Fano factor in pure argon

Nuclear Instruments and Methods m Physics Research 227 (1984) 311-317 North-Holland, Amsterdam

311

FANO FACTOR IN PURE ARGON M. K A S E

RtAen. lnstttute of Physt¢al and Chemical Research, Htrosawa, Wako-shl, Sattama 351, Japan T. A K I O K A ,

H. M A M Y O D A

*, J. K I K U C H I

a n d T. D O K E

S~ lence and Engmeermg Research Laboratory, Waseda Unw, Ktkut~ho, Shmjuku-ku, Tokyo 170, Japan Received 26 March 1984

The Fano factor for 5 3 MeV alpha particles m pure argon has been measured with a grldded Iomzatlon chamber and estimated to be 0 20 +001 The obtained value ~s consistent wtth the theoretical value ff the contribution of elastic nuclear colhs~ons to the Fano -002 factor ~s taken into the consideration There ~s no apprecmble difference between the values for pure argon and for a gas m,xture of Ar+ (10%)CH 4 obtained in the prewous measurement

1. Introduction In 1979, we measured the F a n o factor for 5 3 MeV alpha particles in a gas mixture of Ar + (10%)CH4 with a single gridded iomzatlon c h a m b e r and it was est,mated to be 0.18 + 0 01 [1]. This value is in agreement w~th the one measured for Ar + (0.8%)CH 4 by Alkhazov et al [2] within the experimental errors It has been considered that the F a n o factor m pure argon could be close to that in a gas mixture of Ar + C H 4 when the concentration of m e t h a n e in the mixture is small [2]. In the mixture, the Penning process which reduces the W value and the Fano factor may occur but its effect ~s not significant. Also, an increase of the Fano factor due to the dissociation process of methane is expected to be small. On the other hand, a theoretical estimation of the F a n o factor in pure argon was made by Alkhazov [3] and the result gave the value of 0 16. Recently, Lima et al. [4] have reported that the Fano factor in pure argon is equal to or less than 0 40. They used a gas proportional scintillation counter and measured the F a n o factor for 1 49 keV X-rays. Although their result is not inconsistent with the consideration above, the F a n o factor shown in their experiment is much larger than that expected for pure argon We have measured the F a n o factor for alpha particles in pure argon by the same m e t h o d as in the previous measurement JAr + (10%)CH4], namely, with a gridded ionization chamber. However, when the pure rare gas is used as detecting medium of the ionization * Present address Takasakl Works, Hltach~ Ltd 0168-9002/84/$03.00 © Elsevier Science Publishers B V. ( N o r t h - H o l l a n d Physics Pubhshlng Division)

chamber, there are some difficulties relating to the large agitation energy and slow drift velocity of electrons in the gas under electric field These result m a long collection time of electrons, a high p r o b a b d l t y of electron trapping by grid wires, and so on. We were able to remove these difficulties by using the gated integration technique [5] and by increasing the ratio of fields at both sides of the grid to much larger than Bunemann's criteria [6]

2. Experimental apparatus and techniques 2 1 Detectton system Fig. 1 shows a schematic view of our vacuum system. The system has two vacuum vessels denoted (A) and (B) in the figure. (A) IS the detector container and (B) the gas purifier They were made of stainless steel and metal gaskets were used for every vacuum seal. Before filling, the whole system including a gas supply system was evacuated down to 10 -7 Torr with an oil diffusion p u m p equipped with a liquid nitrogen trap after baking the chamber wall at around 100°C for several days. In fig. 2 the arrangement of detector electrodes, l e collector, grid and cathode, is shown All the electrodes were made of stainless steel and supported by teflon insulators attached to the upper flange or the b o t t o m plate of the vessel (A) The collector was a disk plate of 70 m m in diameter. Its size had been selected relatively small in order to lower the electric noise level by reducing the capacity of the electrode against the ground The sensitive region was cylindrical (60 m m in diameter and

312

M Kase et a l /

,~/ (D) IA)~

Fano fa~tor m pure argon

i~: (F)

~

(K).,~ ~

(H)~..~ (GI

IJI Fig 1 A schematic view of the vacuum system (A) detector container, (B) gas purifier, (C) detector, (D) preamphfler box, (E) pressure gauge, (F) thermocouple, (G) heater, (H) copper plate for getter, (I) copper pipe for supporting the getter plates, (J) coohng water pass. (K) connected to the vacuum pump and gas supply system

29 m m in height). The distance between the cathode a n d the grid, d], was selected so that it would be slightly longer than the range of 5 3 MeV alpha particles in 1100 T o r r argon gas in which the range had the m a x i m u m value in this m e a s u r e m e n t The grid consisted of 0.1 m m diameter stainless steel wires which were spaced 1 m m apart, and located 10.4 m m apart from the collector The distance between the grid a n d the collector, d2, must be long enough to reduce the shielding m e f f l o e n c y of the grid and, at the same time, short enough to keep a high ratio of g r i d - c o l l e c t o r a n d g r i d - c a t h o d e fields at a fixed bias voltage a n d to reduce the collect]on time of electrons The a r r a n g e m e n t gave 1 7% as the shielding inefficiency a n d 1.92 as the critical ratio of grid-collector to g r i d - c a t h o d e fields to e h m l n a t e electron t r a p p i n g by grid wires according to B u n e m a n n et al. [6]. The source of 210 Po was m a d e as follows, first, a small drop

F

>

60ram~{

Collector ~ Grid -->'F"t-~

.

.

.

.

.

~

-

d2 dI

Source Fig 2 The arrangement of the detector electrodes.

of solutLon of 21°po in HCI was put upon a well-pohshed mckel backing plate and, after a whde, the plate was washed m flowing water to remove the residual solvent a n d then dried m air The source, which gave an alpha c o u n t i n g rate of 2 0 - 3 0 c o u n t s / s , was used m the measurement. The source plate was put on the center of the cathode To purify the d e t e c u o n gas, we used a thermal convection type gas purifier, the vessel (B), containing pellets of B a - T l getter alloy. The pellets were put on the eight copper plates (H m fig. 1) which were attached to the copper support (I) a n d contacted the reside wall of the vessel (B) through their edges The pellets were heated by a wire heater w o u n d a r o u n d the outside wall of the vessel The temperature, which was measured w n h a thermocouple ( c h r o m e l - a l u m e l ) in contact with the copper support (I), was kept over 400°C during the evacuation a n d a r o u n d 300°C during the m e a s u r e m e n t T h e vessels (A) and (B) are connected by two watercooled pipes a n d the gas circulation in the detection system was performed by thermal convection through these pipes The t e m p e r a t u r e ms=de the vessel (A) was kept to less than 30°C throughout the m e a s u r e m e n t The purity of the detecting gas was checked by confirming that the drift v e l o o t y was consistent with the available data [7], The drift velocity can be easdy o b t a i n e d from the m a x i m u m pulse duration of the cathode signal It is equal to d l / W ~, where d 1 is the distance between the cathode and the grid and w I the drift velocity of electrons at a field-to-pressure ratio in the cathode-grid region (see fig. 4b) T h e detection system was filled with research grade argon (99 9995% in purity) at pressures of 1180 and 1460 Tort. These pressure values were readings of the B o u r d o n gauge (E) during the o p e r a u o n of the gas purifier The pressure values (at 0°C) which gave densities eqmvalent to these cases were approximately 1100 a n d 1370 Torr, respectively. 2 2 Electromcs

Fig 3 shows the block diagram of electronic circuits used in the measurement. First, the signals from the collector were converted to a low-impedance voltage signals with a charge sensitive p r e a m p h f i e r located on the upper flange of the detector container a n d fed to a m a i n amplifier ( C a n b e r r a 1412) with a seml-Gaussian shaping filter (the shaping time constants, b o t h differential a n d integral, were set to 2 /~s). The o u t p u t signals from the mare amplifier were sent to a single c h a n n e l analyzer (SCA) for the electronic collimation as discussed later a n d also to a gated integrator [5] to eliminate the effect of the collection time variance on pulse height (l e. the rise time effect). The integration has to be initiated just after the a l p h a decay, because a shght current is induced on the collector during the drifting of

313

M Kase et al / Fanofattor m pure argon

Collector ~ r~

lal F

I

amplifier -

-

t

~

) -

"

Cathode

o -HV

Fig 3 A block dmgram of electromc cmrcmts Sohd hncs denote analog slgnals and dashed hnes denotc dmgmtalones

electrons m the space between the grid and the cathode due to the shielding inefficiency of the grid. So the cathode sagnal, whmh was shaped with very short time constant (0 5 ~s), was used as trigger pulse for the gated antegrator. It as suitable for the integration start pulse, because it rises rapidly as soon as alpha decay occurs and independently of the emission angle of the alpha particle. The antegratlon period must be selected as short as possible, because the electronic noise of the total system increases w~th the antegratmn period. The antegratlon was ended just after the tad end of the signals from the main amphfier The integration time was 30/zs. The signal timing chart is shown in fig. 4 2.3 Electromc colhmatlon and grM trappmg

In order to reduce the residual posmve 1on effect and the source effect, it Is required to hm~t the emission angle of alpha particles (defined as the angle between the track of an alpha partmle and the normal line to the cathode surface). It is also effective to reduce the rxse time effect, although the effect is ehmmated efflcmntly with the gated lntegratmn technique Colhmatlon with some mechamcal devices is not preferable m this work, because it probably causes undesirable energy loss of alpha particles. The electromc collimation technique with the cathode pulses, which was used m our previous measrement, has an ambiguity m the collimatmn angles due to the comparatively lugh noise level for the cathode signal and also due to the fact that cathode signals do not exactly follow the parallel-plate approximation, because of the relatively small size of our detection system. Therefore, we selected the electronic colhmatlon using the rise time effect of the collector signals The pulse height spectrum of signals from the main amphfier is shown m fig. 5, together with the result of a computer simulation. The peak m the higher pulse-height

(a)

v(t)l tl

t

t2 t 3

v(t)

(b)

vlt)

t

I/\ to

t2

(c)

(d)

v(tl I

+

to

t4

t

Fig 4 Sketch of time relations of s~gnals at stages shown by (a)-(d) m fig 3 Stgnal wave forms shown by solid hnes are for an ermsslon angle of 0 ° and those shown by dashed hnes for an emission angle of 90 ° to is the time when alpha decay occurs t t = t o + ( d 1 - R ) / w ] , t 2 = t o + d ] / w 1, and t 3 = t o + R / w 1+ d 2 / w 2, where R ts the range of alpha particles and w1, w2 are the drift velootms 6f electrons m the cathode-grid and grid-collector regions, respectively The mtegratmn ~s started at t o and stopped at t 4

M Kase et a l /

314

Fano fa(tor m pure argon

/,2000

(a)

(b)

36000

30000 W Z 24000 z 18000 z

12000

0 .#

6000

j-/

0

I

500

I

600

I

700

I

.....

800 CHANNEL

500 600 NUMBER

700

600

Fig 5 The effect of collecUon time varmnce of collector signals The spectrum (a) is obtained by the measurement m 1100 Torr argon The spectrum (b) ~s the result of the computer simulation for 105 events and the total count ]s normahzed to the spectrum (a)

region of spectrum (a) is distorted due to the source effect which IS significant for alpha particles with emission angle near 90 ° Considering the poor accuracy on the estimations of the drift velocities [7] and the ranges of alpha particles in pure argon [8], the two spectra are consistent with each other The shadowed portion in spectrum (b) corresponds to alpha decays with emission angles ranging from 13 ° to 22 ° . If a portion of the

t0]

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/

~00

99

W 98 OLU > 97 I-',,.-I I,z

"~, 20

3'0 ' FIELD

4'0 RATIO

5'0

*

6'0

F~g 6 The relation between the pulse height of the collector signal and the field ratio, E 2 / E t, m 1370 Torr argon E ] / p was kept constant (0 2 V/cm Torr)

spectrum is selected by the single channel analyzer and used as gate signal, the emission angle can be easily limited from 13 ° to 22 °. In this case, the collimation angles can be defined with an accuracy less than 0 6 ° This method is superior to those using the cathode pulse m view of better accuracy on the collimation angle In order to determine the ratio of electric field m the g r i d - c o l l e c t o r region, E 2, to that m the c a t h o d e - g r i d region, E l, we measured the saturation characteristics of the pulse height against the values of E 2 / E 1. Fig. 6 shows an example of the saturation curve measured for 1370 Torr argon. G o o d saturation can be seen between E 2 / E ~ = 2.9 and 4.5 It means that the electron trapping by the grid wires does not occur over E J E 1 = 2.9 The gradual increase of pulse height over E 2 / E 1 = 5.0 is due to electron multiplication which occurs near the grid wires where the electric field is relatively high. The critical value of E z / E 1 for grid trapping is much higher than the value (1.92) obtained from the formula of B u n e m a n n et al. [6], which is based upon the assumption that electrons move exactly along the field lines and never diffuse transversally. In the measurement with the a r g o n - m e t h a n e gas mixture, where the agitation energy of electrons is very small, the formula gives a good critical value for E 2 / E 1. On the other hand, in the present measurement, electrons In pure argon are so diffusive that the assumption made by Bunemann et al becomes untenable. Recently~ we found that the critical

315

M Kase et al / Fanofa¢tor m pure argon

value for E 2 / E 1 m pure rare gases has a simple relation with the value of D / w l, where D is the diffusion coefficient m the c a t h o d e - g r i d region The details of the experiment wdl be published elsewhere [9]

Table 1 Experimental condmons and results Pressure [Torr]

l 10 × 10 ~

1 37 × l 03

Range [mm] E l ~ p [V/cm Torr]

Ae, "~ [keV] Ae,[keV]

26 9 0 19 3 37 164 +01 105 _ + 0 0 2 36 0 2 121 _+01

21 7 0 19 3 37 165 _+01 107+002 18 0 2 126 _+01

Fano factor

0 19+ 0o] -- 002

E2/E 1

3. Results and data analysis

Aet[keV]

Fig 7 shows a typical pulse height distribution of collector signals stored in the pulse height analyzer ( P H A ) The peak of 5.3 MeV alpha particles was fitted to a Gaussian function by the least-squares method and the peak p o s m o n and the width of the peak were obtained The measurement has been repeated about twenty times and the values were averaged The results are listed m table I together with the experimental conditions The quoted errors are statistical ones. The peak due to test signals from the pulse generator, which was also fitted to the Gausslan function, was used to estimate the electromc noise and to m o m t o r the gain drift of the electromc system. The energy cahbration was done by using the 5 3 MeV peak and the linear relation between pulse height and channel n u m b e r of the PHA In order to obtain the energy spread purely due to

=

,

l

Ae.[keV]

Aep, {keV] Ae, ~1 [keV]

0 20+- - ool 002

a) Aer and Ae, are the estimated contributions of the rise time effect and the source effect t o A e t All energy spreads are shown in fwhm

the ionization fluctuation, we have to estimate the contributlons of other sources which may broaden the alpha peak. The energy fluctuations due to electronic noise can be easily removed from the total energy spread, although their contribution is relatively large in this measurement They are subject to the Gausslan

4L

3600

,3

!

j 3000 I..IJ Z Z

5

-r 2 4 0 0 LD

1800 Z 0 o

1200

600

1800

1810

1820

1830

1840

1980

1990

2000

2010

CHANNEL NUMBER Fig 7 A typical pulse height distribution of collector signals (left) and of test signals (right) The solid hne in the figure is the result of fitting using a Gauss,an distribution The dashed hne is that of fitting usmg the convolution of a Gaussian distribution and the following function, f ( x ) = ( A / a ) e x p ( x / a ) + ( 1 - A) 8 ( x ) for x < 0, and f ( x ) = 0 for x > 0, where 8(x) is a delta function and A, a are fitting parameters Both fitting curves almost agree over the range except for the low energy tail

316

M Kase et al / Fano fa¢tor m pure argon

d l s t n b u u o n a n d the energy spread caused by them can be easdy measured from the spectrum of test mgnals from the pulser (see fig. 7). Since some p e a k - b r o a d e n i n g effects are closely related to the emlsmon angle of a l p h a parUcles, it ~s very useful to mvesUgate the v a r i a u o n of alpha peak against the c o l h m a t l o n angle. In fig. 8, the relatwe locations of a l p h a peaks are shown as a functxon of em/smon angle of a l p h a particles The peak moves shghtly to the higher energy rode as the average em~smon angle increases. However, this tendency m pure argon ~s almost the same as that in Ar + (10%)CH 4 m spite of the large differences m the electron collection time m pure argon c o m p a r e d with those m the mixture. We can conmder that the rise u m e effect is neghglbly small a n d the increase of pulse height m fig. 8 Is mainly due to the pomtwe ion effect. Therefore, the relation m fig. 8 permits the e s u m a t l o n of the pomuve ion effect The distribution of pulse height f l u c t u a u o n due to th~s effect ~s rectangular rather than G a u s s m n If the 21°Po source was uniformly deposited on the source plate, ~t could be thin enough not to cause the self-absorpUon effect for the well c o l h m a t e d a l p h a part~cles If the a l p h a source xtself affects the energy spread l

I

!

I

I

I

Ar

1 004 Z 0 o ~1

0

002 0

1 ooo

0

@ 0

j 0 998

0

I

I

I

I

I

20

30

40

50

60

I

I

AVERAGE

ENIISS[ON

ANGLE

70

(')

1 004

of the alpha peak, th~s may be due to the roughness of the source surface But It ~s difficult to estimate the energy spread assocmted with this effect because of a lack of knowledge about the source roughness The fwhm peak width is s h o w n " a s a function of average emission angle m fig 9, where the range of emission angles for each plot was selected so that the pomtlve ton effect would be nearly constant. It can be considered that the source effect is also related to the emission angle. There is, however, no remarkable increase of peak width over the range of average emission angles from 10 ° to 45 °. The source effect has the feature that tt may cause an asymmetry on the spectrum. Small devlau o n s from the symmetry funcUon (Gaussxan one) can be seen at the tall on the low energy rode of alpha peak This may be attributed to the source effect So we made a n o t h e r fitting for the alpha peak using an asymmetric funcUon, that is, the convolution of a Gausslan function a n d the sum of e x p o n e n u a l and delta functions (see caption of fig 7) This analyms gives the result that the c o n t n b u U o n of the source effect on the F a n o factor a m o u n t s to 3%. But ~t ~s possible that the source effect correlates reversely w~th the pomtlve ~on effect as for the emtss]on angle and the c o n t n b u U o n s of b o t h effects m~ght be partly cancelled out Anyway, ~t =s better for us to conmder the source effect as the negatwe error of the finally o b t a i n e d result As other possible cause of peak broadening, there are the r e c o m b m a u o n in the c a t h o d e - g r i d region and the electron muluphcat~on near the grid wires A sufficient saturation of peak height against E t / p could not be obtained. There remained an increase of pulse height as m u c h as 0 1% against a change of E ] / p from 0 2 to 0 3 V / c m - Torr It is u n k n o w n whether this slope is due to r e c o m b m a u o n or electron mulUphcatlon. However, there is no difference between the results of peak width at E l l p = 0.2 and 0.3 V / c m Torr. Therefore, the cont n b u u o n of these effects to the energy spread is not s~gmflcant

A r + 10% CH4

20

i

=

i

i

, -

Z 0

i

Ar + lO%CH4 >

0

1 002 0

(3.

0

0

1 ooo

0 •

•

,,j-

~:io

O

La.

'~, 0 9 9 8

o

I

I

I

I

I

I

10

20

30

40

50

60

AVERAGE E M I S S I O N

70

ANGLE (')

Fig 8 The variations of the peak pos)tlon against the average emlsmon angle m pure argon (a) and m Ar+(10%)CH 4 (b) Open c~rcles are the experimental data at a pressure of 1100 Torr and sohd ones are those at 1360 Torr The alpha ranges m both gases are nearly equal

I

I

I

10

20

30

AVERAGE

EMSSION

I0

4 ANGLE

i

50

6

70

(+)

Fig 9 The varlat]on of the energy spread of alpha peak against the average emission angle m Ar+ (10%)CH 4 at a pressure of 1360 Torr The contribution of the posmve ion effect to each plot was nearly constant

M Kase et al / Fanofactor m pure argon The energy spread Ae, due to the ionization fluctuation was approximately given by

Ae, = ¢'~e2t

Ae2n--Ae~,

[keVl,

(1)

where Ae t is the energy spread (m fwhm) of the alpha peak and Ae. is that of the pulser peak (l e electronic noise) Aep, is the estimated energy spread (m fwhm) due to the posmve ion effect The error, when eq (1) is used for the rectangular distribution of the positive ion effect, is eshmated to be less than 1% in this measurement. The F a n o factor F can be obtained from the relation Ae, = 2 35 v/-FWE,~ [keV], where W is the mean energy to create an ion pair ( 2 6 4 eV [11] for pure argon) and E,~ is the initial energy of the alpha particle (5.305 MeV) The results finally o b t a i n e d are hsted an table 1. The quoted errors in the F a n o factors involve the statistical one and the a m b l g m t y of the source effect

4. Discussion There is no appreciable difference between the F a n o factors for two pressure values Again, this allows us to consider that the effect of r e c o m b m a u o n ~s neghglble m this m e a s u r e m e n t Also, there ~s n o difference between the F a n o factors for pure argon a n d for a gas mixture of A r + (10%)CH 4 o b t a i n e d m the previous measurement. N o effect of collision processes, which may occur m the mixture, is seen as expected. Our value as shghtly larger than the theoretical value (0 16) by Alkhazov [3]. It is possible that our value of the F a n o factor might contain the fluctuauon m energy loss due to the nuclear elastic colhslons which occur at the end of the alpha particle range m gas medium. According to the theoretical esUmaUon of the effect by L m d h a r d et al [10], this a m o u n t s to a b o u t 6 keV It ts u n k n o w n how it c o n t r i b u t e s to our value, because the energy-loss process by elasuc colhslons is not completely i n d e p e n d e n t of other mare energy-loss processes, ionlzaUons a n d excitations Anyway, if the nuclear elastic collision effect is taken into constderatlon, our value could be close to the theoreucal one of Alkhazov [3]. However, the F a n o factor o b t a i n e d by the proporUonal sclntillaUon m e t h o d is m u c h larger than our value If it ~s taken into account that the F a n o factor for

317

X-rays (namely, for electrons) does not contain the nuclear elasUc colhslon effect, but the F a n o factor for alpha parUcles may contain th~s effect, it seems to us that the proportional sclntlllauon m e t h o d has some source to increase the value of the F a n o factor [12]

5. Conclusion The F a n o factor for 5.3 MeV alpha particles m pure argon has been measured with a single g n d d e d lomzatlon c h a m b e r The reasonable value of 0.20 -+- 0001 02 was obtained. It is supposed that the ionization c h a m b e r technique does not introduce large errors on the measurement of the F a n o factor As for relauvely large correction factors like the electronic noise and the positive 1on effect, precise estimations can easily be m a d e a n d errors associated with other possible sources are smaller than the statistical ones. Smce the F a n o factor for alpha particles may contain the c o n t n b u u o n of elastic nuclear collisions, it could be slightly larger than the F a n o factors for X-rays or electrons. The authors express their t h a n k s to Dr. H M u r a k a l m of Rakkyo university for his helpful suggesuons o n the gated integrator clrcmt References [1] M Kase, J Kakuctu and T. Doke, Nucl Instr and Meth 163 (1979) 289 [2] G D Alkhazov, A P. Komar and A A. Vorob'ev, Nucl Instr and Meth 48 (1967) 1 [3] G.D Alkhazov, Sov Phys Techn Phys 16 (1972)1540 [4] E P De Lma, M S a l e t e S C P Lelte, M.AF Alves and A J P L Pohcarpo, Nucl Instr and Meth 192 (1982) 575 [5] V Radeka, Nucl Instr and Meth. 99 (172) 525 [6] O Bunemann, T.E Cranshaw and J A Harvey, Can. J Res A27 (1949) 191 [7] J C. Bowe, Phys Rev. 117 (1960) 1411 [8] M Bogaardt and B Koudus, Physlca 18 (1952) 249 [9] T Akloka, M Kase, J Kakucha and T Doke, m preparation [10] J Llndhard and V Nielsen, Phys Lett 2 (1962) 209. [11] T E Bortner, G.S Hurst, M Edmundson and J E Parks, ORNL-3422 (1963) [12] A Hashlba, K. Masuda, T Doke, T Takahashl and Y Fujlta, Nucl lnstr and Meth 227 (1984) 305, preceding paper this issue