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Three-photon coincidence and lifetime apparatus for positronium in gases
NUCLEAR
INSTRUMENTS
AND METHODS
37
0965) 51-57; © N O R T H - H O L L A N D
PUBLISHING
CO.
THREE-PHOTON COINCIDENCE AND LIFETIME APPARATUS FOR POS1TRONIUM IN GASES J. BELL, G. J. CELITANS, J. H. G R E E N and S. J. T A O
Department of Nuclear and Radiation Chemistry, University of New South Wales, Kensington, Sydney, Australia Received 1 May 1965 Three-photon coincidence equipment for studies on positron
annihilation in gases is described. The detectors are simple photomultipliers and plastic phosphors which provide shorter pulses and smaller resolving time than NaI phosphors. Side1. Introduction Positronium can be detected by several methods, the determination of positron lifetimes being the one most widely used. Free positron and positronium annihilations can be distinguished in this method by the differences in their annihilation lifetimes. The free annihilation lifetime in gases, in general, is proportional to the density of the annihilating medium and is about 200 ns at 1 atm and 10 ns at 20 atm. Orthoand para-positronium on the other hand, have the definite mean lifetimes of 140 ns and 0.125 ns respectively. However, the most direct way to study positronium is to detect the three photons from orthopositronium annihilations in triple coincidence. The ratio of the number of 3-photon to 2-photon events of the spin averaged free positron annihilations is 1/372. If positronium is formed, this ratio will approach the limit of 3/1 for 100 per cent positronium formations because of the 3 to 1 distribution of triplet to singlet positronium. However, quenching of triplet positronium (ortho) into its singlet (para) state takes place when o-positronium collides with atoms or molecules in a medium. Quenching will reduce the ratio of 3-photon to 2photon events and also the lifetime of the o-positronium. In ordinary gases at low or moderate pressures the quenching effect is not very great, but in condensed materials, especially in metals because of the presence of free electrons, the quenching effect may be quite significant. In the early days, because of the limitation of the resolving time ( ~ l0 ns) in coincidence techniques, the methods used in studying positronium formation were mainly triple coincidence and delayed coincidence 1-3). After the development of fast time-to-amplitude converter*) and multichannel analyzers, the work has been shifted nearly entirely to very short lifetime determinations. Only a few papers in the last few years have described triple annihilation coincidence and long lifetime ( > 100 ns) determinationsS-7). This paper
channel analyzers were incorporated to handle these shorter pukes. Equipment for associated studies of positron lifetime is also described. The range is 360 ns with a resolution of 3.5 ns.
describes the triple-coincidence and long lifetime measuring instruments used by us in the study of positronium formation in gases and of the "shoulder" in the lifetime diagrams for positron annihilation in gasesS-ll). 2. Three photon coincidence The double coincidence method of studying 2-photon annihilation is quite simple, not only because of the simple construction of the coincidence apparatus but also because of the high coincidence rate obtained from a relatively weak source. However, double coincidence normally is only used in determinations of the angular distribution of the two-photon annihilation events. It is seldom used to determine the extent of positronium formation because the relatively small change of the total 2-photon annihilation rate is masked by free positron annihilation. In general, 3-photon coincidence is preferred. The extension of the coincidence method to threephoton annihilations, however, introduces more difficulties. In the case of 2-photon annihilations, energy momentum conservation requires that two y-rays are emitted in very nearly opposite directions. In the case of 3-photon annihilations, momentum conservation requires only that the y-rays are emitted in the same plane and that no more than two are emitted in the same half-plane, This means that with the same intensity of 2-photon and 3-photon annihilation events as measured by 180° 2-photon coincidence and coplanar 3-photon coincidence, respectively, the detection rate of 3-photon events will be far less than that of the 2-photon events. In practice, a source of relatively high strength ( ~ 0.1 mCur) must be used to provide reasonable statistics in a short time. An expression for the triple coincidence rate due to triplet annihilation has been derived by Benedetti and Siegelt2). From his derivation the real triple coincidence rate is proportional to the source strength and independent of resolving time, 51
52
J. BELL et al.
but the random triple coincidence rate is approximately proportional to the cube of the source strength and the square of the resolving time. Obviously, in order to maintain a high signal to noise ratio (true to random coincidences), with a high counting rate, the resolving time must be kept as low as possible.
/
,,,,,?io
\
The apparatus is shown in block diagram form in fig. 2. An E. H. Research Laboratories type 101N coincidence unit, having an ultimate resolution of about 3 ns, was used as the fast coincidence unit. The resolving time was adjusted to 10 ns by means of a clipping line. To operate the unit at this resolution the input required a negative pulse of at least 2 V and a minimum rate of rise of 0.25 V/ns. If photomultipliers of fast rise-time and high gain were available such as RCA 6810A, the 101N coincidence unit would be quite simply operated. However, we used the simpler E.M.I. 6097 B photomultiplier, operated at an E.H.T. of 1.8 kV. These gave a pulse height of about 1 V (137Cs source) and a rise-time of the order of 25 ns, with a transit time of about 10 ns which would hardly meet the requirement of the 101N coincidence unit. Therefore, high speed triggers with small jitter-Moody triggers 14) with minor modifications were used to match the output of the photomultipliers. A n additional pre-amplifier (E 180F) was found necessary, in order to obtain more stability. For maxim u m sensitivity, Moody et al. recommend an E F P 6 0 anode current of 20 mA, well in excess of the rating. Under these conditions, however, the secondary emission tubes did not maintain a stable gain for more than two weeks. By adding the E180F pre-amplifier the anode current could be decreased to about l0 mA and a fivefold increase in the life of the tubes resulted. The
Fig. I. Counter arrangement for the detection of three-photon annihilations. Z2Na was used as a source of positrons. The half-life (2.6 year) is sufficiently long to allow reasonable counting periods without source strength corrections. The positrons are emitted with an upper energy limit of 542 keVla). A 1.276 MeV gamma-ray from the daughter 22Ne released almost simultaneously with the positron, tends to contribute to the background of the three-photon intensity measurements. Three scintillation counters were arranged symmetrically about the source of positrons and co-planar with it (fig. 1). This arrangement simplifies the problem of coincidence detection since all three annihilation photons must now have approximately the same energy, i.e. ~ m c 2. The scintillators were 2" x 2" Naton 136 plastic phosphors (p-terphenylin polyvinyl toluene). These were surrounded by aluminium foil reflectors and optically coupled to the photomultipliers with paraffin oil. A n organic scintillator was chosen in preference to a sodium iodide crystal because of the much shorter decay time obtainable (2 to 3 x 10 -9 see).
PM
~,
P
" ~ "
P
coincidence 10 n sec
Moody trigger
-
coincidence
1
sec
I
3
analyzer 3
t Scaler B
I
Fig. 2. Block diagram of fast-s~owcoincidence system.
THREE-PHOTON
COINCIDENCE
pre-amplifier also isolated the coincidence circuit from the pulse height analysers. Stability was further improved by using two OA85 diodes in parallel instead of one in the circuit, thus increasing their rating. The rise-time of the output pulse was considerably decreased by passing the output signal through a biased diode. In this way, the initial slow-rising part of the wave-form was eliminated. The output of the triggers, which has a risetime of about 10 ns and a pulse height of 10 V was sufficient to operate the fast coincidence unit (fig. 3).
~+250V
÷3sO/
2"/OK
6~K
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.01
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I
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01
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.I
I0 I
82 360 n$
-~"
6AM6 E180F
3XOA85 EFP60
Fig. 3. Circuit diagram of pulse processing unit for triple coincidene:. It has been found that the above combination works satisfactorily provided that a high time stability is maintained. The high time stability has been achieved by regular checking and adjustment as indicated below. The main stability problem was in selecting suitable EFP60 valves, but once selected they were satisfactory for about three months. Obviously, the time resolution of the equipment depends greatly on variations of the input signal pulse height and the triggering level of the Moody triggers. Such variations will change the delay time of the Moody trigger output signal (to the 10IN coincidence unit) and consequently, the relative delay between the three channels. This delay must be kept as small as possible ( < 10 ns) over the range of desired P.M. output voltages. With the aid of a nanosecond double-pulse generator and a dualtrace oscilloscope, it was possible to adjust the gain and discriminator bias on each trigger so that
AND
LIFETIME
APPARATUS
53
the leading edges of any pair of output waveforms would coincide, when the input amplitude was varied between the limits of 0.2 and 0.6 V. Of course, this could only be done with selected EFP60 tubes. The transit-time differences in the three photomultipliers were eliminated by using delay cables before the Moody triggers. The three pulse-height analyzers in the side channels were also based on Moody triggers. The operation of the analyzers is illustrated in block diagram form in fig. 3. Negative pulses from the anode of a photo-multiplier are taken to both the low energy discriminator (top) and the high energy discriminator (bottom). If a pulse enters the analyser with a pulseheight between the levels of the two-discriminators, it will trigger only the low energy discriminator; the positive spike of the differentiated pulse will then fire the output Moody trigger, however, if a large enough pulse triggers both discriminators, no positive spike results on the addition of the two wave-forms and consequently the outputtrigger does not produce a pulse. The advantages of this pulse-height analyser are its simplicity and its ability to handle the P.M. anode pulses directly. However, because of its simple construction, the 1 dB long term stability of the discriminator is not very high compared with some commercial analysers. For our purpose, this was not a very great drawback because regular calibration checks were made and also because of the somewhat diffuse spectrum of photomultiplier output pulses. The pulse height analyzers were calibrated by obtaining pulse height spectra from the individual scintillator-photomultiplier combinations for 131I (364 keV Compton edge), ta7Cs (662 keV) and 22Na (510 keV). Only the low energy discriminators in the analysers were used and, despite the fact that the plastic crystals do not have the resolution of NaI crystals, quite definite Compton edges were obtained for the three gamma-rays. The upper and lower energy discriminators were then set to correspond to 450 keV and 100 keV, respectively. The system was completed by a quadruple coincidence unit of approximately one #s resolving time. A separate scaling pulse generator allows the monitoring of individual channels. The output of the quadrupole coincidence unit is registered by scaler B and represents the triple-coincidence rate with time and energy selection. A fast scaler A, having a 5 #s dead-time, is used for checking purposes. 3. Positron lifetime method
Positronium formation in gases may be investigated
54
J. B E L L et
by the m e t h o & o f positron lifetime measurements, as introduced by Deutsch15). In this method 22N is used as a source from which a positron and a gamma-ray are emitted simultaneously (within 10 -11 sec). If a scintillation counter is arranged to detect this photon, the resulting output pulse from the photomultiplier serves as a zero time indicator. When the positron ends its life in annihilation, more gamma-rays are produced of maximum energy 510 keV. If one of these is detected by another scintillation counter, the time between the first photomultiplier pulse and the second represents the lifetime of the positron. Since the time intervals between these pulses are very short, they are most conveniently measured electronically by a time-to-pulse height converter.
al.
"pulse overlap principle"16). The block diagram of the converter and associated equipment is shown in fig. 4. This is a method widely adopted in constructing a timeto-amplitude converter of very short range ( ~ 20 ns). For such a short range the construction is relatively simple and very high resolutions can be achieved. However, for a range of several hundreds of ns, some difficulties arise. Square pulses of sufficient amplitude and stable width as long as the whole range of the timeto-amplitude converter are required, i.e. > 300 ns.
L
~
3.1. EXPERIMENTAL ARRANGEMENT
The RCA 6810-A photomultipliers used in this system have been specially designed for fast coincidence application. The transit-time spread is about 2 ns (RCA Data) and the overall gain is sufficiently high to allow the use of limiters. The dynode system was arranged according to distribution " A " recommended by RCA for high gain and fast rising pulses. The photomultipliers were optically coupled with paraffin oil directly to 1½" x 2" long plastic phosphors (Naton 136), these being in turn surrounded by aluminium foil to act as reflectors. The foil was continued round the whole length of the tube to act as an electrostatic shield, the whole being kept at cathode potential, as recommended by RCA, to reduce the overall noise level. The crystal-photomultiplier assembly was then made light-tight by wrapping it in black plastic insulating tape. A positron source of low activity (approx. 5 pC) was required in order to obtain a reasonable signal to background ratio. In addition, if the source strength exceeds a certain limit, pile-up may occur because the total range of the instrument has to be at least 300 ns for lifetime measurements in gases. The source was positioned at the centre of a small cylinder, 3" dia. x 4" long, made of x" a aluminium alloy. The source was deposited on a very thin mica sheet ( ~ 2 mg/cm2). An approximate calculation indicated that not more than 1 ~o of positrons would annihilate in the sourceholder. The two photomultipliers were placed on opposite sides of the cylinder in contact with the walls with the source off the centre line. This arrangement gave the maximum possible solid angle and thus offset the low activity of the positron source. The tithe-to-amplitude converter was based on the
C-]
Fig. 4. Block diagram of time-analyser. Ordinary limiters are not very suitable because their outputs cannot meet this requirement very easily. Consequently, we turned to fast triggers. The Moody trigger can provide a reasonably square negative pulse of fast rise-time ( ~ 10 ns) sufficiently long width and high amplitude ( ~ 10 V) which, after application to a suitable limiter tube provides a fairly good pulse for coincidence work. Because the long term stability of the duration of the output pulse of the Moody trigger is not good enough to give a resolving time of nanosecond order, clipping lines were used to determine the pulse length. Incorporating the converter with an ND120 multi-channel analyser a resolving time of better than 4 ns was achieved. The circuit of the square pulse processing unit is shown in fig. 5. The square pulses produced are not ideal in shape (the amplitude of the leading part being slightly higher than that of the falling part) and so a converter insensitive to input amplitude is required to give a linear
THREE-PHOTON COINCIDENCE AND LIFETIME APPARATUS 1K
3gK 2W 10 K 2W
2K
,oo
7
1 _ ~ 4 71~ -150V
I1OK
5K 5W ~ +300V
1K
15K
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In~
55
12
__01~4.7K - ~ O V
6BN6
100 6AG 5
6BQ
Fig. 5. Circuit diagram of square pulse processing unit for converter. response of time-to-pulse height. The converter used is similar in principle to that reported by Neilson and James17). The two control grids of the 6BN6 gatedbeam tube are normally biased to cut off. It therefore requires signals (square pulses) from both photomultiplier A (which detects the 1.28 MeV nuclear gamma-rays) and photomultiplier B (which detects the annihilation gamma-rays) to produce an amplitude limited pulse. The duration of the pulse is equal to the overlap time of the square A and B pulses. The 6BN6 output pulse duration in turn determines the pulse height from a ramp generator (6AG5) thus producing timeto-amplitude conversion. The output of the 6BN6 valve depends mainly on the duration of the overlap of the two pulses on the control grids and is not very sensitive to the variation of the amplitude of the pulses on the grids. Therefore, a fairly linear relationship between the time and the amplitude of the output of the converter can be achieved. The whole range of the converter is readily altered simply by replacing the clipping and delay lines with others of different lengths. Normally, it was operated at a whole range of about 360 ns. Energy discrimination side channels are required in order to define the initial pulse (1.28 MeV ),-rays) and the final pulse (annihilation y-rays) and to reduce the random coincidence rate. A simple fast discriminator is used here. EFP60 pre-amplifiers are used instead of conventional pentodes in order to maintain the same polarity on amplification (the output is taken from the dynode of the EFP60 tube) and Moody triggers are used as fast discriminators. The discriminator level on channel A was set to correspond to an energy of 600 keV (calibrated with 662 keY 137Cs gamma-rays); channel B was set at about 100 keV. The latter setting is not critical; the discriminator was used merely to limit the photomultiplier noise.
The side-channels were combined in triple coincidence (0.75 ps resolving time) with the output of the double coincidence of the converter section to produce a gate pulse for the multi-channel analyser. The output of the triple coincidence section also operated a scaling pulse generator, which could be switched to either channel A or B, double or triple coincidence. 3.2. CALIBRATION OF THE CONVERTER
The converter was calibrated with a nanosecond double-pulse generator and a Tektronix 541 oscilloscope, containing the type CA dual-trace pre-amplifier. With the exception of the two photomultipliers, the complete system was used in the calibration procedure. Negative pulses from the generator were fed to the converter section, while positive signals of lower voltage were admitted to the energy discriminator side-channels. The converter output, plus the gate pulse, was connected to the 512-channel analyser; good resolution was obtained by using only 256 channels for a single determination. The relative delay between the two converter channels was very stable; this was indicated by the fact that no more than two channels recorded counts for a given delay setting. The calibration error was then virtually due to reading the relative delay on the 5" dia. oscilloscope screen. The converter calibration is shown in fig. 6 the relation between delay and pulse height being linear from 0 to 300 ns. A slightly steeper slope is observed from about - 4 0 ns to 0 and the proportionality ends abruptly above 300 ns when maximum overlap of the two square wave-forms is exceeded. Stability of the converter-analyser system was found to be very good, a drift of not more than one channel (in 256) being observed from day to day. When the complete system, including photomultipliers, is used for actual lifetime determinations, the
56
J. BELL et al.
300
~J
c~°2 0 0
# 1~o 0
-50
50
100 150 Channel n u m b e r
200
i
250
Fig. 6. Calibration of the time-analyser.Small circles:calibration with double pulse generator. Large circles: delay cables. slightly different .form of the detector pulses may alter the calibration somewhat. In order to check this possibility, calibrated lengths of delay cables (Telcon PT 29M) were inserted in channel B and the shift of the prompt resolution peak measured. An aluminiumsodium-22 sandwich source was used for this purpose. No significant deviation from the calibration curve was observed for the specific delay cables used (fig. 6). 3.3. PERFORMANCE AND RESULTS The overall detection efficiency for the ~ m c 2 gammarays was estimated to be 0.30 4-0.15 by two independent methods. The performance of the triplecoincidence equipment was then tested by measuring the three-photon intensity in aluminium, where~ as in other metals, the three- to two-photon annihilation events are in the ratio 1/371 and also in Teflon. Preliminary results are reported here. A~"positron source, equivalent to 100___ 7 pC of 22Na; was sandwiched between two T~ i - thick sheets of aluminium or Teflon and positioned at the centre of the detector arrangement, as shown in fig. 1. Lead collimators were used to reduce counter-to-counter scattering, because this adds much to the random coincidence rate. The random coincidence rate was measured by tilting one of the detectors 45 ° out of the common plane maintaining the same source-to-crystal distance. Reproducibility between different runs is quite good for the total and random coincidence rates, although more consistency is observed for the net coincidence rate. The combined rates in aluminium and Teflon were:
Aluminium teflon
Total rate
Random rate
Net coinc, rate
5.36 _+ 0.06 9.35 + 0.07
3.43 ___0.06 3.72 + 0.05
1.95 _+0.09 5.63 + 0.09
(All rates are counts/ksec)
These results gave a Teflon/aluminium ratio of 2.92 ___ 0.15 for the three-photon annihilation intensity. This ratio may be compared with those determined by Graham and Stewart18), (3.4+0.9), by Telegdi et alJ9), (3.08 _ 0.15) and by de Benedetti and SiegeP2), (1.94 + 0.21). Measurements of the three-photon intensity in aluminium showed that a triple coincidence rate could be obtained above that of the random rate. Since this can be done in aluminium, where the fraction of positrons annihilating with three-photon emission is only 1/371, then it is a simple matter to measure the formation of ortho-positronium in gases, or other media, where the probability is ¼f, f being the formation fraction and ¼ the fraction of positronium atoms annihilating with three-photon emission. The same apparatus can also be used to measure double coincidence rates, positron lifetimes and pulse height spectra. Angular correlation measurements of two-photon events are also possible if special collimators are used. Recently, the equipment was used by Celitans and Green ~°) to determine the range distribution of 22Na positrons in argon and nitrogen and the positronium formation in gases ~1). With the lifetime apparatus and using a 6°Co source, the full width at half height of the prompt peak (W~) is about 3.0 ns and the peak-to-background ratio is about 4000 to 1. Although the value of W~ cannot be compared with the performance of fast converters of short whole range, it is sufficiently high to discover the existence of a shoulder in the lifetime diagram of positrons in argong). If the resolving time (W~) was greater than about 6 ns the shoulder would be smeared into the prompt peak and could hardly be detected. This research was assisted by the United States Air Force Office of Scientific Research Grant no. 62-398.
References t) M. Deutsch, Progr. in Nucl. Phys. 3 (1953) 131. 2) S. de Benedetti and H. C. Corben, Ann Rev. of Nucl. Sci. 4 (1954) 191. 3) j. H. Green and J. W. Lee, Positronium Chemistry (Academic Press, N. Y., 1964). 4) R. E. Green and R. E. Bell, Nucl. Instr. 3 (1958) 127. 5) D. C. Liu and W. K. Roberts, Phys. Rev. 130 (1963) 2322. 6) D. A. L. Paul and L. Saint-Pierre, Phys. Rev. Lett. 11 (1963) 493. 7) V. I. Goldanskii, O. A. Karpukhin and G. G. Petrov, Zhur. Eksp. Teor. Fiz. 39 (1960) 1477. s) S. J. Tao and J. H. Green, J. Chem. Phys. 39 (1963) 3160. 9) S. J. Tao, J. Bell and J. H. Green, Proc. Phys. Soc. (Lond.) 83 (1964) 435. 10) G. J. Celitans, S. J. Tao and J. H. Green, Proc. Phys. Soc. (Lond.) 83 (1964) 833.
T H R E E - P H O T O N C O I N C I D E N C E AND LIFETIME APPARATUS ix) G. J, Celitans and J. H. Green, Proc. Phys. Soc. 83 (1964) 823. 12) S. de Benedetti and R. Siegel, Phys. Rev. 94 (1954) 955. 13) B. T. Wright, Phys. Rev. 90 (1953) 159. 14) N. F. Moody, G. J. R. Maclusky and M. O. Deighton, Electronic Eng. 24 (1952) 214. 15) M. Deutsch, Phys. Rev. 82 (1951) 455 and 83 (1951) 866. 16) M. Bonitz, Nucl. Instr. and Meth. 22 (1963) 238.
57
17) G. C. N¢ilson and D. B. James, Roy. Sci. Instr. 26 (1955) 1018. 18) R. L. Graham and A. T. Stewart, Can. J. Phys. 32 (1954) 678. 19) y. L. Telcgdi, J. C. Sens, D. D. Yovanovitch and S. D. Warshaw, Phys. Rev. 104 (1956) 867. 2o) (3. J. Cclitans and J. H. Green, Proc. Phys. Soc. 82 (1963) 1002.
INSTRUMENTS
AND METHODS
37
0965) 51-57; © N O R T H - H O L L A N D
PUBLISHING
CO.
THREE-PHOTON COINCIDENCE AND LIFETIME APPARATUS FOR POS1TRONIUM IN GASES J. BELL, G. J. CELITANS, J. H. G R E E N and S. J. T A O
Department of Nuclear and Radiation Chemistry, University of New South Wales, Kensington, Sydney, Australia Received 1 May 1965 Three-photon coincidence equipment for studies on positron
annihilation in gases is described. The detectors are simple photomultipliers and plastic phosphors which provide shorter pulses and smaller resolving time than NaI phosphors. Side1. Introduction Positronium can be detected by several methods, the determination of positron lifetimes being the one most widely used. Free positron and positronium annihilations can be distinguished in this method by the differences in their annihilation lifetimes. The free annihilation lifetime in gases, in general, is proportional to the density of the annihilating medium and is about 200 ns at 1 atm and 10 ns at 20 atm. Orthoand para-positronium on the other hand, have the definite mean lifetimes of 140 ns and 0.125 ns respectively. However, the most direct way to study positronium is to detect the three photons from orthopositronium annihilations in triple coincidence. The ratio of the number of 3-photon to 2-photon events of the spin averaged free positron annihilations is 1/372. If positronium is formed, this ratio will approach the limit of 3/1 for 100 per cent positronium formations because of the 3 to 1 distribution of triplet to singlet positronium. However, quenching of triplet positronium (ortho) into its singlet (para) state takes place when o-positronium collides with atoms or molecules in a medium. Quenching will reduce the ratio of 3-photon to 2photon events and also the lifetime of the o-positronium. In ordinary gases at low or moderate pressures the quenching effect is not very great, but in condensed materials, especially in metals because of the presence of free electrons, the quenching effect may be quite significant. In the early days, because of the limitation of the resolving time ( ~ l0 ns) in coincidence techniques, the methods used in studying positronium formation were mainly triple coincidence and delayed coincidence 1-3). After the development of fast time-to-amplitude converter*) and multichannel analyzers, the work has been shifted nearly entirely to very short lifetime determinations. Only a few papers in the last few years have described triple annihilation coincidence and long lifetime ( > 100 ns) determinationsS-7). This paper
channel analyzers were incorporated to handle these shorter pukes. Equipment for associated studies of positron lifetime is also described. The range is 360 ns with a resolution of 3.5 ns.
describes the triple-coincidence and long lifetime measuring instruments used by us in the study of positronium formation in gases and of the "shoulder" in the lifetime diagrams for positron annihilation in gasesS-ll). 2. Three photon coincidence The double coincidence method of studying 2-photon annihilation is quite simple, not only because of the simple construction of the coincidence apparatus but also because of the high coincidence rate obtained from a relatively weak source. However, double coincidence normally is only used in determinations of the angular distribution of the two-photon annihilation events. It is seldom used to determine the extent of positronium formation because the relatively small change of the total 2-photon annihilation rate is masked by free positron annihilation. In general, 3-photon coincidence is preferred. The extension of the coincidence method to threephoton annihilations, however, introduces more difficulties. In the case of 2-photon annihilations, energy momentum conservation requires that two y-rays are emitted in very nearly opposite directions. In the case of 3-photon annihilations, momentum conservation requires only that the y-rays are emitted in the same plane and that no more than two are emitted in the same half-plane, This means that with the same intensity of 2-photon and 3-photon annihilation events as measured by 180° 2-photon coincidence and coplanar 3-photon coincidence, respectively, the detection rate of 3-photon events will be far less than that of the 2-photon events. In practice, a source of relatively high strength ( ~ 0.1 mCur) must be used to provide reasonable statistics in a short time. An expression for the triple coincidence rate due to triplet annihilation has been derived by Benedetti and Siegelt2). From his derivation the real triple coincidence rate is proportional to the source strength and independent of resolving time, 51
52
J. BELL et al.
but the random triple coincidence rate is approximately proportional to the cube of the source strength and the square of the resolving time. Obviously, in order to maintain a high signal to noise ratio (true to random coincidences), with a high counting rate, the resolving time must be kept as low as possible.
/
,,,,,?io
\
The apparatus is shown in block diagram form in fig. 2. An E. H. Research Laboratories type 101N coincidence unit, having an ultimate resolution of about 3 ns, was used as the fast coincidence unit. The resolving time was adjusted to 10 ns by means of a clipping line. To operate the unit at this resolution the input required a negative pulse of at least 2 V and a minimum rate of rise of 0.25 V/ns. If photomultipliers of fast rise-time and high gain were available such as RCA 6810A, the 101N coincidence unit would be quite simply operated. However, we used the simpler E.M.I. 6097 B photomultiplier, operated at an E.H.T. of 1.8 kV. These gave a pulse height of about 1 V (137Cs source) and a rise-time of the order of 25 ns, with a transit time of about 10 ns which would hardly meet the requirement of the 101N coincidence unit. Therefore, high speed triggers with small jitter-Moody triggers 14) with minor modifications were used to match the output of the photomultipliers. A n additional pre-amplifier (E 180F) was found necessary, in order to obtain more stability. For maxim u m sensitivity, Moody et al. recommend an E F P 6 0 anode current of 20 mA, well in excess of the rating. Under these conditions, however, the secondary emission tubes did not maintain a stable gain for more than two weeks. By adding the E180F pre-amplifier the anode current could be decreased to about l0 mA and a fivefold increase in the life of the tubes resulted. The
Fig. I. Counter arrangement for the detection of three-photon annihilations. Z2Na was used as a source of positrons. The half-life (2.6 year) is sufficiently long to allow reasonable counting periods without source strength corrections. The positrons are emitted with an upper energy limit of 542 keVla). A 1.276 MeV gamma-ray from the daughter 22Ne released almost simultaneously with the positron, tends to contribute to the background of the three-photon intensity measurements. Three scintillation counters were arranged symmetrically about the source of positrons and co-planar with it (fig. 1). This arrangement simplifies the problem of coincidence detection since all three annihilation photons must now have approximately the same energy, i.e. ~ m c 2. The scintillators were 2" x 2" Naton 136 plastic phosphors (p-terphenylin polyvinyl toluene). These were surrounded by aluminium foil reflectors and optically coupled to the photomultipliers with paraffin oil. A n organic scintillator was chosen in preference to a sodium iodide crystal because of the much shorter decay time obtainable (2 to 3 x 10 -9 see).
PM
~,
P
" ~ "
P
coincidence 10 n sec
Moody trigger
-
coincidence
1
sec
I
3
analyzer 3
t Scaler B
I
Fig. 2. Block diagram of fast-s~owcoincidence system.
THREE-PHOTON
COINCIDENCE
pre-amplifier also isolated the coincidence circuit from the pulse height analysers. Stability was further improved by using two OA85 diodes in parallel instead of one in the circuit, thus increasing their rating. The rise-time of the output pulse was considerably decreased by passing the output signal through a biased diode. In this way, the initial slow-rising part of the wave-form was eliminated. The output of the triggers, which has a risetime of about 10 ns and a pulse height of 10 V was sufficient to operate the fast coincidence unit (fig. 3).
~+250V
÷3sO/
2"/OK
6~K
lO-q~K IK .01
.01
~_~
2.SK~ ~ 0
-IsoV
I
I IK ~[
÷l~
01
~8
.I
I0 I
82 360 n$
-~"
6AM6 E180F
3XOA85 EFP60
Fig. 3. Circuit diagram of pulse processing unit for triple coincidene:. It has been found that the above combination works satisfactorily provided that a high time stability is maintained. The high time stability has been achieved by regular checking and adjustment as indicated below. The main stability problem was in selecting suitable EFP60 valves, but once selected they were satisfactory for about three months. Obviously, the time resolution of the equipment depends greatly on variations of the input signal pulse height and the triggering level of the Moody triggers. Such variations will change the delay time of the Moody trigger output signal (to the 10IN coincidence unit) and consequently, the relative delay between the three channels. This delay must be kept as small as possible ( < 10 ns) over the range of desired P.M. output voltages. With the aid of a nanosecond double-pulse generator and a dualtrace oscilloscope, it was possible to adjust the gain and discriminator bias on each trigger so that
AND
LIFETIME
APPARATUS
53
the leading edges of any pair of output waveforms would coincide, when the input amplitude was varied between the limits of 0.2 and 0.6 V. Of course, this could only be done with selected EFP60 tubes. The transit-time differences in the three photomultipliers were eliminated by using delay cables before the Moody triggers. The three pulse-height analyzers in the side channels were also based on Moody triggers. The operation of the analyzers is illustrated in block diagram form in fig. 3. Negative pulses from the anode of a photo-multiplier are taken to both the low energy discriminator (top) and the high energy discriminator (bottom). If a pulse enters the analyser with a pulseheight between the levels of the two-discriminators, it will trigger only the low energy discriminator; the positive spike of the differentiated pulse will then fire the output Moody trigger, however, if a large enough pulse triggers both discriminators, no positive spike results on the addition of the two wave-forms and consequently the outputtrigger does not produce a pulse. The advantages of this pulse-height analyser are its simplicity and its ability to handle the P.M. anode pulses directly. However, because of its simple construction, the 1 dB long term stability of the discriminator is not very high compared with some commercial analysers. For our purpose, this was not a very great drawback because regular calibration checks were made and also because of the somewhat diffuse spectrum of photomultiplier output pulses. The pulse height analyzers were calibrated by obtaining pulse height spectra from the individual scintillator-photomultiplier combinations for 131I (364 keV Compton edge), ta7Cs (662 keV) and 22Na (510 keV). Only the low energy discriminators in the analysers were used and, despite the fact that the plastic crystals do not have the resolution of NaI crystals, quite definite Compton edges were obtained for the three gamma-rays. The upper and lower energy discriminators were then set to correspond to 450 keV and 100 keV, respectively. The system was completed by a quadruple coincidence unit of approximately one #s resolving time. A separate scaling pulse generator allows the monitoring of individual channels. The output of the quadrupole coincidence unit is registered by scaler B and represents the triple-coincidence rate with time and energy selection. A fast scaler A, having a 5 #s dead-time, is used for checking purposes. 3. Positron lifetime method
Positronium formation in gases may be investigated
54
J. B E L L et
by the m e t h o & o f positron lifetime measurements, as introduced by Deutsch15). In this method 22N is used as a source from which a positron and a gamma-ray are emitted simultaneously (within 10 -11 sec). If a scintillation counter is arranged to detect this photon, the resulting output pulse from the photomultiplier serves as a zero time indicator. When the positron ends its life in annihilation, more gamma-rays are produced of maximum energy 510 keV. If one of these is detected by another scintillation counter, the time between the first photomultiplier pulse and the second represents the lifetime of the positron. Since the time intervals between these pulses are very short, they are most conveniently measured electronically by a time-to-pulse height converter.
al.
"pulse overlap principle"16). The block diagram of the converter and associated equipment is shown in fig. 4. This is a method widely adopted in constructing a timeto-amplitude converter of very short range ( ~ 20 ns). For such a short range the construction is relatively simple and very high resolutions can be achieved. However, for a range of several hundreds of ns, some difficulties arise. Square pulses of sufficient amplitude and stable width as long as the whole range of the timeto-amplitude converter are required, i.e. > 300 ns.
L
~
3.1. EXPERIMENTAL ARRANGEMENT
The RCA 6810-A photomultipliers used in this system have been specially designed for fast coincidence application. The transit-time spread is about 2 ns (RCA Data) and the overall gain is sufficiently high to allow the use of limiters. The dynode system was arranged according to distribution " A " recommended by RCA for high gain and fast rising pulses. The photomultipliers were optically coupled with paraffin oil directly to 1½" x 2" long plastic phosphors (Naton 136), these being in turn surrounded by aluminium foil to act as reflectors. The foil was continued round the whole length of the tube to act as an electrostatic shield, the whole being kept at cathode potential, as recommended by RCA, to reduce the overall noise level. The crystal-photomultiplier assembly was then made light-tight by wrapping it in black plastic insulating tape. A positron source of low activity (approx. 5 pC) was required in order to obtain a reasonable signal to background ratio. In addition, if the source strength exceeds a certain limit, pile-up may occur because the total range of the instrument has to be at least 300 ns for lifetime measurements in gases. The source was positioned at the centre of a small cylinder, 3" dia. x 4" long, made of x" a aluminium alloy. The source was deposited on a very thin mica sheet ( ~ 2 mg/cm2). An approximate calculation indicated that not more than 1 ~o of positrons would annihilate in the sourceholder. The two photomultipliers were placed on opposite sides of the cylinder in contact with the walls with the source off the centre line. This arrangement gave the maximum possible solid angle and thus offset the low activity of the positron source. The tithe-to-amplitude converter was based on the
C-]
Fig. 4. Block diagram of time-analyser. Ordinary limiters are not very suitable because their outputs cannot meet this requirement very easily. Consequently, we turned to fast triggers. The Moody trigger can provide a reasonably square negative pulse of fast rise-time ( ~ 10 ns) sufficiently long width and high amplitude ( ~ 10 V) which, after application to a suitable limiter tube provides a fairly good pulse for coincidence work. Because the long term stability of the duration of the output pulse of the Moody trigger is not good enough to give a resolving time of nanosecond order, clipping lines were used to determine the pulse length. Incorporating the converter with an ND120 multi-channel analyser a resolving time of better than 4 ns was achieved. The circuit of the square pulse processing unit is shown in fig. 5. The square pulses produced are not ideal in shape (the amplitude of the leading part being slightly higher than that of the falling part) and so a converter insensitive to input amplitude is required to give a linear
THREE-PHOTON COINCIDENCE AND LIFETIME APPARATUS 1K
3gK 2W 10 K 2W
2K
,oo
7
1 _ ~ 4 71~ -150V
I1OK
5K 5W ~ +300V
1K
15K
Iro AAZ
In~
55
12
__01~4.7K - ~ O V
6BN6
100 6AG 5
6BQ
Fig. 5. Circuit diagram of square pulse processing unit for converter. response of time-to-pulse height. The converter used is similar in principle to that reported by Neilson and James17). The two control grids of the 6BN6 gatedbeam tube are normally biased to cut off. It therefore requires signals (square pulses) from both photomultiplier A (which detects the 1.28 MeV nuclear gamma-rays) and photomultiplier B (which detects the annihilation gamma-rays) to produce an amplitude limited pulse. The duration of the pulse is equal to the overlap time of the square A and B pulses. The 6BN6 output pulse duration in turn determines the pulse height from a ramp generator (6AG5) thus producing timeto-amplitude conversion. The output of the 6BN6 valve depends mainly on the duration of the overlap of the two pulses on the control grids and is not very sensitive to the variation of the amplitude of the pulses on the grids. Therefore, a fairly linear relationship between the time and the amplitude of the output of the converter can be achieved. The whole range of the converter is readily altered simply by replacing the clipping and delay lines with others of different lengths. Normally, it was operated at a whole range of about 360 ns. Energy discrimination side channels are required in order to define the initial pulse (1.28 MeV ),-rays) and the final pulse (annihilation y-rays) and to reduce the random coincidence rate. A simple fast discriminator is used here. EFP60 pre-amplifiers are used instead of conventional pentodes in order to maintain the same polarity on amplification (the output is taken from the dynode of the EFP60 tube) and Moody triggers are used as fast discriminators. The discriminator level on channel A was set to correspond to an energy of 600 keV (calibrated with 662 keY 137Cs gamma-rays); channel B was set at about 100 keV. The latter setting is not critical; the discriminator was used merely to limit the photomultiplier noise.
The side-channels were combined in triple coincidence (0.75 ps resolving time) with the output of the double coincidence of the converter section to produce a gate pulse for the multi-channel analyser. The output of the triple coincidence section also operated a scaling pulse generator, which could be switched to either channel A or B, double or triple coincidence. 3.2. CALIBRATION OF THE CONVERTER
The converter was calibrated with a nanosecond double-pulse generator and a Tektronix 541 oscilloscope, containing the type CA dual-trace pre-amplifier. With the exception of the two photomultipliers, the complete system was used in the calibration procedure. Negative pulses from the generator were fed to the converter section, while positive signals of lower voltage were admitted to the energy discriminator side-channels. The converter output, plus the gate pulse, was connected to the 512-channel analyser; good resolution was obtained by using only 256 channels for a single determination. The relative delay between the two converter channels was very stable; this was indicated by the fact that no more than two channels recorded counts for a given delay setting. The calibration error was then virtually due to reading the relative delay on the 5" dia. oscilloscope screen. The converter calibration is shown in fig. 6 the relation between delay and pulse height being linear from 0 to 300 ns. A slightly steeper slope is observed from about - 4 0 ns to 0 and the proportionality ends abruptly above 300 ns when maximum overlap of the two square wave-forms is exceeded. Stability of the converter-analyser system was found to be very good, a drift of not more than one channel (in 256) being observed from day to day. When the complete system, including photomultipliers, is used for actual lifetime determinations, the
56
J. BELL et al.
300
~J
c~°2 0 0
# 1~o 0
-50
50
100 150 Channel n u m b e r
200
i
250
Fig. 6. Calibration of the time-analyser.Small circles:calibration with double pulse generator. Large circles: delay cables. slightly different .form of the detector pulses may alter the calibration somewhat. In order to check this possibility, calibrated lengths of delay cables (Telcon PT 29M) were inserted in channel B and the shift of the prompt resolution peak measured. An aluminiumsodium-22 sandwich source was used for this purpose. No significant deviation from the calibration curve was observed for the specific delay cables used (fig. 6). 3.3. PERFORMANCE AND RESULTS The overall detection efficiency for the ~ m c 2 gammarays was estimated to be 0.30 4-0.15 by two independent methods. The performance of the triplecoincidence equipment was then tested by measuring the three-photon intensity in aluminium, where~ as in other metals, the three- to two-photon annihilation events are in the ratio 1/371 and also in Teflon. Preliminary results are reported here. A~"positron source, equivalent to 100___ 7 pC of 22Na; was sandwiched between two T~ i - thick sheets of aluminium or Teflon and positioned at the centre of the detector arrangement, as shown in fig. 1. Lead collimators were used to reduce counter-to-counter scattering, because this adds much to the random coincidence rate. The random coincidence rate was measured by tilting one of the detectors 45 ° out of the common plane maintaining the same source-to-crystal distance. Reproducibility between different runs is quite good for the total and random coincidence rates, although more consistency is observed for the net coincidence rate. The combined rates in aluminium and Teflon were:
Aluminium teflon
Total rate
Random rate
Net coinc, rate
5.36 _+ 0.06 9.35 + 0.07
3.43 ___0.06 3.72 + 0.05
1.95 _+0.09 5.63 + 0.09
(All rates are counts/ksec)
These results gave a Teflon/aluminium ratio of 2.92 ___ 0.15 for the three-photon annihilation intensity. This ratio may be compared with those determined by Graham and Stewart18), (3.4+0.9), by Telegdi et alJ9), (3.08 _ 0.15) and by de Benedetti and SiegeP2), (1.94 + 0.21). Measurements of the three-photon intensity in aluminium showed that a triple coincidence rate could be obtained above that of the random rate. Since this can be done in aluminium, where the fraction of positrons annihilating with three-photon emission is only 1/371, then it is a simple matter to measure the formation of ortho-positronium in gases, or other media, where the probability is ¼f, f being the formation fraction and ¼ the fraction of positronium atoms annihilating with three-photon emission. The same apparatus can also be used to measure double coincidence rates, positron lifetimes and pulse height spectra. Angular correlation measurements of two-photon events are also possible if special collimators are used. Recently, the equipment was used by Celitans and Green ~°) to determine the range distribution of 22Na positrons in argon and nitrogen and the positronium formation in gases ~1). With the lifetime apparatus and using a 6°Co source, the full width at half height of the prompt peak (W~) is about 3.0 ns and the peak-to-background ratio is about 4000 to 1. Although the value of W~ cannot be compared with the performance of fast converters of short whole range, it is sufficiently high to discover the existence of a shoulder in the lifetime diagram of positrons in argong). If the resolving time (W~) was greater than about 6 ns the shoulder would be smeared into the prompt peak and could hardly be detected. This research was assisted by the United States Air Force Office of Scientific Research Grant no. 62-398.
References t) M. Deutsch, Progr. in Nucl. Phys. 3 (1953) 131. 2) S. de Benedetti and H. C. Corben, Ann Rev. of Nucl. Sci. 4 (1954) 191. 3) j. H. Green and J. W. Lee, Positronium Chemistry (Academic Press, N. Y., 1964). 4) R. E. Green and R. E. Bell, Nucl. Instr. 3 (1958) 127. 5) D. C. Liu and W. K. Roberts, Phys. Rev. 130 (1963) 2322. 6) D. A. L. Paul and L. Saint-Pierre, Phys. Rev. Lett. 11 (1963) 493. 7) V. I. Goldanskii, O. A. Karpukhin and G. G. Petrov, Zhur. Eksp. Teor. Fiz. 39 (1960) 1477. s) S. J. Tao and J. H. Green, J. Chem. Phys. 39 (1963) 3160. 9) S. J. Tao, J. Bell and J. H. Green, Proc. Phys. Soc. (Lond.) 83 (1964) 435. 10) G. J. Celitans, S. J. Tao and J. H. Green, Proc. Phys. Soc. (Lond.) 83 (1964) 833.
T H R E E - P H O T O N C O I N C I D E N C E AND LIFETIME APPARATUS ix) G. J, Celitans and J. H. Green, Proc. Phys. Soc. 83 (1964) 823. 12) S. de Benedetti and R. Siegel, Phys. Rev. 94 (1954) 955. 13) B. T. Wright, Phys. Rev. 90 (1953) 159. 14) N. F. Moody, G. J. R. Maclusky and M. O. Deighton, Electronic Eng. 24 (1952) 214. 15) M. Deutsch, Phys. Rev. 82 (1951) 455 and 83 (1951) 866. 16) M. Bonitz, Nucl. Instr. and Meth. 22 (1963) 238.
57
17) G. C. N¢ilson and D. B. James, Roy. Sci. Instr. 26 (1955) 1018. 18) R. L. Graham and A. T. Stewart, Can. J. Phys. 32 (1954) 678. 19) y. L. Telcgdi, J. C. Sens, D. D. Yovanovitch and S. D. Warshaw, Phys. Rev. 104 (1956) 867. 2o) (3. J. Cclitans and J. H. Green, Proc. Phys. Soc. 82 (1963) 1002.