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Recent progress in neutron polarizers
208
Nuclear Instruments and Methods in Physics Research A284 (1989) 208-211 North-Holland, Amsterdam
RECENT PROGRESS IN NEUTRON POLARIZERS O. SCHAERPF
ILL, BP 156 X, F-38042 Grenoble Cedex, France
N. STUESSER
HMI, Ghemcker Strasse 100, D-1000 Berlin, Germany
In the following we shall show the state of the art of supermrror polarizers and of proton filters and, very briefly of the 3 He filter. What interests us primarily is the comparison of the achievable transmission and polarization of these three methods for the different energy and collimation ranges and their availability . 1. Improvement of the angular range of reflectivity of polarizing supermirrors Supermirrors use the extension of the region of total reflection by artificial Bragg reflection on multilayers with a gradient of layer thicknesses which matches the angular region just above the Bragg cutoff angle 9c. The idea stems from Turchin [1]. The name supermirror stems from Mezei, who actually rediscovered the idea and also made the first superrmrrors [2]. The reachable extension of this region is always given as a factor which compares this region to the cutoff angle for nickel 0N'. It is simultaneously the B~/X value of this region if Bc is given in deg/rim. The polarizer of the superbender type [3] needs an absorbing antireflecting layer to exclude the reflection of the neutrons with the wrong spin reflected by the glass substrate or their transmission through the curved substrate. The maximum reachable 9e ff~tive depends on the technically possible thinnest cobalt layers that remain still magnetic. The loss of magnetism has nothing to do with the so-called magnetic dead layers . It is only the problem of interdiffusion which gives this limit in our case, i.e. the thinnest layers are much thicker than magnetic dead layers . For a long time we tried to shift this limit to thinner layers oxidising the titanium every 20 layers, a process which gave good results in the production of nickel titanium supermirrors just by venting the chamber after each 20 layers after finishing a titanium layer [4]. This process did not work with cobalt-titanium layers . After many trials there were indications that the part of the cobalt layers, which after the alloying with titanium by interdiffusion still remains magnetic, becomes too thin for the necessary supermirror structure. So it was tried what would result, if one increases the cobalt layer 0168-9002/89/$03 .50 C Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
thickness and diminishes the titanium layer thickness. Different trials showed that the best results can be achieved with a 0.7-0.8 rim change in both thicknesses with the cobalt layers thicker and the titanium layers thinner [3]. As now this first step of improvement succeeded immediately we came again back to the venting technique which gave always good results with nickel-titanium. And now, in combination with the thickness changes mentioned before also this technique succeeded. Fig. 1 shows the behaviour of the reflectivity with 300 layers theoretically calculated using the method described in ref. [5] and the first achieved experimental reflectivity curve with the above described techniques. It shows that it is possible with this technique to extend the reflectivity far beyond the region of the 80 layer supermirrors . But the remaining problem in this case is the technical feasibility of the production of many such mirrors. Fig. 2 shows examples of a series showing that one not always gets results of the same quality. The
b)
0
n
1 5 GRAZING ANGLE OVER WAVELENGTH CDEG/nm7
3
Fig. 1. Reflectivity of (a) a theoretically calculated supermirror with 300 layers and (b) first achieved experimental reflectivity with the technique described in the text.
209
O . Schaerpf N. Stuesser / Recent progress in neutron polanzers 100
H H Û W
Z O H y rn H L ZZ Q
bdL , 1n two representative
w
0
1 .5 GRAZING ANGLE OVER WAVELENGTH CDEG/nm7
3
Fig. 2. The reproducibility of the reflectivity curves is still not ideal. There are still many bad ones. region of extension is 2.6 that of 9c of nickel . But the reflectivity is sometimes relatively low. 2. Properties of the polarizers using these new mirrors What is now the behaviour of polarizers using such mirrors? We already have a number of such even double-sided coated mirrors sufficient for the construction of a full polarizer i.e . nearly 200 mirrors. One can think of two possible advantages using this sort of mirrors: 1) The extension of the angular aperture i.e . the angular range of neutrons polarized; and 2) the extension of the energy range that is transmitted . The following figures show what can be achieved. Fig. 3 shows the possible extension of the energy range. On the cost of the transmission of the long wavelengths one can now easily enter the region of polarizing 0.1 rim wavelength neutrons or even below using spacers of 0.4 mm thickness, something easily possible . In that case even the flipping ratio at 0.08 rim is still higher than 10 even if one takes into account the diminished absorption of gadolinium for this energy . The other possible extension is in the angular region. Fig. 4 shows a calculation for the use of a polarizer behind a focusing monochromator with an angular range
100)
20050
10
2
collimated boom
Z 0 H N H E Z a
Y
0 .0055 rad
I 0x
0
eV spacer thl kness l mm 0 .6mm 0 .4mm 0 .3mm 0 .2mm
r
0 .5
WAVELENGTH
Max . 0x
measured without spin flip
Cnm7
1 .0
Fig. 3. Possible extension of the energy range transmitted by a polarizer in a setup described in ref. [31 using the above described mirrors.
10
2
Ip0V
beam collimatlon 0 .014 rad spacers 0 .6 m
r
reflectivity curves
200 50
mln .
WAVELENGTH
80
I
300 layers
Cnm7
Fig. 4. Use of the polarizer with the improved mirrors behind a focusing monochromator with ±0 .014 rad collimation shows that there is not much gain .
of ±0 .014 rad as a function of the wavelength . The curves are calculated using the measured reflectivity curves for the mirrors of fig. 2 showing a maximum and a minimum curve of reflectivities . In between those two curves the reflectivity of the applied mirrors are to be found. One sees that supermirror polarizers extended their region of possible applicability into the region of higher energies of 100 meV with the advantage to polarize the whole spectrum without energy selection and the ease of application and reliability avoiding dependences on any other features . But one has to choose between the higher angular range and the higher energy range of transmission . The still lower reflectivity of the 300 layer mirrors gives an overall loss of intensity so that the gain by the extended angular region of reflectivity is not yet evident. 3. Use of proton filters for polarization If one wants both a larger angular and a higher energy region of polarization one has to choose different filters . The working principle of the polarized proton filter for the neutron polarization can easily be described by some simple formulas . We shall show their behaviour just by some figures. The principle of the polarized proton filters is : polarized protons have two different neutron scattering cross sections for spin parallel or antiparallel to the nuclear spin of the proton. This is valid for the coherent and the incoherent part of the cross section shown in fig. 5 which is a plot of the known formulas as a function of the polarization of the proton target PH [6] acoh = 4m bz + bb
2 12P2
a , c = 4m(0 .25bNI(I + 1) - 0 .256NIPnPH 2 -0 .25bNI 2PH), with Pn the neutron polarization and PH the proton VI . NEUTRON SOURCES/DETECTORS
O. Schaerpf, N. Stuesser / Recent progress in neutron polanzers
210
z O
EM 21
1 SE-
0
0
0 U O Z H H U W O
G??
z Z
w
w
Z 0 H rQ N H
w
FfH
a J Z o a a
GTl
0 w
z p
r-
U = O U
0 0
TARGET POLARISATION
PH
1
Fig. 5. Behaviour of the coherent and incoherent scattering cross section of polarized hydrogen as a function of proton polarization for neutron spin parallel or antiparallel to the nuclear spin . polarization . Fig. 6 shows the behaviour of the total cross section for neutron spin parallel (a r r ) or antiparallel (a ? 1) to the nuclear spin of the target respectively with rr =-1 ) .
a rt- acoh(Pn =-1 )+Qinc(pn One sees that 0 r r becomes small and the other 0 r 1 goes up to a high value. Thus one spin is strongly scattered out of the beam and the other spin is transmitted nearly undisturbed only attenuated by the remaining coherent part of the scatterer. If one now has this cross section the attenuation of the respective beam is given by the exponential law exp(-o,Nt) with N the density of the scatterer in the target and t the thickness of the target. This immediately gives the relation of the remaining neutrons for both spin states and thus the polarization of the transmitted (= filtered) beam : exp(- a rr Nt)-exp(- a r 1 Nt) P(neutron) _ exp( - O rr Nt)+exp( - 0 r1 Nt), which is given for some thicknesses in fig. 7.
TARGET POLARISATION
PH 1
Fig. 7. Achievable neutron polarization for some proton filter thicknesses as a function of proton polarization . The resulting transmission of the neutron beam is then easily given by the transmission of the two parts: Trr(t)=exp(-6X10 28 tUrr), Tr 1 (1)=exp(-6 X102810 r1 ), i.e . Ttotal(t) = (exp(-6
X
+exp(-6
10 28 10 r ? ) X
1028ta T 1))/2,
where t and 0 have to be specified in [m] and [m2 ], respectively . This gives the behaviour described in fig. 8 for some different thicknesses. In order to achieve a neutron polarization above 95% using propanediol with a density of 6 X 10 28 m-3 of protons we selected for our filter a target 5 mm thick with a proton polarization of 95% . This is achievable following Niinikoski et al . [7,8] who polarized at CERN hydrogen targets of propanediol of 2 kg protons successfully with even higher polarization. One needs a cryostat with a cooling power of about 4.5 mW at 0.3 K to arrive within 10 h at a target polarization of 95% using a pumping frequency of 70 GHz in a magnetic field of 2.5 T with a homogeneity of 10 -4 in the region of the filter with a size of 3.5 cm X 3.5 cm. This gives a transmission T T T - 0.59 with a polarization of the neutrons of 95% . 1002 a-
D 0 H H L z Z Q H 0
PH
TARGET POLARISATION
1
Fig. 6. Behaviour of the total cross section for neutron spin parallel or antiparallel to the nuclear spin.
0
TARGET POLARIZATION
PH
I
Fig. 8. Transmission of neutrons as a function of target polarization for some thicknesses.
O. Schaerpf, N Stuesser / Recent progress to neutron polarizers All facilities to operate such a filter including a powerful refrigerator with a suitable pumping station and a superconducting magnet can be ordered from Oxford Instruments for a price of 1000000 DM . This system is developed in collaboration with T .O . Niinikoski from CERN and also allows one to freeze in the achieved proton polarization at a temperature of 50 mK using a field of 1 T and no ultrahigh frequency for a week . Within 1 .5 years after the order you can use it . It polarizes a wide range of energies . For the higher energies the thickness must be increased because of decreasing cross sections : it is no more the bound nucleus cross section but the free nucleus cross section which is A/(A + 1) times smaller for the higher energies . And there is a transition region in the range of 1 eV [9] . The principle of the polarized 3 He filter is very similar to that of the proton filter ; one only has an absorption instead of a scattering cross section which is different for the two spin eigenstates [10-12] . But the absorption cross section goes down with energy being only 800 b for 1 eV and is going even further down with still higher energies. We see that there are different approaches to polarization of neutrons . Supermirror type polarizers are very simple in their use and very reliable, they need no service, no power, and they are always ready. Their adjustment is simple, like that of each collimator . You can do it directly optically . Their polarizing efficiency is very good, flipping ratios of 50 being normal without any trouble. Their use extends now into the range of always shorter wavelengths or higher divergency . For extreme conditions where one wants both high energy and large angular range as in a multidetector for short wavelengths, one has to select the technically more complicated way of a filter, either proton or 3 He . The proton filter can directly be bought, is technically al-
ready well performing. The 3 He filter can also work in principle . With such a filter of 5 cm thickness and the already achieved polarization of 73% one can already achieve the same results as with the above described proton filter if one can reach a pressure of polarized 3 He gas of 4 atm in this volume. But for this still some technical problems have to be solved [10-12] .
References [1] V .F . Turchin, At . Energy 22 (1967) no. 2, deposited paper ; F . Mezer, Inst. Phys. Conf. Ser. No . 42 (1978) 162 . [2] F . Mezer, Comm . Phys . 1 (1976) 81 F . Mezei and P.A. Dagleish, Commun . Phys . 2 (1977) 41 . [3] O. Schaerpf, Physica B156&157 (1989) 639. [4] M . Rossbach, O. Schaerpf, W . Kaiser, W . Graf, A. Schirmer, W . Faber, J . Duppich and R . Zeissler, Nucl. Instr . and Meth. B35 (1988) 181 . [5] O . Schaerpf, Physica B156&157 (1989) 631 . [6] H . Glaettli and M . Goldman, in : Methods of Experimental Physics, vol . 23C, Neutron Scattering, eds . K. Skoeld and D .L . Price (Academic Press, London, 1987) p . 250 . [7] T .O . Niinrkoski and F . Udo, Nucl . Instr . and Meth. 134 (1976) 219 . [8] W . de Boer and T .O . Niimkoskr, Nucl. Instr . and Meth. 114 (1974) 495 . [9] V.I . Lushokov, Yu.V . Taran and F .L. Shapiro, Sov . J. Nucl . Phys . 1 0 (1970) 669 . [10] T .E . Chupp, M .E. Wagshul, K .P . Coulter, A .B. McDonald and W . Happer, Phys . Rev . C36 (1987) 2244. [111 K .P. Coulter, A.B . McDonald, W. Happer, T.E . Chupp and M .E . Wagshul, Nucl . Instr . and Meth . A270 (1988) 90 . [12] C.L . Bohler, L .D . Schearer, M . Leduc, P.J . Nacher, L. Zachorowski, R.G . Milner, R .D. Mckeown and C .E . Woodward, J. Appl. Phys . 63 (1988) 2497 .
VI . NEUTRON SOURCES/DETECTORS
Nuclear Instruments and Methods in Physics Research A284 (1989) 208-211 North-Holland, Amsterdam
RECENT PROGRESS IN NEUTRON POLARIZERS O. SCHAERPF
ILL, BP 156 X, F-38042 Grenoble Cedex, France
N. STUESSER
HMI, Ghemcker Strasse 100, D-1000 Berlin, Germany
In the following we shall show the state of the art of supermrror polarizers and of proton filters and, very briefly of the 3 He filter. What interests us primarily is the comparison of the achievable transmission and polarization of these three methods for the different energy and collimation ranges and their availability . 1. Improvement of the angular range of reflectivity of polarizing supermirrors Supermirrors use the extension of the region of total reflection by artificial Bragg reflection on multilayers with a gradient of layer thicknesses which matches the angular region just above the Bragg cutoff angle 9c. The idea stems from Turchin [1]. The name supermirror stems from Mezei, who actually rediscovered the idea and also made the first superrmrrors [2]. The reachable extension of this region is always given as a factor which compares this region to the cutoff angle for nickel 0N'. It is simultaneously the B~/X value of this region if Bc is given in deg/rim. The polarizer of the superbender type [3] needs an absorbing antireflecting layer to exclude the reflection of the neutrons with the wrong spin reflected by the glass substrate or their transmission through the curved substrate. The maximum reachable 9e ff~tive depends on the technically possible thinnest cobalt layers that remain still magnetic. The loss of magnetism has nothing to do with the so-called magnetic dead layers . It is only the problem of interdiffusion which gives this limit in our case, i.e. the thinnest layers are much thicker than magnetic dead layers . For a long time we tried to shift this limit to thinner layers oxidising the titanium every 20 layers, a process which gave good results in the production of nickel titanium supermirrors just by venting the chamber after each 20 layers after finishing a titanium layer [4]. This process did not work with cobalt-titanium layers . After many trials there were indications that the part of the cobalt layers, which after the alloying with titanium by interdiffusion still remains magnetic, becomes too thin for the necessary supermirror structure. So it was tried what would result, if one increases the cobalt layer 0168-9002/89/$03 .50 C Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
thickness and diminishes the titanium layer thickness. Different trials showed that the best results can be achieved with a 0.7-0.8 rim change in both thicknesses with the cobalt layers thicker and the titanium layers thinner [3]. As now this first step of improvement succeeded immediately we came again back to the venting technique which gave always good results with nickel-titanium. And now, in combination with the thickness changes mentioned before also this technique succeeded. Fig. 1 shows the behaviour of the reflectivity with 300 layers theoretically calculated using the method described in ref. [5] and the first achieved experimental reflectivity curve with the above described techniques. It shows that it is possible with this technique to extend the reflectivity far beyond the region of the 80 layer supermirrors . But the remaining problem in this case is the technical feasibility of the production of many such mirrors. Fig. 2 shows examples of a series showing that one not always gets results of the same quality. The
b)
0
n
1 5 GRAZING ANGLE OVER WAVELENGTH CDEG/nm7
3
Fig. 1. Reflectivity of (a) a theoretically calculated supermirror with 300 layers and (b) first achieved experimental reflectivity with the technique described in the text.
209
O . Schaerpf N. Stuesser / Recent progress in neutron polanzers 100
H H Û W
Z O H y rn H L ZZ Q
bdL , 1n two representative
w
0
1 .5 GRAZING ANGLE OVER WAVELENGTH CDEG/nm7
3
Fig. 2. The reproducibility of the reflectivity curves is still not ideal. There are still many bad ones. region of extension is 2.6 that of 9c of nickel . But the reflectivity is sometimes relatively low. 2. Properties of the polarizers using these new mirrors What is now the behaviour of polarizers using such mirrors? We already have a number of such even double-sided coated mirrors sufficient for the construction of a full polarizer i.e . nearly 200 mirrors. One can think of two possible advantages using this sort of mirrors: 1) The extension of the angular aperture i.e . the angular range of neutrons polarized; and 2) the extension of the energy range that is transmitted . The following figures show what can be achieved. Fig. 3 shows the possible extension of the energy range. On the cost of the transmission of the long wavelengths one can now easily enter the region of polarizing 0.1 rim wavelength neutrons or even below using spacers of 0.4 mm thickness, something easily possible . In that case even the flipping ratio at 0.08 rim is still higher than 10 even if one takes into account the diminished absorption of gadolinium for this energy . The other possible extension is in the angular region. Fig. 4 shows a calculation for the use of a polarizer behind a focusing monochromator with an angular range
100)
20050
10
2
collimated boom
Z 0 H N H E Z a
Y
0 .0055 rad
I 0x
0
eV spacer thl kness l mm 0 .6mm 0 .4mm 0 .3mm 0 .2mm
r
0 .5
WAVELENGTH
Max . 0x
measured without spin flip
Cnm7
1 .0
Fig. 3. Possible extension of the energy range transmitted by a polarizer in a setup described in ref. [31 using the above described mirrors.
10
2
Ip0V
beam collimatlon 0 .014 rad spacers 0 .6 m
r
reflectivity curves
200 50
mln .
WAVELENGTH
80
I
300 layers
Cnm7
Fig. 4. Use of the polarizer with the improved mirrors behind a focusing monochromator with ±0 .014 rad collimation shows that there is not much gain .
of ±0 .014 rad as a function of the wavelength . The curves are calculated using the measured reflectivity curves for the mirrors of fig. 2 showing a maximum and a minimum curve of reflectivities . In between those two curves the reflectivity of the applied mirrors are to be found. One sees that supermirror polarizers extended their region of possible applicability into the region of higher energies of 100 meV with the advantage to polarize the whole spectrum without energy selection and the ease of application and reliability avoiding dependences on any other features . But one has to choose between the higher angular range and the higher energy range of transmission . The still lower reflectivity of the 300 layer mirrors gives an overall loss of intensity so that the gain by the extended angular region of reflectivity is not yet evident. 3. Use of proton filters for polarization If one wants both a larger angular and a higher energy region of polarization one has to choose different filters . The working principle of the polarized proton filter for the neutron polarization can easily be described by some simple formulas . We shall show their behaviour just by some figures. The principle of the polarized proton filters is : polarized protons have two different neutron scattering cross sections for spin parallel or antiparallel to the nuclear spin of the proton. This is valid for the coherent and the incoherent part of the cross section shown in fig. 5 which is a plot of the known formulas as a function of the polarization of the proton target PH [6] acoh = 4m bz + bb
2 12P2
a , c = 4m(0 .25bNI(I + 1) - 0 .256NIPnPH 2 -0 .25bNI 2PH), with Pn the neutron polarization and PH the proton VI . NEUTRON SOURCES/DETECTORS
O. Schaerpf, N. Stuesser / Recent progress in neutron polanzers
210
z O
EM 21
1 SE-
0
0
0 U O Z H H U W O
G??
z Z
w
w
Z 0 H rQ N H
w
FfH
a J Z o a a
GTl
0 w
z p
r-
U = O U
0 0
TARGET POLARISATION
PH
1
Fig. 5. Behaviour of the coherent and incoherent scattering cross section of polarized hydrogen as a function of proton polarization for neutron spin parallel or antiparallel to the nuclear spin . polarization . Fig. 6 shows the behaviour of the total cross section for neutron spin parallel (a r r ) or antiparallel (a ? 1) to the nuclear spin of the target respectively with rr =-1 ) .
a rt- acoh(Pn =-1 )+Qinc(pn One sees that 0 r r becomes small and the other 0 r 1 goes up to a high value. Thus one spin is strongly scattered out of the beam and the other spin is transmitted nearly undisturbed only attenuated by the remaining coherent part of the scatterer. If one now has this cross section the attenuation of the respective beam is given by the exponential law exp(-o,Nt) with N the density of the scatterer in the target and t the thickness of the target. This immediately gives the relation of the remaining neutrons for both spin states and thus the polarization of the transmitted (= filtered) beam : exp(- a rr Nt)-exp(- a r 1 Nt) P(neutron) _ exp( - O rr Nt)+exp( - 0 r1 Nt), which is given for some thicknesses in fig. 7.
TARGET POLARISATION
PH 1
Fig. 7. Achievable neutron polarization for some proton filter thicknesses as a function of proton polarization . The resulting transmission of the neutron beam is then easily given by the transmission of the two parts: Trr(t)=exp(-6X10 28 tUrr), Tr 1 (1)=exp(-6 X102810 r1 ), i.e . Ttotal(t) = (exp(-6
X
+exp(-6
10 28 10 r ? ) X
1028ta T 1))/2,
where t and 0 have to be specified in [m] and [m2 ], respectively . This gives the behaviour described in fig. 8 for some different thicknesses. In order to achieve a neutron polarization above 95% using propanediol with a density of 6 X 10 28 m-3 of protons we selected for our filter a target 5 mm thick with a proton polarization of 95% . This is achievable following Niinikoski et al . [7,8] who polarized at CERN hydrogen targets of propanediol of 2 kg protons successfully with even higher polarization. One needs a cryostat with a cooling power of about 4.5 mW at 0.3 K to arrive within 10 h at a target polarization of 95% using a pumping frequency of 70 GHz in a magnetic field of 2.5 T with a homogeneity of 10 -4 in the region of the filter with a size of 3.5 cm X 3.5 cm. This gives a transmission T T T - 0.59 with a polarization of the neutrons of 95% . 1002 a-
D 0 H H L z Z Q H 0
PH
TARGET POLARISATION
1
Fig. 6. Behaviour of the total cross section for neutron spin parallel or antiparallel to the nuclear spin.
0
TARGET POLARIZATION
PH
I
Fig. 8. Transmission of neutrons as a function of target polarization for some thicknesses.
O. Schaerpf, N Stuesser / Recent progress to neutron polarizers All facilities to operate such a filter including a powerful refrigerator with a suitable pumping station and a superconducting magnet can be ordered from Oxford Instruments for a price of 1000000 DM . This system is developed in collaboration with T .O . Niinikoski from CERN and also allows one to freeze in the achieved proton polarization at a temperature of 50 mK using a field of 1 T and no ultrahigh frequency for a week . Within 1 .5 years after the order you can use it . It polarizes a wide range of energies . For the higher energies the thickness must be increased because of decreasing cross sections : it is no more the bound nucleus cross section but the free nucleus cross section which is A/(A + 1) times smaller for the higher energies . And there is a transition region in the range of 1 eV [9] . The principle of the polarized 3 He filter is very similar to that of the proton filter ; one only has an absorption instead of a scattering cross section which is different for the two spin eigenstates [10-12] . But the absorption cross section goes down with energy being only 800 b for 1 eV and is going even further down with still higher energies. We see that there are different approaches to polarization of neutrons . Supermirror type polarizers are very simple in their use and very reliable, they need no service, no power, and they are always ready. Their adjustment is simple, like that of each collimator . You can do it directly optically . Their polarizing efficiency is very good, flipping ratios of 50 being normal without any trouble. Their use extends now into the range of always shorter wavelengths or higher divergency . For extreme conditions where one wants both high energy and large angular range as in a multidetector for short wavelengths, one has to select the technically more complicated way of a filter, either proton or 3 He . The proton filter can directly be bought, is technically al-
ready well performing. The 3 He filter can also work in principle . With such a filter of 5 cm thickness and the already achieved polarization of 73% one can already achieve the same results as with the above described proton filter if one can reach a pressure of polarized 3 He gas of 4 atm in this volume. But for this still some technical problems have to be solved [10-12] .
References [1] V .F . Turchin, At . Energy 22 (1967) no. 2, deposited paper ; F . Mezer, Inst. Phys. Conf. Ser. No . 42 (1978) 162 . [2] F . Mezer, Comm . Phys . 1 (1976) 81 F . Mezei and P.A. Dagleish, Commun . Phys . 2 (1977) 41 . [3] O. Schaerpf, Physica B156&157 (1989) 639. [4] M . Rossbach, O. Schaerpf, W . Kaiser, W . Graf, A. Schirmer, W . Faber, J . Duppich and R . Zeissler, Nucl. Instr . and Meth. B35 (1988) 181 . [5] O . Schaerpf, Physica B156&157 (1989) 631 . [6] H . Glaettli and M . Goldman, in : Methods of Experimental Physics, vol . 23C, Neutron Scattering, eds . K. Skoeld and D .L . Price (Academic Press, London, 1987) p . 250 . [7] T .O . Niinrkoski and F . Udo, Nucl . Instr . and Meth. 134 (1976) 219 . [8] W . de Boer and T .O . Niimkoskr, Nucl. Instr . and Meth. 114 (1974) 495 . [9] V.I . Lushokov, Yu.V . Taran and F .L. Shapiro, Sov . J. Nucl . Phys . 1 0 (1970) 669 . [10] T .E . Chupp, M .E. Wagshul, K .P . Coulter, A .B. McDonald and W . Happer, Phys . Rev . C36 (1987) 2244. [111 K .P. Coulter, A.B . McDonald, W. Happer, T.E . Chupp and M .E . Wagshul, Nucl . Instr . and Meth . A270 (1988) 90 . [12] C.L . Bohler, L .D . Schearer, M . Leduc, P.J . Nacher, L. Zachorowski, R.G . Milner, R .D. Mckeown and C .E . Woodward, J. Appl. Phys . 63 (1988) 2497 .
VI . NEUTRON SOURCES/DETECTORS