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The primary specific ionization in gases of positrons and electrons II Sample, John Thomas 1950

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(is* 6% THE PRIMARY SPECIFIC IONIZATION IN GASES of POSITRONS AND ELECTRONS II by John Thomas Sample A Thesis Submitted In Partial.Fulfilment Of The Requirements For The Degree Of MASTER OF ARTS In The Department of PHYSICS THE UNIVERSITY OF BRITISH, COLUMBIA October, 19^ 0 THE UNIVERSITY OF BRITISH COLUMBIA VANCOUVER. CANADA I P A R T M E N T O F P H Y S I C S October 12,.1950. Dr. L. W. Dunlap, Librarian, University of Brit i s h Columbia. Dear Dr. Dunlap: This letter w i l l certify that the thesis of Mr. John Thomas Sample has been carefully studied by the under-signed, and that the thesis meets the required standards and an abstract has been approved by the Department. Yours sincerely, G. M. Shrum Head of the Department GMS:1c G. G. Eichholz Assistant Professor of Physics . THE PRIMARY SPECIFIC. IONIZATION IN GASES  OF POSITRONS. AND ELECTRONS II ' by John Thomas Sample ABSTRACT By u t i l i z i n g the dependency of the efficiency of a Geiger counter upon the primary ionization of a counted par-t i c l e , the minimum primary specific ionization of electrons in several gases-has been determined. The values obtained are: Gas ion pairs/centimeter/atmosphere Helium 5-47 ± 0-09 Neon 11.6 £ 0 . 4 Argon 29.8 £ 1.5 Ethylene 40.1. 1 .0 Ethyl alcohol vapour 61.5 . •+ 1.5 The dependence of specific ionization upon the energy of the primary electron has been investigated between the energies of 0.158 and 0.351 Mev". The primary specific ionization of positrons and electrons of the same energy has been found to be the same to within 1%. Abstract By u t i l i z i n g the dependency of the efficiency of a Geiger counter upon the primary ionization of a counted par-t i c l e , the mimimum primary specific ionization of electrons in several gases has been determined. The values obtained are: Gas ion pairs/centimeter/atmosphere Helium 5.4-7 t 0.0? Neon 11 .6 * 0.4 Argon 29.8 + 1.5 Ethylene 40.1 I 1.0 Ethyl alcohol vapour 6 l . 5 * 1.5 The dependence of specific ionization upon the energy of the primary electron has been investigated between the energies of O.158 and 0.351 MeY. The primary specific ionization of positrons and electrons of the same energy has been found to be the same to within 1%. Acknowledgments This work has been made possible by the award of a National Research Council Bursary to the author, and by the privilege of using some of the equipment of the Nuclear Techniques Laboratory set up with funds provided by the Defence Research Board. It i s a.pleasure to acknowledge the guidance given by Dr. J.B. Warren, under .whose supervision this work was carried out.- . . The help of Miss L. Silver in fabricating the counter sis gratefully acknowledged. Table of Contents Chapter Page I Introduction 1 II Relativistic Quantum Theory of Specific Ionization . . . . . . . 3 III Experimental Verification of the Theory . . . . 10 . IV Review of Experimental Methods 13 V Considerations Relating to the Counter Efficiency Method . . . . . . . . . . . . . 14 VI Apparatus 18 VII Preliminary Investigations 22 VIII Results and, Conclusions 26 Bibliography 28 Figures 1. Beam distribution from the Magnetic Analyser. 2. Circuit diagram of the t r i p l e coincidence mixer. 3. Graph of equation (16) for mixtures of helium and ethylene. 4. Graph of equation (l6) for mixture*of neon and ethylene. y . Counter efficiency as a function of voltage. 6. Counter plateau with and without external quenching. 7. Table of Results. 8. Variation of p. s . i . with energy. THE PRIMARY SPECIFIC., IONIZATION. IN GASES OF POSITRONS AND ELECTRONS - II CHAPTER I  Introduction The primary specific ionization, henceforth written p.s.i., of a particle moving through a gas is the number of ion pairs per centimeter of path, produced by direct c o l l i s i o n of the particle with molecules, divided by the pressure of the gas (0°C) in atmospheres. Theory predicts a relation between p.s.i. and velocity of the primary particle of the form: p.s.i. o 1 . A f l n M ; 2 ) - + B? where r3 i s the velocity of the particle as a fraction of the velocity of light, and p i s the pressure of the gas in atmos-pheres (0°C). Vdepends on the charge of the particle, the density of atomic electrons, and the average ionization poten-t i a l of the gas. "B'depends on the average ionization potential and on the maximum .energy transferred to a molecule i n a c o l l i s -ion. The theoretical curve of p.s.i. in air versus (3 has a minimum at (3 ~ .°6, corresponding to an energy of 1.5 MeV for electrons. By measurement of the efficiency of a Geiger-counter, the p.s.i. of the gas in the counter can be obtained. This has been done for several gases. A magnetic analyser was used to select electrons of the energy for which the p. s . i . i s a minimum. The values found were 5.47 * 0.09, 11.6 i 0.4, 29.8 t 1.5, 40.1 t 1.0, and 61.5 .£ 1.5 respectively for helium, neon, argon, ethylene, and ethyl alcohol vapour. The variation of p.s.i. with energy has been inves-tigated for energies between 0.158 MeV and O.351 MeV. The shape of the curve of p.s.i, versus energy i s similar to that of the theoretical curve. The efficiency of a counter was found to be the same to within 0.25% for electrons and positrons of the same energy, as predicted by theory. 3 CHAPTER II Relativistio Quantum Theory ofrspecifio Ionization 1. Bohr (1) obtained relativist!© and non-relativistio expressions for the energy lost per centimeter by a charged par-t i c l e passing through matter*According to these expressions, energy loss per centimeter varies directly as the density of atomic electrons and the square of the charge on the particle, and inversely as the square of the velocity of the particle. In quantum mechanical theories the dependence on electron den-sity and .charge i s the same, but the dependence on velocity i s somewhat different. 2. A non-relatiyistic quantum-mechanical relation was derived by Bethe (2). This may be expressed: s = 0.285 / 2TTNZ,z2e4 \ In ( 42 mv2 ) (1) mv2I I where s = p.s . i . N = number of atoms/unit volume. 2 = atomic ..number of the target atom, ez = charge of incident particle e » electronic charge m = electron mass v = velocity of incident particle I • average ionization potential of the electrons of the target atom. 3. A true r e l a t i v i s t i o quantum mechanical treatment was f i r s t presented by Bethe (3), an outline of which i s given 4, below. More detailed derivations have been given by Miller (4), and Bethe and Fermi. (5). A free electron, with energy E, momentum p may be described by the Dirac eigenfunction T = f(p) exp i (p . R - Et) (2) n" where #>(p) has four components ^ , -—, 4^, dependent only upon — • momentum and spin orientation, not upon position vector R. From the eigenfunctions before and after a c o l l i s i o n with an atom,, the charge and current densities are constructed (Miller, (4)}: P = -e Y t p ^ y t p ) «= -eA .o(p, pl) exp i [(p^pl) .R-(E-El)t7 _» S j = - e c a ^ p 1 ) exp i np^pM.R - (E-Sl)t^ (?) where c = velocity of light ao= f*(pl ) f(p) a = - ^ ( p 1 ) ^ f(p) c ot = Dirac velocity operator E 1 and p 1 are respectively the. energy and, momentum of the incident electron after the co l l i s i o n . From these the retarded, scalar and vector potentials of the associated electromagnetic f i e l d are computed. Then, for the probability of a c o l l i s i o n in which the incident electron i s scattered into solid angle d<*J at angle©", and the atom i s raised from the ground state (energy E 0, eigenfunction Y 0) to the nth state (energy En, eigenfunction T " n ) , the Born approximation gives: d#n-= 4e4 f l E S 1 dco I fTn(r) 2 exp i [ ( p ^ p 1 ^ ] f(p=pl)2«( E- El) 2/C^ • - - 3 « 5 The integral in (4) i s extended over the coordinates of the atomic electrons. The index j refers to the j atomic electron. a© introduces the effect of the scalar potential, «T . ^ that of the vector potential. .The term ( E - E 1 ) 2 / © 2 ( E n - E ^ e 2 i s due to retardation. If the atom receives energy small compared to mc2, the rest energy of the electron, Schrfldinger rather than Dirac eigenfunotions may be used for 7^ andYn. Even then the effect of the vector potential must not be neglected since the inter-•p action cross-section would then be too large by a factor E a mc approximately. For small scattering angles, a 0 =1, a = v, and, c taking the velocity of atomic electrons as small compared to that of the incident electron, Tn ^ j T 0 d r - - ^ V o =_L_ (S n-E 0) (J>) where Von. signifies- the matrix element of the velocity, -* t ran that of the coordinates, of the j atomic electron. Also, for small scattering angles, we may expand the exponen-t i a l function.in (4) and neglect terms containing higher powers than the f i r s t . Then the integral in (4) i s : Jn - i f~Tn «S f (P-P 1 * En-Eov). r,-] To a t = i x o n / P P 1 - En-Bo p / (6) x0 n I s the electric dipoie moment corresponding to the trans-p i t i o n o .—* n, hence (x©n| t i c a l transition probability. p i t i o n o .—* n, hence (x©n| , except for a factor, i s the op-Geometric considerations give: (p^p 3-) 2 _ (En - E p ) 2 •. 2("p2-E(En-Eo)l (l-oos &) + (En-Ee ) 2m 2cos^+~ o~z~ c2 P 2 (p=pl - En - E o p ) 2 - 2{p 2-En-Eo}(2E 2-m 2c 4) (l-oos^)+(En - E o ) 2 ""E lo2~" 2 4 xffl " 2 l + - - - (7) E 2 p 2 (7) and (6) are next inserted in (4) and the expression inte-grated over the angle & . The upper limit of integration, j i s chosen small enough that expansion of the exponential i n (4) is allowed, large enough that the expressions (7) depend principally on & t not on the transferred energy En-E 0. These conditions are compatible with each other. Integration of (4) under these conditions gives: (1§J0) = 2 TTe4 r x > f m 2p4(l-oos• &B ) - o 2p 21 J° mv21y ' ' I m2C«a-i«)Si TZ"J (8) - 2 7Te mvHRy ' ' *- (En - E o)z(l- J a where W ( = £ 2 (1-cos <%> ) i s the energy, from conservation m laws, transferred to a free electron when the incident electron i s scattered through an angle The energy loss per centimeter i s obtained from (8) by summing over a l l possible states n (including the continuum)j multiplying each term by the energy transferred, En-Eo. This .. gives: - dE = 2 TTQ^ Z f i n 2mv2W . - /3 2 ] ' (9) dx" mv2 I WTl=F) 1 J where E i s the average excitation energy of the target atoms. The p.s.i. i s related to -dE by dx 7 s - -1 dE ) , where d£\ i s that part of dE producing VT dx / ion 3x/ion dx ionization ((8) summed only over states in the continuum), and Vo i s the average energy expended in creating an ion pair. Then (Bethe (2), Williams (6)): s - 0.285 2 7Te4N Z f In 42mv2 - ln(l-£ 2)- ( 3 2 j (10) nv2l I I where I i s the average ionization potential of atomic electrons. The underlying physical assumptions used to obtain (10) are as follows:.. a) The energy transferred to the atom is much less than the rest energy of an electron. (Cloudr?chamber pictures show few high energy secondaries!. b) The scattering angle & ranges., only over values for which the expansion of the exponential in (4) i s valid. (This assum-ption i s also necessary in approximating the scalar and vector potentials),. c) The velocity of atomic electrons i s small compared to that of incident electrons. 4. Williams (6) usesthe method of impact parameters and classical r e l a t i v i t y to obtain a r e l a t i v i s t i c term to be added, to equation. (1). In this manner he obtains equation (10). The necessary physical assumptions are similar to those given above: a) Energy transferred in a co l l i s i o n i s less than W, where I « W « (Imc 2)^ b) The momentum of orbital electrons must be much less than that of incident electrons. 8 Williams estimates that 45% of -dE i s expended in cEx ionization, and that the number of ejected electrons with energy greater than 21 i s negligible. Since Williams obtains equation (10) by applying classical r e l a t i v i t y , experimental verification of equation (10) i s not a verification of r e l a t i v i s t i c quantum.theory, but only of classical r e l a t i v i t y theory, which has been ve r i f -ied for charged particles at least. 5. The r e l a t i v i s t i c terms i n (10) have l i t t l e effect at velocities smaller than 0.°c. However, as v increases, instead of decreasing monotonically as in the non-relativistio case, s, should pass through a minimum and increase as v—«• c. Equating ds to zero leads to the relation: •d(S ln/42mc2)+ l n / _ x \ = 1 (11) K I 7 'l-x' 1-x where x =• {2* , (3> being the value of {3 when s has i t s minimum value. Graphical solution of ( l l ) gives values of the kinetic energy at the minimum ranging from 1.5 MeV for hydrogen to 1.2 MeV for lead. Equation (10) i s almost constant between 0.5 MeV and, 5 MeV. 6. Although equation (10) has been applied to electrons, i t applies s t r i c t l y only to heavy particles, for two reasons: a) For electrons, there is an, appreciable contribution from collisions with scattering angles greater than @° . b) Since incident and atomic electrons are similar particles, exchange forces must contribute to the interaction. Taking these into account, Bethe (7) obtains: -dE ) = 2 ^ 9 % ^ (In mv2T . ( 2 /I-yP - l+^2) l na + 1^2? dx/ion mv2 1 2l2(l-/2*) J (12) where T i s the r e l a t i v i s t i c kinetic energy of the incident electron. From the graphical representation of equation (12) for a i r (Reference (7)), a minimum occurs at 1 MeV, dE being. . dx 10% greater than the minimum at energies of 0.45 MeV and 4.5MeV. The minimum,for lead occurs at about.0.8.MeV. 7. Equations (1), (10), and (12) are similar at low energies, and may be applied to energies as low as 0.2 MeV. Below this energy,, p.s.i. should deorease sharply, due to the inefficiency of energy transfer processes (velocity of the incident particle comparable to that of the orbital (K) electrons) At energies greater than lJMeV, (10) and (12) are s t i l l similar, increasing slowly as energy increases. At 10 MeV, both indicate that the p^s.i. should be a factor 2 greater than the minimum, markedly different from the classical value, nearly zero. 8. If the exchange forces between a positron and an electron differ from those between 2 electrons, the energy loss per centimeter-of positrons would not be given by equation (12). However, equation (9) should apply to positrons as well as i t does to electrons, and experiments cannot as yet distinguish between equations (9) and (12) (or their p . s . i . analogues). 9. I, the average ionization potential, i s d i f f i c u l t to compute accurately, since the wave-functions of multi-electron atoms are unknown. Bloch (8) suggests the approximation: I » (13.5 Z) eV. (13) 10 CHAPTER III . -Experimental Verification of the Theory 1. Although equation (12) should be applied to p.s.i. of a electrons a l l investigators have used/semi-empiriffial form of equation (10): s = A (In K + In -(3*) ( 1 4 ) where A and. K are dependent upon material and particle. 2. Only for hydrogen has p.s. i . been accurately calcul-ated.-'1 Williams. (6) gives the value 2.5 for the minimum i n atomic hydrogen. Assuming, a value of twice that for molecular hydrogen, this i s i n f a i r agreement with the value 5-2 obtained by Williams and Terroux (12), though considerably lower than the value 6.2 obtained by Danforth and Ramsey (13), and 6.0 obtained by Cosyns (i4). Williams (16) found that equation (1) applied to gave hydrogen^results within 10% of the experimental values for electrons with <? « 0.5, 0.75, O.96. 3. Range energy relationships derived from integration of equations (1) and (9) can be fi t t e d empirically to exper-imental data with good results for heavy particles. (Reference 15). "Straggling" makes this method d i f f i c u l t to apply to electrons. 4 . T has been determined by no means other than measure-ments of p.s.i. and dE, so that checks by two different exper-„dx iments are not as yet possible. 5. Classically, p . s . i . i s expected to vary as 1 . v 2 Instead, Williams and Terroux (12) find, for @ between 0.5 and O.96, the relation s = 5.2 Q - 0 , 2 for hydrogen s = 22 (3 - 0 : 2 for oxygen That the exponent in a f i t of this kind i s less than 2, indic-ates the effect of a term such as In/ ) l l -6. Of many investigators, only Corson and Brode (17) and Hereford (18) confirm the r e l a t i v i s t i c Increase i n p.s.i. Corson and Brode show three points beyond the minimum lying close to a curve of form (14). One point near the minimum and three on the low energy side also l i e close to the curve. Hereford shows three points beyond the minimum confirming the increase. Six points near the minimum de f i n i t e l y . l i e below the theoret-i c a l value for hydrogen (I = 13.5 ev") from equation (10). Hazen (19) concludes that the p. s . i . of mesons in air rises only one fourth as rapidly as expected-from theory. In another paper (20) he confirms the r e l a t i v i s t i c increase i n p.s. i . of cosmic ray electrons, but identification of particles i s not certain. Measurements of grain density along cosmic ray tracks in. photographic emulsions do not indicate an increase in den-sity i n the r e l a t i v i s t i c region (26). This could mean that p. s . i . does not increase in this region, or that an unknown effect i n the photographic process prevents an increase i n density. 7. Results quoted i n the literature show considerable divergence, indicating that the accuracy of the cloud-chamber method has been overestimated. The shape of the theoretical curve (14) lias been verified f a i r l y well, though in cases where quantitative-theoretical results are available, agreement i s not good* -CHAPTER IV  Review of Experimental Methods 1. . Most of the p.s.i. values to date are from cloud-chamber data. Brode (21) has f u l l y discussed the cloud-chamber method. In direct measurements of p.s.i.j the chamber i s ex-panded at regular intervals, only sharp tracks being used. In this way, secondary ions are not distinct, forming a cluster around the primary ions. The p. s . i . i s given by the number of clusters per centimeter divided by the post-rexpansion pressure in atmospheres. The energy of the particle i s determined from the curvature of i t s track in a magnetic f i e l d . Inaccuracy arises from estimation of pressure, temperature, concentration of water vapour and alcohol vapour, and track length, and from s t a t i s t i c a l variation. References (6), ( 1 2 ) , (16), ( 1 7 ) , ( 1 9 ) , (20), and (21) refer to the clouds-chamber method. 2. The p.s.i. of the gas in a Geiger counter can be determined by measuring the efficiency of the counter (Chapter V). Few investigators have as yet applied this method, to measurement of p.s.i., but i t has been used by van Allen to estimate the energy of cosmic ray particles, or alternatively to identify particles. With the exception of Hereford (18) and Curran and Reid (22) a l l investigators using the counter method to measure p.s.i. have done so for cosmic rays only, separating neither particles nor energies. References (10),(12), (14), (18), and (22) refer to the counter efficiency method. 3. Although Powell has measured the variation in grain density along tracks in photographic emulsions * this method serves as yet only to identify particles. 14 CHAPTER V Considerations Relating'to. the Counter Efficiency Method. 1. The. relation between counter efficiency and p.s.i. depends upon the assumptions: a) If.an ion pair i s created anywhere within the volume of the counter, a count i s recorded. b) The counter i s not photo-sensitive, that i s , photons from I n i t i a t e atoms excited, by the passage of a f a s t particle do not^indicate a Geiger discharge. This assumption i s reasonable, since quench-ing agents absorb photons, and counter wails can be made to have a high work function. If s i s the p.s.i. in ion pairs per centimeter per atmos-phere, and p (atmospheres) i s the gas pressure in the counter, then spdx i s the probability of forming at least one ion pair -in distance dx (centimeters). The probability of forming no ion pairs in dx is then (l-spdx). I f pv(x) i s the probability of producing^ no ion. pairs in distance x, then: po(x+dx) = p o(x)p 6(dx) = p 0(x)(l-spdx) dp 0 88 p 0(x+dx)-p 0(x) = -p 0(x).spdx Hence p 0 - e " s p x Then, i f £ i s the average path length of particles traversing the counter, the efficiency (the probability that a particle w i l l induce a discharge) i s given by: = l - e - s X P If two gases are present in the counter, this becomes: > « l - e - U ( s l p l + S2P1 (15.) If T is the absolute temperature at which pi and p 2 are measured, we have, from (14T): 31 + £2 s ? 58 l i ••JL. • I l n ( l - e )l . (16) Pi JL 273 Pi where p^, p£ are now measured i n centimeters of mercury. I f 6 is measured for several values of ££, and the quantity on the Pi right of (16) i s plotted against p_2, a straight line should •Pi result, from which s^ and may he calculated. (16) i s also in suitable form for a "least-squares" f i t . 2. In measurements of 6., electrons of a selected energy pass through the counter under investigation (counter 1) into another, (counter 2). If N2 electrons are recorded, by counter 2, the probability of any one-of these i n i t i a t i n g a count from counter 1 i s 6. From Ait ken (9), the. number of counts, c, i n counter 1, coincident with counts in counter 2, obeys a binomial..distribution: p(c) = N 2 £°(1- 6) N2-o with mean c e » 6N2 and standard deviation 6*~= {N26(1- • Hence € is given by..-e = 0 + JNze 41- a)}^ N 2 N 2 • = o i f c ( l - o ))^ (17) N*2 iW2z - W2 J In a typical case, c • lj>,000, N 2 = 20,000 Then 6~= 3.1 z 10**5 = 0.4% of 6 . If a background n2 i s to be subtracted from N2, a further deviation i s introduced. This i s approximately 6~2- = 22.. I f this i s to be of the same magnitude as the N 2 deviation in the example above, ng. <tf.l8. This i s not d i f f i c u l t N2 to achieve. 3. To find the values of 6 for which s t a t i s t i c a l varia-tions have the least effect in determining the right hand side of equation (l£), let x » sip = - l n ( l - £) Then - a £ = 1 . / e ) , 1 -£ N 2% ( l . / putting A € 8 £7 From this i t is obvious that 6 should be as small as possible. To find the values of 6 at which a measurement of £ i s most sensitive to a difference in the value of sip, take 6 = l - e " x 'y —X A.6 = e ^ x ' - (1- e x From this i t i s apparent that (= should be as small as possible. 4. The "dead-times" (time of insensitivity following activation by a count) of counters and electronics necessitate correction of equation (17). The problem may be phrased as follows: Two counters with counting rates Ni,N 2, dead-times x i , x 2 respectively, activate separate channels of a coincid-ence mixer of resolving time Tr, dead-time t. The individual counting rates and the coincidence rate c are recorded by scalers of dead-time y i , y 2, yj respectively. I f counter 2 has a background rate n 2, what is the efficiency of counter 1 in terms of N 1 } N2, o, x^, x 2, T, t, 3£.,.y2, y^, and n 2, given that ylt y 2, y? > x i , x 2 > t > f ? Since yi>X]_, scaler 1 introduces the only loss in . counting rate Ni. Circuit 1 i s "dead" for the fraction Niyi of each minute. Hence the "true rate" i s given by: or N-^ 1 = Ni similarly Ng^ = N 2 1-N 2y 2 Since t<y^, the "true" coincidence rate, c 1, i s given by c 1 = o l - c y 5 "Accidental'* coincidences occur because of f i n i t e resolving time, the rate n c being,given approximately by: n c - 2(N 1-c)(N 2-c)r Coincidences w i l l be lost when counters 1 and 2 are activated by non-coincident counts. Since xj_, x 2>t, the loss i s determined by the counter dead times. To a near approxim-ation, the time during which coincidences cannot be recorded is given by (Nj-c) Xj + (N2-c) x 2. Actually this time i s diminished by overlapping of these terms, but in our case the second term i s negligible, and .hence the overlapping correction. Neglecting the second term then, c 1 suffers a further correct-ion: c 1 1 = c 1 1-lN-j-cjX! From equation ( 17) : e -. «ii - . o . - 2(Ni-c)(N 2-c)T N 2!-n 2 Il - o y 3)q-(N 1-o)x 1 7 n ~ n 2 1-N2y2 Of a l l the corrections, only 1 -(%-C^and n 2 are appreciable. Then: £ = o 11 + (Ni-c)xi7 (18) N 2-n 2 CHAPTER VI  Apparatus 1. A description of the vacuum chamber, wedge magnet-analyser, and other apparatus has been given by L. Silver (10). 2. The electron source used was 2 millicuries of Radium D.-E. precipitated from acid solution onto platinum f o i l . Emax of the electrons from Radium E i s 1.17 MeV. Soft (3-rays from Ra D and oi-rays from Ra F are eliminated by the analyser. The positron source used in one experiment was a f o i l of Cu^ 4 from the Chalk River p i l e . Emax of the positrons i s .66 MeV. 3. To aid in energy selection, and to reduce the 2^-ray intensity from the source, i f any, a lead .baffle was Inserted just before the exit window of the analyser. 4. Figure (l) i s a plot of intensity versus displace-ment, horizontal and vertical, obtained by moving (across the-exit window at a distance of 0.8 cm.) a counter accepting particles through a 3 inch hole. From this the focussing 32 of the analyser was assumed -to be satisfactory. J?. The counters (Reference (23')) to contain the i n -efficient gas mixtures were of two types. Some were made from square brass tubing, about 2 cm. by 2 cm. Others were cylind-r i c a l brass stock bored out and.machined f l a t to augment attaching windows. 2-4 milligram per square centimeter mica was cemented over 3_ inch diameter holes on two sides of each lb-counter. After evacuation, the anode wires were "flashed" at white heat and held at; red heat for ^ 30 minutes. Pressures were measured with a mercury manometer and travelling teles-cope (accuracy i 0.002 cm.). Room temperature at the time was recorded. A diffusion time of 12 hours was allowed. Path length was obtained by direct measurement before the counters were completed. A small correction (0.05 cm.) for sag of the windows is added. The second counter was a standard "bell-counter 1 1 f i l l e d with, 9 centimeters of argon and 1 centimeter of ethyl alcohol. This counter was very nearly 100% efficient, with a plateau slope of 3.5% per 100 volts over a range of 150 volts. It was operated at a few volts above threshold to reduce the probability of "double counts". A cylindrical lead shield 1 inch thick reduced the background rate of this counter to about 7 counts, per minute. 6. To reach the sensitive volume of the inefficient counter, particles must pass through two mica windows, approx-imately 5 milligrams per square centimeter. From Fermi (11), the energy loss of 1 MeV electrons in air i s 1.7 MeV per gram per square centimeter. Assuming a stopping number relative to air of 1.5 for mica, the energy loss i s 0.013 MeV, or about one percent. 7. Since energy i s lost in the window of the counter, there i s some probability that an electron w i l l be ejected from the window into the counter, causing a discharge when electro* the primary^would not i t s e l f do so. About 7000 eV (1 the 2" loss calculated abojvje) i s lost in the window, and, according to Williams (6), about 45% of this produces ionization. Also very few electrons are ejected with kinetic energy greater than 21. Assuming ah average kinetic energy of ;1.5I> and a value of,80 (reference 15) volts for I (that of air) we have, for the number of. secondaries ejected by one primary: n = 7000 x 0.45 = 16 (19) (1.5+1)80 These sixteen electrons have energy about 120 ev", a range in which energy i s rapidly given up to l a t t i c e vibrations. We conclude that the probability of one of these being hit close enough to the inner window surface to escape i s negligible. There remains to consider the few high energy secondaries (a number so small that contribution to energy loss i s considered negligible in a l l theories). In a total of 1800 centimeters of track in air, (p.s.i. -22) Williams and Terroux (12) found evidence of only 51 secondary electrons of energy greater than 10,000 ev. (even at this energy few electrons w i l l leave the window, since most w i l l have a direction unfavourable to ..escape). Hence the fraction of ionizing collisions in which the secondary electron has energy greater than 10,000 ev. i s : n 1 = 51 - 0.0013 1800 x 22 Then from (19), we expect about 0.0013 x 16 = 0.021 energetic secondaries per primary electron. These secondaries w i l l have effect only in those cases when the primary electron does not init i a t e a discharge, a fraction (l-£). If £- = 0.75, this contribution to w i l l be 0.25 x 0.021 = .005, or 0.7% of 6, of the order of magnitude of the standard deviation. The actual contribution w i l l probably be much smaller than this, since only a few of the energetic secondaries w i l l be produced in a direction and position favourable to entering the counter. 8. Two 2000 volt regulated power supplies are connected to potentiometers in the head amplifier chassis, allowing con-tinuous variation of counter voltages. The head amplifiers are single stage plus a cathode follower, (the cir c u i t diagram si1* given in reference ( 1 0 ) ) . The output pulses, from the amplif-iers activate separate channels of the coincidence mixer, the individual and coincidence counts being recorded by three Dynatron model 200 A decade scalers. A Gossor model 1035 double-beam oscilloscope is used to monitor the head amplifier outputs. Figure (2) i s a cir c u i t diagram of the—coincidence mixer. Only, one channel, (A) i s shown. Channels B and C are exactly similar. When properly adjusted, the mixer, i s i n -sensitive to pulse height variation over a range from 5 volts to 100 volts. Except i n the case of the positron experiment, the mixer was operated as a double coincidence by putting one pulse in two channels. Each day pulses from a pulse generator were fed to a l l three mixer channels to check loss of counts by the mixer or scalers. Resolving time of the mixer was measured by means of a tr i p l e pulse generator giving three pulses of variable spacing in time. The result, 0 .66 micro-seconds, agreed with that from counting accidental coincidences and solving for T in N acc. = 2NlN2 T. CHAPTER. VII Preliminary Investigations During the i n i t i a l testing, and in the course of the f i r s t actual runs, several facts, pleasing and otherwise, were discovered: 1. Counters of the same f i l l i n g but different path length gave the same value,within standard deviation, for the right side of equation (16), showing that path length estim-ates were correct. 2. When corrected for dead-time loss, a counter f i l l e d with 9 centimeters of argon and 1 centimeter of alcohol was 99.9% efficient (expected value 99.99%). From this i t would seem there are no unforseen losses of coincidences. 3. Diaphragms, ^ inch diameter, placed over both windows of the inefficient counter, had no significant effect on efficiency. Since these r e s t r i c t possible variation i n path length, i t i s permissible to use the directly measured path length rather than calibrate the counter with known gases. 4. Although accuracy c r i t e r i a derived i n (Gh.V, 3) show that 6 should be very small, this could not be attained i n practice. A certain pressure must be maintained in the counter for proper Geiger operation and the p.s.i. of most quenching agents is large. Values of € used ranged from 0.6j> to 0.85. 5. Figures (3) and (4) show plots of equation (16) for mixtures of helium and ethylene, and neon and ethylene. The fact that a straight line is obtained justifies the assumption that photons do not count, and corroborates the calculation of the contribution to efficiency from the counter windows. 6. When several anomalously low values, of e were measured, investigation showed € to be a smooth function of the voltage applied to the counter. This i s plotted, with the Geiger plateau, in figure (5). From this plot i t seems that a rise i n efficiency, not multiple counts, accounts for the plateau slope over most of the plateau of counters with these particular f i l l i n g s . It was necessary to increase the voltage until efficiency no longer increased appreciably to obtain consistent values for the right side of (l6). This restricted s t i l l further the possible values of £, since the counters required higher, concentrations of quenching.agent to operate, at higher voltages. It seems l i k e l y that this effect is caused by negative ion formation (a molecule captures a secon-dary electron.). Presumably negative ions do not i n i t i a t e a discharge, or at least delay the discharge beyond the coincid-ence resolving time. The probability of negative ion formation is a property of the gas, and decreases as E increases, where p E i s electric f i e l d strength and p i s the total pressure of gas in the counter ( ^ f ) . 7. Counter l i f e and plateau length varied with f i l l i n g . Most f i l l i n g s had l i f e longer than the experiment (about 10^ counts), although some were shorter. Plateaus varied from £0 v to 500 volts. Those shorter than 100 volts were not useful, since <£ was s t i l l increasing at the end of the plateau. Those of $00 volts were not duplicable, and did not remain as great as this for very long. In almost a l l cases, i t was necessary to "age" the counters, that i s , increase the voltage in steps of 25 volts, allowing 10^  counts between each step. I f this was not done, a sufficiently high voltage could not be reached. 8. To overcome the d i f f i c u l t i e s l i s t e d in sections (6) and (7), two quench amplifiers were built* These, upon being triggered by a Geiger pulse feed back a 350 volt, 300 micro-second negative pulse to the counter. Plateaus of a typical counter with and without this quenching action are shown in figure (6). Unfortunately, this circuit i s sensitive to input pulse height, in that the time-delay between input and output pulse could be as great as 2 micro-seconds. Since the coincidence resolving time i s 0.66microseconds, coincidences w i l l be lost, unless the input pulses to .each amplifier are of the same height. This is d i f f i c u l t to achieve, since the inefficient counter must be operated at the top of i t s plateau, the bell counter at the bottom. 9. For the same reason, a quench unit i-^"} capable of quench pulses up to 800 volts was built. It too introduced a.time-delay, though not one dependent on.input pulse. Hence a time delay device i n the bell counter cir c u i t might enable use of this unit. Pure inert gases could then be investigated directly, since a pulse of such size can quench pure argon counters. 10. In measuring the p.s . i . of positrons, i t was found that annihilation radiation contributed so strongly to the background that the method as so far discussed was not usable. By placing another two-windowed counter in front of the inefficient counter, and measuring the tri p l e coincidence rate, and the double coincidence rate of the front counter and b e l l counter, the efficiency of the middle counter can be found. It i s the ratio of the two rates. Background i s eliminated by a this method. When Ra E source i s used, the double and tri p l e coincidence methods give the same value of & , confirming the validity of the corrections applied to the double coincidence method. CHAPTER VIII  Results and Conclusions 1. A "least squares" f i t of the points shown in figure (3) to equation (16) gives the valued 5.4-7 ±.09 and 39.7 + 0.9 ion pairs per centimeter per atmosphere for helium and ethylene respectively. .-The points of figure (4) give the solutions 11.6 t 0.4- and 43.7 t 2.8 for neon and ethylene respectively. The larger standard deviations of the second set of values are due to poorer s t a t i s t i c s . The weighted mean of the two values for ethylene i s 40.1 * 1.0. 2. Using these values, the p.s.i. values of argon and ethyl alcohol were found by direct solution of equation (16). Two such values were found in each case, 29.1 and 30.6 for argon, 61.4 and 6l.7 for ethyl alcohol, giving values 29.8 * 1.5 and 61.5 - 1.5 respectively. Only small pressures of argon could be used, since the counters contained ethylene for quenching and helium to raise the pressure, making the efficiency too high for accuracy. This explains the difference in values for argon. 3. The table (figure (7)) compares these results with those of other investigators. Agreement is f a i r , with the exception of alcohol. Both experimental values for alcohol are much larger than the values 33» obtained by extrapolating through points of p.s.i. versus number of electrons, and 42 obtained by adding the p.s.i.. of chemical constituents. 4. Figure (8) i s a plot of I n ( l - 6)(proportional to p.s.i.) versus energy of electrons. A classical "1" curve, 27 obtained by equating the value for the lowest energy to k , is shown for comparison. Unfortunately, the counter broke down before the.minimum of the curve was reached, and time did not permit another run.. j>. The efficiency of a counter, by the tri p l e coincid-ence method (Ch.VII,. 10) was found to be .786 for positrons of .5 MeV energy and .784 for electrons of the same energy. The difference between these values is. less than the standard deviation. Hence, to the accuracy of the measurement, p.s.i. is the same for positrons and electrons. o ; z 3 f Position of Detector, centimeters. Figure 1. Beam distribution from the Magnetic Analyser. . \ /0H I 33 K IOOH ^ 15 K. +325* IT. fig. 2 CIRCUIT DIAGRAM OF TRIPLE COINCIDENCE MIXER Figure J. Graph of equation for mixtures of helium and ethylene. fo so bo 70 90 <fo 100 110 1x0 130 1+0 \so ibo 110 1 to 2k -JL i n (l-fr) JL 273 pl Figure 4. Graph of equation (16) for mixtures of neon and ethylene. Voltage Figure j5- Counter efficiency as a function of voltage. Voltage Figure 6. Counter plateau with and without external quenching. Gas p.s.i. Reference Author Others Helium 5.47 t 0.09 6.6 19 5.9 14 Neon 11.6 * 0.4 12.6 25 Argon 29.8 + -1.5 29.4 14 29.8 22 Ethylene 40.1 + 1.0 -Ethyl Alcohol Vapour 61.5 I 1.5 79 22 Figure 7. Table of Results. 1-bO ln(l-e) Z-5-5-/ • 4 5 1+0 1-35 0-1 O-Z 0-3 ' Ob O-Energy, MeV Figure 8. Variation of p.s.i. with energy. 28 Bibliography 1. Bohr, N., Phil. Mag. 25, 10, ( 1 9 1 3 ) . Phil. Mag. 3 0 , 581, ( 1 9 1 5 ) . 2. Bathe, H.A., Ann. der Physik, 5 , 325, ( 1 9 3 0 ) . 3 . Bethe, H.A., Zeits. f. Physik, 76, 293, ( 1 9 3 2 ) . 4 . Miller, Chr., Zeits. f. Physik, 70, 786, (1931) . Ann. der Physik, 14, 531, ( 1 9 3 2 ) . 5. Bethe, H.A., and Fermi, E., Zeits. f. Physik, 77, 296, ( 1 9 3 2 ) . 6. Williams, E.J., Proc. Roy. Soc, A 139, 163, ( 1 9 3 3 ) . 7. Bethe, H.A., Handbuch der Physik, p.523* 8. Bloch, F., Zeits. f. Physik, 81 , 363, ( 1 9 3 3 ) . 9. Aitken, A.C., S t a t i s t i c a l Mathematics, p.49. 10. Silver, L.M., M.A. Thesis, University of British Columbia, April, 1949. 11. Fermi, B., Nuclear Physics, p.31. 12. Williams, E.J., and Terroux, F.R., Proc. Roy. Soc. A 126, 289, ( 1 9 3 0 ) . -13. Danforth, W.E., and Ramsey, W.B., Phys. Rev., 4 9 , 854, ( 1 9 3 6 ) . 14. Cosyns, M., Bull. Tech. Ass. Ing. Brux., 173-265, ( 1 9 3 6 ) . 15. Bethe, H.A., and Livingston, M.S., Rev. Mod. Phys. 9 , 261-276, ( 1 9 3 7 ) . 16. Williams, E.J.', Proc. Roy. Soc. A 135, 108, (1931) . 17. Corson, D.R., and Brode, R.B., Phys. Rev., 53, 773, ( 1 9 3 8 ) . 18. Hereford, F.L., Phys. Rev., 74, 574, ( 1 9 4 8 ) . 19. Hazen, W.E., Phys. Rev., 65, 259, (1944). 20. Hazen, W.E., Phys. Rev., 67, 269, (1945). 21. Brode, R.B., Rev. Mod. Phys., 11, 222, (1939). 22. Curran, S.G., and Reid, J.M*, Nature, 160, 866, (1937). 23. Silver, L.M., and Warren, J.B., Rev. Sci. Inst., 21, 95, (1950). 24. Healey, R.H., and Reed, J.W., The Behaviour of Slow Electrons in Gases, p.23. 25. Skramstad, H.K., and Loughridge, D.W., Phys. Rev., 50, 677, (1936). -26. Edinburgh Conference on Elementary Particles, Nature, 165, 54, (1950). 27. Gooke-Yarborough, E.H., Florida, CD., and Davey, C.N., J.S.I., 26, 124, (1949). . ' 

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