Optimization of NaI(Tl) detector performance in high “background” counting rate environments

Nuclear Instruments and Methods in Physics Research A292 (1990) 343-350 North-Holland

343

OPTIMIZATION OF Nal(Tt) DETECTOR PERFORMANCE IN HIGH "BACKGROUND" COUNTING RATE ENVIRONMENTS L. BONNET, M. FREDERIC, P. LELEÜX, I . LICOT and P. LIPNIK

Institut de Physique Nucléaire, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

Received 3 November 1989 and in revised form 23 February 1990

To deal with the high annihilation y background that accompanies a positron-emitting radioactive ion beam, the Nal(TI) response function is carefully matched to a charge-sensing analog-to-digital converter. More specifically, the detection of the 5 MeV l'-ray 13N + p --,140 + is optimized with respect to the annihilation y-rays which cause pileup . arising from the reaction 1f

l. Introduction

This paper reports on a system designed to detect 13N + p 140 + y reaction -* the 5 MeV y-rays from the in the presence cf an intense 0.5 MeV annihilation "background" . This capture reaction is studied using an accelerated radioactive '3 N ion beam . The 5 MeV -y-ray emitted - the signature of this reaction - must be detected in the presence of the 0.5 MeV background arising from the beam particles. Under typical experimental conditions, a 13 N beam of 1 particle nA (6 x l0 y N +/s) will deposit 10-5 of the beam particles close to the target, for various reasons (large-angle scattering by the target, beam halo on the target holder, etc.) ; the deposited 13 N will decay at a rate of 6 x 10 4 decays per second at saturation ; this rate is 10 4 times higher than that expected for the capture yield. Consequently, one will have to cope with a total event-to-signal ratio between 10 4 and 10 5 in the gamma detector . The detection system consists of six 3 in . x 3 in . Nal(TI) crystals . The electronic circuits of the photomultipliers are described in section 2 . Special care was taken to achieve amplification independent of the counting rate. Section 3 deals with general considerations concerning the time response of the Nal(TI) detectors, their energy resolution and the noise affecting the pulse shape. In section 4 the intrinsic pileup of 0.5 MeV -y-rays is studied; a rnmnrnmi-e has been found that maximizes the signal information while minimizing pileup events . The calculations are checked by measurements using positron emitter sources. In section 5 a data acquisition system in an event-by-event mode is discussed, the use of charge-sensing analog-to-digital converters (QDCs) for * Supported by an Interuniversity Research Grant from the Belgian Government .

Nal(TI) detectors is emphasized, and the application of this system to the detection of 8 MeV y-rays from the Y)14 N reaction is presented. 1 H(13C, 2. High-voltage divider and output circuits The basic purpose of a voltage divider is to keep all the voltages across the dynodes as constant as possible, in order to achieve a stable photomuitiplier (PM) gain versus counting rate . The original ohmic voltage divider was modified by providing (i) parallel capacitors to cope with sudden high-peak anode currents, (ii) additional power supply or high-voltage Zener dynodes and (iii) more recently, active dividers consisting of emitter follower transistors . All those improvements were previously limited to the last few dynodes [1-5]. The present layout, displayed in fig. 1 is designed for a 3 in . diameter, 12-stage Philips XP2312B PM, incorporating the following particular features : - Emitter follower transistors are used to stabilize the voltages of all the dynodes. The resistive divider impedance is greatly decreased, by the ß or the h F. factor of the transistors, which is typically 50 . - Particular care is paid to the photocathode-tofirst-dynode potential Vkd1, where the stability is controlled by a low-voltage Zener diode ZF6 in series with a transistor BF471 . The temperature dependence of these devices are opposite and matched in order to get a null dependence . (The prcvious use of a single high-voltage Zener diode gave serious trouble over long runs .) optimized e.g . versus the energy I'kdl can be varied and resolution of a -y-ray line, while keeping the total voltage constant . - The PM mean current is deceased by charging the anode and the last dynode with a high impedance (typically l or 2 kS2) which improves the stability by a

0168-9002/90/$03 .50 ` 1990 -- Elsevier Science Publishers B.V . (North-Hoiland)

L. Bonnet et al. / Optimization of NaI(T/) detector performance

2,2 nF

120 K

120 K

120 K

120 K

120 K

120 K

120

20K

120K

0

120 K

LED (HV on)

gmetal shield Fig. 1. Schematic view of an XP2312B photomultiplier base; all transistors are BF472, except TI (BF471) . TI is used in conjunction with the ZF6.2 low-voltage Zener diode to stabilize the photocathode-to-first-dynode voltage ; this voltage is adjustable for optimum resolution through the 47 K potentiometer. The diodes preventing overbias at the base of the transistors are 1N4146 . The dynode output is a logical one, the anode output is adapted to the 5011 transport line by an emitter follower (EF). factor at least of 20 with respect to the common 50 S1 by permitting to decrease the current in the tube. This implies that an emitter follower has to be included in the voltage divider housing . Apart from the features aiming at a better voltage and gain stability, it should be mentioned that the dynode output is fed to a discriminator with a variable threshold, also included in the divider housing ; a fast logical output (width about 100 ns) is thereby available . The optimal voltage of the PM is around 1100 V (lower than the usual one), for an optimal Vkd1 of 300 V. The average current taken out of the power supply is 1 mA. Experimental results obtained with the setup will be described below (sections 4.4 and 5). 3. Time response, resolution and noise at the Nal output 3.1. Photon statistics and energy resolution In a Nal(TI) crystal, the useful photon yield is 1 photon/24 eV . When the crystal is coupled to a photomultiplier, the light produces a signal with an exponential time dependence : p (t) = (1 /T) exp( -t/T), where T = 250 ns at room temperature . The time integral of this density function measures the information

collected per registered event: P(T)

= f p(t)di=1-exp(-T/T)=1-Q(T) .

The Poisson distribution is the basic law describing photon statistics: P = exp( -1t%~)n/n!, where the expectation value IL is related to the energy deposited, E, by E = l'h , where y [eV/photon] is the calibration constant . By using the central-limit theorem (It >- 30), the Poisson distribution can be approximated by a Gaussian : P =

1/2 ;rit exp[ - ( n -

t1)

2

/21.]

.

In this case p is related to 1c by p = 8 1og 2/1~ . For a time interval T, the useful part of the signal is given by IA(T) = i
The resolution as a function of T is computed using p(T) -= pl P(T) = p[1 + ~' Q(T ), . For T= 3T, the correction factor in this approximation is p(T )lp = 1 .025 . Experimentally, the simplest way to characterise the performances of a detector is by the dimensionless resolution formula p = A/E, where A is

L Bonnet et al. / Optimization ofNal(TI) detector performance the full width at half maximum of a peak with a mean energy E, both being expressed in the same units. The experimental resolution P662 for a -y-ray of 662 keV varies between 6 and 8% for commercially available detectors. If all the emitted photons contribute to the signal, then P662 = (8 log 2/26480)'/ 2 = 1 .4`x. The difference between the theoretical estimate and the actual performance is accounted for by losses in the light collection, limited photocathode efficiency and dispersion in the electron multiplication . 3.2. Factors affecting the signal shape The photomultiplier anode is adapted through an emitter follower to the transport line. The RC of this circuit modifies the original NaI(TI) signal . This modification is calculated using the following convolution : s(t)=fip(t' ; T)g(t, t' ; RC) dt' 1 [exp( -t/RC) - exp(-t/?')], (5) RC - T where g(t, t'; RC) = (1/RC) exp[ - (t - t')/RC ] is a normalized dispersion. For RC --K T, the expression is reduced to the original form s(t) = (1 /T) exp(- t/T ); for RC >> T, the signal is dominated by s(t) = (1 /RC) exp(- t/RC ) . If RC = T, then s(t) = (t/T 2 ) exp( - t/T ), and this simple signal shape depends only on T. Unfortunately, the 50 Hz ripple of the electric power supply is always picked up, to some extent, on the transport line, and the resolution is affected by this noise which is randomly superimposed on the pulse shape. Indeed, if h(t) = h sin(wt) is the shape of the noise, the distribution around AP(T) is modified by adding a random quantity over the (- bT, + bT) interval. The optimal time integration is given by the condition bTQ(T) = min, i .e. b(T - T) exp(- TIT) = 0. Except for the trivial solution b = 0 (no noise), T = T is the best choice, which indicates that there is no net gain beyond one period T. This slow noise component can be filtered out by a capacitive coupling at the input of the QDC analyzer but in this case, the signal shape exhibits an overshoot of the opposite polarity . =

For example, the probability P(n than one event in T' is given by

345 >- 2)

to have more

P(n ~_- 2) = 1-P(n - 1)=I-(I+AT')exp(-AT') . (6) At the 1% limit, this expression gives AT' = 0.1. A fast counting device (T' -< 10 ns) allows A = 10 7 -Y/S . On the time axis, the NaI(TI) light pulses can be described by the individual events : E,(t ) =E,p(t) = (E~/T)exp(-(t'-t,)/T), t=t,- I,' ;-> 0,

where t' is the real time, t, and E, are the time of arrival and the energy of the ith y-event, respectively. Within the counting time T', one obtains n randomly distributed events in a chronologically ordered sampling (ti, t ;,, . ., tn) E T' . The overlap between two -y-events depends not only on their relative time difference At = t, - t;, t' >- t,, but also on their energy ratio E,/E, . By introducing a dynamical energy range as max(E,/E ), the contribution E from a signal E, to the next signal E is given by

f ,'

exp[ - ( t' - t, )/T ] d t'

l(E , IT)

exp [ -(t'-t,)/TJ

( E,/T)

:~t T

r,

+

dt'=E .

(8)

where T = (t,', tl' + T) is a time window located at the beginning of the second pulse . The tail of the first pulse is integrated over the same interval, and one finds as an extreme condition for E :

max( E,/E, )

e x p( -- _% t/ T ) = E .

( 9)

For a dynamical energy range of 10, and for a 5% interference level, one obtains At = 53T . Thus, two light pulses overlap if their separation in time is less than 5T. These criteria correspond to a particular time and energy sequence, i .e. a big pulse followed by a small one. Nevertheless, this upper limit is adapted in the following for any sequence of pulses . Consequently, the time dependence of the exponential shape can be limited to 0
4 . Intrinsic y-ray pileup

E,(t,t,) ,

(10)

4 .1 . Gen ., . . j urmutatton ancî Monte Carlo calculat« .n

E(t)=

in this subsection, we shall consider the summation of the exponential light pulses at the Nal(TI) output. Let us assoeme that the y-events arrive in the Nal(TI) crystal at a uniform rate A [number/s]. One expects then Ic' = AT' events in a time interval T', the distribution of the events within T' is given by the Poisson law .

where each subscript brings in two random numbers. namely E, and t,'. A simulation of pileup events can be done through random generation of the events originating at t, (uniform over T') with an energy factor E, (energy deposited in the Nal) . The number of generated pileup events n follows the Poisson distribution with a

v

L Bonnet et al. / Optimization of NaI(TI) detector performance

346

over a moving window of length W = T is written as

s(A) = (T - Io 1)/T= 1 - Io I/T,

(12)

where B = tW - t; is the time difference between the pulse head and the window head. For a fixed window position, the random variable A E (- T, T) generates a random signal s = s(A) E (0, 1). There is a one-way correspondence between the random origin t; and the random pulse fraction. 'Tae pileup is a sum of such independent random events, each of them being defined only with respect to the beginning of the time window. In case of a multiplicity n, one has n

Sn

Fig. 2. Counting rate X u.,, of pileup events above Ea = 2 MeV for a 500 ns gate window, versus the 0.5 MeV counting rate A . The dashed curves are the Monte Carlo calculations : the lower one corresponds to exponential pulses, the upper one to rectangular pulses. The Monte Carlo calculations were checked by analytical calculations (solid curves) using rectangular pulse shape : the lower solid curve is the result of the complete analytical calculation [eqs. (19) and (20)] and is in very good agreement with the Monte Carlo calculation; the upper solid curve, obtained by setting Fn = 0 in eq. (19), is an upper limit .

mean value IL' =XT'. E(t) can also be considered as a vector representing the sum of the events. To construct the sum distribution versus energy and multiplicity, E(t) must be summed over a signal sampling window W and, at each step, one gets the sum and the multiplicity of the pulse components . Fig . 2 shows the result of a . (the rate per  Monte Carlo simulation yielding AS second of the multiple 0.5 MeV pileup events exceeding a 2 MeV threshold within a 500 ns gate window) versus X (the 0.5 MeV counting rate per second). For the moment, we refer only to the lower dashed curve of fig . 2. 4 .2. Analytical approach

Let us develop an analytical approach which gives an upper limit to this Monte Carlo calculation (lower dashed curve of fig . 2) for the high-energy tail of the pileup events . For that, the complete -y-spectrum can be replaced by a set of monoenergetic events (photopeak) with a rectangular shape p(t) = 1/T. 0 :5 t <- T. The individual events are described by where t, is at the origin of the rectangular shape and T is the pulse length . For a given pulse, the integration

=

, s(Ai)+

(13)

(0, n),

Sn E

and the maximum pileup signal is Sn = n. However, a given sum can be obtained in many ways. For example, in the case n = 2, the same S2 value can be produced by different individual terms in the sum s0 t ) + s0 2 ). A simple presentation of this multidimensional integral can be found in ref. [6], p. 27, where the cumulative function of Sn is given by Isnl Fn(Sn) = -;;T 1:( - 1) k C,k(Sn k=0

k )n,

(14)

where C',k is the binomial coefficient, from which the density function is obtained as Pn(Sn`) =

_

dFn (Sn ) d S~, (n

1 IS,I k k - 1)' ~~(-1) Cn (Sn

-

k)

 -t

,

(15)

where I S I stands for the integer part of S. Due to the symmetry properties of pn(S, ), the expectation value of Sn is obtained by f Sn pn (Sn ) dSn = n/2. Let us clarify the differences between the quantities T', T and W. The random origin t,' is generated over T' and the mean number of events fL' = \T' is independent of the pulse length T. But the overlap of events is strongly related to T and in fact the mean value of the multiplicity is given by ft = 2AT. Finally, the signal sampling window W is arbitrary, and can be used to optimize the single-event detection (pulse height and resolution) with respect to the sum pulse fraction . The weight factors Pn of the normalized densities pn(Sn) are obtained by The pulse length of the exponential shape was previously limited to T = 5T . If we take the sampling window to be W = 2T, one obtains the expression s(d,)=exp(- A1r) .

-T
s(,1)=1-exp(-(T- ®) /T),

0<®
(17) (18)

L. Bonnet et al. / Optimization of Nal(TI) detector performance

347

P(t)

t2

t? t,

T

t1'

-T

t

0

T

Fig . 3 . (a) Exponential and rectangular pulse shape with two examples of a moving window W before (4 5 0) or after (A z 0 ; the pulse head . Pulse and window lengths are chosen to be the same; T = W = 2T . (b) Sampling fraction as a function of A, for an exponential integral (solid curve) or for a rectangular shape (dashed lines) .

which is close to s(A) =1 -- ( B I /T. If the exponential shape is cut after a pulse length of T = 2T, one can try to replace its random sampling by the random sampling of a rectangular shape . In fig . 3a, the two pulse shapes and the moving window are presented . Fig . 3b illustrates the corresponding integrals ; a small difference in the high-energy tail s(A = 0) is obvious . As it is expected, the rectangular shape produces a distribution that is enhanced in the high-energy part with respect to the exponential shape . In that sense, the rectangular shape gives an upper bound to the exponential one in the high-energy end of the pileup spectrum . Using this replacement, the pileup probability of a monoenergetic -y-ray is estimated by P[Eo :5E] =

n = no

Pn[1 - Fn(Eo/0 .5) ],

(19)

where Eo is the energy threshold [MeV] in the event acquisition, n o = ( E010.51 is the integer part of the energy ratio Eo/0.5, and Pn is the Poisson distribution with p. = 2XT. (An even higher upper limit is obtained with Fn = 0, which gives an energy independent probability to have at least n o events in 2T.) P[Eo -< E] is the probability to get one pileup event (pileup) above Eo in the time interval 2T. The density of such events or the sum rate is obtained by o < E1 /2T , Alum = P[E (

20 )

which depends explicitly on the energy threshold E . For E0 , = 2 MeV at least four 0 .5 MeV -y-rays are needed to jump over this threshold, while there remains a gap of 2 MeV from the threshold to the double-escape part of the 5 MeV -y-ray spectrum . Fig . 2 presents X s , as a function of A for this analytical approach ; Monte Carlo calculations using the same rectangular pulse

shape were done also as a check of the computer program . As appears from fig . 2, the agreement is very good . 4.3. Optimization

by

The randomly sampled background spectrum is given

p(s) =

(21)

where each density function [eq . (15)] is weighed by a Poisson factor [eq . (16))] . P, = exp( - Fa ) is absent from this sum as it corresponds to the empty sampling . When the 5 MeV -y-ray is the sampling trigger, P, is just the weight of the undeformed spectrum . The complementary part (1 - PO ) gives the portion of the 5 MeV y-ray signals shifted by the pileup . So the displaced part R .p of the 5 MeV -y-ray is estimated by x (22) Rup = r, PnFn(S =2 )/(Po+Pl+P2) . n=3 This signal-background interference has the effect of dispersing the 5 MeV spectrum towards higher energies by adding a background sum with the probability function p (S ) . Clearly, for It >- 1 the main components of w f _t . 1 .L . rt = 0 . 1, 2 modify only ihe spcciras shape in Oc vi%iënty' of the peaks and the number of total events remains unchanged in the (3 .5, 5 .5) MeV interval . For A = 0 . an optimal overlap between pulse shape and sampling window W can be found from fig . 3a . This corresponds to the 5 MeV y-ray shape integrated by its own trigger through a logic gate . On the contrary. the background enters in a random way into W. To optimize W as a function of A and T, one can minimize _

Bonnet et al. / Optimization of NaI(TI) detector performance

348

(if the energy is factorized, then EnP = jA), P(W) is an upper limit on the background time integral, exp( - AW) replaces Po = exp( -it), and finally the last factor is the complementary part of the 5 MeV signal . For X = 0, any time window can be used, because IL = 0 and the background condition disappears. A simple solution is obtained when the background integral is bounded by P(W) = 1 ; then the condition W exp(- XW ) exp(- WIT) = min gives as solution W = T/(X T + 1) and for AT >> 1, W=1 /A .

1000

c

0 U 500

4.4. Experimental results and verification of the calculat;ons

6 Energy (MeV)

Fig. 4. Smoothed spectrum of 4.4 MeV y-rays from a Ra-Be source close to a 1 F source providing the NaI detector with 4.5 x 10 5 s -1 , 0.5 MeV -y-rays (upper curve), and spectrum of the 18 F source alone (lower curve). The high-energy part of 4.4 MeV -y-spectrum is not affected by the intense 0.5 MeV counting rate. the contribution of the background (Ebg = 0.5 MeV in our case) into the signal (E y ):  f(W; A ) x

= ( E P"2Ebg2T n=1

Pileup calculations were checked by detecting 4.4 MeV y-rays from a Ra-Be source in the presence of the intense 0.5 MeV y-ray flux from a 18 F source. A lower threshold of Eo = 2 MeV was set on the discriminator output of the NaI(TI) detectors ; this logical output was used to construct a 1 lts long gate during which the linear anode output was integrated. The experimental spectrum for the Ra-Be source plus the 0.5 MeV source is shown in fig . 4 as a solid curve; the 0.5 MeV counting rate in the detector was 4.5 x 10 5 counts/s. Fig. 4 shows also the 0.5 MeV source spectrum alone, of which the count rate amounted to 24 s -1 above threshold. The Monte Carlo simulation yielded a pileup rate of 19 s -1 .

P(W) exp(-AW)[EYQ(W) ~] 5. Data acquisition system

where the first factor represents the pileup sum in which each term has a Poisson weight, the mean background energy nE bg/2 is multiplied by the time fraction W/2T

We are preparing to study the capture reaction 13 N + p -_., 14 0 + y at E,, = 544 keV using reverse kine-

matics . In this case the transferred transverse momen-

TRANSPORT LINES

CAMAC DETECTORS Fig . 5. Electronic schematic for six Nal detectors . Only energy and time correlation with respect to the cyclotron rf are measured . 1-he rf signal is entered twice to realise the time definition of TDC START given by the rf signal only.

L. Bonnet et al. / Optimization of NaI(TI) detector performance

349

100 vn C

w

80

60

60

120 Time Fig. 6. Typical two-dimensional spectrum for a NaI detector; the energy (or integrated charge) is displayed versus the time with respect to the rf signal. y-rays of 8 MeV from the 13C(P, Y) °4N reaction are clearly seen. 30

turn is very small with respect to the beam momentum . The 140 fusion residues remain within the angular cone of the beam divergence and are not easily detected . For that reason the only parameters that will be recorded in the present setup are the photon energy and its time correlation with respect to the cyclotron rf. Moreover, the expected cross sections are very low so that a multidetector should be used to cover a large solid angle. Six NaI(TI) crystals will be used in our system, and this number can be extended if necessary. The discriminator built into the voltage divider hardware is used to set a lower threshold on the pulses from the last dynode of each detector . An OR signal of the six discriminators, in coincidence with the 12 MHz

90

rf signals (the tinting is determined by the rf signal), provides a common START for the CAMAC TDCs and a 1 p,s width gate for the CAMAC charge-sensitive ADCs (ADCs) . Each detector activates a STOP input of the TDC. Linear pulses from the detector anodes are integrated by a QDC during the 1 p.s gate; a 2.5 MeV dynode threshold roughly corresponds to an anode pulse height of 300 mV. The anode signals are capacitively coupled to the QDC input to filter out the low-frequency n6se (e.g. 50 Hz). The CAMAC crate is coupled to a microcomputer, and data accumulated in event-by-event mode are stored on tape. It should be stressed that the energy resolution of the detectors is not degraded by this acquisition system, as compared to more conven80

100 U1 C

0 80

60

U

O

0 U w 0

.n

z 60

N

z 40

40

20 20

0

256

512 Channel Nbr

Fig. 7. Full projection of the two-dimensional spectrum of fig. 6 on the time axis.

Channel Nbr

Fig. 8. Projection on the energy axis of the events contained in the regions limited by solid lines (1101), and by dashed lines (background) in fig. 6.

350

L. Bonnet et al. / Optimization of Nal(TI) detector performance

tional ones using e.g. spectroscopy amplifiers . The same conclusion was reached in a recent work [7] dealing with the acquisition of high-energy -y-rays . Fig. 5 presents this very simple electronic layout. No radioactive beam being available at this time, the multidetector system was tested for the detection of 8.06 MeV y-rays from the 1H(13C, .Y)t4N reaction ; this reaction is dominated by a resonance of 38 keV total width and about 10 eV y-ray width, at a center-of-mass energy of 0.51 MeV . A 5 nA intense 3C1 + beam of 8 MeV energy bombarded a thin (= 200 Iig/cm2) polyethylene target . A typical two-dimensional (energy, time) spectrum is displayed in fig. 6; as can be seen, the 8 MeV -y-rays are clearly correlated with the beam. A full projection on the time axis is shown in fig. 7. The FWHM of the peak is about 13 ns, most of which is due to the cyclotron burst width (a subsequent tuning of the cyclotron yielded a 5 ns wide peak). A projection on the energy axis of the events in the region of interest (ROI) is displayed in fig. 8. The spectrum exhibits three structures that can be assigned as the total-energy peak and the single- and double-escape peaks . The background obtained by projecting events from the region next to the ROI is shown in the same figure (lower curve) .

order to measure absolute cross sections, the integration of a Faraday cup in a CAMAC scaler and the correct measurement of the system dead time via an output register have to be included. Although the acquisition rate of the CAMAC system is limited to a few hundred events per second it is sufficient for the needs of the measurement of the 'H( 13N, Y)140 capture cross section. Finally, it should be mentioned that the efforts to build detectors able to sustain high counting rates will be accompanied by the placing of absorbers in front of the detectors (e.g. 5 cm of Pb should attenuate the 5 MeV flux by about 50% while reducing the 0.5 MeV flux by nearly four orders of magnitude). Acknowledgements We wish to thank Dr. W. Galster and Dr. Th. Delbar for their participation in the data acquisition part of the work, and Miss M . André for her involvement in this work during the academic year 88-89. The help of A. Magnus for the development in section 4.2 is greatly appreciated . One of us (P.Le .) is a Research Associate of the National Fund for Scientific Research, Belgium.

6. Conclusion We have constructed a multidetector system which is able to detect energetic (>_ 4 MeV) -y-rays in the presence of a very high flux of 0.5 MeV annihilation -y-rays . The scintillators are conventional NaI(TI) ; the photomultiplier bases are of a novel design and able to cope with a high counting rate while retaining good energy and time resolutions. The simple acquisition system is designed to provide with a clear signature of the -y-rays of interest ; pileup effects in the detectors were measured and compared to calculations. The description of the CAMAC data acquisition system was limited to the detector-related features; in

References [1] C.R. Kerns, IEEE Trans. Nucl. Sci . NS-24 (1977) 353. [2] R.D. Hiebert et al., Nucl. Instr. and Meth. 142 (1977) 467 . [3] W.L. Reiter and G. Stengl, Nucl. Instr . and Meth. 174 (1980) 585 . [4] C. Ohmori et al., Nucl. Instr. and Meth. A256 (1987) 361. [5] C. Zhong et al., Nucl. Instr. and Meth. A281 (1989) 384 . [6] W. Feller, An Introduction to Probability Theory and its Application (Wiley, New York, 1971); see also I.J. Good and T.N. Tindeman, Numer . Math. 30 (1978) 355. [7] J.P. Miller et al., Nucl. Instr. and Meth. A270 (1988) 431 .