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Conduction processes in liquids Maybank, John 1954

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.CONDUCTION PROCESSES IN LIQUIDS. by John. Maybank A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department, o f PHYSICS We accept t h i s t h e s i s as conforming to the s tandard r e q u i r e d from candidates f o r the degree o f MASTER OF SCIENCE. Members o f the Department o f P h y s i c s THE UNIVERSITY OF BRITISH COLUMBIA March, 1954. ABSTRACT In the work described in this thesis attempts have been made to obtain information on three aspects of the behaviour of liquid argon as an ionization counter.. Ionization was produced by alpha particles from a source deposited on the negative electrode of a small parallel-plate chamber in which pure argon was liquefied. The current pulses resulting from move-ment of the liberated electrons in the field applied to the plates were analysed electronically. Firstly, i t was desired to determine the time taken by the electrons originating from distinct ionization events to traverse measured electrode separations and be collected by the positive-electrode. These transit times depend upon the electron mobility in liquid argon, defined as the velocity of the electrons per unit field. From this mobility, the mean free path and collision cross-section of the electrons with respect to argon atoms can be calculated. .Some estimates of transit times and mobilities, and resulting values of mean free path and cross-section are given.. However, i t appears that limitations of. the electrode spacing and the applied field cause the transit time to be so short as to necessitate the use of wide band amplifiers with, consequently, high noise levels. . Secondly, the causes of variation in size of current pulses with angle of emission of the initiating alpha particles were investigated. The effect of greatest interest was that, due to the geometry of the chamber, as; from i t a determination was made of the range of alpha particles in liquid argon.. For 5.3 MeV alpha particles, the weighted centre of ionization was found to be 0.006 cms. from the.source, implying a particle range of about 0.009 cms., The number of electrons contributing to current pulses was also found to be a function of the angle of emission, on account of a variable degree of recombination with the positive ion column. This number was determined, and even under the most advantageous conditions f e l l consider-ably short of the probable total number liberated.. This fact imposes a serious limitation on the potentialities of liquid argon as a useful counter., ACKNOWLEDGEMENTS The research d e s c r i b e d i n t h i s t h e s i s has been supported by grants from the Defense Research Board. The author i s p e r s o n a l l y indebted t o the N a t i o n a l Research C o u n c i l f o r a. bursary h e l d d u r i n g 1952 — 1953* A l s o , the author wishes to express h i s s i n c e r e g r a t i t u d e to Dr„ U.F. Gi a n o l a , under whose s u p e r v i s i o n the e a r l i e r p o r t i o n s of t h i s ; work were done; to- Drs. F.D. Stacey and H.E.D. S c o v i l , who supervised the l a t t e r p o r t i o n s of the work and the w r i t i n g of the t h e s i s ; and to Mr.. R.L.. W i l l i a m s , w i t h whom I worked d i r e c t l y i n the l a b o r a t o r y , f o r h i s great help w i t h the problems encountered. I N D E X ) page I n t r o d u c t i o n T h e o r e t i c a l C o n s i d e r a t i o n s Theory of Pulse Production. A K i n e t i c Theory of M o b i l i t y . .. 6 D i s c u s s i o n of Ramsauer E f f e c t . H Pulse S i z e D i s t r i b u t i o n 13 Determination of Ion P a i r Energy IS Design of Apparatus Argon Chambers. 19 Alpha Source 2A C i r c u i t Components • 25 Electrometer.. 29 A n a l y s i s of Results: Pulses Obtained. 31 R i s e Time Measurements 34 Pulse S i z e D i s t r i b u t i o n 36 V a r i a t i o n of Maximum Pulse S i z e w i t h F i e l d . . . . 42 I o n i z a t i o n Current Measurements 44 D i s c u s s i o n 46 B i b l i o g r a p h y 49 I ILLUSTRATIONS F i g u r e : f o l l o w i n g page II (a-) Input C i r c u i t i . 5 (b) C u r r e n t Pu l se i 51 (c ) Vo l t age Pu l se 5 2 (a) Angu la r A l p h a D i s t r i b u t i o n . 1 4 (b) Cur r en t Pu l se V a r i a t i o n . • 14 (c) ; Vo l t age Pu l se V a r i a t i o n 14 3> Recombinat ion Column... 16' 4 Argon C h a m b e r . . . . . 20 5 Argon Chamber 21. 6 (a) P r e - a m p l i f i e r C i r c u i t 27 (p.). C i r c u i t Diagram • .27 7 E l e c t r o m e t e r C i r c u i t . 29 8. Pu l se Photographs . 31 9 Noise C o r r e c t i o n C i r c u i t . . . . . . . . . . 37 TABLES AND GRAPHS Table [ f o l l o w i n g page 1. Pulse S i z e D i s t r i b u t i o n s , . 36 2 Pulse S i z e Frequency 36 3 Noise C o r r e c t i o n s •.. 38 4 Corrected Pulse S i z e D i s t r i b u t i o n s . . . . . 38 5, Values of Range and E l e c t r o n Number............... . . . 39 6 Recombination E f f e c t 41 7 F i e l d — Maximum Pulse Size.. 42-Graph 1 Pulse S i z e D i s t r i b u t i o n s 36 2- Pulse Size. Frequency 36 3 Noise C o r r e c t i o n s 3& 4. Corrected Pulse S i z e D i s t r i b u t i o n s 38 5 Recombination E f f e c t 41 6, F i e l d —Maximum Pulse S i z e . . . . . 42 7. F i e l d --Maximum Pulse S i z e 44 CONDUCTION PROCESSES IN LIQUIDS INTRODUCTION The theory of conduction pulses began with the work of R'ontgen and J o f f e ( l Q l j ) , H. S c h i l l e r ( 1 9 2 6 ) and G. J a f f a ( 1 9 J 2 ) . The f i r s t experimental observation of such pulses was found by Van Heerden ( 1 9 ^ 5 ) who used single c r y s t a l s of s i l v e r c h l o r i d e . Since that date much work has been done on both c r y s t a l s and semi-conductors and the whole f i e l d has been adequately surveyed by Hofstadter (I949). The explanation of the conduction properties of these materials i s based upon the theory of f i l l e d and empty el e c t r o n energy bands (Williams, 1 9 5 2 ) . I t i s postulated that i n a normal c r y s t a l nearly a l l the electrons occupy l e v e l s i n f i l l e d bands and hence may be considered bound to d i s t i n c t ions i n the c r y s t a l l a t t i c e . When an i o n i z i n g p a r t i c l e such as an alpha p a r t i c l e enters the c r y s t a l , i t gives some of these electrons s u f f i c i e n t energy to enter the conduction band i n which they are free to migrate through the c r y s t a l , subject to c o l l i s i o n with the ions. The holes i n the c r y s t a l l a t t i c e r e s u l t i n g from the removal of such bound electrons can behave as p o s i t i v e l y charged p a r t i c l e s due to the migration of electrons from neighbouring ions to them; t h i s i s equivalent to movement of the p o s i t i v e l y charged s i t e s . In most c r y s t a l theories such holes are assumed to be r e l a t i v e l y immobile, which i s found to be the case i n AgCl at low temperatures. On the other hand the electrons i n the conduction band w i l l , i n the presence of an e l e c t r i c f i e l d , move through the c r y s t a l toward the p o s i t i v e electrode u n t i l they reach i t or are stopped. They may be stopped by recombination with holes, or by being captured by trapping centres due to inhomogeneities or impurities i n the c r y s t a l l a t t i c e . Both these e f f e c t s w i l l decrease the r e s u l t i n g conductivity pulses, trapping centres being the more important. There i s another e f f e c t o c c u r r i n g i n c r y s t a l s which renders t h e i r use as s i n g l e pulse counters more haphazard. This i s the p o l a r i z a t i o n e f f e c t caused by the successive t r a p p i n g of e l e c t r o n s from a l a r g e number of pulses and the subsequent b u i l d i n g up of p o t e n t i a l b a r r i e r s at p o s i t i o n s f i x e d by the t r a p p i n g centres. Simultaneously there occurs an analogous process i n v o l v i n g the p o s i t i v e i o n s formed near the negative e l e c t r o d e . The e f f e c t of these two charged b a r r i e r s i s to oppose the e x t e r n a l f i e l d , thus decreasing the s i z e of subsequent p u l s e s , and i n some cases quenching them completely. F i n a l l y , i n any c r y s t a l , i f a cleavage plane, or crack i s present near the negative e l e c t r o d e i t forms an e f f e c t i v e b a r r i e r to e l e c t r o n p e n e t r a t i o n , r e s u l t i n g i n diminished p u l s e s . Such b a r r i e r s are present i n a l l mosaic c r y s t a l s t r u c t u r e s i n c l u d i n g l i t h i u m f l u o r i d e and the other a l k a l i h a l i d e s , and are regarded by most researchers i n the f i e l d to be the reason why these c r y s t a l s do not a c t as counters although they have l a r g e e l e c t r o n m o b i l i t i e s and hence l a r g e mean f r e e paths - a necessary c o n d i t i o n f o r the o b s e r v a t i o n of p u l s e s . (Hofstadter, 1950) . These three disadvantages present i n c r y s t a l s , v i z . , the presence of t r a p s of the form of vacant l a t t i c e s i t e s ; p o l a r i z a t i o n due to f i x e d t r a p p i n g centres; and cracks forming e l e c t r o n b a r r i e r s , are absent i n a l i q u i d counter. However, there are d e f i n i t e l i m i t a t i o n s on the types of l i q u i d s which can be used. These are set by the f o l l o w i n g c o n d i t i o n s : (.1) The r e s i s t i v i t y of the substance must be h i g h , e.g. % I O 1 7 ohm-cms. (2)., The l i q u i d molecules should have no e l e c t r o n a f f i n i t y , i . e . the energy of heavy negative i o n s should not be l e s s than t h a t of n e u t r a l atoms. (3) As mentioned above e l e c t r o n s i n t h e . l i q u i d should have a l a r g e mean f r e e path. However, t h i s q u a n t i t y i s at present unknown f o r most l i q u i d s . (A) It should be possible to obtain and maintain the liquid in a high state of purity. (5) Finally, i t is advantageous to use materials with a low dielectric constant. The substances which best f i t these conditions and particularly the second are the rare gases in the liquid state. As argon can be easily liquified (boiling point = -185.7 G at one tatmosphere), and is relatively cheap i t has been the one most often used and is the one used here. Besides having none of the three disadvantages mentioned above as present in crystals, liquid argon can be obtained quite pure (99.98$) and therefore with few traps due to the presence of impurity atoms having electron affinity. Pulses of good size have been obtained with i t . An argon counter possesses a l l the advantages of a crystal over gas counters such as the Geiger-Muller type. These are the fast resolving time, and the high efficiency in gamma counting due to the much greater stopping power of liquids and solids over gases. The liquid also lends itself to the using of more compact construction for counting devices; however, this is somewhat offset by the necessity of working at low temperatures. In the following investigations i t was desired to measure the rise times and amplitude distributions of pulses initiated by alpha particles of various field strengths, in order to determine: the voltage - electron mobility relationship; (2) the mobility, and hence the mean free path of electrons in argon and the capture cross-section involved in their removal; (3) / the pulse amplitude distribution and the ionisation current and . hence the energy per ion pair. THEORETICAL CONSIDERATIONS Theory o f pu l se p r o d u c t i o n When an a lpha p a r t i c l e en te r s a medium such as l i q u i d argon i t l o s e s energy by i o n i z i n g the argon atoms w i t h i n a s m a l l c y l i n d e r which i s centred about i t s t r a c k i n the l i q u i d . The r a t e o f l o s s o f energy o f such a p a r t i c l e due t o i o n i z a t i o n reaches a maximum va lue near the end o f i t s pa th , which r a t e i s approx imate ly tw ice the i n i t i a l one; the r a t e o f i o n -i z a t i o n then drops a b r u p t l y t o zero a t the l i m i t o f the a lpha range.. ' However, as t h i s range i s assumed to be shor t w i t h r e spec t to the i n t e r -e l e c t r o d e d i s t a n c e used he re , the assumption w i l l be made, a t l e a s t i n i t i a l l y , t h a t the e l e c t r o n s produced by an a lpha p a r t i c l e through i o n -i z a t i o n are a l l l i b e r a t e d s imu l t aneous ly i n the p lane o f the nega t ive e l e c t r o d e . . I t i s assumed t h a t no secondary i o n i z a t i o n takes p l a c e , i . e . , the re i s no i o n i z a t i o n o f argon atoms by the e l e c t r o n s as t hey move towards the c o l l e c t i n g e l e c t r o d e . These p r imary e l e c t r o n s w i l l then move w i t h random v e l o c i t i e s due t o the rmal a g i t a t i o n . When an e x t e r n a l f i e l d i s a p p l i e d there w i l l be superimposed upon t h i s mot ion a d r i f t v e l o c i t y through the l i q u i d i n the d i r e c t i o n o f the p o s i t i v e or c o l l e c t i n g e l e c t r o d e . Due t o the f a c t t h a t the n e u t r a l argon atom has a negat ive e l e c t r o n a f f i n i t y there w i l l be no capture o f the e l e c t r o n s by such atoms. Hence the o n l y r e d u c t i o n i n the number o f e l e c t r o n s r e a c h i n g the c o l l e c t i n g e l e c t r o d e w i l l be due t o r ecombina t ion w i t h p o s i t i v e argon i o n s and capture by i m p u r i t y atoms posses s ing e l e c t r o n a f f i n i t y . The former process w i l l occur o n l y i n the r e g i o n o f the source as we have assumed t h a t there i s no secondary i o n i z a t i o n by the l i b e r a t e d e l e c t r o n s . The l a t t e r process can be rendered n e g l i g i b l e by u s i n g h i g h l y p u r i f i e d argon, w i t h the oxygen content p a r t i c u l a r l y , reduced to a minimum. I n moving toward the p o s i t i v e e l e c t r o d e these e l e c t r o n s cause a current, i , t o f l o w f o r a time, r , through the e x t e r n a l c i r c u i t . "X , the t r a n s i t time f o r the e l e c t r o n s i s given by where v = the d r i f t v e l o c i t y of the e l e c t r o n s i n the d i r e c t i o n of the a p p l i e d f i e l d and 1 = the e l e c t r o d e spacing d i s t a n c e . This g i v e s r i s e t o a current pulse of the form shown i n f i g u r e 1 ( b ) This i s an approximation as i t w i l l be rounded by a v a r i e t y of e f f e c t s , the most important of which ar e : ( 1 ) The d i f f e r e n c e i n d i s t a n c e t r a v e l l e d by e l e c t r o n s l i b e r a t e d near the s t a r t of the i o n i z i n g p a r t i c l e ' s range and those l i b e r a t e d a t the end f o r an i o n i z i n g t r a c k n e a r l y p e r p i n d i c u l a r to the e l e c t r o d e s . This w i l l be discussed f u r t h e r i n a f o l l o w i n g s e c t i o n . There i s a l s o the d i f f e r e n c e i n time of l i b e r a t i o n by the alpha as the l a t t e r proceeds along i t s t r a c k i n the l i q u i d . . This a l l o w s some e l e c t r o n s t o complete t h e i r path to the c o l l e c t i o n e l e c t r o d e before others and r e s u l t s i n a widening of the whole p u l s e . The h i g h v e l o c i t i e s of alphas of the energy used here x d . l l keep t h i s e f f e c t s m a l l . ( 2 . ) S t r a g g l i n g i n the times of a r r i v a l a t the p o s i t i v e e l e c t r o d e due t o s t a t i s t i c a l f l u c t u a t i o n s i n the number of c o l l i s i o n s encountered by v a r i o u s e l e c t r o n s . However, i n f i e l d s of the magnitude used here ( ^ 10 - 4 -volts/cm.) t h i s e f f e c t i s considered s m a l l . I t t h e r e f o r e i s assumed t h a t f i g u r e 1 ( b ) represents a current pulse which c l o s e l y approximates to the t r u e p i c t u r e . This current w i l l f l o w through the e x t e r n a l c i r c u i t which i s given by f i g u r e l ( a ) w i t h C r e p r e s e n t i n g a l l the s t r a y capacitances a r i s i n g from the chamber, and leads t o the p r e - a m p l i f i e r . R i s the g r i d r e s i s t a n c e to follow page 5 C b o m b e r S o u r c e R T o P r e - a m p F I G . I C a ) I N P U T C I R C U I T C u r r e n t F I G . I ( b ) C U R R E N T P U L S E V o l t a g e —j=^± t , t A T i m e F I G . I <c> V O L T A G E P U L S E 6 • of the input stage of the pre-amplifier. This external circuit shapes the current pulse into a voltage pulse of the form shown in figure 1(c); this pulse is amplified and displayed on an oscilloscope screen on which i t s rise time may be measured. By measuring the rise time of the voltage pulse, i t is possible to find the time of transit of a group of electrons moving through the counter medium a distance t at a velocity v i n the direction of an applied f i e l d of E volts per cm. The electron mobility i n a particular medium i s defined as the d r i f t velocity of electrons per unit f i e l d . Hence the mobility i s given as: ~ frX cm. ^/volt-sec. In this measurement of "T and hence of K i t is important that the time constant of the input impedance, viz. RC, be small with respect to the rise time' "X . This w i l l also be a necessary condition for a l l electronic circuits following this; i n particular, both the pre-amplifier and the amplifier must have uniform amplification over a wide band width. Kinetic Theory of Mobility The kinetic theory of gases, along with Maxwell-Boltznmnn sta t i s t i c s has been applied successfully to liquids for the determination of such quantities as heat conduction and viscosity (see G. Jaffe, 194-9). It i s hoped that such an approach can yield satisfactory results in the problem of electron mobilities and mean free paths for the motion of electrons i n a liquid. Langevin (1950) has shown that for electrons of mass m, and charge e, moving through a gas of neutral atoms of mass M the mobility is given by + m Since nnrv (1) where L is the mean free path of the electrons i n the gas and i s the root mean square velocity of the atoms. where G m is the velocity of the electrons, assuming no f i e l d is acting, equation #1 can be changed to e I- \ / /v' + ™ which, as m << M can be simplified to K = o?ar£-~ (2) If an electric f i e l d is present i t w i l l act only on the electrons and ions present. Hence the velocity 0 f the atoms remains the same, but the expression for electron velocity has a term added to i t due to the electric f i e l d . Then C m depends on both E and T, and the equation for i t must now be found. Equation #2 w i l l s t i l l be valid, provided that C m is replaced by this new f i e l d dependent velocity for the electrons. From the definition of mobility the velocity in the direction of the f i e l d can be written equal to KE, and so the average distance, S, which the electrons move between collisions with the atoms (in the direction of the f i e l d E) i s given by: S = K E -J-V . -m. where C m is the average velocity of the electrons and is - .922 C m. by kinetic theory. Cm now includes both the velocity due to thermal agitation 8 energy and that due to the electric f i e l d . Therefore: L*e E 5 = °^^TS (5) from equation #2. We now define an equivalent potential per unit charge, u, such that U< 5 Q = the energy of the electron due to thermal agitation plus the energy due to the f i e l d . Then jjL g (4) Compton (1923) showed that the fraction f, of the average energy lost i n an electron-atom c o l l i s i o n i s : (5) for - H . = 3kT/2e - the energy of the electron per unit charge due to the thermal agitation. This w i l l hold only for fields large enough to give iL >)-n.. Therefore the change in energy, & u in a distance £ x moved by an electron in the direction of a f i e l d E is given by: or from equations #4 and #5, with M » m. By assuming that a Maxwellian distribution gives a good approx-imation to the electron velocities the above expression in du/dx can be integrated, giving the following equation for u as a function of x: d% - £k + C LL . Jtl -/ (7) where Now as x-*o° the e x p o n e n t i a l s i n equa t ion #7 bo th — t h e -1 and +1 i n the numerator and denominator r e s p e c t i v e l y can be neg l ec t ed , and the e x p o n e n t i a l s c ance l o u t . Th i s g ive s a t e r m i n a l va lue t o u x which i s independent o f x and depends o n l y on the f i e l d , temperature and mean f ree pa th o f the e l e c t r o n s . The d i s t a n c e , d , a f t e r which u x has ob ta ined a f r a c t i o n <£> o f i t s t e r m i n a l energy, say , i s g i v e n by the e x p r e s s i o n : 3u<k> t - q> o F o r L ^ I C T ^ cms. l / a . i s 10~5 cms. and so d i s v e r y s m a l l even f o r >^ = .99. T h i s means t h a t the t e r m i n a l v e l o c i t y o f an e l e c t r o n i s reached v e r y soon a f t e r i t i s l i b e r a t e d , and f o r . a l l p r a c t i c a l purposes we can take u j as the energy o f the e l e c t r o n per u n i t charge f o r the whole t r a n s i t t ime o f the e l e c t r o n . Hence by l e t t i n g x - » - » e q u a t i o n #7 becomes ar = & + [ 4? + it"** X L 4 T G.OJL™ J Thi s g i v e s C m from the d e f i n i t i o n o f u where C m = [lihuUr , and t h i s va lue o f C m may be s u b s t i t u t e d i n t o equa t i on #2, g i v i n g f o r the m o b i l i t y : ^ OVi^ei.  S o l v i n g t h i s f o r L: This equation will hold only for fields such that_TL «^>. In equation #8, k T ^ l O " 1 ^ ergs for T = 87° A, and M-~ 1CT 2 1 gm. for argon atoms. Hence for fields of 10^ volts/cm. or greater and values of the mobility lOcm? per volt-sec. the second term under the root sign is nearly 10 times as large as the f i r s t . Thus, as the equation is valid only for large fields, for which the contribution of temperature to mean free path is negligible with respect to the contribution from the field, we may contract #8 to: L - ( _e* -JK t- (9) This is the same form of equation as that used by Malkin and Schultz (1951) except for the numerical constant. They also assumed that a liquid may be treated as a gas at high pressure and that the mean free path is a constant. Their final equation was: but they had no way of evaluating c which they took to be in the range 2.3 4 C «* A compared with the value or 1,22 used here. Finally there is the equation for the atomic radius, r, which is given by /—j s~L = \JTJTJJ where N is the number of atoms per unit volume. The collision cross-section is then taken as simply the cross-sectional area of the atoms with which the electrons collide. It is thus inversely proportional to L and to KE^. Unlike the gaseous collision cross-section, this quantity for a liquid should be constant with respect to the field, just as L i s . This theory indicates that K%! must be a constant, or that (11) H<C I /ft i n order to give a constant value for the mean free path for a l l fields greater than a certain minimum f i e l d of *^-/ 1C)3 volts/cm.. This theory has the flaw that a l l calculations of mean free path and c o l l i s i o n cross-section depend solely on a measurement of the mobility from the transit time of the electrons. Thus there can be no alternative and independent method of finding these quantities and so checking the v a l i d i t y of the assumption that a l i q u i d behaves as a gas at high pressure at least as far as electron conduction i s concerned. However, one result _ i of this theory i s that the mobility i s not a constant but varies as E~*. This w i l l provide at least one valuable check on whether kinetic theory essentially derived for gases,, can be applied to any extent to a l i q u i d . Malkin's results (1951) do indicate this relationship between K and E, at least i n the range of 104. - 105 volts/ cm. Discussion of Ramsauer Effect In the above theory i t was assumed, as mentioned previously, that the mean free path was independent of f i e l d . This i s not the case for a gas, where L has a minimum value at a particular value of the electric f i e l d . This i s known as the Ramsauer effect. However, no such minimum has been found to occur for l i q u i d argon.. The following i s a qualitative argument to account for i t s absence i n dense media such as liquids.. Wave mechanical theory gives for the cross-section of a co l l i s i o n between an electron of wavelength*=h/l£«%nd momentum f~^S(t-**) , and an atomic f i e l d , the value (Frolich and Mott, 1939): (12) where £ = the e l e c t r o n energy H = Planck's constant = azimuthal quantum number = the phase s h i f t i ntroduced i n the e l e c t r o n waves by such a c o l l i s i o n , i s dependent upon the s c a t t e r i n g p o t e n t i a l V ( r ) and i f t h i s i s s m a l l f o r a d i s t a n c e comparable t o one wavelength we may w r i t e f o r ^ £ the f o l l o w i n g : where the lower, i n t e g r a t i o n l i m i t s are taken to give the integrands a zero l i m i t . According t o Holtsmark (1929) t h i s s c a t t e r i n g p o t e n t i a l V ( r ) i s l a r g e enough i n a gas to introduce as many as three a d d i t i o n a l wavelengths i n an e l e c t r o n wave t r a i n a f t e r c o l l i s i o n . . This would account f o r a l a r g e v a r i a t i o n i n c o l l i s i o n c r o s s - s e c t i o n observed f o r gaseous argon. However, i n a l i q u i d the i n t e r - a t o m i c d i s t a n c e i s so sm a l l compared w i t h t h a t o f a gas, t h a t an e l e c t r o n a t the time of a c o l l i s i o n w i t h a p a r t i c u l a r atom i s s u b j e c t t o the p o t e n t i a l f i e l d s of s e v e r a l surrounding atoms. This p o t e n t i a l may be expressed as U(r) which combines the e f f e c t s due t o a l l the i n d i v i d u a l atomic f i e l d s exerted on the e l e c t r o n a t the time of c o l l i s i o n . U(r) w i l l i n t r o d u c e a term of value - 2mU(r)/ft2: i n t o the second i n t e g r a n d i n the above ex p r e s s i o n f o r f y A l s o , V(r) i n the f i r s t i n t e r g r a n d , w i l l now assume a perturbed value V ' ( r ) . , The two integrands above are t h e r e f o r e of the same form, and (13) differ only in the potential function present in the second term in each. If V (r),iiS U(r) the two integrals will cancel giving 7\ sc. O , and so the cross-section becomes independent of electron wavelength and, therefore, of the electron energy. It seems likely that this is the case for liquid argon, and so the collision cross-section will be small and will change l i t t l e with changes in external field. Thus there should be no Ramsauer type variation of the cross-section for liquids. Pulse Size Distribution In the theory of pulse production described on page 4, i t is assumed that a l l ionization takes place in the plane of the negative electrode, and that each alpha particle produces n0, electrons, a l l of which contribute to the observed pulses. This would result in a uniform pulse amplitude for a l l alphas. Such a result is not the case, and four effects cause variation in this amplitude. The first of these is due to random noise contributions to the pulses. The effect of this noise contribution depends upon the fundamental frequency of the pulses as compared with the band of noise frequencies amplified. If the latter contains a large percentage of high frequency noise, the majority of pulses are recorded at an amplitude greater than their true value, for the noise peaks would cause the pulse to be registered at its maximum height.. If the pulses are of a frequency near to the upper half-power frequency of the amplifier, half of them suffer a decrease in amplitude.. In general the result of the noise is to increase the amplitude spread of the pulses by an amount dependant upon the signal to noise ratio. The actual spread is difficult to calculate theoretically, but may be corrected for experimentally, as is shown later. The second cause of amplitude variation is due to the fact that ( 1 4 ) a lphas are emi t t ed a t a l l angles t o the plane o f the negat ive e lec t rode . . The r e s u l t a n t columns o f e l e c t r o n s t r a v e l v a r y i n g d i s t a n c e s betv/een the e l e c t r o d e s , depending on the e l e c t r o d e s p a c i n g , 1 , and the a lpha range R * .. Davidson and L a r s h ( 1 9 5 0 ) : d i s c u s s e d t h i s e f f e c t , but d i d not g ive an equa t ion r e l a t i n g pu l se h e i g h t Ve- due t o an e l e c t r o n column formed a t angle 9-, w i t h the f r a c t i o n of such a lphas emi t t ed a t angles between 9 and 9- + d9 . We s h a l l at tempt t o do t h i s as f o l l o w s : I n f i g . 2(a); the number o f a lpha p a r t i c l e s emi t t ed i n a r e g i o n d9; about 9- i s g i v e n by where R a\ = range o f a l p h a p a r t i c l e % = t o t a l number o f a lphas emi t t ed per second, or i f NQ.. i s t aken to be the number o f a lphas emi t ted a t angles x< 9, i t i s g i v e n by (& Ne - J A / T cosBdB^ A / - r sin 0 (1) o I f the e l e c t r o n s are cons idered t o be produced u n i f o r m l y a long the t r a c k o f the a l p h a , t hey can be cons idered centred a t R * / 2 , These e l e c t r o n s w i l l move some d i s t a n c e between J and ( l - R 4 / 2 ) before s t r i k i n g the p o s i t i v e e l e c t r o d e , depending upon the angle o f a l p h a e m i s s i o n . I n each case they v a i l g ive r i s e to the same c u r r e n t , n e/r , i n the e x t e r n a l c i r c u i t , l a s t i n g f o r some average t ime t = T - tQ» Thus the square pu l se i l l u s t r a t e d i n f i g . 1(b). becomes t h a t o f f i g . 2 ( b ) . I n such a case the t o t a l charge t r a n s f e r r e d by the e l e c t r o n s w i l l v a r y w i t h Q, becoming equal t o ne o n l y f o r 9-= 0 , f o r which pu l se the p o s i t i v e i o n s now formed adjacent t o the negat ive e l e c t r o d e c o n t r i b u t e n e g l i g i b l e charge t r a n s f e r . Now, f o r a p a r t i c u l a r a l p h a emi t ted a t an angle 9, the e l e c t r o n s to follow page A&9 TL \ source PIG* Z (a) ANGULAR DISTRIBUTION OF ALPHA PARTICLES, Current FIGo 2 (b) CURRENT PULSE VARIATION T T i m 6 FIG. 2 (e) VOLTAGE PULSE VARIATXOB (15) will traverse a distance, 1 - x/2 = 1 ~(R/2)sin ©, in a time t = T - tg* o If v is taken as the terminal velocity of the electrons and is assumed to be reached in a time small with respect to tg., as well as these times are given by and + (U sin 9 RcTsinB The voltage appearing across the resistance R in fig. l(c) will rise as the current n e / f flows in the external circuit. If the time constant, RG of this circuit i s large with respect to T*, the voltage will not reach saturation but will continue to build up until the current drops back to zero.. As shown in fig. 2(c), i f tg. is small, compared to "ZT , the voltage will rise linearly in the region T - t & to and hence the maximum pulse height obtained will be given by: where a and b are empirical constants. They may be found from the equation relating the voltage at any time t to i , R,, C, and t, found from analysis of the input circuit. The current pulse is given by I = o t < o i =o r 7 T the voltage appearing across R in fig 1(c) can be shown to be (16) From the f i r s t of these two equation, the maximum voltage VQ reached during the pulse i s t-te ~ T-te Now \ ^ i t h RC » t , j£~ « • 1 and may be approximated t o by the f i r s t two terms of the exp o n e n t i a l s e r i e s * This gives v/ ot-e T - ta With equations ( l ) ; and (2) s u b s t i t u t e d i n t o t h i s f o r tg and s i n 8, VQ. becomes \ / - / | t - g _ m£- & M> W& " C C SLJ Nr (3) Thus the graph of V©. a g a i n s t Ne/No? should be a s t r a i g h t l i n e , from which i t should be p o s s i b l e t o f i n d both R and n, i f c i s known. The r e l a t i o n s h i p s are U) V«A* = ^ ( 5 ) The t h i r d cause o f pulse s i z e v a r i a t i o n i s recombination. I n f i g u r e 3, we have an alpha emitted a t an angle 9 t o the el e c t r o d e and surrounded by a c y l i n d e r of r a d i u s r , i n which i t i s assumed t h a t a l l i o n i z a t i o n takes place u n i f o r m l y across r , so t h a t we have an even d i s t r i b u t i o n of n,-, p o s i t i v e and no negative i o n s throughout the column. The e l e c t r o n s are then considered t o o r i g i n a t e along the a x i s o f the c y l i n d e r and t o t r a v e l a di s t a n c e x = r sec 9 through i t under the d i r e c t i o n of the a p p l i e d f i e l d . Each of these e l e c t r o n s sweeps out a volume centred about i t s t r a c k , which w i l l be gi v e n by <rx?t where < 7" 1 i s the capture c r o s s -s e c t i o n of the e l e c t r o n w i t h respect to the p o s i t i v e i o n s . We then have: to f o l l o w page 16 SOURCE F I G . 3. ALPHA RECOMBINATION COLUMN (17) Number of electrons captured = (density of positive ions) x (total volume swept out by no electrons) " 77-n-v/?* * Therefore the number of electrons escaping recombination and contributing to the current pulse will be given by: T> - STL ( I • /n**"- & ) 7Z. _ -n. ( J - J (6) Or as VQOC n we should obtain a linear relationship between VQ and sec 9 of the form VQ. — a-b sec 9, applicable to the voltage - number curve obtained after correcting for the first two effects. Equation, (#6), does not hold for large 9.. For those electrons originating in the triangle at the end of the alpha track, as shown in fig. 3, the distance travelled in the presence of positive ions will be less than x, due to the finite length of track. This fraction of the total number of electrons increases as 9 increases until for 9 = 906, a l l the electrons move through an average distance H./2 in which recombination can take place. However, i f r-~R/50 ,the distance d, as shown in f i g . 3, will be only ~>10% of Rot for 9, = 86°> at which point N@ will be > 98$ of Nj, This will mean an insignificant correction to the above theory for a l l except the few pulses initiated by ctf- particles emitted nearly vertically to the plane of the electrodes.. The fourth effect which must be considered, is the variation of no itself due to variation in alpha energy., This will occur i£-Some alphas^ originate within the negative electrode instead of at its surface, thus losing some of their energy in the metal instead of in tbe argon. This may be- avoided by proper formation of the source, and i t is assumed here that Do. is actually a constant for a l l pulses.. (18) Determination of Ion P a i r Energy:. I f i t i s assumed t h a t each alpha p a r t i c l e emitted by the source enters the l i q u i d argon w i t h the same energy, H, and forms the same number e l e c t r o n - i o n p a i r s , no, then where P i s the i o n i z a t i o n energy of l i q u i d argon. The q u a n t i t y x i s the f r a c t i o n of the energy l o s t by the alpha i n one i o n i z i n g event t h a t i s a c t u a l l y used t o f r e e the e l e c t r o n . The r e s t of the energy l o s t appears as the k i n e t i c energy of the e l e c t r o n and ion., Now P has a value of 25.4- ev. f o r gaseous argon, and t h i s i s the maximum value i t can have f o r the l i q u i d . However, i f there i s i n the l i q u i d a conduction or energy band s i m i l a r t o those known to occur i n s o l i d s , P may be co n s i d e r a b l y l e s s than t h i s , s i n c e the i o n i z a t i o n energy o f the gas i s equal t o the i o n i z a t i o n energy of l i q u i d argon p l u s the energy necessary t o remove an e l e c t r o n completely from the l i q u i d . That conduction bands can e x i s t i n l i q u i d s i s demonstrated by the f a c t t h a t Ogg (194.6) has des c r i b e d such an energy band f o r l i q u i d ammonia.. However, nothing i s known of t h i s f o r l i q u i d argon, and so the i o n i z a t i o n p o t e n t i a l i n the above equation i s unknown.. Hutchinson (1948) and G e r r i t s e n (194.8) as w e l l as Davidson and-Larsh (1950) assumed i t t o be 25.4. ev. However, i f no and H are known we can f i n d P/X„ As X I t h i s determines the maximum value of the i o n i z a t i o n p o t e n t i a l ; , i f t h i s i s l e s s than 25.4. e l e c t r o n v o l t s , we may accept the i d e a of conduction band i n l i q u i d argon. A c t u a l e v a l u a t i o n of depends upon determining X. I t has a value o f 0.6 f o r NaCl c r y s t a l s ; and i s thought to be near.to t h i s value f o r other so l i d s ; , no values are known f o r l i q u i d s . . 9 I n order t o f i n d no i t i s necessary to f i n d the l i m i t of n, (19) the number of electrons collected in the largest pulse for a given f i e l d , as the f i e l d approaches i n f i n i t y . Davidson and Larsh (1950) proposed the equation: , V \ Vfc (i) with a an arbitrary constant. Then from equation #5 in the previous section i t should be possible to calculate n 0, corresponding to the V/*,** in equation #1 above. Another possible way of evaluating n 0 is from the D.C. measure-ments of electron current aa found by an electrometer. This should give J = /fv e A / r where Nrp a number of alphas emitted per second; and n = average number of electrons contributing to each current pulse. -This average number of electrons n, w i l l be different from n, due to the variation of recombination with Q. It can be related to n by means of the experimental curves after they have been corrected for noise and variation in pulse height due to G . Again n" should vary with E similarly to the variation i n V Q _ ^ ? , and so permit n 0 to be found by an independent method. DESIGN OF APPARATUS Argon Chambers: Three different chambers were used in the attempts to observe argon pulses. A l l were basically the same, having a pair of plane parallel electrodes with an alpha source deposited on one of them. The f i r s t consisted of a glass dewar flask containing a lucite holder for the brass electrodes, held in place by ceresin wax. The electrical leads entered from below via glass-to-metal seals. The argon was liquefied in a helical glass c o i l immersed in liquid nitrogen and allowed to flow down into the dewar; the two were connected by a ball-and-Bocket connection. This design had several serious drawbacks. The lucite had a large vapour pressure at room temperature which prevented effective degassing of the chamber. The ceresin wax proved very b r i t t l e at liquid argon temperatures, and tended to break loose. Most important was the inefficiency of the heat exchange system. Using liquid nitrogen, the argon tended to freeze i n the coils and block them, while liquid oxygen necessitated a pressure of 1.3 atmospheres in the system, which was not constructed to withstand i t . Furthermore, the liquid argon in the dewar could not be further cooled, and this necessitated keeping the c o i l constantly immersed in liquid nitrogen throughout the t r i a l . The second chamber used is shown diagrammatically i n f i g . k. It was constructed of copper with the negative electrode and alpha source attached directly to the l i d of the chamber. This was fastened to the body of the chamber, by means of screws, tightening down on the "O" ring seal. The collecting electrode was mounted on a kovar seal soldered into the base of the chamber. The chamber i t s e l f was surrounded by a brass cylinder attached to the chamber base plate. This was f i l l e d with liquid oxygen, and served as an efficient heat exchanger. This in turn was surrounded by styrofoam blocks to provide thermal insulation. This chamber was used for some time but several drawbacks forced i t s abandonment. Diff i c u l t y in rendering the "O" ring seal vacuum tight at low temperatures caused considerable trouble on a number of occasions, and the electrode spacing could not be easily varied. The most serious objection however was the manner in which the source was held in place under a copper cap with a small hole i n i t . This placed the source in a recess about 1 mm. deep, and made the electric f i e l d about i t d i f f i c u l t to determine exactly. It was primarily to eliminate this drawback that a new to follow page 20 F I G . 4. ARGON CHAMBER (21) chamber was designed. The third chamber designed was the one with which a l l the results were obtained. It was of brass, as i t was f e l t that the slight advantages obtained from copper, pertaining to i t s thermal and electrical conduction properties, were more than offset by i t s softness. As shown i n f i g . 5» i t consisted of two electrodes i n a small brass cylinder, one of which was situated on a kovar seal set in the base of the cylinder, while the other electrode was attached to the top by a screw thread. They were adjusted into a plane parallel position with respect to each other, whereupon the copper glass, seal was set down and soldered into place. Afterwards the electrode spacing could be easily and accurately varied, the screw pitch on the upper electrode being known. The upper electrode was screwed down unt i l electrical contact was made with the lower electrode and then turned through a measured angle to give the desired spacing. As there were 52 threads to the inch or 2 per mm. i t was possible to set a gap of .1 cms. with an error of less than 50° or k%. The liquid oxygen was contained i n a glass cylinder attached to the chamber base plate by a groove f i l l e d with glycerine. At low temperatures, the glycerine froze to give a tight seal. For the alpha source, a silver wire was snugly f i t t e d through a hole i n the lower electrode and smoothed off to be flush with i t s upper surface. It was upon this that the alpha source was deposited eliminating any odd f i e l d effects present i n the earlier chambers. A l l three chambers were connected to a vacuum system u t i l i z i n g both a mercury diffusion and a backing pump; these provided a vacuum of better than .001 microns. The pressure was measured by means of Pirani gauge down to .1 microns, and with a McLeod below this; the latter was also used to check periodically the, Pirani, which drifted considerably. I n i t i a l degassing was necessary, taking from a few hours to a few days to achieve to f o l l o w page 21 l i FIG. 5-. ARGON CHAMBER (NATURAL SIZE) (22) s a t i s f a c t o r y vacua i n the d i f f e r e n t chambers. D u r i n g the degass ing the chamber was heated to about 200°.. No degass ing was performed between t r i a l s , as argon would be the o n l y gas absorbed. The argon t ank , c o n t a i n i n g argon o f s p e c i f i e d p u r i t y o f 99.98$ was connected t o the system through a t r a p . Th i s l a t t e r was cooled w i t h l i q u i d oxygen p r i o r t o l i q u i f y i n g the a rgon, and was to serve as a t r a p f o r i m p u r i t i e s such as water vapour and CO2. i n the gas . I t was subsequent ly neg lec ted as i t proved to be unnecessary. . A l s o added to the o r i g i n a l system was a rubber b a l l o o n t o p rov ide a s a f e t y r e s e r v o i r o f low pressure a rgon . However, as i t proved i m p o s s i b l e to degas and v a l u e l e s s as a s a f e t y d e v i c e , i t was removed. I n a l l t r i a l s w i t h the second two chambers l i q u i d oxygen was used as the c o o l i n g agent . A t t h i s temperature (-183°C) the vapour pressure o f l i q u i d argon i s 1.3 atmospheres. I t was l i q u i f i e d a t about 2 atmospheres which was near the l i m i t o f what the s topcocks i n the system could t a k e . The pressure was measured on the gauge a t tached t o the tank and the i n f l o w o f gas c o n t r o l l e d by pressure r educ ing va lue a l s o a t t ached t o the t a n k . The l a t t e r gave some t r o u b l e when degass ing u n t i l the p l a s t i c s e a l i n g d i s c i n s i d e i t was r e p l a c e d by l e a d . A f t e r t r i a l s on the f i r s t two chambers, and then s e v e r a l on the t h i r d had f a i l e d to y i e l d any t rue argon p u l s e s , the argon p u r i t y was suspec ted . A c c o r d i n g t o Davidson and L a r s h ( l l W ) , the presence o f one p a r t i n 10^ o f oxygen v r i . l l reduce the pu l se h e i g h t by a f a c t o r o f 10, w h i l e n i t r o g e n to 1 p a r t i n 10^ w i l l reduce the he igh t by 10%. Two methods o f p u r i f i c a t i o n were t r i e d . One u t i l i z e d a s o l u t i o n o f p y r o g a l l o l and potass ium hydroxide i n wa te r . .An a i r t r a p w i t h s topcocks on top and bottom was p l aced i n the system between the- tank and the chamber and degassed. J u s t before a t r i a l , the KOH s o l u t i o n was sucked i n t o the bubbler from the bottom, and the p y r o g a l l o l i n s o l u t i o n added from the top; t h i s was to prevent any atmospheric oxygen from being absorbed by the l a t t e r , which i s o n l y e f f e c t i v e i n a s t r o n g l y b a s i c s o l u t i o n . The argon was then bubbled through the s o l u t i o n , passed through the l i q u i d a i r t r a p , and then t o the chamber. This should have reduced the oxygen content t o w e l l below .001%.. However, as no pulses were then detected, and the p y r o g a l l o l s o l u t i o n tended t o condense i n the l i q u i d a i r t r a p i t was decided to t r y a second method. Magnesium v a i l r e a d i l y 'combine w i t h oxygen and n i t r o g e n a t temperatures of about 500° Cj the products are s o l i d s w i t h low vapour pressures. Consequently a quartz, tube, about one i n c h i n diameter was packed w i t h magnesium t u r n i n g s h e l d i n place by gl a s s wool plugs. The tube was then degassed. During a t r i a l , t h i s tube was heated to about 600° C by a c o i l wound around i t , and the argon was passed s l o w l y over the turnings.. At t h i s temperature magnesium, although s t i l l a s o l i d , has a vapour pressure of 1.mm., and so the p r o b a b i l i t y of any oxygen or n i t r o g e n molecules c o l l i d i n g and r e a c t i n g w i t h a magnesium atom should be very h i g h . The gas was passed through the l i q u i d a i r t r a p andthen to the chamber.. At room temperature, magnesium has a vapour pressure «*10""5 m i t a n d so w i l l cause no t r o u b l e i n the remainder of the system. This p u r i f i c a t i o n procedure was continued f o r some time a f t e r p ulses were observed; i t was then d i s c a r d e d . As no change i n pulse s i z e could be observed, i t had t o be assumed t h a t the argon was alr e a d y e f f e c t i v e l y f r e e of these two gases, and attempts a t p u r i f i c a t i o n were unnecessary.. Alpha Source The alpha p a r t i c l e s were emitted from a polonium (radium F) source at an energy of 5.3 MeV;. t h i s m a t e r i a l has the advantage of y i e l d i n g a s t a b l e end product, viz.- l e a d 206. I t was contained i n a s o l u t i o n c o n s i s t i n g o f radium D, E and F i n 0 .5N HCl.. According t o Rutherford, Chadwick and E l l i s (1912) the polonium can be separated from the other two r a d i o a c t i v e elements by two processes-One method i n v o l v e d the a p p l i c a t i o n o f a s m a l l p o t e n t i a l t o the s o l u t i o n s u f f i c i e n t t o give a current of 25 t o 35 microamps/cm. W i t h i n these values of current and u s i n g two platinum e l e c t r o d e s , o n l y the polonium w i l l be deposited out on the negative electrode.. As i t w i l l be deposited a t a known r a t e , i t should be p o s s i b l e t o get sources of the d e s i r e d s t r e n g t h q u i t e e a s i l y . However, w i t h the s o l u t i o n used, i t was d i f f i c u l t t o keep the current w i t h i n the p r e s c r i b e d l i m i t s ; a l s o i m p u r i t i e s present i n the s o l u t i o n tended to be deposited on the negative e l e c t r o d e as w e l l as polonium. The second method suggested by Rutherford e t e-l was t r i e d s i multaneously w i t h the above one.. As i t was y i e l d i n g good r e s u l t s i t was decided t o abandon the f i r s t process, a l t o g e t h e r . . I n the second'method, use i s made of the f a c t t h a t s i l v e r i s s u f f i c i e n t l y e l e c t r o p o s i t i v e t o d i s p l a c e o n l y the polonium and not the radium D or E from s o l u t i o n . The s o l u t i o n was drawn i n t o a f i n e g l a s s p i p e t t e by means of a piece of rubber t u b i n g closed a t one end and attached to the pipette.. For use i n the f i r s t two chambers the source was placed on a t h i n s i l v e r d i s c about 0 .5 cms., i n diameter. This d i s c was coated w i t h glue and allowed t o dry; a s m a l l hole was then scratched through t o the metal.. This l i m i t e d the source t o a small area of the s i l v e r d i s c - about 1mm. i n diameter.. C o l l o d i o n was a l s o used but was not as e f f e c t i v e as the (25) glue , i n p r e v e n t i n g the source from sp read ing . The d i s c was h e l d f i r m l y under the t i p o f the p i p e t t e and the t u b i n g compressed to b r i n g the s o l u t i o n down so t ha t i t j u s t touched the me ta l but d i d not spread t o form a drop.. The time f o r d e p o s i t i o n was kept s m a l l t o prevent m i g r a t i o n o f the po lonium atoms i n t o the s i l v e r , and averaged s e v e r a l minutes ; t h i s : y i e l d e d sources o f 40 - 100 counts per second w i t h n e g l i g i b l e be ta con tamina t ion from the rad ium D and E. . A f t e r washing the source tho rough ly , i t was i m p o s s i b l e t o reduce source s t r e n g t h by t app ing the d i s c o r p r e s s i n g the source a g a i n s t a second s u r f a c e . Th i s f a c t removes the n e c e s s i t y o f p r e v e n t i n g the e l e c t r o d e s from coming i n t o con tac t v a t h each o the r , as they do when s e t t i n g the e l e c t r o d e s p a c i n g . Fo r the t h i r d chamber the e l e c t r o d e i t s e l f was coated w i t h g l u e , except f o r the end o f the s i l v e r w i r e se t through i t . Much more care was necessary i n t h i s case f o r both rad ium D and E w i l l r e a c t w i t h the z i n c i n the brass . . I t was p o s s i b l e however, to l i m i t contac t o f the s o l u t i o n w i t h the e l e c t r o d e e n t i r e l y t o the s i l v e r . The s i l v e r was exposed to the s o l u t i o n f o r about one minute , y i e l d i n g a source of about 100 counts per second w i t h n e g l i g i b l e be t a con tamina t ion . By the time r e s u l t s were ob t a ined , t h i s had dropped t o 60 - 70 counts per second, as the h a l f l i f e o f polonium i s o n l y 133 d a y s . C i r c u i t Components I n the o b s e r v a t i o n o f the p u l s e s , two c o n s i d e r a t i o n s govern the choice o f the e l e c t r o n i c c i r c u i t s . They are the a m p l i f i c a t i o n and t ime constants necessary i n these c i r c u i t s . I n i t i a l l y the former was under-es t ima ted ; i n the equa t i on g i v i n g p u l s e he igh t i n terms o f the i n p u t parameters and pu l se c u r r e n t , a g a i n o f about 100 was considered adequate. L a t e r i t was found necessary t o change t h i s t o a t l e a s t 400 f o r v i s u a l (26) o b s e r v a t i o n on an o s c i l l o s c o p e hav ing 1 cm. d e f l e c t i o n f o r .05 i n p u t and t o b e t t e r t han 1C-5 f o r s c a l a r r e a d i n g s . The time constants of a l l components were t o be kept < 10" ^  seconds, as i n d i c a t e d by the m o b i l i t y va lues found by M a l k i n and S c h u l t z . i n 1951. T h i s n e c e s s i t a t e d a h a l f power upper frequency l i m i t o f a t l e a s t 10 megacycles . A Hewle t t Packard wideband a m p l i f i e r (model #4-60A) was used i n a l l a t tempts to observe p u l s e s . I t c o n s i s t s of two 5 tube d i s t r i b u t e d a m p l i f i e r s tages arranged i n cascade, w i t h an a t t e n u a t i o n c o n t r o l i n s e r t e d on the i n p u t t o the second s t age . I t s c h a r a c t e r i s t i c s i n c l u d e a v o l t a g e g a i n o f 3.5 to 10 over a range o f f requenc ies from 500 K C / s e c . t o about 90 M C / s e c , w i t h a r i s e t ime l i m i t o f 2.6 x 10"^ seconds. The no i se l e v e l i s ex t remely l o w , around 4-0 m i c r o v o l t s peak t o peak. The i n p u t and output impendances are o n l y 200 ohms, and so the Hewle t t Packard cou ld not be used connected d i r e c t l y to the chamber as a much h i g h e r r e s i s t a n c e was needed a t the i n p u t , t o p r o v i d e a reasonable v o l t a g e va lue f o r a p u l s e . A c c o r d i n g l y , a s m a l l 2 s tage p r e - a m p l i f i e r w i t h an anode f o l l o w e r preceded the Hewle t t Packard a m p l i f i e r . Employing 6AK5 tubes and shunt peak ing c o i l s i t p rov ided a f u r t h e r g a i n o f 10 over a pass band ex tending up to about 10 megacycles per s ec . I t s i n p u t g r i d r e s i s t o r was v a r i o u s l y se t from 500K down to 3K, T h i s a m p l i f i e r had a h i g h no i se l e v e l o f approx imate ly 1 m i l l i v o l t ; a t f i r s t t h i s was thought to be unimpor tant as pu l se s o f 2 — 3 m i l l i v o l t s were expec ted . L a t e r events and c a l c u l a t i o n s showed t h i s t o be i n e r r o r by a f a c t o r o f a lmost 10, and so i t was necessary t o d i s c a r d the a m p l i f i e r i n favour o f one w i t h a h ighe r a m p l i f i c a t i o n and lower no ise l e v e l . . A f i v e stage a m p l i f i e r , p l u s a cathode f o l l o w e r , was designed and cons t ruc ted t o p rov ide a g a i n o f around 400. Shunt peaking was a l s o (27) employed in i t to increase the half power upper frequency limit from 5 megacycles to around 15. This of course resulted i n a f a i r l y large noise voltage, about 3 or 4 times the theoretical limit of amplifier noise set by WJJ - giving 66 microvolts zero to peak for an input resistance of 100K. Many attempts were made to reduce this noise, as well as to smooth the amplification curve - i t \ras constant for only a small portion of the pass band, and dropped off slowly below 5 megacycles when shunt peaking was employed. ' After a l l attempts to measure rise times were discarded, and i t was decided to concentrate on pulse distribution, there was no need for such a wide pass band. A two stage pre-amplifier, plus two cathode followers, one providing feedback to the 1st stage, the other providing an output signal, had been built to act as a pre-amplifier for an Atomic linear amplifier. The c i r c u i t is shown i n f i g . 6(a). The amplification obtained with i t was very constant at a value of 10 up to about 2 megacycles, with i t s pass band extending from lOOKC/sec. to 5MC/sec. The noise level was about 90y^V zero to peak for 100K input impedance, compared to the theoretial limit of 4^ />V. The f i n a l arrangement of c i r c u i t components was that shown in f i g . 6(b). The linear amplifier, model 204C, has an input time constant of 0.2 JJ sec. on the fast range, and employs feedback to further vary the rise time and amplification. It has a high level output, the signal from which was fed into the scaler, and a low level one of 200 ohms output impedance. The scaler was an Atomic, scale of 64, model 10IA, which could handle pulses up to 60 volts. The oscilloscope used, a Tektronix model #517, could be connected directly onto the low level, or as was found necessary due to the gain, via a line attenuator of 20 decibels attenuation. For the best setting of time constant and feedback on the t o f o l l o w page 27 SCALAR HIGH VOLTAGE HEWLETT LINEAR SUPPLY CHAMBER PRE-AMP PACKARD OSCILLOSCOPE FIG. 6 (b) • CIRCUIT DIAGRAM l i n e a r a m p l i f i e r , v i s . t h a t g i v i n g the sharpest p u l s e s , the low l e v e l g a i n was 56 times, g i v i n g a t o t a l g a i n of ^>.S x 10^ a t the low l e v e l output, corresponding to 4.5 m i c r o v o l t s per d i v i s i o n on the s c a l e r . The a m p l i f i c a t i o n s noted above were a l l measured w i t h a T r i p l e t s i g n a l generator, model 7^52, the output of which was attenuated by a f a c t o r of 100. Each a m p l i f i e r was t e s t e d i n d i v i d u a l l y , f o r both pass band and g a i n . They were then checked by means of a square pulse generator w i t h an output pulse of .08 microsecond d u r a t i o n and .05 microsecond r i s e time. I t was f e d through the three a m p l i f i e r s , and each was checked f o r pulse shape and g a i n . The pulse length was doubled by the p r e - a m p l i f i e r , passed unchanged by the Hewlett Packard, and widened again by the l i n e a r a m p l i f i e r . T his widening was l e a s t (0.4 microseconds) f o r input time constant of 0.2 sec as expected, and f o r the intermediate feedback p o s i t i o n ; hence despite the lower a m p l i f i c a t i o n f o r t h i s p o s i t i o n , i t was,:: f e l t to be the best one t o use. The gains of the p r e - a m p l i f i e r and l i n e a r a m p l i f i e r were s l i g h t l y l e s s f o r pulses than f o r the sine wave s i g n a l from the generator. This was f e l t due to the pulse being f a s t e r than the a m p l i f i e r s . As i t was a f a i r l y s mall d i f f e r e n c e ( <10$) and as the argon pulses were thought t o be slower than those used here f o r c a l i b r a t i o n the gains were taken as those of the s i n e wave. The h i g h voltage supply f o r the argon chamber caused considerable t r o u b l e . A b a t t e r y supply c o n s i s t i n g of seven 500 v o l t Eveready Minimax b a t t e r i e s was used w i t h the second chamber. The b a k e l i t e i n s u l a t i o n used i n i t began t o break down a t 2100 v o l t s negative, causing pulses to appear on the o s c i l l o s c o p e . These were at f i r s t roughly of the s i z e expected f o r argon, and as they d i d not appear f o r p o s i t i v e f i e l d s , they were mistaken f o r argon p u l s e s . Much work was done on them; however, a f t e r a w h ile they began t o increase i n s i z e , appear a t the low v o l t a g e s , and f i n a l l y t o appear with positive f i e l d s . They were f i n a l l y traced to the bakelite, which proved to be very faulty as insulation. Lucite was substituted for i t and the spurious pulses disappeared. Later, when the pulses that were finally, obtained were definitely proved to originate i n the liquid argon, a Cintel stabilized power supply, type 18°2, was substituted for the batteries. Its voltage could be more easily varied. The smoothing proved insufficient, and so an external RC f i l t e r was included. It was found that the 2000 volts obtainable from i t was frequently high enough to cause electrons to flow across the kovar seal surface and appear as pulses. These were reduced i f the glass -surface were cleaned with ether, and were almost completely eliminated when the chamber was cooled. It was also found that a f i e l d of 80 kv per cm. caused dielectric breakdown of the argon between the plates; i t was therefore necessary to work at fiel d s of less than this value. The input capacitances of the chamber and pre-amplifier were measured with a Q-meter. The latter had a value of 10.8 picrofarads, while the former was 3-5 picrofarads plus the capacitance due to the electrodes themselves. This varied from 0.5 to 1.2 picrofarads depending on the electrode separation. Electrometer For the detection of a direct current from the pulses such as that done by Gerritsen (1948) and Hutchinson (1948) an electrometer of the type described by Dubridge and Brown (1953) w a s constructed. Its circuit i s shown in f i g . 7. The tube used i s a Victoreen #?800 electrometer tetrode; the input grid resistors are the Victoreen HiMeg type with tolerances of < 1%, The tube was enclosed i n a light metal cylinder which afterwards was t o f o l l o w page 29 (50) f i l l e d with ceresin wax. This prevented the leads and glass from becoming contaminated with moisture and dirt, and eliminated any possibility of spurious photo-electric effects arising. The three ranges provided by the input resistors were connected into the circuit, as was the input lead, via small brass plugs. Each of these was surrounded by a cylinder of ceresin wax, one centimeter i n radius and one centimeter long. This provided a very high resistance to ground (^10^ ohms) and negligible capacitance. A Tinsley type SS6/45 galvanometer, with a sensitivity of 6 x l O " ^ to 6 x 10~^ amps/mm. was connected between the plate and f i r s t grid. In this way any variations i n filement voltage or emission would affect each of these electrodes i n a constant ratio, and thus not disturb the galvanometer reading. To get the electrometer into working condition, the plate and f i r s t grid currents were set at their recommended values} the filament current, If, was varied to find the point at which the galvanometer deflection reached a maximum with respect to If. This was the optimum working point of the tube, but If had then to be within 10% of i t s rated value of 10 milliamps. To achieve this, i t was found necessary to increase the other two currents to well above their recommended values, v i z . to 30 and 42 microamps for the plate and grid respectively. Calibration of the c i r c u i t was accomplished by applying a known voltage from a dry c e l l to a potential divider, and taking a fraction of i t , about 10""^  volts, into the 10® ohms input resistor. This gave a sensitivity for the instrument of 2.2 x 10 _ 15 amps/mm. for the galvanometer at i t s most sensitive setting. Thus i t should be possible to observe a current of as low a value as 2 x 10~^ amperes with the 10*^ ohm input resistor. When the electrometer was in operation, the zero was found to shift considerably with time, and required several hours to settle down. Furthermore grounding was very c r i t i c a l . Thus movement of any large objects, (31) so much as three f e e t away from the i n p u t l e a d , caused l a r g e d e f l e c t i o n s on the galvanometer, even f o r the l e a s t s e n s i t i v e s e t t i n g o f the i n s t r u m e n t . I t was found i m p o s s i b l e t o comple te ly s h i e l d the e l ec t rome te r from t h i s e f f e c t . ANALYSIS OF RESULTS Pu l ses Obtained A f t e r cons ide rab le time had been spent on measurements o f the spu r ious i n s u l a t i o n breakdown p u l s e s , t h e i r o r i g i n was f i n a l l y d iscovered* they were e l i m i n a t e d , and no f u r t h e r p u l s e s were d i s c e r n i b l e , . Argon p u r i f i c a t i o n was at tempted but f a i l e d t o y i e l d r e s u l t s . The next p o s s i b i l i t y was then i n v e s t i g a t e d , v i z : . , the pu l ses were below the no i se l e v e l o f the p r e - a m p l i f i e r . . The l a t t e r was changed, i t s s i g n a l t o noise; l e v e l improved, and pu l se s were then observed . These were f i r s t found w i t h the s i x tube p r e - a m p l i f i e r d e s c r i b e d p r e v i o u s l y on page 26, w i t h i t the s i g n a l t o no i se r a t i o n was o n l y about 2 : 1 . Wi th the t h i r d p r e -a m p l i f i e r used , whose c i r c u i t i s g i v e n i n f i g 6 ( a ) , t h i s r a t i o was improved to around 4 o r 5 t o 1, The a m p l i f i e d pu l se s had the shape shown i n f i g s . 8 (a) and 8 ( b ) . These photographs were t aken w i t h an o s c i l l o s c o p e camera a t 1/50 second exposure, w i t h the o s c i l l o s c o p e sweep t ime se t a t 0.5 microsecond/cm. The pu l se s were ob ta ined w i t h f i e l d s o f 33.3 k i l o v o l t s / c m . f o r f i g . 8(a) and 16 .7 k i l o v o l t s / c m . f o r 8 ( b ) , w i t h the e l e c t r o d e spac ing se t a t 0.03 cms. A. few p i c t u r e s were t a k e n a t 1/5 second exposure, t o i l l u s t r a t e the pu l se d i s t r i b u t i o n , one o f which i s shown i n f i g . 8 ( c ) . Here E = 1 6 . 7 k i l o v o l t s / c m . and the scope sweep t ime was se t a t 0.2 microseconds /cm. The pu l se s i z e s were g i v e n from the o s c i l l o s c o p e c a l i b r a t i o n f i g u r e and FIG. 8(c) ARGON PULSES 1/5 SEC. EXPOS. (32) the a m p l i f i c a t i o n o f the p r e - a m p l i f i e r , the Hewle t t Packard a m p l i f i e r , and the L i n e a r A m p l i f i e r . . . . The o s c i l l o s c o p e s e n s i t i v i t y was se t a t 0 .20 v o l t s / c m * f o r f i g . 8(a) and 0 .10 v o l t s / c m . f o r f i g . 8(b) and 8 ( c ) j the t o t a l a m p l i f i c a t i o n was 490 . These g ive s i z e s f o r the l a r g e s t pu l se s observed on the two photographs o f 450 m i c r o v o l t s and 310 m i c r o v o l t s f o r f i e l d s o f 33.3 and 16 .7 k i l o v o l t s per cm. r e s p e c t i v e l y . . The s i z e of the pu l se s i n f i g . 8(b) had to be es t imated r o u g h l y as the f i l m used was i n s e n s i t i v e t o r e d l i g h t and so the s c a l e d i d not appear. These va lues are s l i g h t l y l a r g e r t han those obta ined by Davidson and L a r s h (1950), whose maximum pu l se s i z e s were 475 m i c r o v o l t s a t 100 k i l o v o l t s per cm. , and 270 m i c r o v o l t s a t 29 k i l o v o l t s per cm.., w i t h an e l e c t r o d e spac ing o f 0,0094 cms. Because the re had been so much d i f f i c u l t y i n o b t a i n i n g p u l s e s , and so many spur ious e f f e c t s observed, i t was necessary t o determine the o r i g i n o f these p u l s e s as c a r e f u l l y as p o s s i b l e . They d i d not occur when the f i e l d was r e v e r s e d ; T h i s was impor t an t , but as mentioned be fo re , break-down w i l l sometimes occur w i t h o n l y one d i r e c t i o n o f v o l t a g e , so i t was not c o n c l u s i v e . The few s m a l l pu l se s o c c u r r i n g w i t h a negat ive f i e l d are g i v e n i n t a b l e #1 and graph #1, and are expected i f the a lpha range i s o f the same order as the e l e c t r o d e s e p a r a t i o n . These were a l s o found by Davidson and L a r s h but no quan t i t ave da ta were g i v e n by them so t ha t comparison i s i m p o s s i b l e * There was no s i g n o f pu l se s when the chamber was evacuated and coo led , p rov ided t ha t the kovar s e a l was p e r f e c t l y c l e a n . T h i s e l i m i n a t e d the p o s s i b i l i t y o f any spur ious e f f e c t s be ing caused by i n s u l a t i o n break-down., A f u r t h e r t e s t proved t h a t the pu l se s occur red i n the l i q u i d argon and then o n l y when i t was pu re . Argon was l i q u e f i e d i n the chamber and pu l se s observed . The a i r t r a p was i s o l a t e d from the chamber and cooled w i t h l i q u i d oxygen; onygen gas was i n t roduced i n t o i t under pressure and l i q u e f i e d . I t was then connected to the chamber and the oxygen allowed to b o i l o f f and recondense i n the chamber. Almost immediately the pulses observed i n the argon disappeared e n t i r e l y . Very l i t t l e oxygen was needed to d e s t r o y them, but no q u a n t i t a t i v e measurements were made. F i n a l l y , i t i s p o s s i b l e t o a t t r i b u t e the pulses w i t h c e r t a i n t y to i o n i z a t i o n o f argon by the alpha p a r t i c l e s . The stren g t h of the r a d i o -a c t i v e source i s g i v e n by:. Nt = A/« *" > r where 1 % = the number of p a r t i c l e s observed per u n i t time a t time t N 0 = the number o f p a r t i c l e s observed per u n i t time a t some a r b i t r a r y zero of time, (t = 0) and X - 0 .693/T where T i s the h a l f l i f e of the element considered. For radium F, the h a l f l i f e i s 138 days. Three t r i a l s were made on the chamber f o r d i f f e r e n t values of the e l e c t r o d e spacing. These were taken 15 and 22 days a f t e r the f i r s t one, and gave values of Ht of 44.OO per min., a t t = 0 , 4.O6O per min. a t t = 15 days and 3930 per min. a t t = 22 days., According t o the equation given above, N15 and N22. should be 4-070 and 3920 r e s p e c t i v e l y , values very close t o the observed ones. Thus i t can be concluded t h a t the pulses observed and counted o r i g i n a t e i n pure, l i q u i d argon when an e l e c t r i c f i e l d i s a p p l i e d t o i t , and are due t o the i o n i z a t i o n of argon atoms by alpha p a r t i c l e s . .An attempt was made to o b t a i n pulses from the a c t i o n of gamma rays on the l i q u i d argon, s i m i l a r to the method used by Davidson and Larsh. However, the chamber was not constructed f o r i t , and could not be e a s i l y changed. Due to the much greater p e n e t r a t i o n of the gamma ra y s , i t i s (34) necessary to have a large gap (about 1cm.) and to place the source about 2cm.. from the electrode centres.. While the fields need not be as large as for alpha particles, they should be greater than 5 kilovolts/cm. to give observable pulses. The kovar seal would not withstand the necessary voltages. However, a cobalt 60 source was placed i n the liquid oxygen out-side the chamber of which the gap was set at 0.1 cms., and a few pulses were observed with a negative f i e l d (as the alpha source remained i n the system, i t was necessary to use a negative f i e l d ) . Doubt resulting from the presence of the alpha source made this no more than suggestive of further work. Rise Time Measurements The d i f f i c u l t y i n observing pulse shape i s the obtaining of sufficient amplification over a wide frequency band. Due to the size of the pulses i t i s imperative to keep the noise level at less than 100 microvolts, zero-to-peak with 104 ohms input resistance of the pre-amplifier, but with a 10 Mc frequency band this i s equivalent to a noise figure, F, of less than 2. Since the constant current pulses are converted by the input stage of the pre-amplifier to voltage pulses characteristic of charging up the input capacitance, the actual pulse durations are given by the rise times of the voltage pulses displayed on the oscilloscope. Some estimates of this rise time were made, using the 6 tube pre-amplifier and the Hewlett Packard amplifier.. These gave rise time X of .10 microseconds at E = 40 Kilovolts/ cm., and 1 = 0.05 cms.., and .06 microseconds at E = 33.3 kilovolts per cm. and 1 - 0..03 cms.. The corresponding mobilities are 12.5 cms2/volt-second and 15 cms2/volts-second respectively. These are slightly smaller than the values obtained by Malkin and Schultz, (1951), which were 15 and 18 cms^/volt-second for the two fi e l d s used above. The mean free path L of the electrons i n l i q u i d argon i s given by (35) the equation #9, on page 9, viz;: f o r K and E i n p r a c t i c a l u n i t s . The values of L are then 1.18 x 10^ cms» £> -6 and 1..38 x 10" cms.., g i v i n g an average of 1.3 x 1 0 " a cms. From t h i s i s obtained a c o l l i s i o n c r o s s - s e c t i o n f o r the e l e c t r o n s w i t h r e s p e c t t o the argon atoms. I t i s given by <T~ ^  — —— I 0 where D i s the number of argon atoms per cxa.\ For l i q u i d argon the d e n s i t y i s 1.4- gms./cm.or 2.11 x 10.^ atoms per cm.3. Therefore, the c o l l i s i o n c r o s s - s e c t i o n i s 3.7 x 10r*"17 cms»^j of course t h i s value i s v e r y rough, as i t depends upon "X , w i t h an e r r o r of perhaps - 20$ i n c . Two d i f f i c u l t i e s appear i n the measurement of T". One i s the apparent i n a b i l i t y o f the o s c i l l o s c o p e used t o t r i g g e r on the edge of the p u l s e . This i s most n o t i c e a b l e on the f a s t e r sweep times. The other i s due to the a c t u a l shape of the p u l s e . As the pulse top has become conside r a b l y rounded a f t e r p a s sing through the a m p l i f i e r s , the r i s e time determination i s subject to l a r g e e r r o r s . I f the capacitance i s f a i r l y l a r g e , "X should be measured t o the peak of the p u l s e , w h i l e i f C i s v e r y s m a l l , the voltage w i l l reach s a t u r a t i o n , and T i s measured t o the p o i n t a t which the pulse v o l t a g e begins t o drop o f f . T h i s d i f f i c u l t y i s i n d i c a t e d i n f i g . 8(a) to ( c ) , although of course these pulses have been shaped by the slower a m p l i f i e r s used, and so t h e i r r i s e times are e s s i n t i a l l y meaningless. The above method could p o s s i b l y be improved by f i n d i n g the optimum e l e c t r o d e spacing. The v o l t a g e i s g i v e n by: and f o r ~C ^ RC,. the e x p o n e n t i a l can be neglected, g i v i n g V p r o p o r t i o n a l t o 1/~C . At the same time, as T. becomes s m a l l , the a m p l i f i e r s must have a wider band width; there should be some value of 1 and E at which the s i g n a l t o noise r a t i o i s a maximum. There are two other c i r c u i t s which could p o s s i b l y be used t o f i n d m o b i l i t i e s . One would employ a p a r a l l e l inductance capacitance i n p u t ; t h i s w i l l give a s i n u s o i d a l output f o r t < ^ , and a phase change a t %. = ~C t o a decaying s i n u s o i d a l wave of the same frequency. I f t h i s could be observed on an o s c i l l o s c o p e , and the phase change were l a r g e enough, t could be found. The other c i r c u i t would d i f f e r e n t i a t e the current p u l s e , producing two sharp b l i p s of opposite s i g n , a t time T a p a r t . I f t h i s s i g n a l could be a m p l i f i e d and f e d i n t o a c i r c u l a r d elay l i n e , and the l a t t e r observed at d i f f e r e n t p o i n t s along i t , a p o i n t could be found a t which the two s i g n a l s t r a v e l l i n g i n opposite d i r e c t i o n s around the l i n e c a n c e l l e d each other., From the p o s i t i o n of t h i s p o i n t T" could be found. However, the l e n g t h of such a l i n e would be too great to be e a s i l y handled. Pulse S i z e D i s t r i b u t i o n s For the d e t e r m i n a t i o n of pulse s i z e d i s t r i b u t i o n s a narrower band of a m p l i f i c a t i o n i s p e r m i s s i b l e , hence i t i s p o s s i b l e t o get the noise down to about 1/4. of the s i g n a l . Three t r i a l s were taken, u s i n g the c i r c u i t of f i g . 6(b), w i t h d i f f e r e n t s e t t i n g s of the e l e c t r o d e gap.. The f i e l d was; v a r i e d and a set of curves of normalized pulse number, N/N-fc a g a i n s t the s i z e V found f o r the d i f f e r e n t values of E, N being the number of pulses of s i z e V or l e s s . Table #1 and graph #1, taken f o r 1 = 0.05 cms., i n d i c a t e the r e s u l t s obtained; the curves of 1 = 0.067 cms. and 1 = 0.03 cans, are s i m i l a r i n shape to these. Table #2 and graph #2 give the v a r i a t i o n of A N / ^ ? w i t h V, obtained from the curve f o r 40 k i l o v o l t s / c m . w i t h to f o l l o w page 36 TABLE 1 PULSE SIZE DISTRIBUTION FOR AN ELECTRODE SEPARATION OF 0.05 CMS. E. = 40KV/CM E. = 30KV/CM E = 20K7/CM p u l s e s i z e : c n N ( m i n ) " 1 N / N T pu l se s i z e , ( V ) N; ( m i n ) - 1 N/NT. p u l s e s i ze ; N T N / N T 452: • 110. .027 416 5 .001 347 - 14 . 0 0 3 438 460 .113 40,7 20. .005> 338 16, . 0 0 4 428.. 850). .209 393 70, .017 325 80 .020, 416. 1560) .384 384 210. .052 315 140 .035 407. 1920 .473 370, 6.70. .165: 302.. 410, .101. 393 2470. .608, 3.61 970, .236. 293' 79a .195 3.84 2680. .660, 347. 16,50 .407 284 1640 . 4 0 4 370 3120 .768. 338 2070, .510 270 2110. .520 361. 3260, .804. 325' 2750, .678 257 2760 .679 347, 3530 .870 315 2940 .724 247 3130 .772. 33.8 3540 .872- 302 3260, .803: 234 3560 .878 315 3820 .942: 293 3480 .857 225: 3590 . 8 8 4 293 3800 .937 278. 3610 .889 211 3710 .913 270 3910 . 9 6 3 270 3680 .907 202. 3940 .972 247 3890 .958 247 3820 .940 179 3970 .978 225 4000 .986, 225 3840 .945 157 4040 .996: 202 4010 .988 202 3960 , .975 134 4040 .996 179 4090 1.009 179 3950 .973 111 4090 1.009 15.7 3970, .978 157 4Q80. 1.007 88. 8500 2.090: 134 4100 1.010. 1 3 4 4080. 1.007 111 3960 .975 111 4050 .997 98 4280 1.057 98 4570 1.160 TABLE 1 (continued) E = /+OKV/CM E. 30KV/CM E. = 20KV^ CM pulse size. ( v) N: (min)-1; pulse size.. .( ,Y). 1 1 N/NT pulse size; (, V). N (min)-l 2 9 3 ; '9 .002 324' 12. . 0 0 3 179 0 278. 4 0 .010 225 4 0 .010 157 20-270. 95; .0235 211 220 . 0 5 5 134 50' 257. 360; .089 202- 620 . 1 5 3 ; 120 60 2 4 7 710 il75 189 1380. . 3 4 0 111 25 70 234 1530, .377 1.79 2200 . 5 4 2 102 3 0 0 225. 2120. .522: 166 2960. .728 98; 380 4 0 0 211 2930 .722. 157 3380, .833! 93 3600, 202; 3240. .798 U3 3 6 4 0 .897 88 5000 5 4 0 0 189 3580 .882 134 3780, .931-179 3820 . 9 4 1 - 120 3 9 3 0 . .968 166, 3.850 .948 111 4 0 4 0 . .995 157. 3860 .951 98 4 2 4 0 I . 0 4 6 . 1 4 3 3980 .981. 88 9500 2 . 3 4 0 134 4 1 0 0 1.010 120 4170 1 . 0 2 6 111 4 1 2 0 1.013; 98 4390 1.083-88 9000 2*200 GRAPH 1. PULSE SIZE DISTRIBUTION FOR 0.05 «M. -ELECTRODE SPACING PULSE SIZE (MICROVOLTS) to f o l l o w page 3 6 TABLE; 2U, PULSE SIZE-FREQUENCY VARIATION FOR E. = 4 0 KV/CM PULSE. N /Nf SIZE. V (uV) . ( u V ) - 1 4 6 2 . . 0 0 1 1 . 452 . 0 0 3 9 443 .,0067 433 .0111 424 .0122 4 1 & .0122 407 . 0 1 1 1 . 397 .0089 389 .0083 379 .0067 370. .0050 361. . 0 0 4 4 352 .0028 343 .0022 334 .0022. 325 .0017 316 .0015 307 . 0 0 1 1 . 298 .0006 288 .0006 279 .0006 270 .0006 to follow page 36 GRAPE 2o PULSE SIZE FREQUENCY CURVE FOR 40 KV/CM. 300 350 400 PULSE SIZE (MICROVOLTS) 450 (37) A T : 9 microvolts. The scaler accuracy was checked with the 60 cycle/second signal supplied i n the instrument; i t gave readings of well within 2% of the true value. Also i t showed that a zero correction of 0 . 5 division was necessary, and a l l curves given here have been so corrected. In calculations of the total number of pulses, N^, the maximum spread i n the values of N used is about 5 - 10$; this is within the accepted experimental error. However, two effects do cause trouble in finding N^. These are noise at the small pulse size readings, and the vary gradual approach of the high f i e l d curves to a steady value of N as the discrimination level i s reduced. The former can be circumvented by discarding or correcting any readings taken at discriminator settings which f a l l below the maximum noise level. To eliminate the latter effect i t is necessary to take only those values of N which definitely have reached a limit, in particular, those which follow some slight drop i n the count. Taking such precautions i t i s possible to get a f a i r l y accurate value of NJJ., e.g., 4o60 counts per minute for the £ a 0 . 0 5 c m s « t r i a l with a standard deviation of + 70 counts per minute. As mentioned previously, three effects w i l l cause a variation of N with the pulse size. The noise correction was the f i r s t to be made, and was accomplished as follows. The output of a pulse generator was fed into the linear amplifier, as shown in f i g . 9, and the pre-amplifier connected to the chamber as before. The Hewlett Packard gain and the pulse generator output were varied to give a signal to noise ratior. approximately the same as that found for a particular pulse distribution curve. Then, with the Hewlett Packard turned off, the distribution of pulses obtained from the generator was recorded. The Hewlett Packard was turned on, introducing the noise, and to follow page 37 PRB-AMP HEWLETT PACKABP FROM C H A M B E R LINEAR AMP ST.AT.AR SIGNAL GENERATOR FIG. 9 NOISE DETERMINATION CIRCUIT (58) the r e s u l t i n g d i s t r i b u t i o n s were obtained. These are given i n t a b l e #3 and graph #3, f ° r s i g n a l to noise r a t i o s of 2 :1 ; 3:1 ; 4 : 1 ; and $tl. The pulse s i z e s are given as i f they o r i g i n a t e d a t the p r e - a m p l i f i e r input i n order to compare them w i t h the a c t u a l argon pulse d i s t r i b u t i o n s . I t was assumed t h a t the pulses from the generator were mono-energetic and any v a r i a t i o n from a v e r t i c a l l i n e was due to s c a l e r inaccuracy and the noise o r i g i n a t i n g i n the l i n e a r a m p l i f i e r . A c c o r d i n g l y , the median pulse height found when no p r e - a m p l i f i e r noise was present was taken as t h e i r t r u e height; the noise c o r r e c t i o n was simply the noise a f f e c t e d pulse s i z e a t any value of N/N^ minus t h i s median v a l u e . Table #4 gives the r e s u l t o f t h i s c o r r e c t i o n when a p p l i e d t o the 10, 20 and 4o k i l o v o l t / c m . curves given i n graph #1; the s i g n a l 0 t o noise r a t i o c o r r e c t i o n s a p p l i e d are those of 2 :1 , 5 s 1 a n < i ktl r e s p e c t i v e l y . I t can be seen from these t a b l e s t h a t they f i t q u i t e w e l l the a c t u a l r a t i o s found f o r the argon p u l s e s . The r e s u l t a n t curves are shown i n graph #4. A l s o c o r r e c t e d were the JO k i l o v o l t / c m . curve f o r •£ = 0.067 cms. w i t h s i g n a l to noise c o r r e c t i o n of 3 : 1 , and the 16.7» 33*3 a n c * 50 k i l o v o l t / c m . curves f o r H s 0 . 0 3 cms., w i t h s i g n a l to noise c o r r e c t i o n s of 3J1> ^il and 5:1 r e s p e c t i v e l y . According to the second cause of pulse s i z e v a r i a t i o n , v i z . , that due to a v a r i a t i o n of t r a n s i t time r e s u l t i n g from the angle of alpha emission, should vary l i n e a r l y w i t h V. A s t r a i g h t l i n e was drawn to f i t as w e l l as p o s s i b l e the curves of graph #4. These l i n e s as shown must f i t the equation which gives t o f o l l o w page 38 TABLE 3.- NOISE. CORRECTION DATA s i g n a l / n o i s e = 5 / L s i g n a l / n o i s e = 4 / 1 pu l ses o n l y pulses-frioise.' pu l se s o n l y pulses-ftioise. pulse ; s i z e N/NT pu l se s ize : W. N/N(r. p u l s e s i z e . N/%. pulse, s i z e N/NT 554 ..000 571 .003- 434 .000, 446 .003 548. •130, 559 .055> 431 .433; 440 .055' 543 .768 54^ .215> 428. .998, 434 .215 537 •9.73:- 537 .590 423 .996 428 .590, 438 1.000 527 .868 400- .996, 423 .868 222. 1.003; 516. .990 285" .995 417 .990 50, -.994 493. 1.010. 170 .998 411 1.010 382. .990 54 .998. 405 .990 277 .997 400 .997 166 1.007 342 1.007 T A B L E - 3 . (cont inued) . s i g n a l / n o i s e = 3/1 pu l ses o n l y pulses+noise. pulse-sizes X*v) N / N T . p u l s e s i z e . N / N T , 325 .000. 353 .001. 322- .001. 348 -004. 319 .188 342:. .011 316 1*000- 336, .045 313 1.000 331 .096 227 1..008 325 .189, 112 1.006, 319 .319 313, .480 308. .705 302 .892 296. . 9 5 3 290 .991 285 ,998 s i g n a l / n o i s e = 2/1. pu l se s o n l y pulses+noise pulse, s i z e N / N T pulse : s i ze : N / N T 233 .000 256 .001 230 .159 250 .004 227 .831 245- .037 224 1.002 239 .066 141- 1 .004 233 .142 227 .318 222 .453 216 .634 210 .760 204 .8:52. " 198 .912. 187. .997 to follow page 38 GRAPH 3, NOISE CORRECTION CURVES _N 0.8(-N T 0.4h 0.2 200 300 ~ 400 PULSE SIZE (MICROVOLTS) 500 to f o l l o w page 38 TABLE 4. PULSE SIZE DISTRIBUTIONS CORRECTED FOR NOISE . • E. = 40Kv/cm E = 20KV/cm E = 10KV/cm p u i s e s i z e s pu l se s i z e s pu l se s i z e s N / N j uncor. . v a l u e s noise c o r r e c . c o r r e c . va lues u n c o r . va lues no i se cor re c . c o r r e c . va lue s u n c o r . va lue s no i se c o r r e c . corre> value: ..001 469 +15 454 347 +36 311 234 +27 207 .oz 454 + 8 446- 325 +22 303 219 +18 201 ..04 448 + 6 442 315 +19' 296 213 +14 199 .10 439 + 3 436 302. +12 290 206 + 7 199 .20 429 0 429 292. + 7 285 197 + A 193 .30 421 - 3 424 285 + 2. 283 190 - 1 191 .40 413. - 4 417 279 - 1 280 I84 - 5 189 .50 404 - 6. 410 272 - 4 276 180 - 9 189 ..60 394 - 8 402 264 - 7. 271. 174 -12 186 .70 381. -10 391 255 -10 265 168 -16 I84 ..80 363 -13 - 376 244 -13 257 159 -21 180 .,86. 347. -13 360 233 -14 247 151 -25 176 .90 325 -15 340 220 -16, 236 142 -29 171 .94 291 -18 309 207 -20 227 132 -33 165 ..98 238 -23 261 179 -25 204 116 -38 154 (39) Thus (Vmax - v"min)/^max should be a constant w i t h r e spec t to the f i e l d and should equa l R*/2: • The va lues o f t h i s f o r the s t r a i g h t l i n e s shown i n graph #4, as w e l l as f o r the o ther t r i a l s , are g i v e n i n t a b l e #5. The average range o f the a l p h a p a r t i c l e s i s 0,012 cms, w i t h a s tandard d e v i a t i o n o f — ,0015 cmsj t h i s i s l a r g e r than the va lue found by Davidson and L a r s h (1950) by a f a c t o r o f 2..4., The d i f f e r e n c e would be reduced i f the weighted centre o f i o n i z a t i o n were: cons idered t o be f u r t h e r a long the a lpha t r a c k than R « /2, T h i s would be i n d i c a t e d by the i o n i z a t i o n curves o f a l p h a p a r t i c l e s , and a va lue o f about 2/3. Rot would p robab ly be c l o s e r t o the centre of the average p o s i t i o n o f e l e c t r o n f o r m a t i o n . T h i s y i e l d s a v a l u e , R « = 0,009 cms, , s t i l l c o n s i d e r a b l y above Davidson and L a r s h ' s (0,005 cms). An attempt was made to determine whether the expansion to the f i r s t two terms o n l y o f the e x p o n e n t i a l i n the equa t ion g i v i n g V i n terms o f the i n p u t c i r c u i t conponents ( equa t ion #2(a), page 15) was j u s t i f i e d . A c c o r d i n g l y exp„ ( - 'Z ' /RC) . was approximated to by three terms w h i l e the expans ion o f exp, (- tg/RC) was kept t o two . T h i s g ives ; which upon s i m p l i f i c a t i o n and s u b s t i t u t i o n f o r t© i s w i t h the term T ^ t © / 2 R ^ C ^ ' neg lec ted as s m a l l i n comparison w i t h the o t h e r s . T h i s g ive s f o r R 4 the f o l l o w i n g equat ion: . an a r b i t r a r y constant , . Hence the c o r r e c t i o n f a c t o r becomes 1 — -k&/*RC VB j - J/dLKC\fE t o f o l l o w page 39 TABLE, 5... VALUES OF R AND n OBTAINED. FOR. VARIOUS FIELDS AND ELECTRODE SEPARATIONS 1. (cms..), E. (KV/CM). Vmax: M l Vmax-Vmin. CuV) R - / 2 1 R. (cms.) C (pF) n. .,067 30 380 37 .097 .013 14 .8 3 . 5 x l o A .05- 40 441 61 .138 .014. 15 .0 4 . 1 .05. 20. 293^ 36 .123- . 012 15 .0 2 .7 .05 10 200 2 ? .115 .0*2 15.0. 1.9 .03. 50 571. 115 .201. . 012 1 5 . 4 5 .5 ..03; 33 .3 462 87 .189 .011 1 5 . 4 4*4 •03 16 . 7 309' .56. .181. . 011 1 5 . 4 3 .0 (4o) This w i l l —> 1 as Q. —> o or E--># «• . I t w i l l have the g r e a t e s t e f f e c t on the curves obtained f o r large e l e c t r o d e spacings and small f i e l d s , and i n a l l cases i t w i l l increase R* , As w i l l be seen from t a b l e #5 there i s no systematic v a r i a t i o n of R« w i t h .4, and the s l i g h t d i f f e r e n c e o c c u r r i n g between the average value of Ret f o r £ = 0.05 c m s « a n <i t h a t f o r £ s 0.05 c m s « would a c t u a l l y be increased by t h i s c o r r e c t i o n due to i t s g r e a t e r e f f e c t on values of R« obtained from the l a r g e r e l e c t r o d e spacing. There i s a s l i g h t increase i n R,* w i t h i n c r e a s i n g f i e l d , which the above c o n s i d e r a t i o n would tend to c o r r e c t . Using, the value T = 10"*^  seconds f o r E a 4o k i l o v o l t s / c m . and ^  a 0.05 cms., T / R C w i l l be 0.067, while f o r 10 k i l o v o l t s / c m . "JT should be only twice as la r g e , g i v i n g T / R C S 0.135J the c o r r e c t i o n terms w i l l be 1.04 and 1.06 r e s p e c t i v e l y . These are e n t i r e l y i n s u f f i c i e n t t o account f o r the d i f f e r e n c e of 0.002 cms. found, and as the c o r r e c t i o n f a c t o r i s so much smaller than the standard d e v i a t i o n observed, t h a t f a c t o r may be neglected. Therefore, f o r » values of R and C used here, the exponential expansions may be l i m i t e d to two terms w i t h n e g l i g i b l e e r r o r i n c a l c u l a t i n g the alpha range i n l i q u i d argon. The t h i r d cause of v a r i a t i o n of N/Nt w i t h pulse height i s now considered. This i s the e f f e c t t h a t the angle of alpha emission w i l l have on the number of e l e c t r o n s c o n t r i b u t i n g to the cur r e n t pulse, due to t h e i r recombination w i t h p o s i t i v e argon i o n s . The equation derived f o r t h i s e f f e c t , as given before ($6, page 17), i s This i s assumed t o hold only f o r Q $ 80°. The d e v i a t i o n s of the d i s t r i b u t i o n curves given by graph #4 f o r N/NT>0.60 ( i . e . f o r s i n 9 > 0.6) were assumed to be due e n t i r e l y to t h i s v a r i a t i o n of n w i t h sec ©j t h a t i s , the d i f f e r e n c e s ( a ) between the observed pulse size and that given by the straight line for various values of N / N T were subtracted from Vmax. If the above equation were multiplied through by e/c, i t would become V = - ^ ( | _ SBC 6 ) V " C - C V TTnflU / and the voltage values obtained above should f i t this straight line, with sec 8 evaluated from N / N ? = sin 9 . Table #6 and graph #5 give the variations obtained, for the two curves corresponding to 1 = 0.05 cms.., E =4.0 kilovolts/cm. and 1 = 0.03 cms., E = 33.3 kilovolts/cm. The curves are very roughly fitted by straight lines, with deviations from this line for both large and small values of sec 9 . The levelling off of the curve for sec 9 > 3.5 is expected, for the pulse aize must approach a minimum value as sec (i.e. as N / N T - + 1 ) . It seems to occur at values of 9 of ~- 65°, or N / N T / ^ * . 9 5 J this would indicate that the effective radius of the ion column is greater than Is/50 of the alpha range. Variation from the straight line for small values of sec 9- could be due to inaccuracy in drawing the straight line representing variation of pulse size with sin 9.. If this line were slightly steeper, the differences between i t . and the actual readings- for N / N T < 0.6: could be made to f i t the straight lines of graph #5. Such a change in slope would yield a smaller value of j however, this change would be < 10$, as the pulse size differences necessary to f i t the points at sec 9 = 1.15 and 1.00 to the straight line are quite small.. As the equation above contains three unknown quantities, viz., the constants no and r, and <r 2 which would vary with field, no attempt was made to derive information from the slopes of the curves. Also, in order to determine either the radius of the ionization column or the capture cross-section, further information about one of them is necessary, as they cannot to follow page 41 TABLE. 6 . VARIATION N/NT (=s in 9) 0: 0..5 0..71 0 .81 0.866. 0 . 9 2 0 .94 0 .96 0 .97 0 .98 IN PULSE SIZE WITH SEC 9- DUE TO RECOMBINATION sec 9 pulse: s i z e (uV) E=40KV/cms. 1=0.05 cms. E=33»3KV/cms* 1=0.05 cms. 1.0 441 4 6 3 1.15 441 463 1.A1 432. 460 1.70 423 452. 2.0, 4 1 1 441 2.55 3 8 6 422, 2 . 9 2 371. 4 1 1 3.56 355 395 4.12 343, 386 5.0: 325> 369 t o f o l l o w page 41 GRAPH 5* PULSE SIZE VARIATION WITH SEC 8 PULSE SIZE (MICROVOLTS) 500 O- 1 - ^ . 0 5 cms. E=40 KV/Cljl S lr-O.03 amo B=33 KV/CM (42) be: isolated in the above equation. The number of electrons produced, n Q, can be isolated and estimated; inspection of the above equation shows that i t would be equal to (Vmax + slope) C/e. This gives a value for r^, which is not large enough to be independent of field, as i t should be. According to the curve fpr 1 =0.03. cms, E = 50 kilovolts/cm., n is 5.5 x- lo\ while iio, found here, the maximum value of n, is only 4.5 x 10^. As the variation in pulse size due to recombination with argon ions is independent of the electrode separation, and the field should have no effect on the number of electrons produced, no should not vary with either 1 or E. No explanation of this discrepancy has been found. Variation of Maximum Pulse Size with Field As shown in table #5, there i s considerable variation in the maximum pulse size obtained for various settings of the field and electrode separation., A relationship between this pulse size and the field was sought, and from table #7 and graph #6., i t seems that the data f i t quite well on a straight line giving maximum pulse size proportional to EV' 2. There are two possible origins of such a variation: one is due to the electron transit time,. ~£ the other is due to the number of electrons contributing to a pulse, n. If,- i n the equation T i s greater than RC, the exponential term is small and may be neglected. This would give V<£ 1/T > or since "C<£ &f \f\ as shown before, the pulse size: will vary inversely with 1 and directly as yHii, She relationship given by graph #6 would seem at first to indicate this.. However, the condition that T be large with respect to RC is directly contrary to the assumption made in deriving the pulse distribution variation with sin 9 (which variation to> f o l l o w page 42 TABLE. 7. VARIATION IN MAXIMUM PULSE SIZE WITH ELECTRONIC FIELD 1 (cms.,) E (KV/cm.) ( V / c m )1 ^ Lnd-Vmax/V, .05 10. 100 200 - . 1 0 ..05 15 123. 250 - .13 .03 16 . 7 129 310 -.16, .05 20. 141 290 - . 1 5 .03 25 158 390 - . 2 1 ..067 30 173 380 - . 2 0 ..05 30 173- 380 - .20 . .03 33 .3 180 4.60 - . 2 5 ..05 4.0 200 440 - . 2 4 -.03 50. 224. 570 - . 3 2 to f o l l o w page 4 2 PULSE SIZE ( H V ) GRAPH 6, MAXIMUM PULSE SIZE VARIATION WITH FIELD 5<M— 400 3001— 200L_ 100\_ 0 1 = 8o05 cans, X 1 = 0,03 omSo E 1 / 2 (VOLT/CM. 100 125 would not e x i s t i f "T ^ R C ) . A l s o , i t would demand t h a t T be l a r g e r t han 1.5 microseconds - a f a c t o r o f 10 g rea te r than any t r a n s i t t ime so f a r measured f o r l i q u i d argon, w i t h e l e c t r o d e spac ings x - " 0.05 cms. Hence the v a r i a t i o n i n V w i t h E cannot be e x p l a i n e d on the b a s i s o f dependence o f F upon the t r a n s i t t ime. . The second p o s s i b i l i t y i s t h a t , w i t h the pu l se s i z e g i v e n by \/ ^ 2£ as s t a t e d p r e v i o u s l y , n w i l l be a f u n c t i o n o f f i e l d , due t o the r ecombina t ion o f e l e c t r o n s w i t h the argon i o n s be ing more f requent a t low f i e l d s . T h i s would n e c e s s i t a t e n i n c r e a s i n g w i t h not l i n e a r l y , but approaching a. s a t u r a t i o n va lue o f no,, a t which no r ecombina t ion w i l l occur and a l l the free: e l e c t r o n s c rea ted by the a lpha p a r t i c l e c o n t r i b u t i n g t o the p u l s e . I f t h i s i s the case, which seems much more l i k e l y t han the f i r s t mentioned cause, the curves g i v e n i n graph #6 r ep resen t o n l y shor t segments of the curve , f o r which no curva ture i s obs e rva b l e . Under such c i rcumstances a l l at tempts t o o b t a i n no from the da ta i s i m p o s s i b l e ; much l a r g e r f i e l d s would be necessary , so t h a t Vmax could be observed to l e v e l o f f and approach a va lue cor responding to n = no . Davidson and L a r s h (1950) used the equa t ion V * = V. (.--e-*6*^ where a i s an a r b i t r a r y constant and Vo was taken as the observed pu l se s i z e i n argon gas, i n which v e r y l i t t l e r ecombina t ion would o c c u r . The l i n e a r r e l a t i o n s h i p o f graph #6 would f o l l o w from t h i s i f | /~S were «1/a f o r a l l f i e l d s used here.. T h i s equa t ion can be changed to and Vo can be c a l c u l a t e d on the assumption t ha t P / x i s 25.4 eV. as i t i s (44) i n a rgon g a s , TOQ i s then equa l t o 2 . x 10^ e l e c t r o n s and Vo.- t o 2100 m i c r o v o l t s , A p l o t o f I n (1 •-• Vmax/Vo) as g i v e n i n t a b l e #7 a g a i n s t y i e l d s a s t r a i g h t l i n e (graph #7) . There i s a s l i g h t c o n c a v i t y toward low va lues o f the l o g a r i t h m i c v a r i a b l e f o r the 1 = 0 ,05 cm. cu rve . I t would be caused by (1 --Vmax/Vo.) be ing too low, i . e . , by Vo be ing too s m a l l . T h i s i n d i c a t e s the p o s s i b i l i t y o f P/x (=H/ho;) be ing sma l l e r than 25 .4 e V . , g i v i n g a conduc t ion band f o r l i q u i d a rgon . However, no such c o n c a v i t y can be found on the curve f o r 1 = 0.03 cms. , so the i s s u e remains i n doubt . The two curves ob ta ined f o r d i f f e r e n t va lue s o f 1, and t h e i r s l i g h t l y d i f f e r e n t s lopes can be e x p l a i n e d by the c o r r e c t i o n term d e r i v e d i n the p r e v i o u s s e c t i o n . . I t g i v e s f o r the maximum pu l se s i z e ob ta inab le f o r p a r t i c u l a r v a l u e s o f spac ing and f i e l d , the equa t ion As the l a s t te rm i n the e x p r e s s i o n has a v a l u e o f o n l y .07 f o r 1 = 0 .05 cms. and E = 40. k i l o v o l t s / c m . . , as found be fo re , i t w i l l not be s u f f i c i e n t to> account f o r the d i f f e r e n c e between the two curves o f graph #6 ( —• 15$) but i t w i l l decrease t h i s . . A f u r t h e r p o s s i b i l i t y i s t h a t p a r t o f t h i s d i f f e r e n c e i s caused by capture o f e l e c t r o n s by i m p u r i t y atoms. U n l i k e r ecombina t ion e f f e c t s , the number of e l e c t r o n s removed by the capture process w i l l v a r y d i r e c t l y w i t h the e l e c t r o d e s p a c i n g . The magnitude o f t h i s p rocess i s unknown but the p u r i f i c a t i o n preformed here had no observable e f f e c t on i t . I o n i z a t i o n Current 'Measurements I n order t o determine the i o n i z a t i o n cu r r en t , the e le&trometer was connected d i r e c t l y to the chamber, and a l lowed s e v e r a l hours t o reach e q u i l i b r i u m . The chamber was coo led , argon i n t roduced and the f i e l d turned on, as b e f o r e . The d e f l e c t i o n s obta ined were v e r y l a r g e (<**10~H amps,) , w h i l e the a c t u a l cu r r en t s c a l c u l a t e d from a va lue o f no o f 2 x 104 e l e c t r o n s to follow page 44 -.10 G R A P H 7C M A X I M U M P U L S E S I Z E V A R I A T I O N W I T H F I E L D -•'15 r--.20 J_ -.25 r--.30 100 O l e 0.05 cms. X l = 0.03 cms. 1 125 150 175 ZOO E V * ( V O L T / S M J 1 / * 225 per pulse w i t h 60 pulses a second should have been about 10"-*"* amps. These l a r g e d e f l e c t i o n s were accompanied a t high f i e l d s w i t h f l u c t u a t i o n s of the same order o c c u r r i n g a t a frequency of about one per second or so. These f l u c t u a t i o n s p e r s i s t e d when the argon was removed. Th e i r s i z e was lessened c o n s i d e r a b l y by removal of the e x t e r n a l f i l t e r i n g supply on the high v o l t a g e , and by thorough c l e a n i n g o f the e x t e r n a l surface of the kovar s e a l . They could not be e l i m i n a t e d , and w h i l e they d i d not appear a t the lower v o l t a g e s , the steady d e f l e c t i o n d i d , and was i t s e l f so much l a r g e r than the currents o r i g i n a t i n g between the e l e c t r o d e s t h a t i t rendered the l a t t e r i m p o s s i b l e 'to,, as c e r t a i n . There i s a strong p o s s i b i l i t y t h a t t h i s steady current was due t o t r a c k i n g currents across the surface of the kovar s e a l , both i n s i d e and outside the chamber* l i k e so many such e f f e c t s i t d i d not occur w i t h equal magnitudes f o r both d i r e c t i o n s of the f i e l d , being l a r g e r when the chamber was p o s i t i v e w i t h respect t o the connection through the s e a l . To overcome t h i s , a l a r g e kovar s e a l i s i n d i c a t e d f o r such use, w i t h the gap between the el e c t r o d e s kept small to enable the u t i l i z a t i o n of lower v o l t a g e s t o o b t a i n the f i e l d s d e s i r e d . A l s o more c a r e f u l c o n s t r u c t i o n of the i n p u t c i r c u i t of the electrometer would probably be advantageous, w i t h the i n p u t r e s i s t o r s completely s h i e l d e d along w i t h the tube i t s e l f . However, the most important change would be the i n t r o d u c t i o n i n t o the chamber of a much stronger alpha source. This was not done, as one y i e l d i n g 50 — 100 counts per second was considered best f o r r i s e time and amplitude measurements. Where only d i r e c t currents need be measured, sources of 100 - 1000 times t h i s a c t i v i t y would be p e r m i s s i b l e . With such a source (about 5000 counts/sec.) the i o n i z a t i o n current should be greater than 10"11 amps f o r f i e l d s of both p o s i t i v e and negative v a l u e s . (The p o s i t i v e i o n s w i l l n a t u r a l l y y i e l d as l a r g e a current i n moving across the gap as the e l e c t r o n s do, although, w i t h t h e i r much lower m o b i l i t i e s , the pulses them-(46) s e l v e s are not d i s c e r n i b l e . ) Wi th such a source i t should be p o s s i b l e to determine the i o n i z a t i o n cu r ren t s cor responding t o d i f f e r e n t va lue s o f e l e c t r o d e spac ing and f i e l d , and thus achieve an independent method o f c a l c u l a t i n g n . DISCUSSION From the at tempts to determine both the t r a n s i t t ime , T*, and the pu l se ampl i tude , u s i n g the same c i r c u i t , i t must be concluded t h a t such an approach i s e s s e n t i a l l y i m p o s s i b l e . The amount o f i n f o r m a t i o n a v a i l a b l e from the v o l t a g e p u l s e , ( r e s u l t i n g from a steady c u r r e n t , o f magnitude n e / T and d u r a t i o n ~C , when i t passes through an RC p a r a l l e l c i r c u i t ) i s l i m i t e d , and due t o the v a l u e s o f n and "T i s too s m a l l t o y i e l d s i g n i f i c a n t r e s u l t s f o r both q u a n t i t i e s . , Some s a c r i f i c e o f e i t h e r t r a n s i t t ime o r ampli tude accuracy i s e s s e n t i a l i f the o ther q u a n t i t y i s t o be a c c u r a t e l y measured.. As a m p l i f i e r s w i t h good s i g n a l t o no i se r a t i o s were a v a i l a b l e , i t was dec ided to pursue p u l s e s i z e d i s t r i b u t i o n da ta and n e g l e c t t r a n s i t t ime measurements, which demand much f a s t e r a m p l i f y i n g equipment . The mean f ree pa th and c o l l i s i o n c r o s s - s e c t i o n o f an e l e c t r o n i n l i q u i d argon were es t imated from the t r a n s i t t ime f o r two va lues o f f i e l d and e l e c t r o d e s p a c i n g . The c r o s s - s e c t i o n was found to be 4 x 10"^ cms .^ ; t h i s compares w e l l w i t h the va lue ob ta ined by M a l k i n and S c h u l t z (1951), but d i f f e r s c o n s i d e r a b l y , as does t h e i r v a l u e , from those p r e v i o u s l y p u b l i s h e d f o r argon gas (Brode 1933);. these g ive a maximum p r o b a b i l i t y o f capture f o r the e l e c t r o n energy va lues used here , due t o the Ramsauer e f f e c t . The observed magnitude o f any pu l se a t a t ime t a f t e r i t s s t a r t has been shown t o be g i v e n by (47) V - ¥ R ( . - « - * / K ) f o r o-{ t "T - tg»- T h i s pu l se s i z e reaches a maximum a t t = T — t g which w i l l not be the same f o r a l l p u l s e s , due t o v a r i a t i o n o f V w i t h s e v e r a l q u a n t i t i e s not e x p l i c i t l y e n t e r i n g the above e q u a t i o n . The noise o f the a m p l i f y i n g components produces f l u c t u a t i o n s i n pu l se s i z e as shown i n -t a b l e #3 and graph #3. The q u a n t i t y t g v a r i e s w i t h the angle o f a lpha e m i s s i o n , 9, as does the number of p u l s e s o r i g i n a t i n g from a lpha p a r t i c l e s emi t t ed a t angles $ 9* Furthermore the number o f e l e c t r o n s c o n t r i b u t i n g t o a pu l se w i l l v a r y y±th sec 9 and w i t h the a p p l i e d f i e l d , due t o recombin-a t i o n . . There w i l l a l s o be second order e f f e c t s , caused by "X be ing p r o p o r t i o n a l t o the e l e c t r o d e s p a c i n g , 1, and i n v e r s e l y p r o p o r t i o n a l t o the square r o o t o f the f i e l d . . F i n a l l y there w i l l be some v a r i a t i o n i n pu l se s i z e due to the a l p h a p a r t i c l e s not be ing comple te ly mono-energet ic , and to e l e c t r o n t r a p p i n g by i m p u r i t i e s . A l l these e f f e c t s have been cons idered i n the a n a l y s i s o f r e s u l t s , and the p o s s i b l e conc lus ions made. The a lpha range, R w , has been found to be 0.012 cms. , or , co r r ec t ed f o r the heav ie r i o n i z a t i o n o c c u r r i n g near i t s l i m i t , t o 0.009 cms. Both va lues are c o n s i d e r a b l y l a r g e r than t h a t suggested by Davidson and L a r s h (1950), v i z . . , 0,005 cms. I n e i t h e r case, the weighted centre o f the e l e c t r o n column can be g i v e n a. 0,006 cms. a long the t r a c k o f the a lpha p a r t i c l e s . The number o f e l e c t r o n s c o n t r i b u t i n g t o a pu l se was found to v a r y between 2 x 10*V and 6 x l O 4 - depending on the f i e l d . I t shows no s i g n o f s a t u r a t i o n a t l a r g e f i e l d s , and cou ld be as h i g h as 2 x: 10^ w i thou t a conduc t ion band b e i n g present . . Thus there i s no reason as y e t to demand conduc t ion bands f o r l i q u i d argon; h i g h e r f i e l d s would be necessary t o determine t h i s . . Finally, from the attempts to measure ionization current, i t is apparent that more care is necessary in the construction and operation of the chamber and the electrometer circuit. Also a much stronger alpha source would be a definite advantage. BIBLIOGRAPHY Brode, R.S., 1 9 3 5 , Rev. Mod. Phys., 5_, 2 6 3 . Comptori, K.T., 1 9 2 3 , Phys. Rev., 2 2 , 333, 4 3 2 . Davidson, N., and Larsh, A.E., 1 9 5 0 , Phys. Rev., 77_, 7 0 6 . Dubridge, C , and Brown, J.L., 1 9 3 3 , R e v . Sci. Inst., 4 , 5 3 2 . Frolich, H. and Mott, N.F., 1 9 3 9 , Prec. Roy. Soc, 171A, 4 9 6 . Gerritsen, A.N., 1 9 4 8 , Physica, 14, 381. Hofstadter, R., 1 9 4 9 , Nucleonics, 4, 2 . Holtsmark, K.E., I929, Zeits. fur Physik, 5J>, 4 3 7 . Hutchinson, G.W., 1 9 4 8 , Nature, 1 6 2 , 6 1 0 . Jaffe, G., I 9 3 2 , Physik Z., j>3_, 3 9 5 . Jaffe, G., 1 9 4 9 , Phys. Rev., 75_, 1 8 4 . Langevin, P., 1 9 5 0 , Ouevres Scientifique de Paul Langevin, (Centre National de la Recherche Scientif.) Malkin, M.S., and Schultz, H.L., 1951, Phys. Rev., 83_, 1 0 5 1 . Ogg, J«, 19^6, J« Amer. Chem. Soc, 6 8 , 155* Rontgen, W.C., and Joffe, A., I9I5, Ann. Physik, 41, 4 4 9 . Rutherford, E., Chadwick, J., and E l l i s , CD., 1912 , Radiations from Radio-active Substances (Cambridge Univ. Press). Schiller, H., I 9 2 6 , Ann. Physik, 81, 3 2 . Van Heerden, P.J., 1 9 4 5 , Physica, 1 6 , 5 0 5 , 5 1 7 . Williams, R.L., 1 9 5 2 , Conduction Processes in Crystals (Masters Thesis for U.B.C.) 

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