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On selected problems in the field of proportional counters
NUCLEAR
INSTRUMENTS
AND
METHODS
112 ( 1 9 7 3 )
I03-I10 ;
©
NORTH-HOLLAND
O N S E L E C T E D P R O B L E M S IN T H E F I E L D OF P R O P O R T I O N A L
PUBLISHING
CO.
COUNTERS
W. B A M B Y N E K
Central Bureau for Nuclear Measurements, EURA TOM, B-2440 Geel, Belgium A brief review is given on s o m e parameters a n d physical effects which influence the m e c h a n i s m o f proportional counters. T h e following topics are discussed: gas amplification, space
charge, recombination, ion and electron transit times, efficiency o f counters operated at high pressure.
1. I n t r o d u c t i o n
the nature of the gas. Fig. 1 demonstrates this dependence for the rare gases. From eqs. (1) and (2) one can calculate
Proportional counters have been used for more than thirty years. They are powerful tools for the detection of nuclear and atomic radiations. Especially, if the intensity of low-energy radiation must be determined, the proportional counter is still the most suitable detector. Such detectors have been described in various excellent books and reviews 1-14) and there are numerous papers reporting on special aspects or applications. The scope of this paper is to give a brief review on some parameters and physical effects influencing the mechanism of gas filled proportional counters. 2. Gas gain
Let us consider cylindrical counters of diameter 2b with the wire of diameter 2a placed on the axis of the cylinder. The wire shall be positively charged in respect to the wall and the counter be filled with a gas or gas mixture of pressure p. Under these conditions the electrical field strength E per unit pressure at the distance r from the center is given by the relation
l n G _ t s(") a(S) dS paS(a) j S(c) p S 2"
(3)
Various relations have been derived for the gas amplification, depending on the function which has been used for the first Townsend coefficient ~/p = f ( S ) . Usually it is assumed that space charge effects, recombination of electron-ion pairs, photoelectric effect at the cathode, and electron attachement due to impurities can be neglected. Rose and Korff 16) calculated the mean energy of the electrons assuming that the most probable energy of the electrons is equal to the ionization energy and that the energy distribution of the electrons is decreasing for energies higher than the ionization energy. Additionally they assumed a linear energy dependence of 28
S(r) = E(r)/p = V/[pr In(b/a)],
(1)
where V is the applied voltage between cathode and anode. Electrons, which are produced inside the sensitive volume of the counter, move in the inhomogeneous field towards the central wire colliding many times with gas molecules but, nevertheless, gaining energy. At a certain distance c from the cylinder axis ionization of the gas molecules takes place. A Townsend avalanche starts and the total number of electrons increases rapidly. The mean amplification factor G is given by the relation
Xe
J
2/,
J
20
J
i/I J
~. 1 2 - - g o.
J
Kr
j__---f
8
4
I i
I
c~d r ,
(2)
f ~
J
' He extrap
In G =
f
200
t,O0
600
800
1000
1200
I/,00
1600 1800
Elp ( v o l t s l c m ' m m Hg)
where e is the number of ion pairs formed by one electron per cm of path (first Townsend coefficient). It has been shown that ~/p is a function of E/p and of
Fig. 1. First T o w n s e n d coefficient ct/p as a function o f the electric field E/p for rare gases according to v o n Enge115). (Courtesy o f Springer Verlag, Heidelberg.)
103 II. P R O P O R T I O N A L
GAS COUNTING
104
W. BAMBYNEK [
i
,
i
i
I
'
,
i
,
I
r
~
~
,
I
I
I
I
,.o I-
,
...o,! .ET.ANE
i
¢C
I0.0
B
9.0
A
(-
L~ v
p/
/
I
'°F,,,,,,,,,, 25.0
#v'
,l'o°o
32~
,°,, ",, ?,, '7,
30.0
35.0
Z.0.0
I/S'(a) ( v o l t s l c m
/.5.0
' m m Hg )112
Fig. 2. Test of the Curran-Craggs modified Rose-Korff theory according to measurements of Kisera7). (Courtesy of Martinus Nijhoff's Uitgeversmaatschappij, 's-Gravenhage.) Our notation is used at the abscissa and the ordinate.
the ionization cross-section and derived (4)
c~/p = ½ C~ S ÷ .
describe the experimental results. Kocharov and Korolev 18) pointed out that the parameter 7 is propor-
Integration of eq. (3) using this relation gives 0.3
In G pa S ( a )
Cz
C~
(5a)
IS(a)] ~"
The constants C a and C2 must be determined from measurements of the gas amplification G. Curran and Craggs 1) slightly modified the R o s e Korff theory and derived the relation In G pa [s(a)] ~
/
= C2 [S(a)] ½ - C1,
(5b)
which is of the same type as eq. (5a). Kiser 17) performed extensive measurements of the gas amplification using various counters and argonmethane mixtures at different pressures. He brought the Curran-Craggs formula to a form which in our notation is written as In G -- (a7) ÷ {C, IS(a)] ~ [pa S (a)] *
-
C2},
(5C)
where y is assumed to be a constant. Fig. 2 shows Kiser's results for pure methane. He concluded from the fact that one single straight line is not obtained that the Curran-Craggs theory does not correctly
°02
<
7
.¢
• ' 3
A
C
0.1
0
I 10
i 15
I 20
(volts/crn. torr) I12
Fig. 3. Experimental verification of the Rose-Korff formula as modified by Curran and Craggs according to Kocharov and KorolevlS). (Courtesy of Consultant Bureau, New York.) (a) Spectroscopically pure argon; (b) 50% A r + 5 0 %CH 4 (data of Kocharov and Korolev): • 1520 mm Hg, x 1140 mm Hg, O 760mmHg, A 410mmHg; (c)0.2% Ar+99.8%CH4 [data of Kiserl7)]: O 597 mm Hg, counter II, x450 mm Hg, counter II, A 375 mm Hg, counter III. Our notation is used at the abscissa and the ordinate.
SELECTED
PROBLEMS
tional to the pressure p. If this pressure dependence is taken into account, Kiser's data agree with the theory o f Curran and Craggs, as is shown in fig. 3. Diethorn 19) assumed a linear relation for the Townsend coefficient
cz/p =
D,S
(6)
and calculated lnG -
pa S(a)
D~[lnS(a)-lnDz].
(7)
The constants D~ and D2 have to be deduced from measurements. A similar relation has been deduced by Zastawny2°), who approximated c~/pby a linear function
B,(S-So),
c~/P =
105
with this relation yields
]
G pal uS(a-~) - K+B1 I In (S(a)~ 4- So - 1 . \ So ! S(a)
The constant K accounts for a small contribution, which arises f r o m the difference between the linear approximation and the real function o f ~/p for S~< S 0. Hendricks 2~) determined the gas amplification for various commercial proportional counters filled with X e - C O 2 or X e - C H 4 mixtures. He found that his results agree equally well with the predictions of both the Diethorn and the Zastawny equation, as is shown in figs. 4 and 5. Williams and Sara 22) used Townsend's 23) semiempirical expression with the two parameters A and B
c~/p = A exp(-B/S),
(8)
where B x and S O are constants. Integration o f eq. (2)
(9)
(10)
which has been proved in homogeneous fields to hold for S(a)% 200-300 (V/cm torr) 15,24), and derived
0 030
lnG
_ A exp
pa S(a)
i
-
--exp
-
.
(11)
B
I
0 025
The second term o f this equation can be neglected for counters filled with gas o f conventional pressure. However, for counters operated at very low pressure
I
95"/o Xe-5*/o COz
0 032 0 020 i ta
0028 I0 °/0 CH~
0.024 .
0015
.
.
.
. i
oo2oo 0010
-/
0016 ,~
,
i 1i_
o.o12
=
0005
o 4 75
500
525
tn S [a) Fig. 4. D i e t h o r n plot o f gas amplification d a t a for xenon-filled proportional counters having CO2 a n d C H 4 q u e n c h gas additives according to m e a s u r e m e n t s o f Hendricks21). (Courtesy o f N o r t h H o l l a n d Publishing C o m p a n y , A m s t e r d a m . ) T h e e m p l o y e d signs correspond to various counters operated u n d e r different conditions. O u r n o t a t i o n is used to denote abscissa a n d ordinate.
_
-4 o
0
f i
02
04
i
Z--,90o)oXe.d/.c /,'
-
-
i
-71
95'/.xe-5./.c0 0.008
t. 50
..de"- __H ~
T 06
I
i
J !
0.8
10
+ ~ J
12
14
tn(S(o.)/S o) ÷ So/S(a) -1 Fig. 5. Z a s t a w n y plot o f gas amplification data for proportional counters operated u n d e r the s a m e conditions as in fig. 4 according to m e a s u r e m e n t s o f Hendricks~l). (Courtesy o f N o r t h - H o l l a n d Publishing C o m p a n y , A m s t e r d a m . ) II. P R O P O R T I O N A L
GAS COUNTING
106
w. BAMBYNEK
it must be taken into account, as Campion 25) has pointed out. Under this condition a peaked gas gain vs pressure curve is obtained. In fig. 6 calculated gas gains as a function of pressure are compared with experimental results of Wilson and Field26). The constants A and B in eq. ( l l ) can be determined from measurements27). For large S values the exponential function in eq. (10) can be expanded and yields for
(12)
o~/p = K , ,
the approximation of Hristov 28) lnG
K1
pa S(a)
--
K
2
-
-
(13)
-
S(a)"
Various authors have performed gas gain measurements 2,16-20,22,26-47) and experimental tests of gas gain formulas. According to Zastawny 2°) one can distinguish about five regions of S with different functional dependences of ct/p on S. Therefore, it depends on the nature of the gas and the value of S in the counter which formula will yield the better results. This is supported by investigations of Specht and Armbruster44), who showed that for a-particles and light fission products in methane filled counters the theory of Rose and Korff ~6) describes the experimental
I ~
I
I
I
I
3. Space charge The influence of space charge has been recently investigated by Campion46), who found a deviation of the exponential gas-gain-voltage relation. There are two types of space charge effect. The "self-induced" space charge effect is due to the retarding influence of the positive ions on the electrons at the head of the electron cloud. It is larger in methane than in argonmethane mixtures. The "general" space charge effect is due to the integrated effect of the positive ions of
1
f
0.I0
p, j.'P'"
10 3 ,~.
I~
I
results very well up to values for S ( a ) = 5 × 10 4 (V/cm torr), as shown in curve A of fig. 7. The generally accepted theory of Diethorn 19) seems to agree only within a limited region of 100 < S(a) < 1000 (V/cm torr) (curve B of fig. 7). Also the widely used theory of Williams and Sara 22) is only valid for S(a) values of less than about 200-300 (V/cm torr), as Campion 46) has shown, and leads to discrepancies for large S(a) values (curve C of fig. 7). Recently, gas gains of up to 10s have been reported for an argon-isobutane mixture to which 0.2% of freon 13B1 has been added48). The exact mechanism for the action of the freon is not yet understood. Similar gases do not produce the same result. Probably, negative freon 13B1 ions have some special affinity for neutralizing positive argon ions.
-.
~._
~
6O 0v
B p p'" /"
6
~ 10
.'..:"
/'
v
"" . . . .
d 0.02
10
20 oressure
30 (torr)
LO
50
Fig. 6. G a s gain as function o f pressure according to Campion25). (Courtesy o f T h e Institute o f Physics, Bristol.) Full lines indicate calculated values using eq. (11), b r o k e n lines those neglecting the second term. T h e calculations were m a d e for a n o d e a n d c a t h o d e radii o f 63.5/~m a n d 1.59 m m , respectively. These values c o r r e s p o n d a p p r o x i m a t e l y to the experimental conditions used to derive the results o f Wilson a n d Field26), which are reproduced as dotted curves.
•_2_-_-2-~_ "~
102
103
I0 ~
IOs
S (a) ( v o t t s / c m ' torr)
Fig. 7. C o m p a r i s o n o f experimentally a n d theoretically obtained gas gains according to Specht a n d Armbruster44). (Courtesy o f Springer Verlag, Heidelberg.) T h e data points are taken f r o m the w o r k o f several a u t h o r s 16, 17, 44). Curve A represents the predictions o f the R o s e - K o r f f theory16), curve B that o f Diethorn's19), a n d curve C that o f the Williams' a n d Sara's 22) theory.
SELECTED
previous discharges as they drift across the counter. This effect depends on the counting rate. It is most prominent in large counters operated at high pressure because the effective counter potential is proportional to pZb3G In (b/a). Gas gain shifts due to space charge influences have been reported by Vogel and Fergason49). Hendricks 5°) has calculated the change of the peak position of X-rays to be proportional to pb 2 G 2 E 2, where E here means the energy of the X-rays. This prediction is in good agreement with his experimental results. Such peak shifts have also been reported by several other authorsS1-53). 4. Recombination Practically no information could be found on recombination of ions in proportional counters. Usually the recombination of two oppositely charged ions is described in terms of their recombination coefficients ft. It is defined as the recombination rate N per unit volume and unit time devided by the ion densities n+ and n_
N = fin+ n _ .
(14)
F r o m the various possibilities for electron-ion recombination the dissociative recombination seems to be the most probable one. It takes place when a radiationless transition occurs to some state of the molecule XY (XV) + + e - --* (XY)* --+ X* + Y*.
(15)
The asterisks indicate that the atoms may be left in excited states. The recombination coefficient for this type of recombination amounts between 10 - 6 and 10 -8 (cma/sec), at gas temperature of 300 K. The coefficient for other modes of recombination, as the radiative, dielectronic, and three-body recombinations, is of the order of 10-1°--10-12 (cma/sec) 54--56). It should be noted that in practice the ions are not uniformly distributed in the volume of a proportional counter. This is especially the case when ionization is produced by heavily ionizing particles like a-particles. In this case the local density of ions is much higher and the recombination will be greater.
PROBLEMS
107
the positive ions. It amounts to only a few percent. The electron transit time t_ in cylindrical counters can be described by the relation
t._ = a S ( a )
i
S(a)
dS/[S2 v _ ( S ) ] ,
where v_ (S) is the drift velocity of the electrons. A very simple expression has been derived 12'62) under the assumption that v_(S)ocS. Another approach 3) assumed vi(S)ozx/S. Such approximations are valid only in a very limited region, because the experimentally determined electron drift velocities 2'58-61) deviate considerably from a linear or parabolic law. In several gases they even have a peaked shape. Direct measurements of the electron transit time under various conditions have been performed by several autors46"69'7°). The transport of the positive ions is much slower due to the longer distance, which extends practically from the anode to the cathode, and also due to the drift velocity v+, which is approximately a thousand times l o w e r 63-65) than that of electrons. A linear 12,62) and also a parabolic 3) dependence on S has been assumed for v +. The transit time t+ of the positive ions can be calculated by a similar relation as eq. (16):
l+ = a S ( a )
i
S(r)
dS/[S2v+(S)].
(17)
d S(b)
6. Efficiency of proportional counters operated at high pressure For many investigations the knowledge of the efficiency of the counter is required. When the
source
2R
5. Ion and electron transit times The collecting times of electrons and positive ions, which are formed in the avalanche near the anode, influence the shape of the formed pulse 57) and are especially of importance when very high counting rates must be measured46). The contribution of the electrons to the total pulse is rather small compared with that of
(16)
J S(r)
sotid
source
2d A
,,t
'l
--
f -
angle
~,
k :
source prate -
J
,
2r
Fig. 8. Arrangement o f the source in the cylindrical counter. II. P R O P O R T I O N A L
GAS COUNTING
108
w. BAMBYNEK
intensity of X-rays has to be measured a large proportional counter operated at high pressure is often used. Mostly X-rays are produced by a nuclide decaying by electron capture. To stop the Auger electrons the source is placed between foils of sufficient thickness. In such a case care must be taken to avoid thin gas layers between the source and the electron absorbers. Already a thin layer of pressurized gas causes a considerable absorption loss. This effect is mostly not taken into account. For X-rays of 5.4 keV and a gas mixture of 90% Ar and 10% CH¢ at 5 atm pressure a gas layer of 0.008 cm results in an absorption of 2 % (gas density at 25 °C p = 1.536 (g/l), absorption coefficient/t = 316. I (cm2/g)). Calculations of the efficiency of X-rays in cylindrical counters have been reported by several authors66'67). We tried to verify experimentally the theoretical predictions for our two-D-shaped counter 6s) and did not get a good agreement. The source was prepared on
a thin plastic foil, mounted onto an A1 ring which was placed in the middle of the source plate, as shown in fig. 8. In a calculation o f the efficiency the definite thickness of the source plate must be taken into account. It cuts out a certain solid angle f2 in which absorption of the X-rays is only partly possible. The total transmission of the X-rays through the cylinder is given by
T = T4,~- Ts~+ TA,
(18)
where T4~ is the transmission through a cylinder in 4~ geometry, Tz is the transmission through that part of the cylinder which is cut out by the solid angle •, and T z is the transmission through the "triangle" which is limited by the solid angle t? and the cylindrical surface of the opening in the source plate. The calculation yields T =
i
(l/R)
arctg
cos0 exp(--I~R/cosO) dO +
j0
+ E 2 (/d) - (R 2 + 12)-½ E2 [it(R 2 + 12)~] _ 1.o ¸
-
½r~
i
arctg
(d/r)
cosO
x
do
x
EK X
exp(-pl/cosOcosq)) d~o dO 0
i
arctg
cos 0 x
- ½rrdo
x
(d/r)
exp(-pR/(cos2Osin2~o+sin20)~)dq)
dO+
LJ ~M
0.9
+
i
arctg
(d/r)
cos 0 e x p ( - / t r / c o s O) dO,
(19)
dO with q ~ = arctg {[(R/1) 2 cos z O - sin 20] ~} and E2(x ) ---- x f x ° (e-tit 2) dt,
0.8 200
I 600
I 1000
I 1400
P P/Pr ( c r u z / g )
Fig. 9. Efficiency of the counter for K X-rays as a function o f the relative pressure times the absorption coefficient. As reference pressure Pr 1 atm has been chosen. The source was situated in the middle of the counter, as seen in fig. 8. The solid curves show calculated efficiencies neglecting (upper curve) and counting for (lower curve) the existence o f the source plate. The latter case agrees very well with the experimental points.
where 2l is the effective length of the cylinder, 2R its diameter, 2d the thickness of the source plate, 2r the diameter of the opening in the source plate, and ¢t the absorption coefficient. The integrals have been computed numerically and the result is shown in fig. 9, together with our experimental points for several radionuclides and various gas pressures. There is an excellent agreement between the measured values and the efficiencies which are calculated taking into account a definite thickness of the source plate.
109
SELECTED PROBLEMS
It is pleasure to acknowledge the experimental assistance given by Mr D. Reher. References 1) S. C. Curran and J. D. Craggs, Counting tubes (Academic Press, London, 1949). 2) B. B. Rossi and H. H. Staub, Ionization chambers and counters (McGraw-Hill, New York, 1949). 3) D. H. Wilkinson, Ionization chambers and counters (Cambridge University Press, Cambridge, 1950). 4) D. West, Progress in nuclear physics, vol. 3 (ed. O. R. Frish; Pergamon Press, London, 1953) p. 18. 5) S. Korff, Electron and nuclear counters (D. Van Nostrand, London, 1955). 6) S. C. Curran, in Handbuch der Physik, vol. 45 (eds. S. Fliigge and E. Creutz; Springer-Verlag, Berlin, 1958) p. 174. 7) W. J. Price, Nuclear radiation detection (McGraw-Hill, New York, 1958). 8) V. Kment and A. Kuhn, Technik des Messens radioakticer Strahlung (Akademische Verlagsanstalt, Leipzig, 1960). 9) C. Gatrousis, R. Heinrich and C. E. Crouthamel, Progress in nuclear energy, Ser. "IX, Analytical chemistry, vol. 2 (ed. C. E. Crouthamel; Pergamon Press, Oxford, 1961) p. 1. 10) W. Franzen and L. W. Cochran, in Nuclear instruments and their uses, vol. I (ed. A. H. Snell; J. Wiley, New York, London, 1962) p. 3. 11) E. W. Emery, in Radiation dosimetry, vol. II (eds. F. H. Attix and W. C. Roesch; Academic Press, New Y o r k / London, 1966) p. 73. 1_2) H. Neuert, Kernphysikalische Messverfahren (G. Braun, Karlsruhe, 1966). 13) S. C. Curran and H. W. Wilson, in Alpha-, beta- a n d g a m m a ray spectroscopy (ed. K. Siegbahn; North-Holland Publ. Co., Amsterdam, 1968) p. 303. 14) D. W. Aitken, IEEE Trans. Nucl. Sci. NS-15 (1968) 10. 15) A. von Engel, in Handbuch der Physik, vol. 21 (ed. S. Fliigge; Springer-Verlag, Berlin, 1956) p. 504. 16) M. E. Rose and S. S. Korff, Phys. Rev. 59 (1941) 850. 17) R. W. Kiser, Appl. Sci. Res. B8 (1960) 183. 18) G. E. Kocharov and G. A. Korolev, Izvest, Akad. Nauk. SSSR, Ser. Fiz. 27 (1963) 301 [Bull. Acad. Sci., USSR, Phys. Ser. 27 (1963) 308]. 19) W. A. Diethorn, NYO-6628 (1956). 20) A. Zastawny, J. Sci. Instr. 43 (1966) 179; A. Zastawny and J. Mizeraczyk, Nukleonika 11 (1966) 685; A. Zastawny, J. Sci. Instr. 44 (1967) 395. 21) R. W. Hendricks, Nucl. Instr. and Meth. 102 (1972) 309. °-e) A. Williams and R. I. Sara, Intern. J. Appl. Radiation Isotopes 13 (1962) 229. 23) j. S. Townsend, Electricity o f gases (Clarendon Press, Oxford, 1915). 24) H. Schlumbohm, Z. Angew. Physik 11 (1959) 156; Z. Physik 184 (1965) 492. 25) p. j. Campion, Phys. Med. Biol. 16 (1971) 611. 26) K. S. J. Wilson and S. B. Field, Phys. Med. Biol, 15 (1970). 657. 27) p. j. Campion and M. W. J. Kingham, Intern. J. Appl. Radiation Isotopes 22 (1971) 703. 28) G. L. Hristov, Dokl. Bulg. Akad. Nauk 10 (1957) 453 29) M. E. Rose and W. E. Ramsey, Phys. Rev. 61 (1942) 199. 30) C. S. Curran, J. Angus and A. L. Crookroft, Phil. Mag. 40 (1949) 36.
31) L. Colli, U. Facchini and E. Gatti, Phys. Rev. 80 (1950) 92. 32) E. Fiinfer and H. Neuert, Z. Angew. Physik 2 (1950) 241. 33) R. Fourage and L. Miramond, J. Phys. Radium 15 (1954) 780. 34) I. Kumabe and M. Sonoda, J. Phys. Soc. Japan 9 (1954) 877. 35) K. Schiitt, Z. Physik 143 (1955) 489. 36) T. A. Chubb, NRL Report 4814 (1956). 37) H. J. Stuckenberg, Dissertation (Universit/it Hamburg, 1958). 3s) K. van Duuren and G. L. Sizoo, Appl. Sci. Res. B7 (1959) 379. :39) S. Ramakrishna, Proc. Indian Acad. Sci. 51 (1960) 117. 4o) R. Engfer, Diplomarbeit (TH Darmstadt, 1960). 41) M. Pasternak and G. Ben-David, IA Report 713 (1962). 42) A. P. Lukirskii, O. A. Ershov and 1. A. Brytov, Bull. Acad. Sci. USSR, Phys. Ser. 27 (1963) 798. 43) A. Spernol and B. Denecke, Intern. J. Appl. Radiation Isotopes 15 (1964) 195. 44) H. J. Specht and P. Armbruster, Nukleonik 7 (1965) 8. 45) R. Gold and E. F. Bennett, Phys. Rev. 147 (1966) 201. 46) p. Campion, Intern. J. Appl. Radiation Isotopes 19 (1968) 219. 47) p. W. Benjamin, C. D. Kemshall and J. Redfearm, Nucl. Instr. and Meth. 59 (1968) 77. 4s) R. J. Sutter, Proc. Banff Summer School Intermediate energy nuclear physics, Banff, Alberta, 17-28 Aug. 1970 (eds. G. C. Neilson W. C. Olsen and S. Varna; University of Alberta, Edmonton, 1970) p. 264. 49) R. S. Vogel and L. A. Fergason, Rev. Sci. Instr. 37 (1966) 934; L. Fergason, Rev. Sci. Instr. 37 (1966) 964. 5o) R. W. Hendricks, Rev. Sci. instr. 40 (1969) 1216. 51) p. G. Burkhalter, J. D. Brown and R. L. Myklebust, Rev. Sci. Instr. 37 (1966) 1267. 52) N. Spielberg, Rev. Sci. Instr. 37 (1966) 1268. 53) p. W. Sanford and J. L. Culhane, Proc. 2nd Symp. Lowenergy X- and gamma-sources and applications, ORNL 11C-10 (27-29 March 1967) p. 376. 54) E. W. McDaniel, Collision phenomena in ionized gases (J. Wiley, New York, 1964). 55) A. D. Danilov and G. S. Ivanov-Kholodny, Soviet Phys. Usp. 8 (1965) 92. 56) j. N. Bardsley, J. Phys. B (Proc. Phys. Soc.) I (1968) 365. 57) G. R. Ricker and J. J. Gomes, Rev. Sci. Instr. 40 (1969) 227. 53) W. N. English and G. C. Hanna, Can. J. Phys. 31 (1953) 768. 59) T. E. Bortner, G. S. Hurst and W. G. Stone, Rev. Sci. Instr. 28 (1957) 103. 60) j. L. Pack, R. E. Voshall and A. V. Phelps, Westinghouse Research Report 62-928-113-R1 (1962). 61) H. Schlumbohm, Z. Physik 182 (1965) 317. 62) H. J. Stuckenberg, Desy Report 69/49 (1969). 63) j. A. Hornbeck, Phys. Rev. 84 (1951) 615. 64) R. N. Varney, Phys. Rev. 88 (1952) 362. 65) G. J~iger and W. Otto, Z. Physik 169 (1962) 517. 66) A. Bisi and L. Zappa, Nuovo Cimento 12 (1954) 211. 67) K. Hohmuth, ZfK-PhA-14 (1964). 68) W. Bambynek, EUR 2632. d (1965). 69) V. I. Korolev, L. A. Kamaeva, V. G. Chaikovskii and A. V. Shapar, Pribory i Tekhn. Eksperim. no. 4 (1970) 46. 7o) M. T. Rainbow, A. G. Fenton and K. B. Fenton, Aust. J. Phys. 19 (1966) 583.
Discussion Buraei: Charles has given the most recent formula on gas gain. The reference is M. W. Charles, J. Phys. E5 (1972) 95.
II. P R O P O R T I O N A L
GAS C O U N T I N G
110
w.
BAMBYNEK
Cervellati: Y o u did not mention the variance o f pulse distributions presumably because of lack o f time. Would you be kind enough to add something on the subject? Bambynek: The variance of the pulse distribution o-2o is determined by the fluctuation of the n u m b e r of primary ion pairs N produced in the ionizing event and by the fluctuation of the gas gain A. These fluctuations become serious when the counter is used to detect soft X-rays. The relative variance is given by (o'0//9)2 = (o'N/N) 2 -I- N -1 (O'A~A)2. According to F a n o (1947)
2 >,
/
~
.I ! I
FWHM : 3070 eV: 52 % " 1000 " 17 *A 600 102 %
r: I
\
330
5.6%
~n
E U
(o'N/N) 2 = FIN, where F is the F a n o factor. If the mean energy to produce an ion pair is W, then a p h o t o n of energy E produces a mean n u m b e r N o f ion pairs, thus N = E/W. We n o w get the relation
o'elo = C/EL The constant C = { W [ F + (aA/A) 2])~ is practically independent of the energy of the incident radiation and depends mainly on the nature of the gas. The relation is experimentally checked and well established [Lukirsky et al. (1963), Campbell and Ledingham (1966), Charles and Cooke (1968), Hink et al. (1970)]. F o r a gas mixture of 90% argon and 10% methane C values between 0.146 and 0.157 and for pure methane C values between 0.168 and 0.175 have been reported. However, it should be noted that additional fluctuations can be introduced by instrumental defects as, e.g., amplifier noise, gaseous impurities, and nonuniformity of the anode wire. The following slide (fig. 10) demonstrates a comparison o f the energy resolution o f different types of detectors. The material is taken from a review article of Aitken (1968). It is probable that the resolution of the Ge(Li) and Si(Li) detectors have been improved since that time.
Bertolini: The resolution of solid state detectors is n o w about half that s h o w n in fig. 10.
3.0
T Kal,a z K!3
;o
energy ( keV )
Fig. 10. Resolution of various detectors to 55Mn K X-rays from 55Fe according to Aitke,naa). The separation o f the two peaks is about 600 eV. - 1/32" NaI(TI) on E M I 9656 R, - - - typical proportional counter, . . . . . . realistically attainable with small Si(Li) or Ge(Li), - . . . . . . best value with Si(Li).
Breyer: I would like to point out that at lower energies, say less than 1 keV, the proportional counter has a better resolution than the semiconductor detector. References U. Fano, Phys. Rev. 72 (1947) 26. A. P. Lukirskii, O. A. Ershov and I. A. Brytov, Bull. Acad. Sci. USSR, Phys. Ser. 27 (1963) 798. J. L. Campbell and K. N. D. Ledingham, Brit. J. Appl. Phys. 17 (1966) 769. M. W. Charles and B. A. Cooke, Nucl. Instr. Meth. 61 (1968) 31. W. Hink, A. N. Scheit and A. Ziegler, Nucl. Instr. Meth. 84 (1970) 244. D. W. Aitken, I E E E Trans. Nucl. Sci. NS-15 (1968) 10.
INSTRUMENTS
AND
METHODS
112 ( 1 9 7 3 )
I03-I10 ;
©
NORTH-HOLLAND
O N S E L E C T E D P R O B L E M S IN T H E F I E L D OF P R O P O R T I O N A L
PUBLISHING
CO.
COUNTERS
W. B A M B Y N E K
Central Bureau for Nuclear Measurements, EURA TOM, B-2440 Geel, Belgium A brief review is given on s o m e parameters a n d physical effects which influence the m e c h a n i s m o f proportional counters. T h e following topics are discussed: gas amplification, space
charge, recombination, ion and electron transit times, efficiency o f counters operated at high pressure.
1. I n t r o d u c t i o n
the nature of the gas. Fig. 1 demonstrates this dependence for the rare gases. From eqs. (1) and (2) one can calculate
Proportional counters have been used for more than thirty years. They are powerful tools for the detection of nuclear and atomic radiations. Especially, if the intensity of low-energy radiation must be determined, the proportional counter is still the most suitable detector. Such detectors have been described in various excellent books and reviews 1-14) and there are numerous papers reporting on special aspects or applications. The scope of this paper is to give a brief review on some parameters and physical effects influencing the mechanism of gas filled proportional counters. 2. Gas gain
Let us consider cylindrical counters of diameter 2b with the wire of diameter 2a placed on the axis of the cylinder. The wire shall be positively charged in respect to the wall and the counter be filled with a gas or gas mixture of pressure p. Under these conditions the electrical field strength E per unit pressure at the distance r from the center is given by the relation
l n G _ t s(") a(S) dS paS(a) j S(c) p S 2"
(3)
Various relations have been derived for the gas amplification, depending on the function which has been used for the first Townsend coefficient ~/p = f ( S ) . Usually it is assumed that space charge effects, recombination of electron-ion pairs, photoelectric effect at the cathode, and electron attachement due to impurities can be neglected. Rose and Korff 16) calculated the mean energy of the electrons assuming that the most probable energy of the electrons is equal to the ionization energy and that the energy distribution of the electrons is decreasing for energies higher than the ionization energy. Additionally they assumed a linear energy dependence of 28
S(r) = E(r)/p = V/[pr In(b/a)],
(1)
where V is the applied voltage between cathode and anode. Electrons, which are produced inside the sensitive volume of the counter, move in the inhomogeneous field towards the central wire colliding many times with gas molecules but, nevertheless, gaining energy. At a certain distance c from the cylinder axis ionization of the gas molecules takes place. A Townsend avalanche starts and the total number of electrons increases rapidly. The mean amplification factor G is given by the relation
Xe
J
2/,
J
20
J
i/I J
~. 1 2 - - g o.
J
Kr
j__---f
8
4
I i
I
c~d r ,
(2)
f ~
J
' He extrap
In G =
f
200
t,O0
600
800
1000
1200
I/,00
1600 1800
Elp ( v o l t s l c m ' m m Hg)
where e is the number of ion pairs formed by one electron per cm of path (first Townsend coefficient). It has been shown that ~/p is a function of E/p and of
Fig. 1. First T o w n s e n d coefficient ct/p as a function o f the electric field E/p for rare gases according to v o n Enge115). (Courtesy o f Springer Verlag, Heidelberg.)
103 II. P R O P O R T I O N A L
GAS COUNTING
104
W. BAMBYNEK [
i
,
i
i
I
'
,
i
,
I
r
~
~
,
I
I
I
I
,.o I-
,
...o,! .ET.ANE
i
¢C
I0.0
B
9.0
A
(-
L~ v
p/
/
I
'°F,,,,,,,,,, 25.0
#v'
,l'o°o
32~
,°,, ",, ?,, '7,
30.0
35.0
Z.0.0
I/S'(a) ( v o l t s l c m
/.5.0
' m m Hg )112
Fig. 2. Test of the Curran-Craggs modified Rose-Korff theory according to measurements of Kisera7). (Courtesy of Martinus Nijhoff's Uitgeversmaatschappij, 's-Gravenhage.) Our notation is used at the abscissa and the ordinate.
the ionization cross-section and derived (4)
c~/p = ½ C~ S ÷ .
describe the experimental results. Kocharov and Korolev 18) pointed out that the parameter 7 is propor-
Integration of eq. (3) using this relation gives 0.3
In G pa S ( a )
Cz
C~
(5a)
IS(a)] ~"
The constants C a and C2 must be determined from measurements of the gas amplification G. Curran and Craggs 1) slightly modified the R o s e Korff theory and derived the relation In G pa [s(a)] ~
/
= C2 [S(a)] ½ - C1,
(5b)
which is of the same type as eq. (5a). Kiser 17) performed extensive measurements of the gas amplification using various counters and argonmethane mixtures at different pressures. He brought the Curran-Craggs formula to a form which in our notation is written as In G -- (a7) ÷ {C, IS(a)] ~ [pa S (a)] *
-
C2},
(5C)
where y is assumed to be a constant. Fig. 2 shows Kiser's results for pure methane. He concluded from the fact that one single straight line is not obtained that the Curran-Craggs theory does not correctly
°02
<
7
.¢
• ' 3
A
C
0.1
0
I 10
i 15
I 20
(volts/crn. torr) I12
Fig. 3. Experimental verification of the Rose-Korff formula as modified by Curran and Craggs according to Kocharov and KorolevlS). (Courtesy of Consultant Bureau, New York.) (a) Spectroscopically pure argon; (b) 50% A r + 5 0 %CH 4 (data of Kocharov and Korolev): • 1520 mm Hg, x 1140 mm Hg, O 760mmHg, A 410mmHg; (c)0.2% Ar+99.8%CH4 [data of Kiserl7)]: O 597 mm Hg, counter II, x450 mm Hg, counter II, A 375 mm Hg, counter III. Our notation is used at the abscissa and the ordinate.
SELECTED
PROBLEMS
tional to the pressure p. If this pressure dependence is taken into account, Kiser's data agree with the theory o f Curran and Craggs, as is shown in fig. 3. Diethorn 19) assumed a linear relation for the Townsend coefficient
cz/p =
D,S
(6)
and calculated lnG -
pa S(a)
D~[lnS(a)-lnDz].
(7)
The constants D~ and D2 have to be deduced from measurements. A similar relation has been deduced by Zastawny2°), who approximated c~/pby a linear function
B,(S-So),
c~/P =
105
with this relation yields
]
G pal uS(a-~) - K+B1 I In (S(a)~ 4- So - 1 . \ So ! S(a)
The constant K accounts for a small contribution, which arises f r o m the difference between the linear approximation and the real function o f ~/p for S~< S 0. Hendricks 2~) determined the gas amplification for various commercial proportional counters filled with X e - C O 2 or X e - C H 4 mixtures. He found that his results agree equally well with the predictions of both the Diethorn and the Zastawny equation, as is shown in figs. 4 and 5. Williams and Sara 22) used Townsend's 23) semiempirical expression with the two parameters A and B
c~/p = A exp(-B/S),
(8)
where B x and S O are constants. Integration o f eq. (2)
(9)
(10)
which has been proved in homogeneous fields to hold for S(a)% 200-300 (V/cm torr) 15,24), and derived
0 030
lnG
_ A exp
pa S(a)
i
-
--exp
-
.
(11)
B
I
0 025
The second term o f this equation can be neglected for counters filled with gas o f conventional pressure. However, for counters operated at very low pressure
I
95"/o Xe-5*/o COz
0 032 0 020 i ta
0028 I0 °/0 CH~
0.024 .
0015
.
.
.
. i
oo2oo 0010
-/
0016 ,~
,
i 1i_
o.o12
=
0005
o 4 75
500
525
tn S [a) Fig. 4. D i e t h o r n plot o f gas amplification d a t a for xenon-filled proportional counters having CO2 a n d C H 4 q u e n c h gas additives according to m e a s u r e m e n t s o f Hendricks21). (Courtesy o f N o r t h H o l l a n d Publishing C o m p a n y , A m s t e r d a m . ) T h e e m p l o y e d signs correspond to various counters operated u n d e r different conditions. O u r n o t a t i o n is used to denote abscissa a n d ordinate.
_
-4 o
0
f i
02
04
i
Z--,90o)oXe.d/.c /,'
-
-
i
-71
95'/.xe-5./.c0 0.008
t. 50
..de"- __H ~
T 06
I
i
J !
0.8
10
+ ~ J
12
14
tn(S(o.)/S o) ÷ So/S(a) -1 Fig. 5. Z a s t a w n y plot o f gas amplification data for proportional counters operated u n d e r the s a m e conditions as in fig. 4 according to m e a s u r e m e n t s o f Hendricks~l). (Courtesy o f N o r t h - H o l l a n d Publishing C o m p a n y , A m s t e r d a m . ) II. P R O P O R T I O N A L
GAS COUNTING
106
w. BAMBYNEK
it must be taken into account, as Campion 25) has pointed out. Under this condition a peaked gas gain vs pressure curve is obtained. In fig. 6 calculated gas gains as a function of pressure are compared with experimental results of Wilson and Field26). The constants A and B in eq. ( l l ) can be determined from measurements27). For large S values the exponential function in eq. (10) can be expanded and yields for
(12)
o~/p = K , ,
the approximation of Hristov 28) lnG
K1
pa S(a)
--
K
2
-
-
(13)
-
S(a)"
Various authors have performed gas gain measurements 2,16-20,22,26-47) and experimental tests of gas gain formulas. According to Zastawny 2°) one can distinguish about five regions of S with different functional dependences of ct/p on S. Therefore, it depends on the nature of the gas and the value of S in the counter which formula will yield the better results. This is supported by investigations of Specht and Armbruster44), who showed that for a-particles and light fission products in methane filled counters the theory of Rose and Korff ~6) describes the experimental
I ~
I
I
I
I
3. Space charge The influence of space charge has been recently investigated by Campion46), who found a deviation of the exponential gas-gain-voltage relation. There are two types of space charge effect. The "self-induced" space charge effect is due to the retarding influence of the positive ions on the electrons at the head of the electron cloud. It is larger in methane than in argonmethane mixtures. The "general" space charge effect is due to the integrated effect of the positive ions of
1
f
0.I0
p, j.'P'"
10 3 ,~.
I~
I
results very well up to values for S ( a ) = 5 × 10 4 (V/cm torr), as shown in curve A of fig. 7. The generally accepted theory of Diethorn 19) seems to agree only within a limited region of 100 < S(a) < 1000 (V/cm torr) (curve B of fig. 7). Also the widely used theory of Williams and Sara 22) is only valid for S(a) values of less than about 200-300 (V/cm torr), as Campion 46) has shown, and leads to discrepancies for large S(a) values (curve C of fig. 7). Recently, gas gains of up to 10s have been reported for an argon-isobutane mixture to which 0.2% of freon 13B1 has been added48). The exact mechanism for the action of the freon is not yet understood. Similar gases do not produce the same result. Probably, negative freon 13B1 ions have some special affinity for neutralizing positive argon ions.
-.
~._
~
6O 0v
B p p'" /"
6
~ 10
.'..:"
/'
v
"" . . . .
d 0.02
10
20 oressure
30 (torr)
LO
50
Fig. 6. G a s gain as function o f pressure according to Campion25). (Courtesy o f T h e Institute o f Physics, Bristol.) Full lines indicate calculated values using eq. (11), b r o k e n lines those neglecting the second term. T h e calculations were m a d e for a n o d e a n d c a t h o d e radii o f 63.5/~m a n d 1.59 m m , respectively. These values c o r r e s p o n d a p p r o x i m a t e l y to the experimental conditions used to derive the results o f Wilson a n d Field26), which are reproduced as dotted curves.
•_2_-_-2-~_ "~
102
103
I0 ~
IOs
S (a) ( v o t t s / c m ' torr)
Fig. 7. C o m p a r i s o n o f experimentally a n d theoretically obtained gas gains according to Specht a n d Armbruster44). (Courtesy o f Springer Verlag, Heidelberg.) T h e data points are taken f r o m the w o r k o f several a u t h o r s 16, 17, 44). Curve A represents the predictions o f the R o s e - K o r f f theory16), curve B that o f Diethorn's19), a n d curve C that o f the Williams' a n d Sara's 22) theory.
SELECTED
previous discharges as they drift across the counter. This effect depends on the counting rate. It is most prominent in large counters operated at high pressure because the effective counter potential is proportional to pZb3G In (b/a). Gas gain shifts due to space charge influences have been reported by Vogel and Fergason49). Hendricks 5°) has calculated the change of the peak position of X-rays to be proportional to pb 2 G 2 E 2, where E here means the energy of the X-rays. This prediction is in good agreement with his experimental results. Such peak shifts have also been reported by several other authorsS1-53). 4. Recombination Practically no information could be found on recombination of ions in proportional counters. Usually the recombination of two oppositely charged ions is described in terms of their recombination coefficients ft. It is defined as the recombination rate N per unit volume and unit time devided by the ion densities n+ and n_
N = fin+ n _ .
(14)
F r o m the various possibilities for electron-ion recombination the dissociative recombination seems to be the most probable one. It takes place when a radiationless transition occurs to some state of the molecule XY (XV) + + e - --* (XY)* --+ X* + Y*.
(15)
The asterisks indicate that the atoms may be left in excited states. The recombination coefficient for this type of recombination amounts between 10 - 6 and 10 -8 (cma/sec), at gas temperature of 300 K. The coefficient for other modes of recombination, as the radiative, dielectronic, and three-body recombinations, is of the order of 10-1°--10-12 (cma/sec) 54--56). It should be noted that in practice the ions are not uniformly distributed in the volume of a proportional counter. This is especially the case when ionization is produced by heavily ionizing particles like a-particles. In this case the local density of ions is much higher and the recombination will be greater.
PROBLEMS
107
the positive ions. It amounts to only a few percent. The electron transit time t_ in cylindrical counters can be described by the relation
t._ = a S ( a )
i
S(a)
dS/[S2 v _ ( S ) ] ,
where v_ (S) is the drift velocity of the electrons. A very simple expression has been derived 12'62) under the assumption that v_(S)ocS. Another approach 3) assumed vi(S)ozx/S. Such approximations are valid only in a very limited region, because the experimentally determined electron drift velocities 2'58-61) deviate considerably from a linear or parabolic law. In several gases they even have a peaked shape. Direct measurements of the electron transit time under various conditions have been performed by several autors46"69'7°). The transport of the positive ions is much slower due to the longer distance, which extends practically from the anode to the cathode, and also due to the drift velocity v+, which is approximately a thousand times l o w e r 63-65) than that of electrons. A linear 12,62) and also a parabolic 3) dependence on S has been assumed for v +. The transit time t+ of the positive ions can be calculated by a similar relation as eq. (16):
l+ = a S ( a )
i
S(r)
dS/[S2v+(S)].
(17)
d S(b)
6. Efficiency of proportional counters operated at high pressure For many investigations the knowledge of the efficiency of the counter is required. When the
source
2R
5. Ion and electron transit times The collecting times of electrons and positive ions, which are formed in the avalanche near the anode, influence the shape of the formed pulse 57) and are especially of importance when very high counting rates must be measured46). The contribution of the electrons to the total pulse is rather small compared with that of
(16)
J S(r)
sotid
source
2d A
,,t
'l
--
f -
angle
~,
k :
source prate -
J
,
2r
Fig. 8. Arrangement o f the source in the cylindrical counter. II. P R O P O R T I O N A L
GAS COUNTING
108
w. BAMBYNEK
intensity of X-rays has to be measured a large proportional counter operated at high pressure is often used. Mostly X-rays are produced by a nuclide decaying by electron capture. To stop the Auger electrons the source is placed between foils of sufficient thickness. In such a case care must be taken to avoid thin gas layers between the source and the electron absorbers. Already a thin layer of pressurized gas causes a considerable absorption loss. This effect is mostly not taken into account. For X-rays of 5.4 keV and a gas mixture of 90% Ar and 10% CH¢ at 5 atm pressure a gas layer of 0.008 cm results in an absorption of 2 % (gas density at 25 °C p = 1.536 (g/l), absorption coefficient/t = 316. I (cm2/g)). Calculations of the efficiency of X-rays in cylindrical counters have been reported by several authors66'67). We tried to verify experimentally the theoretical predictions for our two-D-shaped counter 6s) and did not get a good agreement. The source was prepared on
a thin plastic foil, mounted onto an A1 ring which was placed in the middle of the source plate, as shown in fig. 8. In a calculation o f the efficiency the definite thickness of the source plate must be taken into account. It cuts out a certain solid angle f2 in which absorption of the X-rays is only partly possible. The total transmission of the X-rays through the cylinder is given by
T = T4,~- Ts~+ TA,
(18)
where T4~ is the transmission through a cylinder in 4~ geometry, Tz is the transmission through that part of the cylinder which is cut out by the solid angle •, and T z is the transmission through the "triangle" which is limited by the solid angle t? and the cylindrical surface of the opening in the source plate. The calculation yields T =
i
(l/R)
arctg
cos0 exp(--I~R/cosO) dO +
j0
+ E 2 (/d) - (R 2 + 12)-½ E2 [it(R 2 + 12)~] _ 1.o ¸
-
½r~
i
arctg
(d/r)
cosO
x
do
x
EK X
exp(-pl/cosOcosq)) d~o dO 0
i
arctg
cos 0 x
- ½rrdo
x
(d/r)
exp(-pR/(cos2Osin2~o+sin20)~)dq)
dO+
LJ ~M
0.9
+
i
arctg
(d/r)
cos 0 e x p ( - / t r / c o s O) dO,
(19)
dO with q ~ = arctg {[(R/1) 2 cos z O - sin 20] ~} and E2(x ) ---- x f x ° (e-tit 2) dt,
0.8 200
I 600
I 1000
I 1400
P P/Pr ( c r u z / g )
Fig. 9. Efficiency of the counter for K X-rays as a function o f the relative pressure times the absorption coefficient. As reference pressure Pr 1 atm has been chosen. The source was situated in the middle of the counter, as seen in fig. 8. The solid curves show calculated efficiencies neglecting (upper curve) and counting for (lower curve) the existence o f the source plate. The latter case agrees very well with the experimental points.
where 2l is the effective length of the cylinder, 2R its diameter, 2d the thickness of the source plate, 2r the diameter of the opening in the source plate, and ¢t the absorption coefficient. The integrals have been computed numerically and the result is shown in fig. 9, together with our experimental points for several radionuclides and various gas pressures. There is an excellent agreement between the measured values and the efficiencies which are calculated taking into account a definite thickness of the source plate.
109
SELECTED PROBLEMS
It is pleasure to acknowledge the experimental assistance given by Mr D. Reher. References 1) S. C. Curran and J. D. Craggs, Counting tubes (Academic Press, London, 1949). 2) B. B. Rossi and H. H. Staub, Ionization chambers and counters (McGraw-Hill, New York, 1949). 3) D. H. Wilkinson, Ionization chambers and counters (Cambridge University Press, Cambridge, 1950). 4) D. West, Progress in nuclear physics, vol. 3 (ed. O. R. Frish; Pergamon Press, London, 1953) p. 18. 5) S. Korff, Electron and nuclear counters (D. Van Nostrand, London, 1955). 6) S. C. Curran, in Handbuch der Physik, vol. 45 (eds. S. Fliigge and E. Creutz; Springer-Verlag, Berlin, 1958) p. 174. 7) W. J. Price, Nuclear radiation detection (McGraw-Hill, New York, 1958). 8) V. Kment and A. Kuhn, Technik des Messens radioakticer Strahlung (Akademische Verlagsanstalt, Leipzig, 1960). 9) C. Gatrousis, R. Heinrich and C. E. Crouthamel, Progress in nuclear energy, Ser. "IX, Analytical chemistry, vol. 2 (ed. C. E. Crouthamel; Pergamon Press, Oxford, 1961) p. 1. 10) W. Franzen and L. W. Cochran, in Nuclear instruments and their uses, vol. I (ed. A. H. Snell; J. Wiley, New York, London, 1962) p. 3. 11) E. W. Emery, in Radiation dosimetry, vol. II (eds. F. H. Attix and W. C. Roesch; Academic Press, New Y o r k / London, 1966) p. 73. 1_2) H. Neuert, Kernphysikalische Messverfahren (G. Braun, Karlsruhe, 1966). 13) S. C. Curran and H. W. Wilson, in Alpha-, beta- a n d g a m m a ray spectroscopy (ed. K. Siegbahn; North-Holland Publ. Co., Amsterdam, 1968) p. 303. 14) D. W. Aitken, IEEE Trans. Nucl. Sci. NS-15 (1968) 10. 15) A. von Engel, in Handbuch der Physik, vol. 21 (ed. S. Fliigge; Springer-Verlag, Berlin, 1956) p. 504. 16) M. E. Rose and S. S. Korff, Phys. Rev. 59 (1941) 850. 17) R. W. Kiser, Appl. Sci. Res. B8 (1960) 183. 18) G. E. Kocharov and G. A. Korolev, Izvest, Akad. Nauk. SSSR, Ser. Fiz. 27 (1963) 301 [Bull. Acad. Sci., USSR, Phys. Ser. 27 (1963) 308]. 19) W. A. Diethorn, NYO-6628 (1956). 20) A. Zastawny, J. Sci. Instr. 43 (1966) 179; A. Zastawny and J. Mizeraczyk, Nukleonika 11 (1966) 685; A. Zastawny, J. Sci. Instr. 44 (1967) 395. 21) R. W. Hendricks, Nucl. Instr. and Meth. 102 (1972) 309. °-e) A. Williams and R. I. Sara, Intern. J. Appl. Radiation Isotopes 13 (1962) 229. 23) j. S. Townsend, Electricity o f gases (Clarendon Press, Oxford, 1915). 24) H. Schlumbohm, Z. Angew. Physik 11 (1959) 156; Z. Physik 184 (1965) 492. 25) p. j. Campion, Phys. Med. Biol. 16 (1971) 611. 26) K. S. J. Wilson and S. B. Field, Phys. Med. Biol, 15 (1970). 657. 27) p. j. Campion and M. W. J. Kingham, Intern. J. Appl. Radiation Isotopes 22 (1971) 703. 28) G. L. Hristov, Dokl. Bulg. Akad. Nauk 10 (1957) 453 29) M. E. Rose and W. E. Ramsey, Phys. Rev. 61 (1942) 199. 30) C. S. Curran, J. Angus and A. L. Crookroft, Phil. Mag. 40 (1949) 36.
31) L. Colli, U. Facchini and E. Gatti, Phys. Rev. 80 (1950) 92. 32) E. Fiinfer and H. Neuert, Z. Angew. Physik 2 (1950) 241. 33) R. Fourage and L. Miramond, J. Phys. Radium 15 (1954) 780. 34) I. Kumabe and M. Sonoda, J. Phys. Soc. Japan 9 (1954) 877. 35) K. Schiitt, Z. Physik 143 (1955) 489. 36) T. A. Chubb, NRL Report 4814 (1956). 37) H. J. Stuckenberg, Dissertation (Universit/it Hamburg, 1958). 3s) K. van Duuren and G. L. Sizoo, Appl. Sci. Res. B7 (1959) 379. :39) S. Ramakrishna, Proc. Indian Acad. Sci. 51 (1960) 117. 4o) R. Engfer, Diplomarbeit (TH Darmstadt, 1960). 41) M. Pasternak and G. Ben-David, IA Report 713 (1962). 42) A. P. Lukirskii, O. A. Ershov and 1. A. Brytov, Bull. Acad. Sci. USSR, Phys. Ser. 27 (1963) 798. 43) A. Spernol and B. Denecke, Intern. J. Appl. Radiation Isotopes 15 (1964) 195. 44) H. J. Specht and P. Armbruster, Nukleonik 7 (1965) 8. 45) R. Gold and E. F. Bennett, Phys. Rev. 147 (1966) 201. 46) p. Campion, Intern. J. Appl. Radiation Isotopes 19 (1968) 219. 47) p. W. Benjamin, C. D. Kemshall and J. Redfearm, Nucl. Instr. and Meth. 59 (1968) 77. 4s) R. J. Sutter, Proc. Banff Summer School Intermediate energy nuclear physics, Banff, Alberta, 17-28 Aug. 1970 (eds. G. C. Neilson W. C. Olsen and S. Varna; University of Alberta, Edmonton, 1970) p. 264. 49) R. S. Vogel and L. A. Fergason, Rev. Sci. Instr. 37 (1966) 934; L. Fergason, Rev. Sci. Instr. 37 (1966) 964. 5o) R. W. Hendricks, Rev. Sci. instr. 40 (1969) 1216. 51) p. G. Burkhalter, J. D. Brown and R. L. Myklebust, Rev. Sci. Instr. 37 (1966) 1267. 52) N. Spielberg, Rev. Sci. Instr. 37 (1966) 1268. 53) p. W. Sanford and J. L. Culhane, Proc. 2nd Symp. Lowenergy X- and gamma-sources and applications, ORNL 11C-10 (27-29 March 1967) p. 376. 54) E. W. McDaniel, Collision phenomena in ionized gases (J. Wiley, New York, 1964). 55) A. D. Danilov and G. S. Ivanov-Kholodny, Soviet Phys. Usp. 8 (1965) 92. 56) j. N. Bardsley, J. Phys. B (Proc. Phys. Soc.) I (1968) 365. 57) G. R. Ricker and J. J. Gomes, Rev. Sci. Instr. 40 (1969) 227. 53) W. N. English and G. C. Hanna, Can. J. Phys. 31 (1953) 768. 59) T. E. Bortner, G. S. Hurst and W. G. Stone, Rev. Sci. Instr. 28 (1957) 103. 60) j. L. Pack, R. E. Voshall and A. V. Phelps, Westinghouse Research Report 62-928-113-R1 (1962). 61) H. Schlumbohm, Z. Physik 182 (1965) 317. 62) H. J. Stuckenberg, Desy Report 69/49 (1969). 63) j. A. Hornbeck, Phys. Rev. 84 (1951) 615. 64) R. N. Varney, Phys. Rev. 88 (1952) 362. 65) G. J~iger and W. Otto, Z. Physik 169 (1962) 517. 66) A. Bisi and L. Zappa, Nuovo Cimento 12 (1954) 211. 67) K. Hohmuth, ZfK-PhA-14 (1964). 68) W. Bambynek, EUR 2632. d (1965). 69) V. I. Korolev, L. A. Kamaeva, V. G. Chaikovskii and A. V. Shapar, Pribory i Tekhn. Eksperim. no. 4 (1970) 46. 7o) M. T. Rainbow, A. G. Fenton and K. B. Fenton, Aust. J. Phys. 19 (1966) 583.
Discussion Buraei: Charles has given the most recent formula on gas gain. The reference is M. W. Charles, J. Phys. E5 (1972) 95.
II. P R O P O R T I O N A L
GAS C O U N T I N G
110
w.
BAMBYNEK
Cervellati: Y o u did not mention the variance o f pulse distributions presumably because of lack o f time. Would you be kind enough to add something on the subject? Bambynek: The variance of the pulse distribution o-2o is determined by the fluctuation of the n u m b e r of primary ion pairs N produced in the ionizing event and by the fluctuation of the gas gain A. These fluctuations become serious when the counter is used to detect soft X-rays. The relative variance is given by (o'0//9)2 = (o'N/N) 2 -I- N -1 (O'A~A)2. According to F a n o (1947)
2 >,
/
~
.I ! I
FWHM : 3070 eV: 52 % " 1000 " 17 *A 600 102 %
r: I
\
330
5.6%
~n
E U
(o'N/N) 2 = FIN, where F is the F a n o factor. If the mean energy to produce an ion pair is W, then a p h o t o n of energy E produces a mean n u m b e r N o f ion pairs, thus N = E/W. We n o w get the relation
o'elo = C/EL The constant C = { W [ F + (aA/A) 2])~ is practically independent of the energy of the incident radiation and depends mainly on the nature of the gas. The relation is experimentally checked and well established [Lukirsky et al. (1963), Campbell and Ledingham (1966), Charles and Cooke (1968), Hink et al. (1970)]. F o r a gas mixture of 90% argon and 10% methane C values between 0.146 and 0.157 and for pure methane C values between 0.168 and 0.175 have been reported. However, it should be noted that additional fluctuations can be introduced by instrumental defects as, e.g., amplifier noise, gaseous impurities, and nonuniformity of the anode wire. The following slide (fig. 10) demonstrates a comparison o f the energy resolution o f different types of detectors. The material is taken from a review article of Aitken (1968). It is probable that the resolution of the Ge(Li) and Si(Li) detectors have been improved since that time.
Bertolini: The resolution of solid state detectors is n o w about half that s h o w n in fig. 10.
3.0
T Kal,a z K!3
;o
energy ( keV )
Fig. 10. Resolution of various detectors to 55Mn K X-rays from 55Fe according to Aitke,naa). The separation o f the two peaks is about 600 eV. - 1/32" NaI(TI) on E M I 9656 R, - - - typical proportional counter, . . . . . . realistically attainable with small Si(Li) or Ge(Li), - . . . . . . best value with Si(Li).
Breyer: I would like to point out that at lower energies, say less than 1 keV, the proportional counter has a better resolution than the semiconductor detector. References U. Fano, Phys. Rev. 72 (1947) 26. A. P. Lukirskii, O. A. Ershov and I. A. Brytov, Bull. Acad. Sci. USSR, Phys. Ser. 27 (1963) 798. J. L. Campbell and K. N. D. Ledingham, Brit. J. Appl. Phys. 17 (1966) 769. M. W. Charles and B. A. Cooke, Nucl. Instr. Meth. 61 (1968) 31. W. Hink, A. N. Scheit and A. Ziegler, Nucl. Instr. Meth. 84 (1970) 244. D. W. Aitken, I E E E Trans. Nucl. Sci. NS-15 (1968) 10.