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A position-determining scintillator for small angle neutron scattering measurements
N U C L E A R I N S T R U M E N T S AND METHODS
I35
(I976) 483-487; © N O R T H - H O L L A N D P U B L I S H I N G CO.
A P O S I T I O N - D E T E R M I N I N G SCINTILLATOR FOR SMALL ANGLE N E U T R O N SCATTERING MEASUREMENTS* V. GIORDANO, C. MANDUCH1,
M . T . RUSSO-MANDUCHI and G. F. SEGATO
lstituto di Fisica dell' Universit&, Padova, Italy, and lstituto Nazionale di Fisiea Nucleare, Sezione di Padova, Italy Received 25 February 1976 A position-determining device has been developed for studying small-angle scattering of fast neutrons. The detector essentially consists of two photomultiplier tubes looking at a liquid scintillator: the time difference between both signals of the phototubes is used to determine the position of the light-producing region. The quality of the performance is illustrated by measuring absolute cross section and polarization of 2.5 MeV neutrons scattered by Bi. A critical examination is made of the properties of the device.
1. Introduction
The elastic scattering of fast neutrons into angles below 10° is the subject of both theoretical and experimental studies1). Previous measurements of smallangle neutron scattering have examined the electromagnetic interaction between the incident neutron and the scattering nucleus. The presence of this interaction introduces into the scattering amplitude a spin dependence even in those cases when the contribution from the specifically nuclear interaction is independent of the spin. In first order perturbation theory, the resulting increment in cross-section is
Aa(O) = Jim
hs(0)] 2 ,
where hs(0) = -½(i7) ctg ½0, and 7 is a constant depending on the neutron magnetic moment /~, and the atomic number Z of the target nucleus: ]) :
I~lnl Z(e2/rrlC2).
The differential neutron scattering cross-section a(0) and the corresponding polarization P(~9) are related by
tial cross-section, as calculated in terms of an optical model plus electromagnetic interaction, and as measured, do not agree. It has been suggested that an additional contribution may come from the electric polarizability of the neutron2). A possible long-range component of the nuclear potential has also been postulated3), but agreement with experimental data is still lacking. Only when sufficient data are available to yield reasonable optical model predictions of the scattering, it will be possible to definitely determine the existence of anomalies in small-angle scattering. Described herein is a new device for measuring small-angle scattering of fast neutrons. The experimental equipment is basically a shielded-source geometry, where the neutron detector is a positiondetermining scintillator. The detector essentially consists of a liquid scintillator encapsulated in a glass cylinder, with both end-faces in optical contact with two photomultipliers. The glass cylinder is enclosed in a light-tight stainless steel tube. The time difference between both output signals of the phototubes, owing to the different optical paths, may be well approximated by a linear function of position of the lightproducing region. An important feature of this method
tr(0) P(~) -- K Im hs(~)(aJ21r), where K is the wave number of the neutron, and a t the neutron total cross-section. It follows that the polarization could be computed by measuring the total cross-section, when the differential cross-sections were well known. However, there is some evidence that the absolute magnitudes of the differen* Work performed at the Laboratori Nazionali di Legnaro.
FM
e '° Fig. 1. Sketch of detector assembly showing: glass cylinder (1); stainless steel container (2); viewing windows (3); light pipes (4); expansion chambers (5).
484
v. G I O R D A N O
_1 "0°. -I
I -...p_ MIXER
l-
XP 2020
XP2020
Ic.F.T.
NE--213
start_l
-I Start
et al.
I". A,C. 1
1 1 2_ o,.2.Z 3.L Fig. 2. Block diagram o f the electronics used with the positional spectrometer.
is that data may be taken simultaneously in the total angle of acceptance of the scintillator,
height is, in general, a linear function of the lightsource position.
2. Positional spectrometer
2.2. COUNTING PROPERTIES Relevant factors affecting time resolution are the light-emission to energy-loss relation and the finite transfer time in the phosphor, the quantum efficiency and time dispersion in the photomultiplier. Circuitry design is sufficiently advanced so that at present the electronics external to the photomultiplier contribute a negligible width to the ultimate resolving times obtainable. The position measurement is independent of fluctuations in light production, since both phototubes look at the same light emission center and the predicted position depends only on the different transit times for light incident upon both photocathodes. The resolution of the system was tested with collimated beams of 3 MeV and 15 MeV neutrons, using a wide dynamic range. The spectrometer could be moved in a normal direction to the beam. The resolution is better than 1.16 ns at 3 MeV and 0.57 ns at 15 MeV (corresponding to _+4 cm and + 2 cm respectively) for all counter elements except the end ones. Here the intrinsic features of the detector introduce a small degradation on the time resolution.
2.1. DESIGN The cross-sectional diagram of the counter assembly is illustrated in fig. 1. The glass cylinder, 80 cm in length and 30.8 mm in diameter, is filled with NE 213 liquid scintillator. ]-he ends of the cylinder are hermetically sealed to a stainless steel container, 34.1 mm inside diameter and 3.9 mm thick. Two viewing windows, at the end-faces of the scintillator cylinder, are in optical contact with XP 2020 photomultipliers, through 5 cm long light pipes. Special attention has been paid to light collection factors, scintillator stability and oxygen removal facilities. The NE 213 liquid scintillator has been chosen owing to pulse shape discrimination properties, in spite of the disadvantageous aspects associated with the poor scintillator decay properties. The XP 2020 photomultipliers were selected for their excellent timing performance. The electronic system is shown in fig. 2. Constant fraction triggers (CFTs) provide good time resolution for a wide dynamic range. The logic signal from the trigger output of phototube 2 is delayed and correlated to the signal from phototube i through a time-topulse-height converter (TAC). The resulting time spectrum is expanded by a biased amplifier: the pulse
2.3. PERFORMANCETESTS Performance tests, and measurements, were carried
POSITION-DETERMINING
out at the L N L Van de Graaff accelerator. The accelerator operation in the pulsed mode was used for energy separation by conventional time-of-flight techniques, and pulse shape discrimination was applied to reduce the y-ray contamination. In the experimental arrangement the whole spectrometer configuration was an array of ten contiguous elements, 8 cm in length. Each counter element was classified by the corresponding pulse-height range in the time spectrum, and categorized into one of the 16 groups of a 2-dimensional (16x16) analyzer, together with the associated time-of-flight spectrum. The 7-n discriminator was connected as a gating signal (see fig. 2). The efficiency of the spectrometer does not depend to a great extent on position, as may be seen from the distribution in fig. 3, concerning a uniform spectrum of 3 MeV neutrons produced in the D(d,n) reaction. Two typical pulse-height distributions, at the same neutron energy, are presented in fig. 4: (a) corresponds to a nearly uniform neutron distribution with a slab of paraffin interposed; (b) represents a measurement taken with the first counter element near the neutron source, the axis of the scintillator being perpendicular to the deuteron beam. The smooth curves in fig. 4 are the profiles expected from the geometry of the system, while the circles indicate experimental data, corrected for finite time resolution and relative efficiency. The data points plotted as " s t a r s " in (b) are obtained by scanning a stilbene scintillator, 1.3 cm in length and 3.8 cm in diameter, in the same positions as the counter elements.
485
SCINTILLATOR
polarized neutrons are produced in the target (T). The target chamber strongly supports both the entrance (accelerator beam) and the exit (neutron) collimators. Neutrons produced at 45 ° to the incident accelerator beam pass through a polyethylene collimator, 62 cm in length, inserted into a stainless steel tube connected to the scattering chamber. The neutron collimator flares from a minimum of 8.6 x 6.0 m m 2 at the entrance end to a maximum of 20.0 x 14.7 m m 2 at the exit end (about 77 cm from the source target). The profile of
1
2
3
4
(
( :
5
6
.~cbu.nt~r.,'-
7
8
9
10
': - 0
3
" 2 _~ ~ 1 ='~
(a) c o u n t e r elements ~ .
( ,'. ~ : ¢opn_~e,
', ': {1
22 o z la ~" Z O U
3. Small-angle scattering apparatus
14
The experimental setup is shown in fig. 5. Partially o' 1 p-
10
3 >.4
r~ m
(b)
Ill I-ey
2 O Z
O
i
i
I
i
I
i
1
2
3
4
5
6
i
i
7 8 counter
i
I
9
10
elements
Fig. 3. Pulse-height d i s t r i b u t i o n for a nearly u n i f o r m flux of 3 MeV neutrons.
I
I
I
I
1
2
3
4
5
6
i
i
i
i
7
8
9
10
Fig. 4. Pulse-height di s t ri but i ons for 3 MeV neutrons from the D (d,n) reaction: (a) a nearly u n i f o r m n e u t r o n di s t ri but i on with a slab of paraffin interposed; (b) first c ount e r element near the n e u t r o n source. Circles are e xpe ri me nt a l data. The curves are the profiles expected from the geometry of the system. The da t a points plotted as " s t a r s " are from a m e a s u r e m e n t pe rforme d with a stilbene scintillator.
486
v. GIORDANO et al.
the neutron beam indicates an angular divergence in the horizontal plane of ,-~ 1.3 °. The neutron scatterer is at a distance of 80.8 cm from the neutron source. The scattering sample is a cylinder, positioned with its symmetry axis parallel to the neutron beam: all neutrons leaving the collimator are intercepted by the scatterer. Scattered neutrons are detected by the positionsensitive scintillator, at 227 cm from the scattering sample. Owing to the possible use of the system as a
neutron polarimeter, the scintillator is symmetrically disposed with respect to the neutron beam direction in the horizontal plane. In order to achieve a shieldedsource geometry, the scintillator is mounted above the reaction plane, the minimum scattering angle being determined only by a practical compromise with the requirements of the exit beam profile. The spectrometer is free to rotate about a centre pivot, so that the counter elements can be interchanged. A stilbene detector, at 390 cm from the'neutron source, is used to monitor the neutron yield][through the collimator.
/ 1°
2°
3 °
4°
5°
6 °
7°
8°
9 °
i 7°
i 8°
I 9°
10 °
5.2
T
\ ".'?':~.'...: :' -,...::. / ~"~ 4.8 Z 0
IU 4.4 I 09 0
5
U 4.0
angle
(degree)
C~ -- 0.1
--0.2 Z o
,~0.3 < .J o
0.4
--0.5
-- 0.6
1 = 1°
Fig. 5. Schematic d i a g r a m o f the experimental arrangement: (1) paraffin shield; (2) polyethylene shield; (3) b e a m ; (4) collim a t o r ; (5) n e u t r o n scatterer; (6) positional spectrometer; (7) stilbene scintillator; (8) cathetometer.
| 2 °
Fig. 6. Preliminary trons by Bi at 2.50 curve refers to a n the solid curve is
i 3 °
i 4 °
i 5 °
i 6 °
0 1 o
results from small-angle scattering o f neuMeV. (a) Differential cross-sections: the solid optical model calculation. (b) Polarizations: calculated from the formulae o f Schwinger.
POSITION-DETERMINING
Absolute cross-sections can be measured by comparison of the scattered flux with the incident flux at the scatterer position, as deduced from the monitor data. 4. Measurements
In order to evaluate the validity of the technique described in this paper, the absolute values of the differential cross-section and the polarization of neutrons elastically scattered by Bi have been measured at 2.50 MeV. The results are shown in fig. 6, where the assigned standard deviations include, in addition to counting statistics, other sources of uncertainties: specifically, uncertainties in the time resolution corrections. Measured cross-sections are compared with calculations based on a scattering potential that includes only the terms due to nuclear and Schwinger interactions. Polarization data, obtained from the asymmetry in the scattering of neutrons to the right and to the left of the neutron beam, are compared with Schwinger's predictions. Although the experimental procedure was limited to an exemplification test, the agreement with the previous results 4) appears fairly good. The calculated differential cross-sections are systematically lower than the experimental ones: this effect was also observed at other energiesS).
SCINTILLATOR
487
In spite of the poor resolution, the position-determining scintillator described here proves helpful for a variety of applications, especially where a high detection efficiency combined with n-~ discrimination is of great importance. Results of theoretical considerations of the effect of transfer times in the scintillator 6) indicate that this is probably the limiting factor in obtainable time resolution. Research on the development of scintillators with very short transfer times, together with suitable properties for pulse shape discrimination, would be of great value for positional accuracy.
References J) R. B. Galloway and R. M. A. Maayouf, Nucl. Phys. A212 (1973) 182. 2) G. V. Anikin and I. I. Kotukhov, Yad. Fiz. 12 (1970) [English transl.: Sov. J. Nucl. Phys. 12 (1971) 614]. a) R. Fox, Nucl. Phys. 43 (1963) 110. 4) L. Drigo, C. Manduchi, G. Moschini, M. T. Russo-Manduchi, G. Tornielli and G. Zannoni, Nuovo Cimento 13A (1973) 867. s) F. T. Kuchnir, A. J. Elwin, J. E. Monahan, A. Langsdorf and F. P. Mooring, Phys. Rev. 176 (1968) 1405. 6) G. Present, A. Schwarzschild, I. Spirn and N. Wotherspoon, Nucl. Instr. and Meth. 31 (1964) 71.
I35
(I976) 483-487; © N O R T H - H O L L A N D P U B L I S H I N G CO.
A P O S I T I O N - D E T E R M I N I N G SCINTILLATOR FOR SMALL ANGLE N E U T R O N SCATTERING MEASUREMENTS* V. GIORDANO, C. MANDUCH1,
M . T . RUSSO-MANDUCHI and G. F. SEGATO
lstituto di Fisica dell' Universit&, Padova, Italy, and lstituto Nazionale di Fisiea Nucleare, Sezione di Padova, Italy Received 25 February 1976 A position-determining device has been developed for studying small-angle scattering of fast neutrons. The detector essentially consists of two photomultiplier tubes looking at a liquid scintillator: the time difference between both signals of the phototubes is used to determine the position of the light-producing region. The quality of the performance is illustrated by measuring absolute cross section and polarization of 2.5 MeV neutrons scattered by Bi. A critical examination is made of the properties of the device.
1. Introduction
The elastic scattering of fast neutrons into angles below 10° is the subject of both theoretical and experimental studies1). Previous measurements of smallangle neutron scattering have examined the electromagnetic interaction between the incident neutron and the scattering nucleus. The presence of this interaction introduces into the scattering amplitude a spin dependence even in those cases when the contribution from the specifically nuclear interaction is independent of the spin. In first order perturbation theory, the resulting increment in cross-section is
Aa(O) = Jim
hs(0)] 2 ,
where hs(0) = -½(i7) ctg ½0, and 7 is a constant depending on the neutron magnetic moment /~, and the atomic number Z of the target nucleus: ]) :
I~lnl Z(e2/rrlC2).
The differential neutron scattering cross-section a(0) and the corresponding polarization P(~9) are related by
tial cross-section, as calculated in terms of an optical model plus electromagnetic interaction, and as measured, do not agree. It has been suggested that an additional contribution may come from the electric polarizability of the neutron2). A possible long-range component of the nuclear potential has also been postulated3), but agreement with experimental data is still lacking. Only when sufficient data are available to yield reasonable optical model predictions of the scattering, it will be possible to definitely determine the existence of anomalies in small-angle scattering. Described herein is a new device for measuring small-angle scattering of fast neutrons. The experimental equipment is basically a shielded-source geometry, where the neutron detector is a positiondetermining scintillator. The detector essentially consists of a liquid scintillator encapsulated in a glass cylinder, with both end-faces in optical contact with two photomultipliers. The glass cylinder is enclosed in a light-tight stainless steel tube. The time difference between both output signals of the phototubes, owing to the different optical paths, may be well approximated by a linear function of position of the lightproducing region. An important feature of this method
tr(0) P(~) -- K Im hs(~)(aJ21r), where K is the wave number of the neutron, and a t the neutron total cross-section. It follows that the polarization could be computed by measuring the total cross-section, when the differential cross-sections were well known. However, there is some evidence that the absolute magnitudes of the differen* Work performed at the Laboratori Nazionali di Legnaro.
FM
e '° Fig. 1. Sketch of detector assembly showing: glass cylinder (1); stainless steel container (2); viewing windows (3); light pipes (4); expansion chambers (5).
484
v. G I O R D A N O
_1 "0°. -I
I -...p_ MIXER
l-
XP 2020
XP2020
Ic.F.T.
NE--213
start_l
-I Start
et al.
I". A,C. 1
1 1 2_ o,.2.Z 3.L Fig. 2. Block diagram o f the electronics used with the positional spectrometer.
is that data may be taken simultaneously in the total angle of acceptance of the scintillator,
height is, in general, a linear function of the lightsource position.
2. Positional spectrometer
2.2. COUNTING PROPERTIES Relevant factors affecting time resolution are the light-emission to energy-loss relation and the finite transfer time in the phosphor, the quantum efficiency and time dispersion in the photomultiplier. Circuitry design is sufficiently advanced so that at present the electronics external to the photomultiplier contribute a negligible width to the ultimate resolving times obtainable. The position measurement is independent of fluctuations in light production, since both phototubes look at the same light emission center and the predicted position depends only on the different transit times for light incident upon both photocathodes. The resolution of the system was tested with collimated beams of 3 MeV and 15 MeV neutrons, using a wide dynamic range. The spectrometer could be moved in a normal direction to the beam. The resolution is better than 1.16 ns at 3 MeV and 0.57 ns at 15 MeV (corresponding to _+4 cm and + 2 cm respectively) for all counter elements except the end ones. Here the intrinsic features of the detector introduce a small degradation on the time resolution.
2.1. DESIGN The cross-sectional diagram of the counter assembly is illustrated in fig. 1. The glass cylinder, 80 cm in length and 30.8 mm in diameter, is filled with NE 213 liquid scintillator. ]-he ends of the cylinder are hermetically sealed to a stainless steel container, 34.1 mm inside diameter and 3.9 mm thick. Two viewing windows, at the end-faces of the scintillator cylinder, are in optical contact with XP 2020 photomultipliers, through 5 cm long light pipes. Special attention has been paid to light collection factors, scintillator stability and oxygen removal facilities. The NE 213 liquid scintillator has been chosen owing to pulse shape discrimination properties, in spite of the disadvantageous aspects associated with the poor scintillator decay properties. The XP 2020 photomultipliers were selected for their excellent timing performance. The electronic system is shown in fig. 2. Constant fraction triggers (CFTs) provide good time resolution for a wide dynamic range. The logic signal from the trigger output of phototube 2 is delayed and correlated to the signal from phototube i through a time-topulse-height converter (TAC). The resulting time spectrum is expanded by a biased amplifier: the pulse
2.3. PERFORMANCETESTS Performance tests, and measurements, were carried
POSITION-DETERMINING
out at the L N L Van de Graaff accelerator. The accelerator operation in the pulsed mode was used for energy separation by conventional time-of-flight techniques, and pulse shape discrimination was applied to reduce the y-ray contamination. In the experimental arrangement the whole spectrometer configuration was an array of ten contiguous elements, 8 cm in length. Each counter element was classified by the corresponding pulse-height range in the time spectrum, and categorized into one of the 16 groups of a 2-dimensional (16x16) analyzer, together with the associated time-of-flight spectrum. The 7-n discriminator was connected as a gating signal (see fig. 2). The efficiency of the spectrometer does not depend to a great extent on position, as may be seen from the distribution in fig. 3, concerning a uniform spectrum of 3 MeV neutrons produced in the D(d,n) reaction. Two typical pulse-height distributions, at the same neutron energy, are presented in fig. 4: (a) corresponds to a nearly uniform neutron distribution with a slab of paraffin interposed; (b) represents a measurement taken with the first counter element near the neutron source, the axis of the scintillator being perpendicular to the deuteron beam. The smooth curves in fig. 4 are the profiles expected from the geometry of the system, while the circles indicate experimental data, corrected for finite time resolution and relative efficiency. The data points plotted as " s t a r s " in (b) are obtained by scanning a stilbene scintillator, 1.3 cm in length and 3.8 cm in diameter, in the same positions as the counter elements.
485
SCINTILLATOR
polarized neutrons are produced in the target (T). The target chamber strongly supports both the entrance (accelerator beam) and the exit (neutron) collimators. Neutrons produced at 45 ° to the incident accelerator beam pass through a polyethylene collimator, 62 cm in length, inserted into a stainless steel tube connected to the scattering chamber. The neutron collimator flares from a minimum of 8.6 x 6.0 m m 2 at the entrance end to a maximum of 20.0 x 14.7 m m 2 at the exit end (about 77 cm from the source target). The profile of
1
2
3
4
(
( :
5
6
.~cbu.nt~r.,'-
7
8
9
10
': - 0
3
" 2 _~ ~ 1 ='~
(a) c o u n t e r elements ~ .
( ,'. ~ : ¢opn_~e,
', ': {1
22 o z la ~" Z O U
3. Small-angle scattering apparatus
14
The experimental setup is shown in fig. 5. Partially o' 1 p-
10
3 >.4
r~ m
(b)
Ill I-ey
2 O Z
O
i
i
I
i
I
i
1
2
3
4
5
6
i
i
7 8 counter
i
I
9
10
elements
Fig. 3. Pulse-height d i s t r i b u t i o n for a nearly u n i f o r m flux of 3 MeV neutrons.
I
I
I
I
1
2
3
4
5
6
i
i
i
i
7
8
9
10
Fig. 4. Pulse-height di s t ri but i ons for 3 MeV neutrons from the D (d,n) reaction: (a) a nearly u n i f o r m n e u t r o n di s t ri but i on with a slab of paraffin interposed; (b) first c ount e r element near the n e u t r o n source. Circles are e xpe ri me nt a l data. The curves are the profiles expected from the geometry of the system. The da t a points plotted as " s t a r s " are from a m e a s u r e m e n t pe rforme d with a stilbene scintillator.
486
v. GIORDANO et al.
the neutron beam indicates an angular divergence in the horizontal plane of ,-~ 1.3 °. The neutron scatterer is at a distance of 80.8 cm from the neutron source. The scattering sample is a cylinder, positioned with its symmetry axis parallel to the neutron beam: all neutrons leaving the collimator are intercepted by the scatterer. Scattered neutrons are detected by the positionsensitive scintillator, at 227 cm from the scattering sample. Owing to the possible use of the system as a
neutron polarimeter, the scintillator is symmetrically disposed with respect to the neutron beam direction in the horizontal plane. In order to achieve a shieldedsource geometry, the scintillator is mounted above the reaction plane, the minimum scattering angle being determined only by a practical compromise with the requirements of the exit beam profile. The spectrometer is free to rotate about a centre pivot, so that the counter elements can be interchanged. A stilbene detector, at 390 cm from the'neutron source, is used to monitor the neutron yield][through the collimator.
/ 1°
2°
3 °
4°
5°
6 °
7°
8°
9 °
i 7°
i 8°
I 9°
10 °
5.2
T
\ ".'?':~.'...: :' -,...::. / ~"~ 4.8 Z 0
IU 4.4 I 09 0
5
U 4.0
angle
(degree)
C~ -- 0.1
--0.2 Z o
,~0.3 < .J o
0.4
--0.5
-- 0.6
1 = 1°
Fig. 5. Schematic d i a g r a m o f the experimental arrangement: (1) paraffin shield; (2) polyethylene shield; (3) b e a m ; (4) collim a t o r ; (5) n e u t r o n scatterer; (6) positional spectrometer; (7) stilbene scintillator; (8) cathetometer.
| 2 °
Fig. 6. Preliminary trons by Bi at 2.50 curve refers to a n the solid curve is
i 3 °
i 4 °
i 5 °
i 6 °
0 1 o
results from small-angle scattering o f neuMeV. (a) Differential cross-sections: the solid optical model calculation. (b) Polarizations: calculated from the formulae o f Schwinger.
POSITION-DETERMINING
Absolute cross-sections can be measured by comparison of the scattered flux with the incident flux at the scatterer position, as deduced from the monitor data. 4. Measurements
In order to evaluate the validity of the technique described in this paper, the absolute values of the differential cross-section and the polarization of neutrons elastically scattered by Bi have been measured at 2.50 MeV. The results are shown in fig. 6, where the assigned standard deviations include, in addition to counting statistics, other sources of uncertainties: specifically, uncertainties in the time resolution corrections. Measured cross-sections are compared with calculations based on a scattering potential that includes only the terms due to nuclear and Schwinger interactions. Polarization data, obtained from the asymmetry in the scattering of neutrons to the right and to the left of the neutron beam, are compared with Schwinger's predictions. Although the experimental procedure was limited to an exemplification test, the agreement with the previous results 4) appears fairly good. The calculated differential cross-sections are systematically lower than the experimental ones: this effect was also observed at other energiesS).
SCINTILLATOR
487
In spite of the poor resolution, the position-determining scintillator described here proves helpful for a variety of applications, especially where a high detection efficiency combined with n-~ discrimination is of great importance. Results of theoretical considerations of the effect of transfer times in the scintillator 6) indicate that this is probably the limiting factor in obtainable time resolution. Research on the development of scintillators with very short transfer times, together with suitable properties for pulse shape discrimination, would be of great value for positional accuracy.
References J) R. B. Galloway and R. M. A. Maayouf, Nucl. Phys. A212 (1973) 182. 2) G. V. Anikin and I. I. Kotukhov, Yad. Fiz. 12 (1970) [English transl.: Sov. J. Nucl. Phys. 12 (1971) 614]. a) R. Fox, Nucl. Phys. 43 (1963) 110. 4) L. Drigo, C. Manduchi, G. Moschini, M. T. Russo-Manduchi, G. Tornielli and G. Zannoni, Nuovo Cimento 13A (1973) 867. s) F. T. Kuchnir, A. J. Elwin, J. E. Monahan, A. Langsdorf and F. P. Mooring, Phys. Rev. 176 (1968) 1405. 6) G. Present, A. Schwarzschild, I. Spirn and N. Wotherspoon, Nucl. Instr. and Meth. 31 (1964) 71.