A new 4πβ-multiwire proportional counter for the 4πβ − γ coincidence measurement

International Journal of Applied Radiation and Isotopes, 1973,Vol. 24, pp. 65--72, Pergamon Press. Printed in Northern Ireland

A New 4TC ,-Multiwire Proportional Counter for the 4g -Y Coincidence Measurement j. PLCH, J. ZDERADI~KA and L. KOKTA Institute for Research, P r o d u c t i o n a n d Application of Radioisotopes, Prague, Czechoslovakia

(Received 17 April 1972; in revisedform 29 September 1972) A new multlwire p r o p o r t i o n a l counter was proposed to reduce the resolving t i m e in the 4zrfl -- 7 coincidence m e t h o d . O n the basis of the calculation of the i o n - n u m b e r distribution a n d the inefficiency, t h e lowest h e i g h t of the c o u n t e r was estimated a n d it was shown t h a t it c a n n o t b e considerably r e d u c e d below 10 m m . A counter with a c o u n t i n g volume of 60 × 60 × I0 m m in one h a l f a n d with 11 wires of 2 0 / ~ m d i a m e t e r was tested. T h e counter, filled with technical-grade m e t h a n e , exhibited good t i m i n g properties; the F W H M o f the t i m e s p e c t r u m was 18 nsec a n d the full base w i d t h was 100 nsec w h e n new fast i n t e g r a t e d electronics was used. A fast R C - s h a p i n g e n a b l e d a short d e a d time of a b o u t 2/~sec in the b e t a - c h a n n e l to b e applied. A good c o u n t i n g plateau, of a b o u t 400 V with the slope less t h a n 0.2~o/I00 V for ~°Co a n d less t h a n 0.1 ~o/I00 V for 9°Sr, was m e a s u r e d even at h i g h c o u n t i n g rates.

UN

NOUVEAU COMPTEUR PROPORTIONNEL 4~rfl A M U L T I F I L POUR LA MESURE DE COINCIDENCE 4rrfl--7

O n proposa u n n o u v e a u c o m p t e u r p r o p o r t i o n n e l ~ multifil p o u r r6duire le temps de r6solution dans le m d t h o d e de coincidence 4~rfl -- 7- Sur la base d u calcul de la distribution des n o m b r e s d'ions et de l'inefficacit6, on estima le m i n i m u m de h a u t e u r d u c o m p t e u r et il fur m o n t r 6 quececi n e pouvait 6tre rdduit ~ b e a u c o u p moins de I0 m m . O n fit des essais avec u n c o m p t e u r a y a n t u n volume de c o m p t a g e de 60 × 60 × 10 m m dans u n e moitid et 11 ills de 2 0 / 2 m de diam6tre. Le c o m p t e u r , r e m p l i de m d t h a n e de qualit6 technique, m o n t r a de bonnes caract6ristiques de temps; la v a l e u r F W H M d u spectre de temps rut 18 nsec et la largeur totale de base rut 100 nsec l o r s q u ' o n se servait de nouvelles et rapides pi6ces 61ectroniques intdgrdes. U n e formation R C r a p i d e p e r m i t l ' a p p l i c a t i o n d ' u n t e m p s - m o r t b r e f d ' e n v i r o n 2 /~sec dans le canal ft. O n m e s u r a u n b o n p l a t e a u de c o m p t a g e d ' e n v i r o n 400 V a y a n t u n e p e n t e de moins de 0,2 ~o/I00 V p o u r le ~°Co et moins de 0,I ~ / 1 0 0 V p o u r le ~°Sr, m~me p o u r les t a u x de compte 61evds.

H O B b I I ~ 4~rfl-MHOFOHHTHM17I C t t E T t l H H I I P O H O P I H / I O H A J I b H O F O T H I I A )~JIH H 3 M E P E H I / I H 4 , r f l - - 7 C O B I I A ~ E H H Y I Ilpe;moaoa~e~ noBL~II IIpOnOplDIOHaJIbULn] CqeTtlHK coKpaTI4Tb p a a p e m a m m e e BpeMH B MeTo~e 4~rfl -- ~ C0BHa~eHH~. H a 0CHOBeB~I~HcaeHHHpacrlpe~eJIeHHHq~caaHOHOBHad~eHTHBH0CTtl ~aeTc~I OI~eHHa HaH6oJiee iti43HOl~ BLIC0T]bI, 1]0Ha3alI, qTO He B03MOH~HO 3tIaqHTeJII)H0e yMeHhmeH~e Hnme 10 MM. I/IcHHTaH CqeTqHK C C~IeTHI)IM06~eMOM 60 × 60 × 10 MM B O~HOI~ n0~0BMHe I4 C 11 np0BOJIOKaMH ~ a M e T p a 20 /~M. Hano~HeI~nJ,ifi c TexHI~qecI~IM MeTaHOM ctIeTql4H xapaRTep~aoBaH xopoILII4MH CBOi~CTBaMH xponHpoBa~Hn; xapaKwepMcTnRa (HIIIBM) BpeMeHHOrO cneKwpa 6Liaa 18 HceH, a noaHaa 6asoBau m ~ i p ~ a 6Liaa 100 Hce~ npH IlpI4MeHeHI4~ 5~ICTpO~etlCTBy~)mei~ nnverp~posamloi~ a~eHTpOKHHH. BLICTpoe ~OpM~IpOBaH~Ie I~C ~aeT BOSMOH~HOCTI~IIptlMeHHTb HopoTHoe BpeMH Balla3~,iBaH~I~ ~ 2 /*cen B 6eTa-I~aHa~ie. ~ a m e n p a n a a ~ BI)ICOH~IX cHopocTm] cqewa ~aaMepeHo xopomoe c~eTnoe n a a ~ o ~ 4 0 0 s c n a ~ a o n o ~ < 0 , 2 ~o/100 t3 ~ a a ~°Co, a < 0 , 1 × / 100 B ~zla ~°Sr. 65

66

J. Plch, J. Zderadi&a and L. Kokta

EIN NEUER 47r/%MEHRDRAHT-PROPORTIONALER Z A H L E R Z U R 47r/3 -- 7 K O I N Z I D E N Z Z A H L U N G Ein neuer proportionaler Mehrdraht-Z/ihler wird vorgeschlagen, um die Auflbsungszeit bei der 4rrla -- y Koinzidenzmethode zu verktirzen. Auf der Grundlage einer Berechnung der Ionenzahl-Verteilung und der Unwirtschaftlichkeit wurde die kleinste H6he des Z/ihlers gesch/itzt und es zeigte sich, dass sic nicht viel unter 10 mm verringert werden kann. Ein Z/ihler mit einem Z/ihlvolumen von 60 × 60 × 10 mm in einer H~ilfte nnd mit 11 Dr~ihten von 20 /*m Dm. wurde erprobt. Der mit Methan technischer QualitM gefiillte Z~ihler hatte gute Zeitgebereigenschaften; die F W H M des Zeitspektrums war 18 nsec, und die volle Basisbreite war 100 nsec, wenn eine moderne schnelle integrierte Elektronik benutzt wurde. Schnelles RC-Formen erbracht eine kurze Totzeit von etwa 2 /~sec im Betakanal. Ein gutes Z/ihlerplateau von etwa 400 V mit einer Neigung von unter 0,2 ~/100 V fiir 6°Co und unter 0,1 ~/100 V fiir 90Sr wurde selbst bei hohen Z~ihlgeschwindigkeiten gemessen.

1. I N T R O D U C T I O N THE 4¢rfl - - y coincidence m e t h o d is c u r r e n t l y r e c o g n i z e d as a m e t h o d p r o v i d i n g the most accurate primary measurement of a radioactive sample. T h e m e t h o d is used in most l a b o r a t o r i e s a n d has been discussed b y several authors. (1-6) T h e a c c u r a c y of the a c t i v i t y d e t e r m i n a t i o n is l i m i t e d b y the a c c u r a c y of corrections a p p l i e d to the result of the m e a s u r e m e n t as well as b y the statistical error. T h u s the u n c e r t a i n t y in the c o r r e c t i o n for c o m p l e x d e c a y scheme a n d the inaccuracies o f the i n s t r u m e n t a l c o r r e c t i o n for d e a d time a n d a c c i d e n t a l coincidences cont r i b u t e to the total error. T h e c o r r e c t i o n t e r m due to resolving time d o m i n a t e s in the ins t r u m e n t a l correction. T h e i m p r o v e m e n t follows from r e d u c i n g the time j i t t e r o f the b e t a c h a n n e l pulses w h i c h effectively d e t e r m i n e s the resolving time of the system. (7-9) T h e cause o f the inferior time p r o p e r t i e s o f the b e t a - c h a n n e l lies p r i m a r i l y in the c o m m o n l y used p i l l - b o x or a n o d e - l o o p c o u n t e r w i t h one wire as there a r e large parts of the c o u n t i n g v o l u m e w i t h a low intensity o f the electric field a n d therefore w i t h a r a t h e r long collection time of electrons. T h e muhiwire proportional counter (MWPC) proposed b y C H A R P A K for a p p l i c a t i o n in high e n e r g y physics (1°-14) enables a r e d u c t i o n in the collection time. T h e M W P C combines the p r o p e r t i e s of the c y l i n d r i c a l a n d p a r a l l e l - p l a t e c h a m b e r s . Thus, even n e a r the c a t h o d e the field is such t h a t the electron drift velocity is saturated.(l~) T h e design o f the c o u n t e r a n d the electronic

system as well as e x p e r i m e n t a l d e s c r i b e d in the p a p e r .

2. C O U N T E R

DESIGN

results a r e

AND

CONSTRUCTION I n o r d e r to decrease the collection time the c o u n t e r h e i g h t should be r e d u c e d as m u c h as possible. H o w e v e r , w h e n r e d u c i n g the ionization p a t h we m a y c o m e to a p o i n t w h e r e fast b e t a - p a r t i c l e s do not c r e a t e sufficient n u m b e r o f ions. T h e i o n - n u m b e r d i s t r i b u t i o n was calc u l a t e d (see A p p e n d i x ) to d e t e r m i n e the r e l a t i o n b e t w e e n the necessary sensitivity a n d the l e n g t h o f the i o n i z a t i o n p a t h . O n the basis o f the d i s t r i b u t i o n function, shown in Fig. 1, the following sensitivities for r e a c h i n g 99"9 p e r cent efficiency were c a l c u l a t e d : Ionization path (ram) 10 Sensitivity (number of ions) 29

8

6

5

22

14

11

4

3

7 4

2'5 1

T h e c o u n t e r h e i g h t also relates to the c o u n t e r w i d t h w h i c h m u s t be a b o u t 5 c m in o u r case d u e to the s a m p l e d i a m e t e r . By r e d u c i n g the h e i g h t we increase the r a t i o b e t w e e n the m a x i m a l a n d m i n i m a l ionization, i.e. the d y n a m i c r a n g e of the pulse-heights; consequently the c o u n t i n g p l a t e a u deteriorates. As a c o m p r o m i s e b e t w e e n these different requirem e n t s the height of 10 m m was chosen w h i c h ensures a collection time of a b o u t 40 nsec a n d gives a d y n a m i c r a n g e of a b o u t 1 : 300, while the sensitivity for r e a c h i n g the p l a t e a u should be

A new 4,rfl-multiwire proportional counterfor the 4rrfl -- 7 coincidence measurement

s e p a r a t e h o l d i n g t u b e a n d small i n s u l a t o r (see Fig. 3). This system is m o r e c o m p l i c a t e d t h a n the usual m e t h o d of soldering the wires to a p r i n t e d b o a r d b u t t h e s i m p l i c i t y of wire r e p l a c e m e n t in the case o f c o n t a m i n a t i o n should b e t a k e n into a c c o u n t . G r e a t a t t e n t i o n was p a i d to the tolerances o f the wire s p a c i n g a n d to k e e p i n g the wires at the s a m e distance from the central plane. A standard deviation of the spacing o f 0.07 m m was o b s e r v e d ; t h e m a i n cause is the wire d i s p l a c e m e n t in the h o l d i n g tubes.

0.25

0-20

0.15

3. E L E C T R O N I C

O.IO

00 "0 5

0

67

IO

20 3,0 Number of ions

40

FIG. 1. The ion-number distribution for the ionisation path equal to 5 mm in methane. The distribution involves both the statistical nature of ion formation and the statistics of the gas-multiplication. Curve (1) represents the Landau distribution p(Ni) for the ionisation path equal 5 mm (N~ = 23); curve (2) represents the gas-amplification distribution P(n, Ni) ; curve (3) shows the resulting distribution Q(n) and curve (4) shows the efficiency W(n) as a function of the sensitivity expressed in terms of ion number. a b o u t 30 ion-pairs w h i c h c a n b e a c h i e v e d w i t h fast electronics a n d a c c e p t a b l e gas a m p l i f i c a t i o n . T h e w i r e s p a c i n g a n d d i a m e t e r influence the field d i s t r i b u t i o n . As no space resolution was r e q u i r e d w e used a s p a c i n g o f 4-6 m m a n d a d i a m e t e r o f 20 # m . F i g u r e 2 shows the field d i s t r i b u t i o n in the p r o p o s e d c o u n t e r . T h e field s t r e n g t h is less t h a n 760 V / c m in a small v o l u m e b e t w e e n the wires w h e r e the electron velocity is n o t s a t u r a t e d . I t constitutes a b o u t 0.1 p e r cent o f the t o t a l v o l u m e . T h e c o u n t e r c o n s t r u c t i o n was b a s e d on t h e a b o v e considerations as well as on g o o d exp e r i e n c e w i t h the p i l l - b o x t y p e (n) w h i c h has b e e n used for years. T h e new c o u n t e r is a m u l t i w i r e version o f the p i l l - b o x w i t h 11 wires, e a c h w i t h a

SYSTEM COUNTER

O F T H E 4n[3-

I n o r d e r to get a g o o d c o u n t i n g p l a t e a u the electronic system should fulfil the following r e q u i r e m e n t s : it should h a v e a sensitivity o f about 5 mV and exhibit good overloading properties, i.e. it should n o t g e n e r a t e false a d d i t i o n a l pulses w h e n a large pulse a p p e a r s . As r e g a r d s the t i m i n g p r o p e r t i e s fast circuits w i t h the rise t i m e o f several nsec a r e d e s i r a b l e not to spoil the q u a l i t y o f the c o u n t e r . Io"

td

E

/

,o~

\y,,y.o,

//E.(x-s/2)\

Vy

l

)

Cai'hode

I V ~........ t~ ...... z~ oxis x

~_ ~- sd

Io'[0

I

1

I

I

1

|

2

3

4

5

Distance

f r o m c e n t r e of

w i r e - x , y , , mm

FIG. 2. Electric field as a function of the distance from the centre of the wire; H V = 3 k V ; d=20#m; L =5mm.

68

J. Plch, J. Zderaditka and L. Kokta

FIG. 3. Counter construction. The pulse shaping is of primary importance for solving the problems mentioned above. The induced current pulse from the counter consists of two components:(lO) the fast one caused by ion motion in the cylindrical field and the slow one by motion in the homogeneous field. The slow component, which lasts 70 psec constitutes about 60 per cent of the total charge. This slow part must be reduced as much as possible to get a suitable pulse for high counting-rate measurements. This can be done using a short RCshaping constant in the input network and further differentiation in the amplifier. As the initial part of the pulse is very fast a short RCconstant can be used without losing much charge. A calculation indicates that the pulse height corresponding to 20 per cent of the total charge is gained when the first time constant is 200 nsec and the second one 400 nsec. Such a fast shaping is desirable to reduce the influence of the undershoot on the system dead time.(lg) The dead time of about 2 ,usec is long enough to eliminate any influence of the undershoot. The input pulses taken from the counter by means of the emitter follower are shown in Fig. 4 for the case when the counter was irradiated by alphaparticles. When beta-particles are detected the initial part of the pulse is built up from small, statistically distributed sub-pulses; the length of the fast component does not exceed 50 nsec here either. In order to realize KAWADA’S(~~) principle of the gamma-sensitivity measurement, the elec-

tronic system was separated into two independent channels, connected to the upper and lower halves of the counter respectively, and provided with logical summing at the output. A lower input capacity and therefore higher charge sensitivity can be reached in this way. The choice of the circuits was determined by the major requirements concerning the rise time, the stability of the delay and the reliability of the beta-channel. The design was based on the use of the integral circuit SN 75 108 as a discriminator. Its minimal sensitivity is about 5 mV and the delay of the output pulses is nearly stable. The videoamplifier SN 72 733 with the gain of about four increases the input sensitivity. The discrimination level is adjustable from 2 to 10 mV. The multivibrators SN 74 121 form the logic pulses and determine the dead time of the system which is about 2 psec. Attention was paid to the stability of the delay between the input and output pulses. The delay depends on the amount by which a pulse exceeds the discriminator level. If the pulse exceeds the level by a few per cent only the line receiver SN 75 108 creates an additional delay up to 30 nsec while for the pulses exceeding the level by 20 per cent the delay is stable to within a few nsec. The complete circuit diagram and the other technical information are given in Report NO. 2 of The Institute for Research, Production and Application of Radioisotopes (UVVVR) .

FIG. 4. Pulses from one-half of the counter alpha-particles, HI’ = 3 kV; 100 mV/cm; resistor I kR.

after an emitter follower, 100 nsec/cm; input

68

A new 4~r~-multiwire proportional counterfor the 4~r[~ - -

V Y N S foil sample

nsec

,I" I1~' 2 5 n s e c

69

coincidence measurement

~

A I - s a n d w i c h sample

1[__[25nsec

Channel n u m b e r

FIO.

5.

Gamma-gamma t i m e spectrum and beta-gamma time spectra; H V = 3 kV;

4. EXPERIMENTAL R E S U L T S 4. I Time spectrum and delay coincidence curve

T h e time spectrum, i.e. the time distribution of the output pulses from the beta-channel with respect to a fixed reference time, was measured with the 6°Co-sources. T h e reference time was taken from the gamma-channel, where the NaI(T1) scintillation probes, the spectrometric amplifier and the cross-over timing single channel analyzer were used. T h e g a m m a g a m m a time spectrum in Fig. 5 was obtained by means of two identical gamma-channels while the b e t a - g a m m a spectra by the described beta-system and one gamma-channel. T h e intrinsic F W H M of the beta-channel is about 22 nsec. T h e shortest resolving time of the coincidence circuit necessary for reaching 100 per cent efficiency can be estimated from the full base width of the time spectrum. T h e base width of the spectrum given in Fig. 5 equals 100 nsec. T h e spectrum is rather asymmetric due to an additional delay created by the small pulses. For similar reasons there is a shift of about 10 nsec when the spectrum is measured at the beginning of the counting plateau. T h e shape of the time spectrum depends on the sample quality. T h e results given in Fig. 5 were obtained by measuring a 6°Co sample sandwiched between Al-foil of 500 Fg/cm 9" and by measuring a e°Co sample on a gold coated VYNS film of about 30/zg/cm s. The greater

20 nsec/cm.

n u m b e r of delayed pulses is caused by a more frequent occurrence of soft particles. T h e fullwidth of the time spectrum is about the same. Figure 6 shows the curve of the delayed coincidences measured with the ~°Co-sandwichsample and with a resolving time of 206 nsec. I t is obvious that 100 per cent of the " t r u e " coincidences are registered. In order to compare the time properties of the new system with those of the old one, the time spectrum of the channel with the pill-box type counter was measured. T h e old system is equipped with medium-speed electronics (the rise time is about 0.1/~sec); the pill-box has a 0.8 0.7 =206nsec

0.6 0.5 z 0.4 z ~

o 0.3 :~ n.-

0,2 0.1 - 0

-[00

0

t00 Delay,

L

,

200

3OO

nsec

FIG. 6. Delay coincidence curve; beta-counting rate of about 1.6 × 104sec-1; coincidence resolving time is 50 nsec and 206 nsec.

70

J. Plch, J. Zderadi&a and L. Kokta

6 0 m m diameter and is 2 0 m m high. A comparison of the time properties is given in Table I.

P64

TABLE 1. Comparison of time distributions I-7o

~63

-

Distribution (nsec) Counter

Electronics

MWPC MWPC Pill box

FWHM

New Old Old

Base width

25 53 100

100 200 400

o b69 -~n ~0" 1"68

o o

It was observed that the plateau exhibits the

slope of the plateau was higher for the 6°Co-

sample prepared on the VYNS-film. When very soft particles were absorbed in the Al-foil the slope drops; this can be seen in Fig. 8 showing --

/

6°Co Scale on the I ~ t

6.[ -

~

-

0.2%/100

5'9

/

70

09 to

5"8

to ~ O × 5'7

8-1 80, 79 --- 7.8

Scale on the right

== o o

5.6

7"7

5.5

7.6

54

7,5

"3 _~ E Z

5.3 5.2

-- 7"q

1 l

2"7

,62 ,6,

_~w

/ /------~-

l

Scale onfhe left

159

0~ 1.65

[58

1.64

-- 157

- 156

1"63

I

2.7

28

T

29

I

50

High voltage,

~

3t

i

52

1

55

3"4

kV

FIG. 8. Counting plateau with a sample of 6°Co in an Al-sandwich of 500 #g/cm 2. The influence of the electronic dead time.

8'3 8.2

6-0

Scale onthe right

;o2,/ 1

!.67

166

smallest slope when the sensitivity was about 4 mV. If the gold-coated film was not sufficiently conductive there was a tendency to create discharging small pulses, especially when the sample had high activity. As Fig. 7 shows, the

-~:325~c

[

x m

4.2 The counting plateau

6"2 F

/

the plateaus of the 6°Co-sandwich-sample with two dead times. As both the slope and the length are independent of the dead time there are no spurious pulses caused by the electronics. The plateau has small slope and a sufficient length up to very high c o u n t i n g rates;

this is

shown in Fig. 8 giving the result of a measurement with an activity of 1.4 × 10~ sac-1. The length and the slope of the plateau are about the same as in our old system with the pillbox counter which indicates that there are no essential differences in the gas amplification of individual wires. This was also proved by means of the collimated alpha-particles when the variation of ± 1.3 per cent in the peak position was found. It should be stressed that technicalgrade m e t h a n e was used in all measurements.

The gas amplification changed from 3"2 × 10 5 to 3 × 106 w h e n the high voltage was varied

]

2"8

!

2:9

T

3"0

High voltage,

I

1

3-2

31

l 3-3

7.3 3'4

kV

FIG. 7. Counting plateau with a sample of 9°Sr-k 90y and with a sample of 6°Co on gold-coated VYNS-foil of 30 ffg/cm z.

from 2.7 to 3.3 kV. 5. C O N C L U S I O N S The experimental results show that the use of a Charpak type multiwire counter and fast electronics reduces the coincidence resolving

A new 4rr~-multiwire proportional counter for the 4~r[1 -- 7 coincidence measurement time to 200 nsec; this constitutes a b o u t ~- of the resolution g a i n e d i n the system with the pill-box type counter. T h e n e w system exhibits good c o u n t i n g plateaus with the slope less t h a n 0-2 ~ [ 100 V for 6°Co a n d less t h a n 0.1 ~ / 1 0 0 V for 9°Sr. T h a n k s to the fast shaping the defined dead time was r e d u c e d to 2/zsec. Acknowledgements--J. Plch would like to thank Prof. G. CHARPAK, Dr. MINTEN and all the members of the SFM-group in CERN for all their support and help during his stay in CERN. The authors are indebted to Dr. CAMPION for helpful comments during the preparation of the manuscript. The authors are obliged to Mrs. BOUKALOVA,Mrs. VLADYKOVAand Miss STI~fTESKAfor their assistance in the elaboration of the manuscript.

REFERENCES I. PUTMAN J. L. U.K. Atomic Energy Research Establishment, Report I/M 26 (1957). 2. CAMPIONP . J . Int. J. appl. Radiat. Isotopes 4, 232 (1959). 3. GANDY A. Int. J. appl. Radiat. Isotopes 11, 75 (1961). 4. CAMPIONP. J . and TAYLORJ. G. V. Int. J. appl. Radiat. Isotopes 10, 131 (1961). 5. KAWADAY. Int. J. appl. Radiat. Isotopes 20(6), 1961. v 6. BU~INAI., PLCH J., ZDERADICKAJ . and MARSAL J. dadernd energie 15, 369 (1969). 7. KARLSSONL. Nucl. Instrum. Meth. 93, 563 (1971). 8. WILLIAMS A. and CAMPION P. J. Int. J. appl. Radiat. Isotopes 16, 555 (1965). 9. MIGUEL M. and HOUTERMANSH. Proceedings of Symposium on Standardisation of Radionuclides, Vienna 1966, SM-79/60, pp. 135. 10. CHARPAK G. Ann. Rev. nucl. Sci. 20, 195 (1970). 11. CHA.RPAKG. et al. Time degeneracy of MWPC, CERN (1971). 12. MINTEN A. The split-field magnet facility, CERN/ISZC]71-79. 13. FISCHERG. and PLCH J. The high-voltage readout for MWPC, CERN (1971). 14. CHARPAK G. et al. Some features of large MWPC, CERN (1971). 15. CAMPIONP . J . Int. d. appl. Radiat. Isotopes 19, 219 (1968). 16. BERGER M. J. and SELTZER. Nucl. Sci. Series, Report No. 39 National Academy of Sciences, Washington (1964). 1 7 . C U R R A N S . C . e t al. Phil. Mag. 40, 929 (1949). 18. CHARLESH. W. and COOKE B. A. Nucl. Instrum. Meth. 61, 31 (1968). 19. PLCHJ. Int. J. appl. Radiat. Isotopes 22, 281 (1971).

71

20. KAWADAY. Int. J. appl. Radiat. Isotopes 20, 413 (1969). 21. BR~ONCE P. Rapport du directeur sur II'activitd et la gestion du Bureau International des Poids et Mesures, 2e S6rie, Tome 34, p. 68 (1966).

APPENDIX The ion-number distribution and the effciency of the electrondetection In order to simplify the calculation we shall assume that 1.3-MeV electrons are detected. The sensitivity is expressed in terms of the number of ions collected on the cathode. There are fluctuations of ion-number caused both by the statistical nature of the ion creation and by the gas-multiplication process. The particle loses a small amount of energy when the ionisation-path is much shorter than the range of the particle in the absorption medium. I n this case, the energy loss distribution can be expressed by the Landau function: p(co) --

1__ . e--ll 2(°J+e-°~) ~/2~r

(1)

where the energy loss w is expressed in terms of a universal variable o : o~ =

A L0 - - /23

(2)

a.R

A .

The term w xs the most probable energy loss equal to (1 -

~ 2 ) . i2

+ 1.12

)

(3)

where Z 1 a = 0.153. p ~ . ~-~

(MeVlcm)

(4)

p, Z, A are the density, atomic number and weight of the absorption medium; R is the length of the ionisation path I is the mean ionisation potential. The Landau function is assymetrical; the mean value of~5 is equal to 1.2704 while ~ocorresponding to the most probable loss is equal to zero. From our point of view the most important is the most probable ion number and the smallest number of ions produced on the ionisation path. We need to know the most probable energy loss but there are great discrepancies between the experimental data and the theory and as far as methane is concerned no experimental results have been published. Therefore a theoretical value, equal to 2-222 M e V . cm 2 . g-X was used for methane and minimal ionising electrons of 1.3 MeV according to the calculation in ref. 16.

J. Plch, J. Zderadi~ka and L. Kokta

72

T h e data necessary for the calculation are given in Table 2. The m i n i m u m numbers of ions Ni_99 and Ni_999 were calculated from the L a n d a u function by numerical integration determining the levels c%9, e%99 which are exceeded with probabilities of 0.99 and 0.999 respectively. Finally, the corresponding numbers of ions were computed. TABLE 2. T h e most probable energy loss ~, the most probable ion n u m b e r Ni, the mean n u m b e r of ions Ni and the lowest n u m b e r of ions Ni_99, Ni_999 for 1.3-MeV electrons and different ionisation path lengths R

?o

(mm)

(eV)

Ni

Ni

Ni-99

Ni-999

5 4 3 2 1

670 515 377 243 114

23 18 13 8 4

26 20 14.5 9.4 4.43

19.9 15-2 11-1 7.1 3.3

19 14.5 10-5 6.7 3.1

P(n, Ni)

It is obvious that the pulse-spectrum would be identical with the L a n d a u function if the gas amplification had no fluctuations. In fact the gas amplification process spreads this distribution. It was pointed out by CURRAN (17) that the probability distribution of the variable x, for instance the distribution of the pulse-height from the proportional counter, can be described by the function

P(x) = 1 . xN.,,_1. e-X tl m

--

3 2

= N.m.

(5)

(6)

As it is easier to express the sensitivity in terms of the number of primary ions, we shall assume that the gas-amplification factor equals one; this " u n i t " gas amplification transforms the n u m b e r of primary ions N/ into the n u m b e r of ions n with the probability P(n, Ni). It is clear that the probability function P(n, Ni) is identical with equation (5) when ~ = N i. T h e n we can write nNi -1

R

where

is the normalisation-factor equal to the Gamma-function, i.e. ~ = r(N. m) N i s the number of primary ions. The mean value of the variable x is equal to

. e -n

r(~v/)

(7)

The resulting ion-distribution Q(n), can be gained by multiplying the probability P(n, Ni) by p(Ni), which describes the probability of occurrence of the ion number equal to Ni, and summing the results for all N/. Thus we come to the equation

q(n) =

f0

P(n, Ni) . P( Ni) . dNi

(8)

where P(Ni) is the Landau function with the variable ~o expressed in terms of the ion number. The numerical integration leads to the results given in Fig. 2. I f the function Q(n) is integrated from the level n to the infinity in the following way W(n) =

f7

Q(n) . dn

(9)

then the term W(n) represents the probability of the electron detection when the sensitivity is equal to n-ion pairs.