A discriminator for use with NaI(Tl) detectors at high counting rates

NUCLEAR

INSTRUMENTS

AND

METHODS

III

(I973) 365-373;

© NORTH-HOLLAND

PUBLISHING

CO.

A D I S C R I M I N A T O R F O R USE W I T H NaI(TI) D E T E C T O R S AT H I G H C O U N T I N G RATES* A L L E N P. M I L L S , Jr.

Brandeis University, Department of Physics, Waltham, Massachusetts 02154, U.S.A. Received 9 M a r c h 1973 A discriminator is described which is suitable for use in a multiple NaI(TI) coincidence spectrometer at high c o u n t i n g rates. T h e device generates pulses whose lengths convey energy information,

and energy c o m p e n s a t e d timing pulses for use in multiple fast coincidence m e a s u r e m e n t s .

1. Introduction

information loss at counting rates approaching 1/8r 5 x 10 s s -1.

This laboratory has recently set up an experiment using a multiple Nal(T1) detector t) system. Since the data collection rate is proportional to the single detector counting rate, we wanted to maximize that rate without seriously impairing the time and energy resolution and without introducing large dead time losses. We, therefore, have designed a discriminator for NaI(T1) detectors which would be nearer to optimal at high counting rates than the commercially available electronics which typically has long integration times. The usefulness of a NaI(TI) scintillation detector for measuring the time of arrival of a y-ray and its energy is strongly limited by the finite mean number m of photoelectrons per pulse, the long scintillator decay time r ~ 220 ns, and the photomultiplier (PM) tube characteristics. In particular, r places an upper limit on the tolerable counting rate of the system, if a fast discriminator is set at a level corresponding to say n photoelectrons, then a dead time tD of several times must be introduced to prevent double pulsing on a single event. For example, for n = 2 there is a 68% probability of double pulsing with a dead time of t68% o = tln[(tr/z)½m],

where tr is the 10-90% step function rise time of the PM tube. For ~37Cs y-rays corresponding to m = 3000, to=6Z= 1.3/~s. Similarly, in a conventional pulse height analyser, the anode current pulses must be integrated for about 3 r to prevent the deterioration of the pulse height information. Since a dead time t per pulse implies a pile up loss of I - exp( - 22t) at a counting rate 2, we conclude that the pulses from NaI(T1) detectors require carefui handling in order to prevent * W o r k s u p p o r t e d by the National Science F o u n d a t i o n , the I,r.s. A r m y Research Office, D u r h a m , and a grant from T h e Research Corporation.

365

In this paper we present our solution to the problem of using NaI(T1) detectors at high counting rates (up to 2 x 105 s-a). To reduce the deadtime we have used a partial deadtime for the fast trigger and a variable integration time for the pulse height integrator; this allows pulses separated by intervals as short as r to be correctly analyzed. The time and energy information is made available in a form which allows its use in a multiple counter system. The fast timing pulses are individually pulse height compensated and thus can be used over a wide range of y-ray energies in simple multiple overlap fast coincidence circuits. Also, the energy information is translated into the length of a short pulse ( < 200 ns) which can be easily routed for pulse height analysis. In addition, both the fast discriminator trigger level and the PM gain are stabilized by negative feedback to allow long term operation without adjustment. In the following section we discuss the design of the pulse height compensated fast discriminator. An analysis of the voltage to time converter (VTC) is given in section 3, and section 4 shows how to perform pulse height analysis using the VTC pulses. Section 5 describes the overall performance of the discriminator. 2. The fast discriminator

It is known that the best time resolution using NaI(T1) counters is obtained by triggering on the first photoelectron in the anode current pulse2). Fig. 1 shows schematically typical anode current pulses corresponding to a single photoelectron S ( t ) and to a y-ray being absorbed in the NaI(TI) crystal, I(t). The line marked A corresponds to a trigger level which is just above the single electron noise current. The signal B is the output of an ideal discriminator with a threshold at A. To

366

ALLEN

P. M I L L S ,

prevent the multiple pulsing shown in B, one m a y completely turn off the discriminator for several T following t = 0. However, it is really only necessary to add to the anode current pulse I(t) a second pulse I ' (t) such that I'(t) + I(t) > 0 for all t > 0. This will allow a second pulse of sufficient magnitude to fire the discriminator while preventing multiple pulsing on the fluctuations associated with a single input pulse. Let us estimate the magnitude o f the fluctuations in l(t). Suppose that the anode current pulse is given by I(t)

=

f

+~

1 -

-

x

- ~ (2 ~o-2)~ k

xexp[-(t-t')2/2a

z] ~ q i f ( t l - t ' ) d t ',

(l)

i=1

where 2(2 In 2)~a ~ tr is the full width at half m a x i m u m of the single electron anode response, and the single electron pulse arrival times ti are distributed exponentially with probability 3)

P(tl) = (1/z)e -n/~ O(ti). k is the total n u m b e r of single electron pulses in l(t), with charges qi, i = 1, 2, ..., k. We assume that k differs from pulse to pulse but has a mean value of m and follows a Poisson distribution. Neglecting the finite rise time, we find of course that the average value o f I(t) is exponential,

( l ( t ) ) = m ( q ) ( 1 / z ) e -t/~ O(t). We also find that the mean square anode pulse is (12(t))

(I(t)) 2

=

0

~-

I

i

__~k~sl,1

(q2) -I-

(I(t))

- -

(q)

(4niT2) ~-"

2r I

_ __

X/

U

Thus, the fractional rms fluctuation in the anode current is given by

Alrms(t) _ 1 (q2)-~ __z~e -t/zr O(l), (l(t)) m ~ ( q ) (4rco2) ~' and the correct form for the dead time pulse l'(t) should be

l'(t) = [(/(t))l +3Alrm~(t = 0)e -'/2~ O(t), where the factor of 3 should reduce the double pulse probability to a few percent per pulse. For (q2)~/ ( q ) ~ 1 and a = 2 ns we find that Alrms(O)/(l(O)) =0.3 and 0.13 for pulses from 100 keV and 500 keV y-rays respectively. In practice, the pulse I(I(t))l may be obtained sufficiently accurately by integrating each anode current pulse for a time long compared to a, but shorter than r. The integration introduces a delay which allows the fast discriminator to trigger before subtraction occurs and also smooths each l(t) to reduce fluctuations. The second part of the dead time pulse I ' (t) may be approximated sufficiently accurately by some average value of 3Alrm~(t = 0) times an exponential decay which may be generated by a capacitor discharge with RC = 2 r. Fig. 2 shows the block diagram of the variable dead time discriminator. The current amplifier A2 driving the tunnel diode discriminator is similar to that described in ref. 2 and the use of the Ge diode biased G a A s tunnel diode T D I has been described by Whetstone et al.*). The pulse I(l(t))[ is generated by the operational amplifier A l, and the pulse for surpressing fluctuations is generated by the univibrator U 1 which pumps the 220 pF capacitor. These two sensi-

-(l(t)>

5T I

V

JR.

k/

t

\A

7

Fig. 1. The response B of an ideal fast discriminator to a long photomultiplier pulse. The pulse S(t) is a typical single photoelectron response and l(t) is a pulse of decay time ~ containing about 64 single photoelectron pulses. The width of S(t) was chosen to be about z[8 for this illustration. The discrimination level A has been set just above the single electron pulse height.

Anode In

50:

Fig. 2. A block diagram of the variable dead time discriminator.

DISCRIMINATOR

FOR

USE

tivity reducing pulses are summed at the low impedance input of the current amplifier, A2. It is difficult to maintain the correct bias level on the tunnel diode over long periods of time when it is triggering very close to the anode noise level. Not only is the noise output of the tube not constant and the tunnel diode temperature sensitive, but also if the tunnel diode starts to oscillate due to a transient or temperature fluctuation, we have observed that it is not likely to stop of its own accord owing to hysteresis in its sensitivity. Consequently, it is desirable to have some means for stablizing the tunnel diode trigger level. Fig. 3 indicates how we have chosen to stabilize it. A slow discriminator consisting of a 710 IC is set to trigger at a low level on the output of A1. Since this element is quite stable and not triggering in the noise, its output makes a good reference with which to compare the triggering rate of TD1. This comparison is effected by the set-reset flip-flop. The output Z will be low after TD1 only fires, and Z will be high after an event in which both T D I and the 710 fire, since the 710 output is longer than the reset pulse X from U1. Z is integrated and inverted by A3 and then added to the current in T D I . Typically, a perturbation in the bias level of T D I equivalent to 100 keV results in a change of only 4% in the firing rate of TD1 with this circuit. Since some double pulsing of TD1 must be tolerated a rate variation of 4%/100 keV is quite modest. Finally, it is desirable that the fast timing output derived from T D I be compensated to reduce the time shifts associated with different 7-ray energies, Ez). The time centroid of the output pulses from a fast discriminator triggering on the leading edge of NaI(TI) counter pulses is observed to shift roughly as lIE. The shift of a few ns in the range 100-500 keV is sufficient to double the time resolution of an uncompensated system observing the energy pairs 100+500 keV and 500+ 100 keV simultaneously. A number of compensation schemes have been devisedS), the simplest being the addition of energy pulse heights to the output of a time to pulse height converter (TAC). This method requires the use of many T A C ' s for n counters, and hence might not be practical in a many counter system. In such a system it is better if the fast timing pulses are compensated before their analysis by a set of fast overlap coincidence circuits. Fig. 4 indicates how this may be accomplished. In this circuit, a germanium tunnel diode, TD2, is set in the low voltage state by the leading edge of the signal from TD1. After a time t~ L/R, TD2 returns to the high voltage state. Since t depends on the current bias on TD2, it may be adjusted to compensate for time shift with pulse height by adding

NaI(T1)

WITH

DETECTORS

367

a fraction of the pulse height signal from A1 to the input of the current amplifier A4 which drives TD2. This effects a linear compensation which is an adequate approximation to 1/E provided that the energy range is not too great. The pulse from TD2 is clipped at the output of the current amplifier A5, and the resulting positive pulse is the compensated one. TD2 is biased in the high voltage state so that the trailing edge of its output will be a sharp pulse. 3. The voltage to time converter

In order to determine the energy E lost in the NaI(Tl) scintillator for each 7-ray we must measure the total charge collected by the anode during each pulse I(t) given approximately by eq. (1). For the present discussion we will neglect the single electron response time, a-> 0, the non-uniformity of the scintillator and photocathode, the non-exponential decay of the scintillator light, the possible correlated single photon emission of the scintillator and the light feedback gain and ion after pulse gain of the PM tube. The statistical results of most of these effects may be accounted for in eq. (1) by using an effective mean value re(E) of photoelectrons per pulse of energy E which is lower than the measured value. k

Integrating the anode pulse Im(t ) = ~ q~f(tl--t) i=1

over all time gives the total charge collected at the k

anode,

Qm = ~ qi. The average total charge is i=l

(Qm) =re(q), where ( q ) is the average charge in a m

~

30~f

15F Hy

Fro

~.. }~---~ ~Z ' -7 1 0

To

A3

TDI

Reset LevelAdjustment Fig. 3, The fastdiscriminatortriggerlevelstabilizer. R

y

From " ~ TDI

II t

L

-]

~>---A4

~

F-- ~ p

u

Fast

t A5

TD~

From AI Fig. 4. The block diagram of the fast discriminator pulse height compensator.

368

A L L E N P. MILLS, JR.

single electron anode pulse. If m (E) is proportional to E, then Om gives a good estimate of E for each pulse with a variance given by

~

m ~"

Using a value for +/estimated to be 1.2 we find that the full width at half maximum of the distribution of Q is w+ = 2(2 ln2) + (AQ2>+ ~ 2.8 m -+



To make this expression account for a typical resolution of 8% for a 662 keV photopeak, we must set m/E= 1.7 photoelectrons per keV, which of course does not agree with estimates of m/E= 5 2) obtained by actually dividing the area of the anode pulse by the area of a single electron pulse. If the principal line broadening effect is the scintillator non-uniformity, then it may be that an individual pulse is w/3 times smoother than one would expect from measurements of the total variance of Q. In this case one would be able to obtain estimates of Q in each pulse consistent with AQrm~ without completely integrating l(t). Such an effect has indeed been observed6). If Ira(t) is being integrated on a capacitor C, the average voltage on the capacitor at time t is

< Vm(t)> =

(m /C)(l

- e-'/~),

and the fluctuation of Vm(/) at time t is given by

(AV2(t)> < Vm(/)> 2

= (l-e-'/~) -'

2 '

which indicates that with an integration time of r one would expect 25% poorer pulse height resolution than would be obtained with an infinite integration time. The voltage to time converter described below incorporates some of the features of the pile up correction systems proposed by Blatt et al.7). These systems were to use linear gates and integrating amplifiers to subtract undesirable pulses from the pulses of interest which were to be analyzed. Such systems should be capable of correcting piled up pulses with a time resolution determined by the time required to estimate the amplitude of the correction pulse. If the pile up pulses have amplitudes comparable to the pulses of interest, then the sampling time must be comparable to the pulse height analyzer integration time if spectrum distortion of closely spaced pulses is to be avoided. Furthermore, if one wishes to know the amplitude of each pulse, the

pile up correction resolving time cannot be less than the pulse height analysis time. The voltage to time converter produces for each input pulse a pulse whose length is proportional to the total anode charge collected. The pulse height integration time is ~ 3r for pile up free pulses, but is reduced to the double pulse separation when pile up occurs. Since the time required to effect the amplitude to time conversion is ~ r for this design, the pile up correction resolution time is ~ z also. Thus, each pulse is analyzed with the maximum accuracy consistent with a double pulse resolution time of y r . Since the facsimile pulse generation required for pulse height correction does not require the use of linear gates, the circuitry of the present design is simpler than that proposed by Blatt et al. Furthermore, with the amplitude information in the form of logic pulses of variable length, pulse height analysis in a multiple counter system is simplified since non-linear logic gates may be used to route the pulses. An amplitude may be converted to a time interval by integrating the input pulse and then measuring the time required to reset the integrator with a constant current input, as shown in fig. 5. However, if the integrator is reset at times comparable to the input pulse decay time r, there will be an error due to the incomplete integration of the input. Also, after reset, the tail of the input will interfere with the amplitude determination of the succeeding pulses. It is possible to overcome this difficulty by placing a resistance R in series with the integrating capacitor C' of fig. 5 such that RC'= r. Such an integrator produces a step function response to an exponentially decaying input. However, this arrangement would pass all the short term anode current fluctuations and it is therefore necessary to partially integrate the input first as shown in fig. 6. Effectively, the decay time of the scintillator

Input - " ~ " w " - - t ~

~~

,

Reset

Reset

Time ~

Current

Fig. 5. A block diagram indicating the principle of amplitude to time conversion. The pulse labeled "input" is integrated by the operational amplifier and capacitor C'. The capacitor is then discharged by a constant current source. The discharge time tR is then proportional to the area of the input pulse.

DISCRIMINATOR

FOR USE W I T H

pulse is reduced to RC, allowing the integrator to be reset at any time greater than 3RC without introducing appreciable systematic errors in the amplitude information. The integrator of fig. 6 is reset by a facsimile pulse which is generated by integrating a constant current pulse in the RC-circuit as shown. The time required for the facsimile pulse to zero the integrator is proportional to the input pulse area. Since A6 gives a constant output for input pulses with decay time r, once it is reset, the output remains at zero ready for the analysis of the next pulse. Integrating anode current pulses Ira(t) in the circuit of fig. 6 results in a voltage Wm(t) which has an average value of (Wm(t) ) = (m ( q ) / C ' ) ( l --e-'/"c), which has a faster rise time than the pulse of fig. 5, V,,(t) if RC < r. However, the noise content of Win(t) is greater than that of Vm(t), as one would expect. For t >>RC, we find

(AWd(t))

[l + (Qm) 2

(Win(t)) 2

e -- t/r q

l,

x = RC/~.

x(2-x)3

Therefore, if the resolution is to be no more than, say, 5% greater than the minimum resolution, the resetting of Wm(t ) must not end before tl = rln[10/x ( 2 - x ) ] . A reasonable choice o f x =½ results in t 1 = 2.9r = 640 ns. Those pulses which are reset at t = r due to pile up will have a variance 30% greater than the minimum value. However, this is an upper limit considering the results of ref. 6. The resetting of A6 is initiated by the trailing edge of a long pulse from a univibrator U2 which is triggered by U l (fig. 2) and is reset early by the same pulse that triggers U1 if a pile up occurs. The tunnel diode TD3 is normally biased in the high voltage state just above the peak current I v and is set in the low voltage state by the trailing edge of the U2 pulse. The output

R

C'=rlR

Start Pulse

NaI(TI) D E T E C T O R S

369

of TD3 when amplified by A7 becomes the reset current pulse which is terminated as soon as the output of A6 causes the current in TD3 to exceed lp. The voltage across TD3 is brought up to standard T T L logic levels by another amplifier; this pulse is the voltage to time converter output.

4. Pulse height analysis The analysis of the time coded pulse height information contained in the pulses from the voltage to time converter (VTC) described in the last section is initiated by routing the VTC pulse of interest through a gate as shown in fig. 7. A fast coincidence pulse opens the gate, letting through the next VTC pulse and only this pulse since its trailing edge closes the gate. The gated VTC pulse may then be integrated and analyzed by a conventional pulse height analyzer. Alternatively, the pulse height information in the gated VTC pulse may be analyzed directly by a slow chronotron 8) circuit such as that of fig. 8. The leading edge of the gated VTC pulse is sent down a delay line with n outputs D i spaced at intervals T. If t is the length of the VTC pulse, then the outputs of the coincidence circuits C~ with i < t i t will be high while the outputs with i > tiT will be low after the VTC pulse has ended. A typical pulse height window of width l and lower level k isa gate whose outputis Wkl = S*Ck*Ck+~,, where S is the widened trailing edge of the VTC pulse. The pulse height coincidence circuits are reset by a pulse R which is the trailing edge of S while the window coincidence circuits are reset by R', the leading edge of S. While this scheme results in very long window output pulses, the resolving time of a coincidence system including a slow coincidence requirement on the slow window pulses is determined by the fast coincidence resolving time provided that there is a VTC pulse for each fast coincidence input pulse. This will indeed be the case since the VTC pulse generation is initiated by a pulse derived from the fast discriminator of fig. 2. A simplified version of the above slow chronotron may be used to stabilize the overall system gain by VTC

Pulse In

-U-

c;

L'

)

Gate -

Gated Output

Pulse In

>

Reset Current Pulse

Fig. 6, The block diagram of the voltage to time converter. The I-V plot shows the quiescent bias point of TD3.

Fig. 7. A logic gate for routing the time coded "energy" pulses from a voltage to time converter.

~'~

A L L E N P. M I L L S , JR. 2R VYC

Zo

Leading Edge

Pulse-] F

JI_ Delay ~ Line

i t-h Coinc.

~ /-

t

D2 i

JI

T

S

Dn Ck ~

F

~

~

~

'' Wkl

Window Coinc Width = 1

R"

Lower Level = k

Fig. 8. A slow c h r o n o t r o n circuit for the analysis o f the time coded " e n e r g y " pulses from a voltage to time converter.

sitting on a photopeak with two adjacent pulse height windows P_ and P +, a well known method of spectrum stabilization9). The outputs of the two windows

P_ = S~gCk~gCk+l and P+ = S*Ck+l~gCk+2 control a set-reset flip-flop whose output is integrated by A9 as shown in fig. 9. The averaged voltage drives a lampphotoresistor high voltage transistor combination in the photomultiplier high voltage divider chain. The result of this feedback network is a very stable energy to time conversion coefficient for the VTC.

5. Performance

The operation of the pulse height compensated discriminator described in section 2 is indicated in fig. 10. Two counters consisting of 2" x 2" NaI(TI) on 8575 PM's were positioned to detect the 27 annihilation photons from a ZZNa source. The anode pulses from

Nsec.

3.0

2.5

-HV IOHf

I

2.0

b, U ncom pensated

:>

P÷

=E

1.5

,q

~9

÷

o

L0 33K

ToPM Voltage

TD 714

o lu n,"

0.5

Divider

o IP-IP+I

Fig. 9. A high voltage stabilizing system for use with the slow c h r o n o t r o n o f fig. 8. T h e tunnel diode T D 7 1 4 is used to detect the o u t p u t level o f the amplifier A9 a n d causes A9 to execute a very slow oscillation f r o m m a x i m u m to m i n i m u m o u t p u t until a peak in the pulse height distribution is detected a n d locked onto.

I-.-

-0.5 = 0

I

I

I

I

0.1

0.2

0.3

0.4

I 0.5 Mev

Pulse Height

Fig. 10. T h e Nal(TI) time shift vs pulse height curves for the fast discriminator with (a) a n d without (b) pulse height compensation.

DISCRIMINATOR

these counters were connected to two identical discriminators whose fast outputs were driving a time to pulse height converter (TAC). The TAC was gated by energy windows derived from the dynodes. Fig. 10 shows the time shift of the centroid of the TAC output as a function of E 2 (the energy detected by counter 2) with E1 fixed at 511 keV. The curve marked "uncompensated" was obtained using the leading edges of the fast discriminator outputs, while the " c o m p e n s a t e d " curve was obtained using the trailing edges. In the energy range from 125 keV to 5ll keV the uncompensated time shift is 3.2 ns while the compensated timeshift is between +0.5 and - 0 . 3 ns. The pulse height compensated time resolution is about 25% wider than the uncompensated results when narrow energy windows are used. With both counters detecting the 511 keV photopeaks the time resolution (fwhm) was found to be 1.85 ns compensated versus 1.46 ns uncompensated at singles rates of 24k and 33k s -1. When the singles rates were 170k and 220k s -~ the resolutions became 1.98 and 1.68 ns, respectively. However, when wide energy windows are used, the pulse height compensated resolution is slightly better than the uncompensated resolution. Furthermore, if the two counters are observing simultaneously pairs of x

o

10 4

xXXX

~

x

o

=

o

o

170

# o, 160

-& to 150

Perturbation

I

I

I

I

2

3

4

5

Feedback

I

I

6ma

Current

I

I

I

I

i Singles

10 4

o

Rate

I

o

x

~

o

..... ,,

c c

x

I..

tJ

o x

Q.

=,OO]o !

.. ;-*"

w o

FW I / 2 M

/

/\

t

o

:

,~,

= I.Tx 105sec. -I

\

x

o

~, io 3

o

o

13.

o

o

x

x

C x

io 2

I

I

o

o

3

0 -x

® x

x

o

?

x

o o°

o

u

180

./"".,

x

o

o

I

x

t 1° 3

J90

o

x

o

o

o

x

o •

o o

o

sec, - I

o

ox

o o

7-rays with high and low energies, the compensated resolution is more than a factor of two better. Fig. 11 shows the time resolution curves obtained with E 1 in the range 100-150 keV and E 2 on the 511 keV photopeak and conversely. For the pulse height compensated curve we find that the fwhm is 2.9 ns and the fw-ft6-mis 6.2 ns whereas the uncompensated widths are 8.0 and 11.7 ns, respectively.

Fig. 12. T h e performance o f the trigger level stabilizer s h o w i n g that a large disturbance o f the trigger level produces only a small change in the triggering rate.

x o

XO

b o

371

o

0 o

NaI(Tl) D E T E C T O R S

F O R USE W I T H

o°

•

o

Xx x

zx

~

Singles

°o

=

x •

104sect I

o •

x

Ra'te = 2 5 x

o

x

102

o

0

/

7 3 key Pb X r a y

511 ke

/

x xx x x •

-I0

,

,

i

I

,

i

i

-5

i

I

,

0 Delay

Time ~

,

,

,

I

.5

,

,

20

ix I0 nsec

Fig. 11. T h e N a l ( T l ) t i m e r e s o l u t i o n o b t a i n e d u s i n g t w o fast d i s c r i m i n a t o r s w i t h (a) a n d w i t h o u t (b) p u l s e h e i g h t c o m p e n s a t i o n . T h e e n e r g i e s d e t e c t e d w e r e c h o s e n to be 1 0 0 - 1 5 0 k e V f o r one counter a n d 511 k e V f o r t h e o t h e r a n d t h e c o n v e r s e .

40

60

80

Pulse H e i g h t ,

lOG Channels

I

i

17'0

140

=

Fig. 13. T h e Nal(T1) pulse height spectra obtained using time converted energy pulses f r o m one c o u n t e r gated by 2y annihilation coincidences from a second counter. A c o m p a r i s o n o f the two curves obtained at different singles rates m a y be used to estimate the pile up resolving time o f the system.

A L L E N P. M I L L S , JR.

.5/2,

The performance of the trigger level stabilizer is shown in fig. 12 which is a plot of the fast discriminator triggering rate as a function of the feedback current to the tunnel diode. Ordinarily the tunnel diode would %

I10

I I00

u

.5

have begun oscillating at about 1 mA. However, the negative feedback keeps the rate increase to only 4.5% per 100 keV of threshold change. The differential linearity of the voltage to time converter (VTC) was measured to be + 3 % in the range 50-500 keV. Fig. 13 shows the VTC spectra of one counter gated by 27 coincidences with a second counter. The gated VTC output was integrated and analyzed on a 400 channel R I D L analyzer. The energy resolution is 9.6% at low counting rates and becomes 10.0% at a singles rate of 170k s -1. The pile up fraction at the high counting rate may be estimated to be about 7.5% from the increase in counts with energy above the 511 keV photopeak. From this we determine that the pile up resolution time is approximately given by

@

2r = 0.075/170 000 = 440 ns.

E ~a ta z~ o~ 90

80

i

1750

1

1800 High Voltage

t

1850

1900

~,

Finally, the pulse height stabilization plateau is shown in fig. 14. A 100 V change in the high voltage causes less than 0.1% change in the gain. The slopes of the curve outside the stabilization range indicate that a 10 V change would ordinarily cause a 4% gain shift which means that the stabilization factor is ~ 400. A summary of the above results and a few additional specifications are listed in table 1.

Volts

Fig. 14. T h e pulse height stabilization plateau s h o w i n g the over all system gain as a function o f the high voltage applied to the photomultiplier voltage divider.

Appendix Since some of the above circuitry requires the use of fast temperature stabilized amplifiers we present here -24

-}2

2.2K t 47,

-12 47

'~ I

^"¢~-~I~-('-~') MPs6518 T C .-- L /-q_=5., I ^~^^~ J"

9Volt ,5 Zener

..~K

.02 'F--¢ MPS6518

I.SK

+lz

~;

I

t

r

I+,2 {

J .O2T

"7I

:.02

390

I0,~ In

IO,t2 Out

Fig. 15. A circuit d i a g r a m o f the high slew rate low drift operational amplifier used for amplifier AI o f fig. 2 a n d A6 of fig. 6.

DISCRIMINATOR

F O R USE W I T H

TABLE 1 Specifications.

1. Gain stabilizer reduces gain shifts by a factor o f 400. 2. Peak shift versus c o u n t i n g rate ( + 0 . 2 4 4 - 0 . 1 ) % / 1 0 5 cps. 3. Peak c o u n t i n g rate versus t e m p e r a t u r e using 64Cu source with RI~, : 7.25 × 104 s 1 a n d Rpeak : 2.05 × 104 s 1: dRpeak dT

-

+ 0.07O/o/OC.

4. T e m p e r a t u r e d e p e n d e n t time shift o f P H c o m p e n s a t o r = 4- 20 ps/'~C. 5. C h a n g e in RI~, versus threshold = 4 . 5 % / 1 0 0 keV. 6. V T C linearity 50-500 k e V = 4 - 3 % differential, 4-0.3% integral. 7. Pile up resolving time 2 r ~ 440 ns. 8. Pulse height resolution at c o u n t i n g rate o f 1.7 × 105s 1 = 10.0% at 51 l keV.

the circuit diagrams for the two amplifiers we have designed. The basic idea is well known: one uses a slow but stable amplifier (in this case a 709 integrated circuit operational amplifier with an input offset voltage drift of 4- 10 #V/°C) to correct for the thermal drift of a fast amplifier. The first amplifier is shown in fig. 15 and is the circuit used for A 1 of fig. 2 and A6 of fig. 6. This amplifier has an FET source follower (2N3819) input to keep the input offset current low. The 709 measures the input offset voltage through the 1 kf2 resistor and adjusts the voltage on the emitter of the main amplifier transistor Q1 via emitter follower Q2 until the input offset voltage -24 In

47

O2

270

151<

47

o-.-.vw,~ 47

47

47

+1I47 z

02

MPS6518 27O

2N3663 47

o Out

)2i~_ --~1-¢

..q•TT

25 pf

471 IO/~f

~

)2N706

l" I i

IK .o2 47

+12

390 Fig. 16. A circuit d i a g r a m o f the low input offset voltage current amplifier used for amplifier A2 o f fig. 2 a n d A 4 of fig. 4.

NaI(TI) D E T E C T O R S

373

is near zero. Q3 provides a constant current load for Q1. The output from the collector of Q1 drives emitter follower Q4 which in turn drives the output emitter follower pair through the 9 V zener. This amplifier is to be used as an operational amplifier. With 1 kf2 shunted by 8.2 pF in series with the input and with a 10 kf2 feedback resistor (from " o u t " to "in"), the gain is 10, the half power bandwidth is dc to 19 M Hz, the rise time is 20 ns with 10% overshoot, the output voltage range is + 8 to - 3 V, the input offset voltage is typically a fraction of a millivolt, and the slewing rate at the output is 1000 V//~s. The input offset voltage and frequency response of this amplifier can be duplicated by available integrated circuits but these typically specify a slewing rate of ~ 50 V/#s which was too small for our puposes. The second amplifier is shown in fig. 16 and is the circuit used for A2 of fig. 2 and A4 of fig. 4. This is a moderately fast current amplifier (MPS6518-2N3663) whose input offset voltage is held near zero by the 709 IC and 2N706 transistor. The current gain is G ~, 1 + Rr/Rc, where Re is the 270 f2 output transitor (2N3663) emitter resistor and Rf is the 470 £2 feedback resistor. The actual current gain was found to be 2.4. The rise time was 2.4 ns and was limited principally by the plug in printed circuit design we employed. The input impedance is 50 f2 and the output impedance is 1 k~2. References 1) See various articles in Alpha-, beta- and gamma-ray spectroscopy (ed. K. Siegbahn; N o r t h - H o l l a n d Publ. Co., A m s t e r d a m , 1965); J. B. Birks, The theory and practice o f scintillation counting (Macmillan Co., New York, 1964). 2) C. H o h e n e m s e r , R. R e n o a n d A. P. Mills, IEEE Trans. Nucl. Sci. NS-17 (1970) 390, a n d references therein. 3) O(t) is the unit step function, O(t) = St_ ~: ,5(t')dt'. 4) A. W h e t s t o n e a n d S. K o n n o s o , Rev. Sci. Instr. 33 (1962) 423. A. Whetstone, Rev. Sci. Instr. 34 (1963) 412. 5) H. Weisberg, P h . D . Thesis (Brandeis University, 1965) available from University Microfilms, A n n Arbor, Michigan, U.S.A.; H. Verweij, Nucl. Instr. a n d Meth. 41 (1966) 181; P. Thieberger, Nucl. Instr. a n d Meth. 44 (1966) 349; D. A. Gedeke a n d M c D o n a l d , Nucl. Instr. a n d Meth. 55 (1967) 337, 51 (1967) 325, 5 8 (1968) 253. 6) K. Fr~inz and K1. Mfiller, Nucl. Instr. a n d Meth. 22 (1963) 43. 7) S. L. Blatt, J. M a h i e u x a n d D. Kohler, Nucl. Instr. a n d Meth. 60 (1968) 221 ; also, see for example, C. Brassard, Nucl. Instr. and Meth. 94 (1971) 301. 8) W. H. Venable, Jr., Rev. Sci. Instr. 37 (1966) 1443. 9) See, for example, F. R. Lenkszus a n d S. J. R u d n i c k , IEEE Trans. Nucl. Sci. NS-17 (1970) 285.