization p as the incoming beam. These particles were analyzed in the polarimeter filled with 20 bar. The four counting rates (left and right polarimeter detector both measured N O R M and REV) obtained for an incoming beam with spin up, led to the measured assymetry c. Possible " n o n p r o p e r spin flips" can be taken into account by introducing a false assymetry c' in the expression for the measured asymmetry [6] c -- ( p A e f f + e ' ) / ( 1 + e'pA~ff).
Using the same formula for the spin-down case and assuming c' to be the same, the false asymmetry can be eliminated. In all cases e' was only a few percent. The measured points and a least-squares fit of a quadratic polynominal with the error band are shown in fig. 7. An efficiency of - 1.3 × 10 6 p b a r - 1 was determined at Ep = 12 MeV by counting the incoming particles with the scintillator at the entrance of the polarimeter and
The authors very much appreciate the helpful advice of G. Muhr and G. Heimpel and the careful machine work done by L. Drechsler.
References [1] R. Henneck, W. Kretschmer, H. Lt)h, G. Muhr and W. Stach, Nucl. Instr. and Meth. 158 (1979) 391. [2] W. Kretschmer, H. Lrh, A. Rauscher, R. Schmitt and W. Schuster, Nucl. Instr. and Meth. A241 (1985) 480. [3] P. Schwandt, T.B. Clegg and W. Haeberli, Nucl. Phys. A 163 (1971) 432. [4] L.G. Keller and W. Haeberli, Nucl. Phys. A 156 (1970) 465; R.R. Cadmus, Jr. and W. Haeberli, Nucl. Instr. and Meth. 129 (1975) 403. [5] H. Weiss, Zulassungsarbeit, Erlangen (1974) unpublished; N. Stamminger, Zulassungsarbeit, Erlangen (1977) unpublished. [6] G.G. Ohlsen and P.W. Keaton, Jr., Nucl. Instr. and Meth. 109 (1973) 41. [7] H. L~3h, PhD thesis, Erlangen (1981). [8] R. Schmitt, PhD thesis, Erlangen (1986).
Nuclear Instruments and Methods in Physics Research A245 (1986) 438-442 North-Holland, Amsterdam
A HIGH PRESSURE 4He POLARIMETER FOR DOUBLE SCATI'ERING EXPERIMENTS W. K R E T S C H M E R , H. L O H **, A. R A U S C H E R , a n d N. S T A M M I N G E R
R. S C H M I T T ,
W. S C H U S T E R ,
*
W. S T A C H t
Physikalisches lnstitut der Universitiit Erlangen - N~rnbergo D-8520 Erlangen, FRG
Received 16 December 1985
We describe the performance of a high pressure (up to 50 bar) 4He polarimeter designed as the second scatterer in nuclear double-scattering experiments for protons and deuterons at energies up to 12 MeV. The main characteristics are an efficiency of - 3 x 10-5 and an effective analyzing power of 0.7-0.8 for protons (measured at a pressure of 20 bar). For deuterons the efficiency is estimated to be of the same order of magnitude whereas the effective analyzing power is about half the magnitude. The polarimeter is equipped with several beam monitoring devices and can be moved along its symmetry axis as well as rotated around it.
I. Introduction Measuring the depolarization, i.e. the spin transfer coefficient K y', is a way to investigate the spin dependence of the nuclear forces. For this purpose one has to carry out a double-scattering experiment which determines the polarization of the incoming beam as well as that of the scattered particles. The Erlangen double* Work supported by the Deutsche Forschungsgemeinschaft. ** Now at AOA Apparatebau Gauting, GmbH, FRG. t Now at Kraftwerk Union, Erlangen, FRG.
Double
scattering arrangement (see fig. 1) consists of three main parts: the sliding seal chamber [1], the magnetic spectrometer [2] and the 4He polarimeter to be described. The sliding seal chamber contains the target T1 as the first scatterer. Furthermore, T1, together with symmetrically arranged surface barrier detectors, serves as the polarimeter for the incoming beam. The chamber is designed very compact (diameter 14 cm) to obtain a large solid angle (20 msr) accepted by the following spectrometer. The exit to the first quadrupole can be turned around - 1 0 ° up to - 1 2 0 ° without loss of vacuum.
Scattering Arrangement
•t I n c i d e n t
o
/
Fig. 1. Principle of double-scattering arrangement in Erlangen. 0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Polcrimeter
ilOCml
W Kretschmer et aim / A high pressure
The magnetic spectrometer consists of a first quadrupole, a bending magnet and a second quadrupole. This m o m e n t u m analysis (dispersion A x ( A p / p ) -1 = 1.3 m) separates the desired particles from those scattered inelastically or by T1 contaminants. This is necessary because the expected low counting rates in a double-scattering experiment require thick targets and large accepted solid angles which leads to considerable energy straggling due to energy loss and reaction kinematics. The quadrupoles are installed to enlarge the accepted solid angle, to improve the image, and to obtain a narrow and parallel beam in the polarimeter region.
2. Requirements The polarimeter has been designed for protons and deuterons with energies less than 12 MeV. Of course a polarimeter should have a high analyzing power but moreover this polarimeter should have a high efficiency too, since it is used as a second scatterer causing the problem of low counting rates. Thus the scattering medium should have a large target thickness and the detectors should accept a large solid angle. This requires a scatterer with a high analyzing power over a wide energy and angle range. In this polarimeter 4He under high pressure is used. The polarimeter is mounted at the end of a spectrometer and hence it has to provide beam monitoring devices to adjust the proper fields of the magnets. Furthermore it should be movable along the beam axis
l/ Icintillator I
Iightgalde
4He polarimeter
439
to achieve a double focus of the spectrometer at the polarimeter entrance. To avoid systematic errors due to instrumental asymmetries, it is common practice to measure with two symmetrically arranged detectors once with the polarization vector being parallel to ki, × kou t and then being antiparallel. Since after the first scattering the polarization vector cannot be flipped easily, the polarimeter has to be turned around its symmetry axis by 180 ° .
3. Performance For the following description see figs. 2 and 3. The polarimeter tube is fixed at the end of a rod which contains two pipes for gas inlet and outlet. The rod passes through the slide mechanism holder and the plastic sleeve, where it can move along its axis but not rotate around it. The sleeve is running in needle bearings and can be turned around the symmetry axis together with the rod, the mechanism holder and the slide motion motor. The rotary motion is managed by another motor that is fixed at the cover plate of the polarimeter housing. The sleeve and a few electrical plugs pass vacuum-sealed through this plate. Each motion motor simultaneously turns a potentiometer to determine the actual position. The slide motion covers a length of 86 mm and can be stopped at an arbitrary position. The rotary motion has three stops at 0 ° ( " N O R M " ) , 90 ° ( " V E R T I C A L " ) and 180 ° ( " R E V E R S E " ) respectively. The positions of both motors can be set via remote control from the Tandem
cover plate of pol~rlmeter housing
mu-metal eh)eld containing photomultlpJler
needle hearing toothed wheel for rotlr~ motion
gt=
L
~oeabl~ I=mella holder
etoo[ foil
i
1
lntor=edltte piece
etHp
dotector tlot
Fig. 2. Vertical section through the polarimeter.
holder
turn-elide ro6
"
tdth ftrtdt¥ CUp end guide rill for po*ition oeneltive detector
slide mechanlem
pipe
T~ovldur =loevo
tooth rack for elide motion
)
5 Om
I
440
I~ Kretschmer et al. / A high pressure 4He polarimeter
Fig. 3. Photographs of the polarimeter. The mu-metal shield and additionally, in the right photograph, the position sensitive detector have been removed.
Fig. 4. Photograph of the polarimeter insert. The four detectors have been removed.
W. Kretschmeret al. / A highpressure 4He polarimeter
441
control room. Furthermore, the rotation can be operated by a P D P l l computer to turn the polarimeter periodically during a measurement. The polarimeter tube itself has an oval entrance window of 6 x 20 m m 2 which is vacuum-sealed by a 25 # m high grade steel foil. The maximum pressure in the tube is 50 bar. The insert in the tube (see fig. 4) consists of an intermediate piece and the lamella and detector holder. The intermediate piece contains the Faraday cup and a slot to move in two vertical strip detectors side by side. This allows the determination of a possible disalignment of the beam in the polarimeter. The lamella holder may be exchanged depending on the particles to be analyzed, protons or deuterons. Essentially it is built of four L-shaped profiles with 10 (for deuterons, 5) slots to hold the lamellae (see next section. The lamellae are 0.3 mm thick, nonmagnetic VA-steel sheets with a depth of 6 (for deuterons, 10) mm and a height of 16 mm for the top and bottom and of 22 mm for the left and right detectors. These surface barrier detectors are mounted directly behind the lamellae whereby the top and bottom detectors have been installed additionally to determine a t o p - b o t t o m asymmetry. The active target zone has a length of 50 m m and the effective surface of the left-right detectors is 459 mm 2.
axis and rotate around it together with the whole tube, it is possible to determine the beam position and spread in the polarimeter region, both in the horizontal and in the vertical direction. This ensures the optimal settings of the spectrometer magnets and a narrow and nearly parallel beam in the polarimeter region.
In front of the tube is a 200 # m thick scintillator which covers the whole entrance window. The light of this scintillator is guided to a photomultiplier on top of the polarimeter. The multiplier is surrounded by a mumetal shield to protect it against the fringe field of the second quadrupole. A fast coincidence of the polarimeter detector signals with the pulses from the photomultiplier drastically reduces the background (see fig. 5) and thus any subsequent subtraction becomes superfluous. The position-sensitive detector is guided in a rail which is fixed on the surface of the scintillator flange. By means of an electric motor which can be operated from outside, the detector can be slid into the beam line. Since the detector can move along the polarimeter
A eff = ( oA )eff/Oeff
,
i
r
r
:ts
oo
4. Calculations and measurements
The three parameters O0, b and l decisive in designing the lamellae are shown in fig. 6. For a scattered particle, the probability W(O) to reach the detector is zero for a scattering angle smaller than a, it then rises linearly up to 1 at an angle of O 0 and then falls linearly to zero for a scattering angle of B or larger. Using measurements of the analyzing power A(O, E) and the differential cross section o(O, E) of 4He(p, p)4He [3] and 4He(d, d)4He [4] the efficiency e, the effective analyzing power Aeff and the figure of merit f can be approximated at a given energy assuming an ideal linear beam: e = number of particles, detected in both the left and right d e t e c t o r / n u m b e r of incoming particles
= C~#o(O, E)W(O) d~2,
c2 fBo( O, E)W( O )A( @, E) dFg ~Bo( O, E)W( O) d~2 f = a2effe, with C1, C 2 being constant for a given pressure, temperature and azimuthal accepted angle. The parameters O0, b and I were varied to give a maximum figure of merit [5]. This leads to the following values for protons, b : l = 7 : 10, O o = 135 °, 90 ° ~< Op 153 ° . The values for deuterons are b: l = 6 : 1 0 and O0 = 126°, 89° ~< @d ~ 146°. Here a larger counting rate due to reaction kinematics can be obtained by detecting the recoil 4He nuclei instead of the deuterons. The effective analyzing power Aerf for protons was
.'4.. .'.:.
./--- detector .- /
\
,\.
lO z ~ , ' ~ ~ ~ ~ - ' - -
I00
200
300
400 500 chin
I00
200
300
400 500 chart
Fig. 5. Spectra of polarimeter detector after the scattering 27Al(p, p)27A1 at 11 MeV. Left: with coincidence to the entrance ZlE scintillator, right: without coincidence.
.
.
.
.
lame I la
.
beam line
~
b
J
Fig. 6. Definition of the geometrical parameters for the lamellae.
442
W. Kretschrner et al, / A high pressure
4He polarirneter
the scattered particles in the polarimeter detectors. Since we are mostly interested in protons the effective analyzing power for deuterons has only been estimated with the above mentioned formula to range from 0.23 at 10 MeV to 0.35 at 4 MeV and the efficiency should give values of about 3 and 10 × 10 -6 p bar -1, respectively.
A.. .8-
.6-
5. Applications .4
I
I
L
10.5
11
11.5
F:. ,~,2
Fig. 7. Aeff of the polarimeter reaction 4He(p, p)4He vs the energy of the protons in front of the scintillator. Measured points and least-squares fit of a quadratic polynominal with error band.
With the polarimeter described above we succcessfully measured the depolarization in the elastic scattering of polarized protons on 27A1 at 10.35 MeV [6], on 27A1 and 89y at 11 MeV and on 1H at 12 MeV [7].
Acknowledgments measured in a double-scattering experiment. A proton beam with known polarization was scattered in the sliding seal chamber from a 2°8pb target. Since Pb at forward angles has a very small analyzing power and since the depolarization is 1, the outgoing scattered particles have the same polarization p as the incoming beam. These particles were analyzed in the polarimeter filled with 20 bar. The four counting rates (left and right polarimeter detector both measured N O R M and REV) obtained for an incoming beam with spin up, led to the measured assymetry c. Possible " n o n p r o p e r spin flips" can be taken into account by introducing a false assymetry c' in the expression for the measured asymmetry [6] c -- ( p A e f f + e ' ) / ( 1 + e'pA~ff).
Using the same formula for the spin-down case and assuming c' to be the same, the false asymmetry can be eliminated. In all cases e' was only a few percent. The measured points and a least-squares fit of a quadratic polynominal with the error band are shown in fig. 7. An efficiency of - 1.3 × 10 6 p b a r - 1 was determined at Ep = 12 MeV by counting the incoming particles with the scintillator at the entrance of the polarimeter and
The authors very much appreciate the helpful advice of G. Muhr and G. Heimpel and the careful machine work done by L. Drechsler.
References [1] R. Henneck, W. Kretschmer, H. Lt)h, G. Muhr and W. Stach, Nucl. Instr. and Meth. 158 (1979) 391. [2] W. Kretschmer, H. Lrh, A. Rauscher, R. Schmitt and W. Schuster, Nucl. Instr. and Meth. A241 (1985) 480. [3] P. Schwandt, T.B. Clegg and W. Haeberli, Nucl. Phys. A 163 (1971) 432. [4] L.G. Keller and W. Haeberli, Nucl. Phys. A 156 (1970) 465; R.R. Cadmus, Jr. and W. Haeberli, Nucl. Instr. and Meth. 129 (1975) 403. [5] H. Weiss, Zulassungsarbeit, Erlangen (1974) unpublished; N. Stamminger, Zulassungsarbeit, Erlangen (1977) unpublished. [6] G.G. Ohlsen and P.W. Keaton, Jr., Nucl. Instr. and Meth. 109 (1973) 41. [7] H. L~3h, PhD thesis, Erlangen (1981). [8] R. Schmitt, PhD thesis, Erlangen (1986).