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The primary specific ionization of gases of positrons and electrons Silver, Lorna Margaret 1949

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THE PRBILARY SPECIFIC MIZATIOir IK GASES Of P0SITR01TS AED ELECTRONS Lorna Margaret S i l v e r A Thesis Submitted I n P a r t i a l F u l f i l m e n t Of The Requirements For The Degree Of MASTER OF ARTS I n The Department of PHYSICS {$ THE UBIVERSITY OF BRITISH COLUMBIA A p r i l , 1949 ACKNOWIJCDGM&NTS . This work has been made possible by the award of. a National Research Council Bursary to the author, and by a National Research Council research grant. The author has had the privilege of using some of the equipment and f a c i l i t -ies of the Nuclear Physics Techniques Laboratory set up with funds provided by the Defense 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 given by Mr. W. Pye and Mr. A. Fraser i n the fabrication of the counters and vacuum system used i s grate-f u l l y acknowledged. TABLE OF CONTENTS. Chapter Page I. Abstract 1. II. Theory of Specific Ionization 3 . III. Methods of Measurement of Specific Ionization and Available Results. 9• IV. Experimental Arrangement A) General Scheme 14. B) Design of the -ray Energy Analyser ...... 15. C) Choice of Sources 17. D) intensity Considerations 19. E) Counter Design 19* F) Counter Construction and F i l l i n g Techniques 22. G) Electronic Equipment 24. V. . Results 25. Appendices 1. The Energy Transfer Relations 32. 2. Magnet Design 55. 3 . Magnet Performance 35* 4. Magnetic Refocussing of Electron Paths 36. Figures 1. Impact Parametec in a Coulomb Field 4. 2. Ionization - Energy Curve 8. To follow page 3. layout of Apparatus , . . . 16. 4. Triple Counter 22. 5. Rectangular and Square - Counters 22. 6. Schematic Electronic Arrangement 25. Table of Contents ( c o n t . ) . F i gures To f o l l o w page 7. C h a r a c t e r i s t i c Curves of Various Counters .'. 25. 8. Magnetjfior Spectrometer .. 35. 9. Magnet C a l i b r a t i o n at High F i e l d s 35. 10. Magnet C a l i b r a t i o n at Low F i e l d s 3$. P l a t e s 1. Layout of Apparatus 16. 2. E l e c t r o n i c Counter T e s t i n g Equipment 24. 3. Dead Time Measurement • 24. 4. Spectrometer and E l e c t r o n i c Equipment 25. C i r c u i t Diagrams Page 1. S t a b i l i z e d Power U n i t 29. 2. Head A m p l i f i e r . . . . . . . . . 3 0 . 3. Quench U n i t f o r S e l f Quench Geiger 31. B i b l i o g r a p h y 59. 1M_ A B S T R A C T Theories of P . S . I . * produced "by electrons passing through gases show that one would expect the number of primary ion p a i r s formed to vary with the electron density i n the gas and with the mean i o n i z a t i o n p o t e n t i a l of the gas. to vary inversely as the square of the v e l o c i t y of the electron at low energies reaching a minimum value approximately at a k i n e t i c energy equal to the res t energy and to be independent of the sign of the beta p a r t i c l e producing the i o n i z a t i o n . I t i s consequently of i n t e r e s t to obtain measurements of the P . S . I , of beta p a r t i c l e s at energies at which i t i s a minimum i n various gases which are used f o r f i l l i n g counters and i o n i z a t i o n chambers including hydrogen, helium, neon, xenon, methane, chlorine and other quenching vapors such as methyl chloride which may be-come of p r a c t i c a l concern f o r counters designed to operate over a wide temperature range. Present data on P/afS.I. of electrons and mesons i s l i m i t e d to but few gases and the r e s u l t s are not i n good accord. As mentioned, the P . S . I , i s independent of the sign of the charge of the i o n i z i n g p a r t i c l e and, since a l l the i n d i r e c t evidence and the p r i n c i p l e of conservation of charge indicates the equality of the charge on the positron and negatron, i t would be expected that the values of the P . S . I , would be i d e n t i c a l f o r the two part-i c l e s . However while i t i s known that the value of e/m f o r both p a r t i c l e s i s i d e n t i c a l to within 2%, there i s some possible theo-r e t i c a l i n d i c a t i o n that t h e i r masses might be s l i g h t l y d i f f e r e n t . * The primary s p e c i f i c i o n i z a t i o n w i l l hereafter be denoted by P . S . I 2. Moreover the only direct estimation of the value of e + i s the measurement of P.S.I, from the original cloud chamber ob-servation of a cosmic ray positron by Anderson4which established the charge equality of e + and e" to within 20%. Thus i t appeared of some fundamental importance to compare with precision the P.S.I, of both positive and negative electrons of similar velocities in a gas of high atomic number such as neon and a gas of low atomic number such as helium. Finally i t was hoped that the apparatus set up would be suitable for an investigation of the relation between the P.S.I, and velocity of the electron especially in the r e l a t i v i s t i c reg-ion in which the data i s very meagre. This w i l l need high en-ergy beta sources (e.g. B 1 2) which w i l l "become available when the U.B.C. electrostatic generator i s in operation. Apparatus has been set up to determine 13ae P.S.I, of elec-trons i n various gases by determining the inefficiency of a Geiger counter f i l l e d with gas. To eliminate the difficulty, of a variable path length of the particle through the ordinary cy-l i n d r i c a l counter, rectangular and square envelope counters with thin windows have been constructed. The presence of a large thin window, even when a conducting surface, has been found to affect the spread of the discharge and results in the appearance of two size pulses analagous to the effect of an insulating bead oh the centre of the wire. Thus, contrary to the usual theory of Geiger operation, i t seems that the spreading of the discharge does in-volve a cathode mechanism i n this design. In order to select beta particles of homogeneous energy from the radioactive source, a small wedge shaped magnetic spec-trograph has been b u i l t . 3. The counter i n e f f i c i e n c y i s d e t e r m i n e d "by p a s s i n g t h e 'beta p a r t i c l e s through the i n e f f i c i e n t counter into a 100% e f f i c i e n t counter operating at normal pressures» and recording the coincidence rate as a f r a c t i o n of the " e f f i c i e n t counter" r a t e . C o 5 6 was chosen as the most suitable positron emitter* and has been prepared i n the Berkeley cyclotron by the re" r e a c t i o n . RaE has been used as a negatron emitter. I I . THEORY OF SPECIFIC IONIZATION The P.S.I, i s defined to be the number of primary ion p a i r s formed per cm. length of track i n the gas, reduced to U.T.P. Two . other si m i l a r quantities sometimes measured are the t o t a l s p e c i f i c i o n i z a t i o n ; i . e . , the t o t a l numbers of ion p a i r s (primary, secon-dary, t e r t i a r y , etc.) formed per cm. at N.T.P., and the probable s p e c i f i c i o n i z a t i o n ; i . e . , the number of primary ion p a i r s plus the number of secondary ion p a i r s having a s p e c i f i e d upper l i m i t to t h e i r energy which are formed per cm. at 3ST.T.P. J.J.Thomson has calculated the energy transfer Q r e s u l t i n g from a c o l l i s i o n of a p a r t i c l e of mass M, k i n e t i c energy T, and charge ze, and an electron of mass m and charge e, when the el e c -tron suffers a d e f l e c t i o n through an angle e. His expression de-r i v e d c l a s s i c a l l y i s (flt<»f~ (See appendix 1.) The closeness of c o l l i s i o n can be s p e c i f i e d by the impact parameter p: 4. F* ffig.l. Impact Parameter i n a Coulomb F i e l d . Prom conservation of momentum, i t follows that f o r any p, ca e = V 4 t — x e ) therefore (See appendix 2.) where ze - charge on the "bombarding p a r t i c l e v • incident v e l o c i t y T l m PVk) T. An i o n i z i n g event r e q u i r i n g an i o n i z a t i o n energy W w i l l occur whenever P»* = ( ^ j - - iX^p^:} T' » W and i f then TW '' ,The number of electrons which w i l l be removed from the atoms i n 1 cm. of track ( i . e . , the P.S.I.) w i l l equal the p r o b a b i l i t y that the i o n i z i n g p a r t i c l e w i l l come within radius p 0 of any electron, m u l t i p l i e d by the number of electrons per cc. i n the gas; i . e . , . . . . . . . . . . . . ( i ) 5 . Thomson's formula therefore s t i p u l a t e s that; (1) For a given incident v e l o c i t y , P.S.I, i s Independent of M. (2) P.S.I, i s proportional to v"1 (3) P.S.I, i s proportional to z xe 4 ( 4 ) P.S.I, i s independent of the sign of ze. (5) If.S.I. i s proportional to (M/tef>)2 f o r i o n i z i n g p a r t i c l e s of mass M selected by t h e i r Hf i n a magnetic momentum analyser. The equality of the magnitude of charge on positrons and negatrons was f i r s t established to a rough degree of approxim-i .. 'ne-at ion by Anderson by a comparison of the s p e c i f i c i o n izations of / 3 + and pr of r e l a t i v i s t i c energies such as occur i n cosmic rays. A l l other evidence f o r t h i s equality i s e s s e n t i a l l y i n -d i r e c t and assumes the conservation of charge. The equality of B/m f o r and p' has been established by Zahn and Spees 7to an accuracy of 2%. Barnothy 3has suggested that t h e o r e t i c a l l y the mass of the positron i s 0.354$ l e s s than the mass of the electron due to the difference i n sign of t h e i r mass defects, and a care-f u l examination of the r e s u l t s of Zahn and Spees reveals that i s s l i g h t l y greater than e 7 w . A p r e c i s i o n measurement of fym to t h i s accuracy would, i f t h i s divergence i n s p e c i f i c charge were established, be strong evidence of the exact equality of charge. Since the s p e c i f i c i o n i z a t i o n i s proportional to the square of the mass f o r a given v e l o c i t y , or rather a given Hf , a comparison of P.S.I, f o r positrons and negatrons w i l l give d i r e c t evidence f o r the equality of mass and hence charge of the two p a r t i c l e s . Be the has derived an expression f o r the P.S.I, by a s c r i b -ing hydrogen-like wave functions to the atomic electrons, and 6. r e s t r i c t i n g the v e l o c i t y of the bombarding electron to he much greater than the v e l o c i t y of the atomic electrons i n the Bohr or b i t s * and much l e s s than the v e l o c i t y of l i g h t . His formula is$ p . s . i . - ^ 2 L £ ! ' ( * w ) ( l n ^ E ) . . . . . . . . . . ( i i ) T ' W where W = 13.5 ev. f o r hydrogen and ¥ (Z) s 13.5 Z f o r other gases. The value f o r W, the average e x c i t a t i o n p o t e n t i a l of the whole atom, can be found more accurately empirically from stopping power data than t h e o r e t i c a l l y . The t h e o r e t i c a l expression given lay Livingston i s : Log (¥) s ( l - ^ ' ) l o g I'+^LgJ log I K where I K * average e x c i t a t i o n p o t e n t i a l of the K s h e l l = 1.103 Z^eff. R I J and Ry = i o n i z a t i o n p o t e n t i a l of the hydrogen atom. Z " 0.3 = e f f e c t i v e nuclear charge of the K s h e l l . I '» average e x c i t a t i o n p o t e n t i a l of the electrons out-side the K s h e l l . Z - 1.81 • " e f f e c t i r e " number of electrons. To describe i o n i z a t i o n by r e & a t i v i s t i c p a r t i c l e s , B e t h e H a p p l i e s an ex&ot quantum mechanical treatment to the energy l o s s prob-lem. He considers the d i s t r i b u t i o n of Q, into e x c i t a t i o n and ion-i z a t i o n energies, which v a r i e s with the atom bombarded, and he 7 . shows that -dT/dx » A x ( l n E +- In £i - y ) ... ( i i i ) where K depends inversely on the e f f e c t i v e i o n i z a t i o n p o t e n t i a l of the gas and on whether i t i s primary or probable s p e c i f i c ion-i z a t i o n which i s being described. For P.S.I, i n hydrogen, K ? 10 5 A B 4z2 e4HZ/mc 2 The r a t i o (dT/dx)pri P.S.I. • V 0 a average energy expended per primary ion p a i r produced. V 0 i s a function of the nature of the gas only, and i s independ-ent of the energy and nature of the i o n i z i n g p a r t i c l e . Values f o r d i f f e r e n t gases are given i n Table 1. Tzvble 1- Vo f»»- Different Gates. (revs Vo R o f f e n c e Air-A i r Prot o n A i r j r . ' i A i r i i Hx II 31.0 Ife u ii 3 / - 0 I II « He 1 II ' XO A 1 ) A £ lect row D.O /7 f Kr Alpta ZZ.O Xo Xe II /•3 IX 8. When changed to give P . S . I . , equation ( i i i ) "becomes; P . S . I . : S H Z l ^ M ^ M * W M (iv) . n v v 1 L '~r ' * J where K i s a constant which depends on the gas being ionized, and C depends on the i o n i z a t i o n p o t e n t i a l of the gas. A p l o t of (iv) i s given i n P i g . 2 l o 3 to* fp< /Pu io7 i°* P i g . 2 . Ionization-Energy Curve. The r e l a t i v i s t i c formulae d i f f e r s i g n i f i c a n t l y from the n o n - r e l a t i v i s t i c only when the energy i s several times r e s t en-ergy. The r e l a t i v i s t i c increase i n the s p e c i f i c i o n i z a t i o n i s due to the increasing contraction of the e l e c t r i c f i e l d of the p a r t i c l e toward a plane perpendicular to i t s motion, thus increas-ing the impulse given to atomic electrons by p a r t i c l e s passing at some distance from the atomic centre. An increase i n Rf> by a 9. f a c t o r of 5.104 only doubles the minimum value of the s p e c i f i c i o n i z a t i o n . I l l * Methods of Measurement of S p e c i f i c Ionization and Available Results. A) General Scheme. The primary s p e c i f i c i o n i z a t i o n of electrons, alpha p a r t i c l e s , protons and mesons has been measured by two methods. In the f i r s t a cloud chamber i s used i n which the expansion i s arranged to take place shortly before the passage of the i o n i z i n g p a r t i c l e through the chamber, so that condensation occurs before the ions d i f f u s e an appreciable distance. The secondary electrons of low energies and correspondingly short ranges thus give r i s e to a c l u s t e r of c l o s e l y spaced ions which appears as a blob about the primary ion p a i r . Counting the numbers of blobs per cm. gives the primary s p e c i f i c i o n i z a t i o n . The energy of the p a r t i c l e is-found from a measurement of the curvature of the track i n a magnetic f i e l d . Inaccuracies a r i s e from multiple scattering i n the gas at low energies, and by the uncertainty i n estimating the plane of the track. The amount of water vapor present i s hard to estimate* and hence also introduces an error. Further, the blobs may over-lap, be of various sizes, and "be i r r e g u l a r l y spaced, thus making accurate counting d i f f i c u l t . The second method consists i n measuring the e f f i c i e n c y of a Geiger counter; i . e . , i n f i n d i n g the p r o b a b i l i t y that at l e a s t 1 0 * one ion p a i r i s created i n the gas "by the passing p a r t i c l e . The e f f i c i e n c y may he calculated as follows: Assuming a l l path lengths i n the counter are the same* and equal to i cms. then the average number of ion p a i r s pro-dueed i n the tube 1st n - at p. where s • primary s p e c i f i c i o n i z a t i o n p = gas pressure i n atmospheres. Let coU)s p r o b a b i l i t y that the p a r t i c l e goes a distance i without producing an ion p a i r . Then u>(«U) s<L)0s p r o b a b i l i t y that the p a r t i c l e goes a distance <U without producing an ion p a i r . Therefore u 4 ) l w U ) s p r o b a b i l i t y of i t going a distance U+<U) without producing an ion p a i r Applying the boundary condition , and integrating, we get s c" s P Therefore e f f i c i e n c y • c l i ) * 1- e I f the geometry i s such that there i s a continuous d i s -t r i b u t i o n of path lengths, i t i s possible and necessary to r e v i s e the expression f o r the e f f i c i e n c y as a function of (sp). The p r e c i s i o n i s l i m i t e d i n that the c a l c u l a t i o n s assume that ( 1 ) the presence of one ion p a i r i s s u f f i c i e n t to i n i t i a t e a discharge (which, i s believed to be true i n a properly operated Geiger counter), and ( 2 ) that neglegibly few e n t i t i e s capable of exc i t i n g a discharge are ejected by the p a r t i c l e s from the inner surface of the counter c y l i n d e r . To check whether or not condition ( 2 ) i s s a t i s f i e d , an e f f i c i e n c y measurement could be made using a gas filllng^known P.S.I, and by checking the form of the func-t i o n a l r e l a t i o n by varying the f i l l i n g pressure. 01. ti Ramsey has pointed out that a single segmented court er could be used to measure the F.S.I* By applying different volt-ages to different segments* one segment can be operated in the proportional region giving a current proportional to the number of ion pairs formed, while another segment i s operated in the Geiger region giving a current which i s proportional to the number of ion-izing particles passing through i t . The ratio of these two curr-ents i s proportional to the P.S.I, and i s independent of the number of particles i n the beam. To obtain the absolute value of P.S.I, for any gas, a calibration of the apparatus must be carried out using a gas of lenown P.S.I. The results of several investigators are given in Table 2 . Table 2. Available Data \. Cloud Clqtunlaeir. P.S.I (NTP) W i l l i A wis %"Xerrou.x ~ J O 4 e ' / c £T.X \\ •< ~ \0L A »v ~ I0 q Corner-*- * Biroit^ Air C?) tt--is-We Elee-fc L.L •• He Mesons >v>" LS-N* £\ectr e « t>co-aioo Kcv/. /9 l| M He II tu>-7.io0 Ke»/ ta.L J. Counter Eff,'cienc J)ev»vfi>r"tk * Ramsey Mr M«a^ «.» * £ It i t row -? 11 « 7 Cos ^ t\S  7 A .. f ? •II He I I " ? sr.l ii It. 1 * il ? Lt> t 0.2-Curt-fc.^ * Reic l Elf cty>»\f « > . ^ M e v . 7? i . •« A M I I *s-IS ft I I 12. Williams and Terroux claim an error of 2% i n t h e i r measurement of Hp, and an error of 5% due to the presence of water vapor and other gas impurities. They estimate that the error i n judging the number of blobs per cm. produced by f a s t -electrons i s I n s i g n i f i c a n t compared to the error of the f i r s t two causes. For slow electrons the method i s very inaccurate be be-cause of the s c a t t e r i n g . They f i n d the v a r i a t i o n of P.S.I, with v e l o c i t y can be given by - \.S tO.T-P.S.I. a 5.2 /B f o r hydrogen. P.S.I. = 22 /?~ M ±*"* f o r oxygen. Their r e s u l t s show that equation ( i ) predicts the correct order of magnitude f o r P.S.I, but t h e o r e t i c a l values are s i x times lower than experimental. E . J.Williams^found that equation ( i i ) gave values w i t h i n 10/£ of the experimental values f o r electrons having p a 0.50, 0.75 and 0.96. Kunze d i d not f i n d the expected increase of P.S.I, with T e l o c i t y at energies greater than 2Hev«, nor d i d Anderson?' who ob-tained a value of 31 ion p a i r s per cm. f o r energies greater than 1 0 ' ev. As BrodeVint's out. t u . may be due to an error in the operation of the cloud chamber, giving a r e s u l t which i s too low by a f a c t o r of 2. This same mistake was made by Corson and Erode and i s due to the f a c t that they were observing condensation on pos-i t i v e ions alone, instead of on ion p a i r s . Hazen quotes a probable error of 1.6% f o r electrons and li7/£ f o r mesons. This covers an estimation of the percentages of alcohol and water vapor present i n the chamber. 13. Skramstad and Loughridge estimate that the r e s o l v i n g power of the observer*s eye l i m i t s the accuracy to 10-15# f o r Bfg. and 7-10^ f o r B e, depending on the v e l o c i t y of the electron. They did not f i n d an increase of P.S.I, with r e l a t i v i s t i c veloc-i t i e s . Their r e s u l t s are expressed as ... ' P.S.I. » 19 f o r nitrogen. P.S.I. = 12.6f h* s ± 9''*' f o r neon. They also observed a few tracks i n oxygen, two or three of which were d e f i n i t e l y due to positrons and others to electrons. The r e -su l t s were indistinguishable i n the two cases, and agreed with the values of Williams and Terroux. The r e s u l t s of Danforth and Ramsey, Cosyns and Hereford, using the counter technique, a l l give a value f o r the P.S.I, of a p a r t i c l e of E/mc 2 * 20, where E i s the t o t a l energy of the p a r t i c l e , which i s an electron i n the case of Hereford and a cosmic ray par-t i c l e i n the other cases. For low energies, Hereford*s r e s u l t s follow c l o s e l y Bethe*s t h e o r e t i c a l curve, the minimum l i e s below the t h e o r e t i c a l curve, and there are three experimental points to indicate that the P.S.I, does increase at r e l a t i v i s t i c v e l o c i t i e s . Hereford*s r e s u l t s appear-ed i n the September 1948 issue of The Physical Review, sometime after the present experiment had begun and he used an experimental set up very similar to the one used by the author, but Hereford.has used c y l i n d r i c a l glass envelope counters with graphite cathodes. The majority of the r e s u l t s quoted i n the l i t e r a t u r e are not i n p a r t i c u l a r accord, which would suggest that the p r e c i s i o n of the cloud chamber has been overestimated. The theory has been checked 14 and v e r i f i e d most c l o s e l y i n the region of the minimum of the ionization-energy curve. IV. Experimental Arrangement. A) General Scheme. In t h i s research the primary s p e c i f i c i o n i z a t i o n of negatrons and positrons i s obtained by measurement of the i n -e f f i c i e n c y of a Geiger counter operating at a low pressure of the gas under in v e s t i g a t i o n . E s s e n t i a l l y the method adopted i s i n -tended to give a d i r e c t comparison of the primary s p e c i f i c ion-i z a t i o n of /3fand .p~ of various v e l o c i t i e s . For t h i s purpose a small magnetic analyser has been set up, the s e l e c t i o n of either ft* or p>~ being made by r e v e r s a l of the f i e l d d i r e c t i o n while a l l other experimental conditions remain unchanged. This method obviously can be applied to study the v a r i a t i o n of P.S.I, with the energy of the bombarding p a r t i c l e and with the nature of the gas through which the p a r t i c l e passes. The gases i t i s proposed to study include argon, helium, chlorine, hydrogen, neon, and quenching vapors such as alcohol, methane and methyl chloride, while the energy range available f o r i n v e s t i g a t i o n i s from 200 Kev. to 1.5 Mev., the lower l i m i t being set by the energy spread intorduced by the mica windows, and the upper l i m i t by the sources at present obtainable. 15 . B) Design of the fs -ray Energy Analyser. The magnet used i s a l/& scale model of the deflection magnet designed for the If .B.C. Van de Graaf generator, hut with different pole pieces to provide a3/4 i n . gap and wedge shaped f i e l d . It i s capable of producing f i e l d s up to )%om gauss over the area of the wedge,i.e., 4 7 sq. cms. Details of the de-sign and performance are given in Appendices 2 and 3. In add-it i o n to i t s simplicity, the main virtue of wedge refocussing i s that i t enables the velocities of the electrons to be analysed without the deflecting magnetic f i e l d straying over into the regions in which the electrons originate and where they are de-tected. Further, the yoke provides some shielding of the detector and the geometry and distances are such that excellent shielding from gamma rays and annihilation radiation from the source can be achieved by use of lead blocks, while s t i l l maintaining a reason-able solid angle and counting rate. The spread, or departure from perfect focus i s given by S • a#c 2sine (See Appendix 4 ) . where, for the wedge used, a = 30 cms. - distance from wedge apex to source. O a 21° • one half the wedge angle, z 5° = one half the collection angle, whence, S = 0.09 cms. -This means that a source 1 cm. wide w i l l have an image of 1.09 cms. which i s just less than the counter window width. The dispersion, or the a b i l i t y to separate two different velocities, as measured by the distance between the points at which 16* central rays corresponding to the two velocities would focus, i s shown to be -D s 2a sine Aj- (See Appendix 4). If we take D s - 0 #6 cms. = window width, then s tD/(2a s i n e ) = ±D/21,48 Now ^ =±fcp/p »±l/2 ( E/E3) =^0.6/21.48 Therefore i &E/E = 11.2/21.48™= £ 6#. Thus, i f the electrons were uniformly distributed in velocity up to the maximum velocity of electrons from the source, the magnet should select a l l those in a 6% band, i.e., 6 i n 100 particles •would enter the counter. The vacuum box of the spectrometer i s made of 3in. by 1 i n . brass wave guide tubing which was cut and bent to a width of " A tin. in order that i t f i t between the pole pieces. The sources are placed on aluminium trays which f i t snugly into a hole in one end plate. A 1/2 i n . diameter mica window in the other end plate serves as exit s l i t f o r tiie electron beam. A lead baffle placed next to the exit flange serves to cut down the amount of scattered radiation i n the beam arising from Compton and photo-electrons e-jected from the walls of the vacuum box by gamma rays from the source and from annihilation radiation from positrons stopped in the walls. Lead blocks are set up to prevent direct gamma rays from the source entering the counters. The general layout of this apparatus i s shown in Fi g . 3 and Plate 1. 17. C) Choice of Sources. RaE, with an Emax of 1.17 Mev. and half l i f e of 5.0 days, was chosen as negatron source owing to i t s a v a i l a b i l i t y . Both pure sources, prepared from RaD by electrochemical deposition on a nickel surface after removal of RaF by a similar electro-chemical deposition on silver, and a source of RaD i t s e l f i n the form of chloride evaporated to dryness on a mica sheet have been used. For purposes of this experiment the alpha emission from RaF and sof beta emission from RaD i t s e l f are not harmful. Reasonably thin sources were used, which were deposited on an area of about 1 cm. diameter, and thick backings. The choice of a positron emitter for these experiments was a d i f f i c u l t one, since there are relatively few positron emitters with Emax. greater "than 1 Mev., s t i l l fewer of these have an adequate half l i f e to be useful for these experiments In Vancouver. Further owing to the ready ava i l a b i l i t y of sources from the Chalk River Pil e i t was preferable that the source should be producable by a neutron reaction in relatively high specific activity. One of the positron emitters producable in a p i l e Cu64. from Cu 6 S(n»y)Cu 6 4 reaotion, has Emax. of 0.66 Mev. and a half l i f e of 12.8 hours. A considerable fraction of the active nuclei decay v i a f emission but the main objection to using this material as source was the cost of continued transport across Canada. Some Zn65 was prepared i n the Chalk River P i l e i n the summer of 1948, while the author was there, by the Zn 64( n,y)zn 6 5 reaction, "but on taking an absorption curve i t was evident that the ratio of Zn6t» nuclei which decayed by emitting a positron to those which 18. decayed "by K capture and emitted a 1 Mev. *ray was in the region of 1 i n 2 0 0 . This source only provides positrons of Emax. of 0 . 4 Mev., hut the half l i f e of 2 5 0 days would have been very suit-able. Owing to the high ratio of gamma rays to positrons this source was not used. Consideration was then given to sources which could be prepared with the aid of a cyclotron. Of these the following were considered: £ o ix r t e Pre p& rist 'i • r T w 0.77 H&V 4,5" <Aivjs L o w E »HI\X 72 s G o o J. 3.1 Mev. WrS. Ty^_ " too s k o r t O.S8' Y[ev. Lrf>UJ E rwjxy 1.0 ^eV. | .0 |VW' I t AN^S E mix ^ d l i ] y U u K Co 0 5 was chosen as the positron emitter. Through the kind-ness of Dr.Hamilton, who i s in charge of the 6 0 i n . cyclotron used at Berkeley for trace preparation, a mtllicurie of Co 5 6 has been prepared for use in this experiment. Sinoe the range of the 25 Mev. deuturons from the Berkeley 60 i n . cyclotron used for the bombard-ment of the iron i s small, the Co 5 6 w i l l be concentrated in a thin surface layer of the target disc, i t has been shown that l/z of the atoms decay by K-capture. The fi* spectrum 1B believed to be simple, and therefore the momentum-number distribution can be 19. given by a Fermi p l o t : i . e . , the p r o b a b i l i t y cj(6,I t It )-=Kf(£'--lK(£ e-£ ) where £=EElectron/m 0c 2, £<>a Eniax/ni 0o 2 From t h i s , the average energy can be shown to be approximately 650 Kev. D) Intensity Considerations. , The wedge magnet i n use has the c o l l e c t i o n angle i n one plane of 2 / l l radian. In the other plane the angle, as l i m i t e d by the ex i t window which i s 1/2 i n . at a distance of 28 i n . , i s approximately l/56 radian. Thus the o v e r a l l s o l i d angle sub-tended by the counter at the source i s (1 / 4 T T ) (1/56) (2/11) = 1/3872 Hence a m i l l i c u r i e source of C o 5 6 can be expected to give (3.7) (10 7) (1/3872) (6/100) (l/3) (1/3) = 50 counts/sec, where the f a c t o r s of 1/3 are allowances f o r K-capture and s e l f -absorption i n the source, while a m i l l i c u r i e source of RaE would be expected to give s l i g h t l y l e s s than 450 counts/sec, depending on the thickness. In f a c t with approximately 1/2 m i l l i c u r i e of RaE the counting r a t e at the optimum value of was found to be 170 counts/sec. E) Counter Design. In order to apply the equation f o r e f f i c i e n c y i t i s necessary to determine p r e c i s e l y the value of the path length through the counter, or to evaluate t h e o r e t i c a l l y the average value of  %l1 pertaining to the p a r t i c u l a r experimental arrange-ment. With the wedge analyser described, the d i r e c t i o n of the electrons leaving the ex i t window are within 5° to the normal to the window, i n order to define with some exactitude the path 20. length through the i n e f f i c i e n t counter i t was decided to use a rectangular envelope, and the whole counter design was based oh use of 3 cm* wave guide brass tubing f o r t h i s envelope* This has the obvious advantage over a c y l i n d r i c a l counter that not only i s the distance between the windows known quite c l o s e l y but that t h i s distance can be made quite small - 1 cm* - so that r e l a t i v e l y large values of P.S.I, can be measured with a not too low f i l l i n g pressure, such as occur with gases l i k e argon* Too low a press-ure i s rather undesirable as the s t a b i l i t y of counter performance over a period of time i s l e s s c e r t a i n , the amount of quenching vapor and hence l i f e of the counter i s low. Again i t i s r e l a t i v e -l y easy to i n s e r t windows of 1/2 i n . by 1 i n . i n mica of thick-ness as low as 2 milligrams/sq. cm. on a f l a t brass surface but almost impossible to do so over a c y l i n d r i c a l surface. F i n a l l y a c l o s e l y packed coincidence arrangement i s e a s i l y set up with such rectangular envelopes, and so enable a larger s o l i d angle to be subtended at the source f o r the same counter volume than i s possible with c y l i n d r i c a l geometry. Curran and Reid have investigated some of the properties of rectangular counters. Using a collimated source they found that the e f f e c t i v e counting volume of the counter coincided with i t s geometrical volume. Because of the reduced lengths of paths a-long which the p o s i t i v e ions pro duced i n a discharge t r a v e l to the cathode, i t was expected to observe shorter dead times than found i n c y l i n d r i c a l counters of comparable cross sectional area, and t h i s e f f e c t they v e r i f i e d . There i s a lower l i m i t to the r a t i o of the length of the walls of a rectangular counter which i s imposed by the f a c t that 21. the f i e l d must not be too high i n the short d i r e c t i o n to pro-duce overshooting and yet the f i e l d i n the long d i r e c t i o n must be s u f f i c i e n t f o r an avalanche to occur. Curran and Reid point out that the r a t i o of maximum to minimum f i e l d strengths e f f e c t -ive i n a rectangular counter i s given by - -(my*0) + p1* where f>- 3 wire radius * distance at which m u l t i p l i c a t i o n process begins i s length of short w a l l . For the counters, used i n the present experiment i • 1 cm. f> = 0.01905 cm. hence M » 1.002 One can therefore conclude that tiieee counters should operate comparatively as w e l l as c y l i n d r i c a l . The plateau lengths found were of the order of 60 V o l t s . This i s more than adequate f o r accurate counting when the counter voltage can be derived wrom a w e l l s t a b i l i z e d voltage supply. The power u n i t constructed f o r t h i s purpose (See c i r c u i t diagram page.^9) has a v a r i a t i o n of l/2% f o r a 10^ v a r i a t i o n i n mains voltages, and a f t e r 15 minutes warming up period had l e s s than 1 v o l t i n 2000 d r i f t over the next several hours. Two square section brass counters, one with 3/8 i n . square mica windows and one without, have also been b u i l t , p a r t l y f o r comparison with the rectangular shaped envelope, and show rather better plateau c h a r a c t e r i s t i c s and l e s s "window e f f e c t " (see para-graph "Results"). Ordinary b e l l type counters have been used f o r 22. the second 100$ e f f i c i e n t counter. F u r t h e r , as an a l t e r n a t i v e scheme f o r determining P.S.I*» a t r i p l e segmented counter ( F i g . 4) has been c o n s t r u c t e d t o f u n c t i o n along the l i n e s suggested by Ramsey. This has been op-erated s u c c e s s f u l l y as three counters i n one. I n order to be used f o r a c t u a l measurement of P.S.I., i t s t i l l needs to be s u p p l i e d w i t h an end window, and s u f f e r s from the r a t h e r s m a l l s o l i d angle of e l e c t r o n s i t w i l l accept. F) Counter C o n s t r u c t i o n and F i l l i n g Techniques. Scale diagrams of the counters used are given i n F i g 5. The r e c t a n g u l a r wave guide has the b r a s s end p l a t e s s i l v e r s o l d e r -ed i n t o p l a c e . The Kovar s e a l s and f i l l e r tube are then s o f t s o l -dered w i t h a c i d core solder and a hand t o r c h (gas and oxygen). Care i s taken t o keep the solder c l e a n by w i p i n g i t w i t h a wet r a g before and a f t e r the s e a l s are i n s e r t e d . The c e n t r a l w i r e of 0.005 i n . diameter tungsten, spot welded onto advance w i r e of 0.02 I n . diameter, i s then s o f t soldered i n p l a c e , b e i n g p u l l e d t a u t w h i l e the s o l d e r i s hardening. The counter i s now cleaned by p l a c -i n g i t i n a hot s o l u t i o n of 1, IT. HNO^. G l y p t a l i s f i r s t coated on top of the s o f t solder to prevent i t being corroded by the a c i d . A f t e r the b r a s s i s n i c e l y etched, the counter i s q u i c k l y t r a n s f e r -r e d to a water b a t h , where i t i s thoroughly r i n s e d . F i n a l l y the counter i s r i n s e d w i t h e t h y l a l c o h o l and allowed to dry i n a vacuum d e s s i c a t o r . The next procedure i s t o s e a l mica windows onto the counter. B e s t Ruby mica i s used which has been s p l i t under warm water by a v e r y sharp tungsten needle. The t h i n sheets of mica are examined under p o l a r i z e d l i g h t to s e l e c t those of uniform t h i c k n e s s . The s e a l used i s Gelva V-7, a V i n y l Acetate R e s i n , Fill«r TuLe Tungst en- <J l*cs$ Silver solder G k s s Sleeve. O.0O5" Tungsten. S 0015 " Tungsten Spring Cowto^ cts Glctss Beads Tjrex Envelope. cLiam.. Cu coXkodes. Si l ve r Solder. R e c t t ^ n c j u . 1 evr -E n v e l o p e s : \ x \ **+ brass W a v e c j a i d e t u . b i « < j Wihct-OWS \ " X 2. S^ u^re. Envelopes:\*% U~fr.ss t u b i n g W i rvdows - VjH >• 'ya 1 1 stuF»k.ff . Kove^r- Glctss Fil|«rTubc < Soft S o U e r (Acl«9' -»H«\r<f S i l v e r S o l d e r - > $ t u p t k l ( o f f S c & l -* O.oos" Tungsten M\co.or M -» Window -RoundedL Ed^es Cknd Corners. •^o.oi Advance 23. which i s mixed i n acetone. A thin layer i s applied at a distance of l/8 i n . from the edge of the hole to both mica and brass, and then freed from air bubbles "by heating at 150° C. for 1/2 hour. After this, the window i s placed on the counter and weighted i n position while the Gelaa i s baked to hardness at 150° C. for 3/4 hogr. Fina l l y the mica i s trimmed down and a coat of glyptal applied to the edges. The heating process causes the solder to soften and the wire to p u l l in and hence to require resoldering. The cylindrical counters having Cu cylinders are cleaned "by a chromic acid passivizing process. The mica window is then put i n place and the glass b e l l (plus wire) i s waxed onto the flange. The f i l l i n g and testing apparatus i s shown i n Plate 2. Taper joints are used to attach the counters to the system to f a c i l i t a t e the r e f i l l i n g process. The counters are thoroughly outgassed with the aid of the mercury diffusion pump, and the wires are glowed to burn off sharp points or d i r t particles ad-hering to their surfaces. They are then f i l l e d i n the usual way by allowing the organic vapor 1/2 hour to diffuse before adding the main Inorganic component. Several hours are l e f t for diffusion and absorption by the counter surfaces to be complete before testing the counters e l e c t r i c a l l y . This ageing process seems frequently to be necessary, counters often showing a much better plateau, etc., after this time than shortly after f i l l i n g . The operating voltage does not noticeably alter during this time. The counter operation i s tested before i t i s removed from the f i l l i n g system. 2 4 . G) Electronic Equipment. The electronic equipment used for testing, as shown i n Plate 2, includes ahead amplifier, stabilized power supply, a scaling unit and a pulse oscillograph which can be used with a triggered or self running sweep. The head amplifier avoids the necessity of a long cable to the other apparatus with consequent large capacity across the oounter and i t s resultant small output pulse size. It consists of a single 6AC7 amplifying stage with a low anode load to follow a rapid pulse r i s e , important in coincidence work, and also with simple negative feed back to extend the input voltage size over which the amplifier w i l l work before saturating. The second stage is a 6AG7 cathode follower adequate to drive a long cable capac-i t y so that the rate of r i s e of the pulse reaching the coincidence mixer i s not appreciably deduced below the i n i t i a l rate of f a l l of potential on the counter wire. Measurements confirm the ex-pected amplifier voltage gain of U and maximum output pulse size p f Ztf volts, and also that the r i s e time with 6 f t . of cable i s less than 1/2 microsec. The •Triggered* time base enables the start of the time base to be coincident with the arrival of the pulse, so that on the screen with a high counting rate the appearance i s as shown in Plate 3t A delay time of l/4 micro sec. in the signal lead en-ables the time base to be started ahead of the v e r t i c a l displace-ment of the beam so the rate of rise of the pulse may. be studied. This provides a very convenient means of measuring dead time and recovery time of a counter and of detecting multiple counts and pulses of different heights, and i n fact of deducing most of the 25. troubles which arise i n the counter* The electronic equipment used in the main experiment i s shown schematically i n F i g . %, and a photograph i s shown in - -Plate 4. The head amplifier and stabilized power unit are of the same types as those mentioned previously. The coincidence mixer i s a t r i p l e channel mixer but i s used at present as a double channel mixer* Without special adjustment of the coincidence mix-er, the resolving time was found to be 0.8 microsec, by feeding random pulses from two Geiger counters activated each by i t s own source into the mixer and counting the coincidences. Prom the usual formula U 0 B Z&x^gff the resolving time ~T was deduced. V. Results. Graphs of observed counting rates for typical specimen ~ counters against voltage are given in Fig. $r. The b e l l type of counter and the rectangular and square gamma counters have useful plateaus, while the rectangular and square beta counters show very poor •plateaus'. One rectangular gamma counter was tested at reduced press-ures and even with a total pressure of only 1 cms. had a plateau slope of n % over a range of 100 volts. A square /J-counter of \.< cms. total pressure showed a slope of over ioo volts. Although our value of M as previously calculated was 1.002 for the rectangular ^ -counters and hence, on the basis of Curran and Reid*s report, should have operated successfully, i t can be seen by the graph that this was not the case* The rectangular ^-oounters having windows of either A l or mica*when operated i n Fig (p. S c h e m a t i c Electronic ftrr^emerv Counter 1 Stabilized! H . I Counter Z Double BeM*| O s c i l l o s c o p e U n i t 1 M l Coincidence Miver 3 Fig. *7 (co»x,t3 26. t h e i r 'Geiger* region, gave pulses of two d i s t i n c t heights analogous to the e f f e c t of a head at the centre of the wire, as was checked "by p l o t t i n g counting rate against scalar d i s -criminator s e t t i n g . This e f f e c t was only p a r t i a l l y improved when the mica was made conducting on the outside by coating i t with graphite, which seems to indicate, contrary to the usual theory, that a cathode mechanism such as the eje c t i o n of electrons from the cathode by quanta emitted i n the i n i t i a l avalanche, i s involv-ed i n the spread of the discharge. To check t h i s l a s t hypothesis a point 43 source was placed against the window centre and the count-ing rate noted, then the source was moved to the window's edge and the counting rate again recorded. The value of the r a t i o E f f i c i e n c y at Edge was 1.54 f o r a graphite covered mica window, E f f i c i e n c y at Centre and was 1.91 f o r the same window without graphite. The e f f i c i e n c y r a t i o s were found to be the same when counting only large pulses and when counting both large and small pulses and also f o r a gamma source. Thus i t would appear that the e f f i c i e n c y of the counter i n the c e n t r a l region where the windows are i s very low, even when the f i e l d d i s t r i b u t i o n i n t h i s region i s made uniform. A further check was made by moving a point gamma source along the narrow edge of the counter and again the e f f i c i e n c y was found to drop i n the c e n t r a l region. Tests made with oollimated beta sources d i d not show any s i g n i f i c a n t change i n large to small pulse s i z e as the region into which the betas were f i r e d through the window was charged. These r e s u l t s f o r c e one to believe that the cathode mechan-ism and not merely the f i e l d d i s t o r t i o n prevents the c e n t r a l region 2 7 . from h a v i n g the same G e i g e r o p e r a t i n g v o l t a g e as the r e s t o f the c o u n t e r . N a t u r a l l y t h i s r e s u l t s i n v e r y poor p l a t e a u s f o r . t h e s e b e t a c o u n t e r s so f a r t e s t e d . An attempt was made t o measure the r e a l e f f i c i e n c y o f such a c o u n t e r by p l o t t i n g t he v a l u e o f N , t h e c o i n c i d e n t c o u n t i n g r a t e , a g a i n s t v o l t a g e on the r e c t a n g u l a r c o u n t e r , t h e b e l l c o u n t e r v o l t a g e b e i n g a d j u s t e d t o be a t t h e s t a r t o f i t s s l o p e . The s p u r -i o u s c o u n t s w h i c h a r i s e i n the r e c t a n g u l a r c o u n t e r as the v o l t a g e i s r a i s e d s h o u l d n o t a f f e c t t he c o i n c i d e n c e r a t e s i g n i f i c a n t l y u n t i l t h e s t a t e o f almost c o n t i n u o u s d i s c h a r g e i s r e a c h e d , f o r N c = 2 NxN2t , w i t h N2 = 5 0 c o u n t s p e r s e c . and hence N c s h o u l d a l s o be about 5 0 c o u n t s p e r s e c , and w i t h = ( 1 / 2-HlO) D s e c , N-^  can be 5 = 1 0 ^ c o u n t s p e r s e c . b e f o r e t h e chance 12)150)11/2)110 >-«• ' s p u r i o u s ' c o i n c i d e n c e r a t e amounts t o 1 0 % o f the r e a l r a t e . The r e s u l t s t a b u l a t e d below bear t h i s out and i n d i c a t e t h a t even a t the h i g h e s t v o l t a g e s r e a c h e d b e f o r e d i s c h a r g e s e t s i n the c o u n t e r e f f i c i e n c y was o n l y 96foiLinstead o f the computed f i g u r e o f 1 0 0%mfor t h e f i l l i n g . 118 : coit n^s in 2 my K .i Con. L B V t k cj roav\d 20 11 *, *. * 1* ft « C u. irr«rvt (Amps) 0.1 D.I O./S' OAST COO-KTS/ 1 iH in-S-7f- I38-& N A Counts 1% »v»im IS5-I Eff i c J c R c y = % 28. I t was obvious at t h i s stage that further work was needed to improve the behaviour of the rectangular beta counters. F i r s t l y i t i s intended to sputter copper onto the mica i n an attempt to equalize the work functions of the cathode materials and hence make the counter 100^ e f f i c i e n t , and secondly to use a "quench u n i t " to reduce voltage on counter by 250 v o l t s once d i s -charge has occurred and keep i t at t h i s 'below Geiger threshold' l e v e l f o r 300 microsec. to eliminate multiple pulses and so f l a t t e n the plateau and so be sure that both counters w i l l f i r e once only when an i o n i z i n g p a r t i c l e passes through t h e i r s e n s i t i v e volumes. A u n i t has been made up to the c i r c u i t shown and appears to work s a t i s f a c t o r i l y . S T A B I L I Z E D POWER U N I T - T . R E . H F S I ^ H E A D A M P L I F I E R 32. APPENDIX 1. THE ENERGY TRANSFER RELATIONS. 1) C o l l i s i o n E q u a t i o n s . >_ C o n s e r v a t i o n o f momentum r e q u i r e s t h a t &) M 2V' 2 cos 20> - m 2 u 2 cos 2© - 2MVmu c o s e + M 2V 2 b) M2V2 sin2<(> = m 2 u 2 s i n 2 e 2 2 hence c) MV* = m 2u 2 - 2 MVmu co s e + M 2V 2 C o n s e r v a t i o n o f Energy r e q u i r e s t h a t d) 1/2 MV"'2 = 1/2 MV 2 - 1/2 mu 2 Combining C) and d) we get, e) M 2V' 2 = M 2Y 2 - Mmu2 f ) (Mm + m 2) u 2 = 2M7'mu cos t h e r e f o r e u = * ^  cos © o r Q, = energy t r a n s f e r r e d = l / 2 m u 2 = ^ ^ 0 Z c o s 2 e = _^U0 L / 2 M V 2 c o s 2 e 2) Impact Parameter i n Coulomb F i e l d . The p a r t i c l e w i l l be a t t r a c t e d towards t h e e l e c t r o n s w i t h a f o r c e o f z e 2 / r 2 and w i l l d e s c r i b e a h y p e r b o l a w i t h respab t t o the second p a r t i c l e , as shown below: I n t h i s s k e t c h q = c l o s e s t d i s t a n c e o f approach. p = impact parameter = c l o s e s t d i s t a n c e o f approach i f p a r t i c l e were not d e f l e c t e d . k = d i s t a n c e o f f o c u s o f h y p e r b o l a f rom o r i g i n . cj> = a n g l e o f d e f l e c t i o n o f i n c i d e n t p a r t i c l e . & = a n g l e o f d e f l e c t i o n o f e l e c t r o n w i t h r e s p e c t t o • the i n c i d e n t d i r e c t i o n . The energy r e l a t i o n s h i p a t t h e c l o s e s t d i s t a n c e o f approach i s 1/2 mv 2 = 1/2 mv 2 + z e 2 / q where v = v e l o c i t y o f p a r t i c l e a t an i n f i n i t e d i s t a n c e and v 0 = v e l o c i t y o f p a r t i c l e a t o r i g i n . L e t K = z e 2/mv 2 -~ hence v 2 / v 2 = 1 - 2 K/q From a n g u l a r momentum c o n s i d e r a t i o n s we have mvp - mv 0q t h e r e f o r e v 2 / v 2 = p / q 2 whence p 2 / q 2 = l - 2 K / q (A) From h y p e r b o l a geometry q = e ( l + cos e ) and e = p / s i n e t h e r e f o r e q = p(l+cos£ ) / ( s i n e ) 34. and P 2 / q 2 = ( 1 - o o s 2 © )/ ( l + c o s © ) 2 = (1-cos e ) (1+cos e;) By s u b s t i t u t i n g i n (A) and m u l t i p l y i n g by (1+cos ©) we get (1-cos e) = 1+cose - ( 2 k / p ) ( s i n e ) hence 2k/p = 2 cos©/sine and p/k = t a n © now tan 2© = s i n 2 0 / c o s 2 0 = ( 1 - c o s 2 e )/cos2© t h e r e f o r e 1 = cos 2.e ( l + p 2 / K 2 ) t h e r e f o r e c o s 2 0 = 1/(1+ 5) E v a l u a t i o n o f the Parameter p. .2„ „_„/,„,_,2 m//,. ™*p*_ v + , Q=4mM/(M-m)2 T c o s 2 9 =4mM/(M-m)2 T / ( l + ) hence m 2 p 2 v 4 / z 2 e 4 =( (4mMT/© -(M+m) 2 - 1 ) ) and p 2 = (4T'/Q - I ) 2 e / 4 T ' 35-APPENDIX 2. MAGNET DESIGN. The 1 / 6 model of the magnet designed f o r the U . B . C . Van de Graaff generator has been modified to have an a i r gap of 3 / 4 i n . Not shown i n the diagram Fig.tf) are the c o i l s which have been wound w i t h woo turns of No.13 gauge formex copper wire and provided w i t h a water c o o l i n g l a y e r such t h a t a max-imum current of It amps, can be passed through without s e r i o u s overheating. Hence N*max = '7,£t>o amp. turns Therefore M.M.F.j^^. = 4TTNI / 1 0 = 12, (ot g i l b e r t s = ^ a i r ! a i r + H i r o n ^ r o n Assuming a maxumum value f o r H j _ r o n of 4 0 Oersteads to correspond to 1 0 , 0 0 0 lines/sq.cm. i n the i r o n y o l k used which i s made of laminated low carbon s t e e l , then M.M.F.maX =22, 10k = ( 1 1 ) ( 2 . 3 4 ) + ( 4 0 ) 1 7 2 ) ( 2 . 3 4 ) l b 6 Therefore ^ a i r - " Kilog^uss With the model as used, s a t u r a t i o n would a b v i o u s l y occur i n the poles which are not tapered to a l l o w f o r leakage f l u x . However as i t i s a 'model* w i t h enlarged a i r gap, c l e a r l y the l i m i t a t i o n l i e s not i n i r o n s a t u r a t i o n but t n the current which can be passed through the c o i l s . APPENDIX 3. MAGNET. PERFORMANCE. This magnet.'s performance i s given i n the f o l l o w i n g graphs, as found by a b a l l i s t i c galvanometer and search c o i l . On the next diagram f o r comparison i s shown the performance of the magnet when modified to have wedge shaped pole pieces of approx-imate l y the same t o t a l area as the square t i p s . APPENDIX 4 . MAGNETIC REFOCUSSING OF ELECTRON PATHS. WEDGE MAGNETS. 1 1 3 The e l e c t r o n p a t h s i n the wedge a r e a r c s o f c i r c l e s w h i c h a r e ta n g e n t a t t h e edges o f t h e f i e l d t o t h e e n t r a n c e and e x i t d i r e c t i o n s . . C o n s i d e r a homogeneous beam o f e l e c t r o n s o f v e l o c i t y v e n t e r i n g t h e e n t r a n c e s l i t A making t h e a n g l e © w i t h , t h e base l i n e and e n t e r i n g the f i e l d a t P p e r p e n d i c u l a r t o OPQ. I f t h e f i e l d H i s s e t t o t u r n the beam i n t o an a r c o f r a d i u s R where R « a s i n © = OP = OW where HR = mv/e t h e n the c e n t r e o f c u r v a t u r e o f the a r c w i l l be 0, and t h e e x i t beam w i l l l e a v e t h e wedge f a c e a t W p e r p e n d i c u l a r t o OWV" and e n t e r t h e c o l l e c t o r a t B on the a x i s . A l l o t h e r beams e.g. AQJ, w i t h s i m i l a r v e l o c i t y and w i t h t h e a n g l e - * t o AP w i l l be r e f o c u s s e d so as t o c r o s s v e r y c l o s e t o B. That i s , the b e s t r e f o c u s s i n g f o r a d i v e r g e n t p e n c i l f r o m A o c c u r s a t B, where b = a s i n e / s i n ^ The d e p a r t u r e f rom p e r f e c t f o c u s - t h e Spread -S = UB s i n K, where UB i s the s p r e a d a l o n g the 37, u B base l i n e due t o beams making a n g l e s o f - •< w i t h t h e c e n t r a l p a t h APtyB. I f one c o n s i d e r s a beam o f v e l o c i t y v+ &v s t a r t i n g a l o n g AP, i t s r a d i u s o f c u r v a t u r e w i l l be l a r g e r and i t w i l l i n t e r s e c t t h e base l i n e a t C. The a b i l i t y t o s e p a r a t e two d i f f e r e n t v e l o c i t i e s i s c a l l e d t h e d i s p e r s i o n - D -D = BC s i n * D and S a r e d e f i n e d as l e n g t h s p e r p e n d i c u l a r t o the r a y p a t h as t h e s l i t o f t h e c o l l e c t o r w i l l n o r m a l l y be p l a c e d perpen-d i c u l a r t o the p a t h . The r a t i o D/S g i v e s a measure o f t h e t h e o r -e t i c a l r e s o l v i n g power. D e r i v a t i o n o f E q u a t i o n f o r S: L e t AOB be the x - a x i s and AY t h e y - a x i s . C o n s i d e r the . p a t h AQ,vTJ o f the beam a t + «*° t o t h e normal beam.. C o o r d i n a t e s o f Q,: X]_ = a cos ©cos (© + «<)/cos* 2v C o o r d i n a t e s o f T: x 2 = a ( ( c o s ©cos (© +°<)/eos»< + s i n © s i n ( e y 2 = a( (cos 6 s i n ( 0 + )/eos°< - s i n o cos( ©+<><))) C o o r d i n a t e s o f V: .2 X3 = + 2 ( x 2 * y 2 c o t * + a cot^ t f ) + 4 ( x 2 + y 2 c o t y + a c o t ^ jr )' 9 2 2 2 P ? 2 -4 c o s e c ^ Y (X2 +y 2 + 2 a y 2 c o t X + a c o t ^ j r - a ^ s i n e) 2 c o s e c ' y : y^ = ( x ^ - a) c o t y o b t a i n e d f r o m i n t e r s e c t i o n o f a c i r c l e about T: o p 2 . 2 . sr. and second edge o f wedge: y = (cotY)x - a c o t Y C o o r d i n a t e s o f U : {where i n t e r s e c t s A O ) x 4 = 2:3 +' l y 5 - y 2 ) / U ^ - z 2 ) y 4 = 0 Hence S - >s» sin.V = ( a + b - x ^ j s i n Y - alsin if * . sin e ) - s i n t ((zj + y 3(y 5-y 2')/(x 5-x 2) -)') • ' On expa n d i n g i n powers o f << and d r o p p i n g terms i n *3f e t c < S • a <<2/2 ((sin 2©/sin y + s i n 2 y / s i n e ) ) When 3 = * , S = a * 2sin© When © « V = 90° , S =• a * 2 the u s u a l 180° f o c u s s i n g c a s e . D e r i v a t i o n o f E q u a t i o n f o r P i I n c r e a s e o f AV i n v i n c r e a s e s R by A R where A R / R =AV/V i f H i s k e p t f i x e d . I f t h i s i s drawn i n , one can f i n d a.new p o s i t i o n and new a n g l e a t w h i c h t h e beam l e a v e s t h e f i e l d a n d . i t s i n t e r c e p t on ZOB. (Same proce d u r e as b e f o r e ) . E x p a n d i n g g i v e s : D = a sin©/sin V -av/v ( s i n © + s i n y ) Whan G = y, D = 2a s i n e - A v / v When 0 = y= 90°, D = 2a A V / V . R e s o l v i n g Power: D/S i s p l o t t e d as a f u n c t i o n o f © arid y i n u n i t s o f ( 2 A 2 ) ( A V / V ) . The maximum v a l u e o c c u r s f o r v a l u e s s u c h t h a t 2sin y = sin©, g i v i n g t h e r a t i o D/S = 1-1/3 t i m e s . t h a t f o r 180° case o f 0 = 43°, Y= 43° c a s e . BIBLIOGRAPHY, (1) Anderson, C. D., Phys. Rev. 44, 406, 1933. (2) A n d e r s o n , C. D., Phys. Rev. 30, 263, 1936. (3) B a r n o t h y , Phys. Rev.. 74, 844, 1948. (4) Bethe H., Handbuch d e r P h y s i k , V o l . 24, 1, p 323, 1933. (3) Brode, R. D., Rev. Mod. Phys. 11, 222, 1939-(6) Corson, D. R. and Brode, R. "D., Phys. Rev. 33, 733, 1938. (7) Cosyns, M., B u l l . Tech. A s s . I n g . Brux., 173-263, 1936. (8) S u r r a n , S. C. and R e i d , J . M., N a t u r e 160, 866, 1947. (9) C u r r a n , S. C. and R e i d , J . M., Rev. Sc. I n s t . 19, 67, 1948. (10) D a n f o r t h , W. E., and Ramsey, W. E., Phys. Rev. 49, 834, 1936. (11) ,Gray, I i . H., P r o c . Camb. P h i l . Soc. 40, 7.2, 1944. (12) Gurney, R. W., P r o c . Roy. Soc. A 107, 332, 1923. (13) Hazen, W. E., Phys. Rev. 63, 107, 1943. (14) Hazen, W. E., Phys. Rev. 63, 239, 1944. (13) Hereford,. F. L., Phys. Rev. 74, 374, 1948. (16) Kunze, P., Z e i t s . f . P h y s i k , 83, 1, 1933. (17) L i v i n g s t o n , Kev- r W . ?kys., J u l ^ , 1137. p.AtS" (18) Nicodemus, D. B., PhD. T h e s i s , S t a n f o r d , 1946. (19) Ramsey, W. E., Phys. Rev., 6 l , 97, 1942. (20) S c h n i e d e r , K., Ann. der P h y s i k , 33, 443, 1939. (21) Skramstad, H. K. and L o u g h r i d g e , D. H., Phys. Rev.30,677, 136. (22) Stephens, W. E., Phys. Kev. 43, 313, 19:3#-(23) Thomson, J . J . , P h i l . Mag. 23, 449, 1912. • .• . . (24) W i l k i n s o n , D. H., Phys. Rev. (23) W i l l i a m s , E. J . , P r o c . Roy. Soc. A 133, 108, 1931. (26) W i l l i a m s , E. J . , and T e r r o u x , F.R., Proc.Roy.Soc.A126,289,1929 (27) Zahn, C.T. and Spees, A.H.,. Phys. Rev., 38, .861, 1940. 

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