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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 T h e s i s S u b m i t t e d I n P a r t i a l F u l f i l m e n t Of The Requirements F o r 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 p r i v i l e g e 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. I t i s a pleasure to acknowledge the guidance given by Dr.. J . B;. Warren, under whose supervision t h i s work was carried' out. The help given by Mr. W. Pye and Mr. A. Fraser i n the f a b r i c a t i o n of the counters and vacuum system used i s gratef u l l y acknowledged.  TABLE OF CONTENTS. Chapter I.  Page 1.  Abstract  II.  3.  Theory of S p e c i f i c Ionization  III.  Methods of Measurement of S p e c i f i c Ionization and Available Results.  IV.  9•  Experimental Arrangement A) General Scheme B) Design of the  14. -ray Energy Analyser  ......  15.  C) Choice of Sources  17.  D) i n t e n s i t y Considerations  19.  E) Counter Design  19*  F) Counter Construction and F i l l i n g Techniques  22.  G) E l e c t r o n i c Equipment  24. 25.  V. . Results Appendices 1.  32.  The Energy Transfer Relations  2. Magnet Design  55.  3 . Magnet Performance  35*  4. Magnetic Refocussing of Electron Paths  36.  Figures 1.  Impact Parametec i n a Coulomb F i e l d  4.  2. Ionization - Energy Curve  8. To follow page  3 . layout of Apparatus  ,  16. 22.  4. T r i p l e Counter 5. Rectangular and Square  ...  - Counters  6. Schematic Electronic Arrangement  22. 25.  Table o f Contents  (cont.).  Figures 7.  To f o l l o w page  C h a r a c t e r i s t i c Curves o f V a r i o u s Counters  8. Magnetjfior S p e c t r o m e t e r  .'. ..  25. 35.  9. Magnet C a l i b r a t i o n a t H i g h F i e l d s  35.  10. Magnet C a l i b r a t i o n a t Low F i e l d s  3$.  Plates 1.  16.  L a y o u t o f Apparatus  2. E l e c t r o n i c Counter T e s t i n g Equipment 3 . Dead Time Measurement 4. S p e c t r o m e t e r and E l e c t r o n i c Equipment C i r c u i t Diagrams 1.  S t a b i l i z e d Power U n i t  2. Head A m p l i f i e r . 3 . Quench U n i t f o r S e l f Quench G e i g e r Bibliography  24. •  24. 25. Page 29. ........30. 31. 59.  ABSTRACT  1M_  T h e o r i e s of P . S . I . * produced "by e l e c t r o n s p a s s i n g through gases show t h a t one would expect the number of primary i o n p a i r s formed t o v a r y w i t h the e l e c t r o n d e n s i t y i n the gas and w i t h the mean i o n i z a t i o n p o t e n t i a l of the gas. t o v a r y i n v e r s e l y as the square of the v e l o c i t y of the e l e c t r o n a t low e n e r g i e s r e a c h i n g a minimum v a l u e approximately a t a k i n e t i c energy e q u a l t o the r e s t energy and t o be independent of the s i g n of the b e t a p a r t i c l e p r o d u c i n g the  ionization.  I t i s consequently of i n t e r e s t to o b t a i n measurements of the P . S . I , of b e t a p a r t i c l e s a t e n e r g i e s a t which i t i s a minimum i n v a r i o u s gases which a r e used f o r f i l l i n g c o u n t e r s and  ionization  chambers i n c l u d i n g hydrogen, h e l i u m , neon, xenon, methane, c h l o r i n e and other quenching v a p o r s such as methyl c h l o r i d e which may  be-  come of p r a c t i c a l concern f o r c o u n t e r s designed t o operate over a wide temperature range.  P r e s e n t d a t a on P/afS.I. of e l e c t r o n s  and  mesons i s l i m i t e d t o b u t few gases and the r e s u l t s a r e not i n good accord.  As mentioned,  the P . S . I , i s independent  of the s i g n of the  charge of the i o n i z i n g p a r t i c l e and, s i n c e 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 c o n s e r v a t i o n of charge i n d i c a t e s the e q u a l i t y of the charge on the p o s i t r o n and negatron, i t would be  expected  t h a t the v a l u e s of the P . S . I , would be i d e n t i c a l f o r the two icles.  However w h i l e i t i s known t h a t the v a l u e of e/m  part-  for both  p a r t i c l e s i s i d e n t i c a l t o w i t h i n 2%, t h e r e i s some p o s s i b l e theor e t i c a l i n d i c a t i o n t h a t t h e i r masses might be s l i g h t l y  different.  * The p r i m a r y s p e c i f i c i o n i z a t i o n w i l l h e r e a f t e r be denoted by  P.S.I  2.  Moreover the only d i r e c t estimation of the value of e  +  is  the measurement of P.S.I, from the o r i g i n a l cloud chamber observation of a cosmic ray positron by Anderson which established 4  the charge equality of e  and e" to within 20%.  +  Thus i t appeared  of some fundamental importance to compare with p r e c i s i o n the P.S.I, of both p o s i t i v e and negative electrons of similar v e l o c i t i e s i n a gas of high atomic number such as neon and a gas of low atomic number such as helium. F i n a l l y i t was hoped that the apparatus set up would be suitable f o r an investigation of the r e l a t i o n between the P.S.I, and v e l o c i t y of the electron especially i n the r e l a t i v i s t i c region i n which the data i s very meagre. ergy beta sources (e.g. B ) 1 2  This w i l l need high en-  which w i l l "become available when  the U.B.C. e l e c t r o s t a t i c generator i s i n operation. Apparatus has been set up to determine 13ae P.S.I, of electrons i n various gases by determining the i n e f f i c i e n c y of a Geiger counter f i l l e d with gas.  To eliminate the d i f f i c u l t y , of  a v a r i a b l e path length of the p a r t i c l e through the ordinary cyl i n d r i c a l counter, rectangular and square envelope counters with t h i n windows have been constructed.  The presence of a large t h i n  window, even when a conducting surface, has been found to a f f e c t the spread of the discharge and r e s u l t s i n the appearance of two size pulses analagous to the e f f e c t of an i n s u l a t i n g 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 i n volve a cathode mechanism i n t h i s design. In order to select beta p a r t i c l e s of homogeneous energy from the radioactive source, a small wedge shaped magnetic spectrograph 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 i n t o a e f f i c i e n t counter o p e r a t i n g a t normal pressures»  100%  and r e c o r d i n g  the c o i n c i d e n c e r a t e as a f r a c t i o n of the " e f f i c i e n t c o u n t e r " rate.  Co  5 6  was  chosen as the most s u i t a b l e p o s i t r o n e m i t t e r *  and has been prepared i n the B e r k e l e y c y c l o t r o n by the re" reaction.  II.  RaE has been used as a negatron e m i t t e r .  THEORY OF SPECIFIC IONIZATION  The P.S.I, i s d e f i n e d to be the number of p r i m a r y i o n p a i r s formed per cm. l e n g t h of t r a c k i n the gas, reduced to U.T.P. Two . other s i m i l a r q u a n t i t i e s sometimes measured a r e the t o t a l  specific  i o n i z a t i o n ; i . e . , the t o t a l numbers of i o n p a i r s (primary, secondary, t e r t i a r y , e t c . ) formed per cm. a t N.T.P., and the p r o b a b l e s p e c i f i c i o n i z a t i o n ; i . e . , the number of p r i m a r y i o n p a i r s p l u s the number of secondary i o n p a i r s h a v i n g a s p e c i f i e d upper  limit  t o t h e i r energy which are formed per cm. a t 3ST.T.P. J.J.Thomson has c a l c u l a t e d the energy t r a n s f e r 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 e l e c t r o n of mass m and charge e, when the e l e c t r o n s u f f e r s a d e f l e c t i o n through an angle e .  H i s e x p r e s s i o n de-  rived classically i s  (flt<»f~  (See appendix 1.)  The c l o s e n e s s o f 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 c o n s e r v a t i o n ca  of momentum, i t f o l l o w s t h a t f o r any p,  e =V  4t  —  )  xe therefore (See appendix where ze v  •  Tl  m  charge on the "bombarding  2.)  particle  incident v e l o c i t y  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 e l e c t r o n s which w i l l be removed from t h e atoms i n 1 cm. of t r a c k ( i . e . , the P.S.I.) w i l l e q u a l t h e p r o b a b i l i t y t h a t the i o n i z i n g p a r t i c l e w i l l come w i t h i n r a d i u s p  0  of any e l e c t r o n ,  m u l t i p l i e d b y the number of e l e c t r o n s p e r c c . i n the gas; i . e . , ............(i)  5. Thomson's f o r m u l a t h e r e f o r e s t i p u l a t e s t h a t ; (1)  For a given  (2)  P.S.I, i s p r o p o r t i o n a l to  (3)  P.S.I, i s p r o p o r t i o n a l to z e  (4)  P.S.I, i s independent of the s i g n of  (5)  If.S.I. i s p r o p o r t i o n a l t o (M/tef>) f o r i o n i z i n g p a r t i c l e s  i n c i d e n t v e l o c i t y , P.S.I, i s Independent of  x  1  4  s e l e c t e d by t h e i r Hf  The  +  rays.  i  .. 'ne-  a comparison of the s p e c i f i c i o n i z a t i o n s  pr of r e l a t i v i s t i c  A l l other  energies  for  such as occur i n cosmic  evidence f o r t h i s e q u a l i t y i s e s s e n t i a l l y i n -  d i r e c t and assumes the c o n s e r v a t i o n /m  and  f i r s t e s t a b l i s h e d to a rough degree of approxim-  at i o n by Anderson by / 3 and  i n a magnetic momentum a n a l y s e r .  e q u a l i t y of the magnitude of charge on p o s i t r o n s  negatrons was  B  ze.  2  of mass M  of  v"  M.  of charge.  The  and p' has been e s t a b l i s h e d by Zahn and  accuracy of 2%.  e q u a l i t y of Spees to 7  an  B a r n o t h y h a s suggested t h a t t h e o r e t i c a l l y the 3  mass of the p o s i t r o n i s 0.354$ l e s s than the mass of the  electron  due  a care-  to the d i f f e r e n c e i n s i g n of t h e i r mass d e f e c t s , and  f u l examination of the r e s u l t s of Zahn and i s s l i g h t l y g r e a t e r than  e  7 . w  Spees r e v e a l s  A p r e c i s i o n measurement of  that 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 e s t a b l i s h e d , be  strong evidence of the exact  e q u a l i t y of charge.  S i n c e the s p e c i f i c i o n i z a t i o n i s p r o p o r t i o n a l to the square of the mass f o r a g i v e n v e l o c i t y , or r a t h e r a g i v e n H f  , a comparison  of P.S.I, f o r p o s i t r o n s and negatrons w i l l g i v e d i r e c t evidence for  the e q u a l i t y of mass and hence charge of the two Be the has  ing hydrogen-like  particles.  d e r i v e d an e x p r e s s i o n f o r the P.S.I, by a s c r i b wave f u n c t i o n s t o the atomic e l e c t r o n s ,  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 e l e c t r o n t o he much g r e a t e r t h a n the v e l o c i t y of the atomic e l e c t r o n s  i n the Bohr  o r 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  )  ..........(ii)  T'W  where  W = 13.5  and  ¥  The  (Z)  ev. 13.5  s  v a l u e f o r W,  atom, can be  f o r hydrogen Z  f o r other gases.  the average e x c i t a t i o n p o t e n t i a l of the whole  found more a c c u r a t e l y  power d a t a than t h e o r e t i c a l l y . lay L i v i n g s t o n  Log  where  and  Ry  ( l -^ ' ) l o g  I'+^LgJ  log  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 Z^eff.  RIJ  =  1.103  =  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  I  t h e o r e t i c a l expression given  is :  (¥) s  IK *  The  e m p i r i c a l l y from s t o p p i n g  '»  = e f f e c t i v e n u c l e a r charge of the K  average e x c i t a t i o n p o t e n t i a l of the s i d e the K  Z - 1.81  lem.  He  electrons  out-  shell.  • " e f f e c t i r e " number of  electrons.  To d e s c r i b e 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 , an ex&ot quantum  shell.  Bethe applies H  m e c h a n i c a l treatment t o the energy l o s s prob-  c o n s i d e r s the  d i s t r i b u t i o n of Q, i n t o e x c i t a t i o n and  i z a t i o n e n e r g i e s , which v a r i e s w i t h the  atom bombarded, and  ionhe  7.  shows t h a t  -dT/dx » A x ( l n E +- I n £i  -y)  ...  ( i i i )  where K depends i n v e r s e l y on t h e 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 t h e gas and on whether i t i s primary o r p r o b a b l e s p e c i f i c  ion-  i z a t i o n which i s b e i n g d e s c r i b e d . F o r P.S.I, i n hydrogen,  K ? 10 A The  B  5  4z2 4HZ/mc  2  e  ratio (dT/dx)pri  P.S.I. • V  0  a average energy expended p e r primary ion pair V  0  produced.  i s a f u n c t i o n of the n a t u r e o f the gas o n l y , and i s independ-  ent o f t h e energy and n a t u r e o f t h e i o n i z i n g p a r t i c l e . f o r d i f f e r e n t gases a r e g i v e n i n Table 1.  Tzvble 1-  Vo f»»- Different G a t e s .  (revs  Vo  R o f f e n c e  AirAir  Prot o n  Air Air Hx Ife  jr.'i ii  31.0  II  u  ii  II  «  He  1  II  A  1  A  £ lect row  Kr  Alpta  Xe  II  3/-0  I ' XO  ) D.O/7f  ZZ.O  /•3  Xo IX  Values  8.  When changed t o g i v e P . S . I . , equation  P.S.I. :SHZ .  l ^ M ^ M * nvv  1  L  ( i i i ) "becomes;  W M  '~r ' *  (iv) J  where K i s a constant which depends on t h e gas b e i n g i o n i z e d , and C depends on t h e i o n i z a t i o n p o t e n t i a l o f t h e gas.  A plot  of ( i v ) i s g i v e n i n P i g . 2  lo  Pig.2.  3  to*  Ionization-Energy  fp<  /P  u  io  7  i°*  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 t h e energy i s s e v e r a l times r e s t energy. due  The r e l a t i v i s t i c i n c r e a s e i n the s p e c i f i c i o n i z a t i o n i s  t o t h e i n c r e a s i n g c o n t r a c t i o n of t h e e l e c t r i c f i e l d o f t h e  p a r t i c l e toward a p l a n e p e r p e n d i c u l a r t o i t s motion, thus i n c r e a s i n g t h e impulse g i v e n t o atomic e l e c t r o n s b y p a r t i c l e s p a s s i n g a t some d i s t a n c e from t h e atomic c e n t r e .  An i n c r e a s e i n Rf> b y a  9.  f a c t o r of 5.10  4  o n l y doubles the minimum v a l u e of the  specific  ionization.  Ill*  Methods of Measurement of S p e c i f i c I o n i z a t i o n and A v a i l a b l e R e s u l t s .  A) G e n e r a l  Scheme.  The p r i m a r y s p e c i f i c i o n i z a t i o n of e l e c t r o n s , a l p h a p a r t i c l e s , protons  and mesons has been measured b y two methods.  I n the f i r s t a c l o u d chamber i s used i n which the expansion i s arranged  to take p l a c e s h o r t l y b e f o r e the passage of the  p a r t i c l e through the chamber, so t h a t condensation the i o n s d i f f u s e an a p p r e c i a b l e d i s t a n c e . of low e n e r g i e s and c o r r e s p o n d i n g l y  The  ionizing  occurs  before  secondary e l e c t r o n s  s h o r t ranges thus g i v e r i s e  to  a c l u s t e r of c l o s e l y spaced i o n s which appears as a b l o b about  the  primary i o n p a i r .  the  Counting the numbers of b l o b s per cm.  primary s p e c i f i c i o n i z a t i o n .  The  gives  energy of the p a r t i c l e i s - f o u n d  from a measurement of the c u r v a t u r e of the t r a c k i n a magnetic field. low  I n a c c u r a c i e s a r i s e from m u l t i p l e s c a t t e r i n g i n the gas  e n e r g i e s , and by the u n c e r t a i n t y i n e s t i m a t i n g the plane  the t r a c k .  The  amount of water vapor present  and hence a l s o i n t r o d u c e s an e r r o r . l a p , be  i s h a r d to  at  of  estimate*  F u r t h e r , the b l o b s may  over-  of v a r i o u s s i z e s , and "be i r r e g u l a r l y spaced, thus making  accurate counting The  difficult.  second method c o n s i s t s 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 t h a t at l e a s t  10*  one i o n p a i r i s c r e a t e d i n the gas "by the p a s s i n g p a r t i c l e . The e f f i c i e n c y may  he c a l c u l a t e d as f o l l o w s :  Assuming a l l p a t h l e n g t h s i n the counter are the same* and e q u a l t o i cms.  then the average number of i o n p a i r s p r o -  dueed i n t h e tube 1st where  n - at p .  s • primary s p e c i f i c  ionization  p = gas p r e s s u r e i n atmospheres. Let  coU)s p r o b a b i l i t y t h a t the p a r t i c l e goes a distance  u>(«U) s<L)0s  Then  i  w i t h o u t p r o d u c i n g an i o n p a i r .  p r o b a b i l i t y t h a t the p a r t i c l e goes a  d i s t a n c e <U w i t h o u t p r o d u c i n g an i o n p a i r . T h e r e f o r e u 4 ) l w U ) s p r o b a b i l i t y of i t g o i n g a d i s t a n c e U+<U) w i t h o u t p r o d u c i n g an i o n p a i r  A p p l y i n g the boundary c o n d i t i o n we get  s  c"  s  , and  integrating,  P  T h e r e f o r e e f f i c i e n c y • c l i ) * 1-  e  I f the geometry i s such t h a t t h e r e i s a continuous  dis-  t r i b u t i o n of p a t h l e n g t h s , i t i s p o s s i b l e and n e c e s s a r y t o r e v i s e t h e e x p r e s s i o n f o r the e f f i c i e n c y as a f u n c t i o n of ( s p ) . The p r e c i s i o n i s l i m i t e d i n t h a t the c a l c u l a t i o n s assume that  ( 1 ) the presence of one i o n p a i r i s s u f f i c i e n t t o i n i t i a t e  a d i s c h a r g e (which, i s b e l i e v e d t o be t r u e i n a p r o p e r l y operated Geiger c o u n t e r ) , and  ( 2 ) t h a t n e g l e g i b l y few e n t i t i e s capable of  e x c i t i n g a d i s c h a r g e are e j e c t e d by the p a r t i c l e s from the i n n e r s u r f a c e of the counter c y l i n d e r . (2)  To check whether or not c o n d i t i o n  i s s a t i s f i e d , an e f f i c i e n c y measurement c o u l d be made u s i n g a  gas f i l l l n g ^ k n o w n P.S.I, and by c h e c k i n g the form of the f u n c t i o n a l r e l a t i o n b y v a r y i n g the f i l l i n g p r e s s u r e .  01. ti Ramsey has pointed out that a single segmented court er could be used to measure the F.S.I*  By applying d i f f e r e n t v o l t -  ages to d i f f e r e n t segments* one segment can be operated i n the proportional region g i v i n g a current proportional to the number of ion p a i r s formed, while another segment i s operated i n the Geiger region g i v i n g a current which i s proportional to the number of ioni z i n g p a r t i c l e s passing through i t .  The r a t i o of these two curr-  ents i s proportional to the P.S.I, and i s independent of p a r t i c l e s i n the beam.  of the number  To obtain the absolute value of P.S.I,  f o r any gas, a c a l i b r a t i o n of the apparatus must be c a r r i e d out using a gas of lenown P.S.I. The r e s u l t s of several investigators are given i n Table 2 . Table 2. Available Data  \. C l o u d Clqtunlaeir.  P.S.I (NTP) Willi  A  wis %"Xerrou.x  \\  ~  ••  A »v Air Elee-fc  He  Mesons  M  J. Counter J)ev»vfi>r"tk  *  tt--isL.L  >v>"  II  tu>-7.io0  Ramsey  Mr  M«a^«.» * £ It i t row  Ke»/  LS/9  ta.L  Cos ^ t\S  ..  f  ?  He  II  "  ?  It.  1 *  il  A  7  •II  ii  Elf cty>»\f  Curt-fc.^ * R e i c l A  •«  sr.l  ? «>.^  Lt> Mev.  t 0.2-  7?  M II  IS  -?  7  «  ft  q  Eff,'cienc  11  i.  I0  £\ectr e « t>co-aioo Kcv/.  He  £T.X  L  C?)  We N*  l|  ~  e'/c  4  ~ \0  •<  Corner-*- * Biroit^  JO  II  *s-  12.  W i l l i a m s and Terroux c l a i m an e r r o r of 2% i n t h e i r measurement of Hp, water vapor  and an e r r o r of 5% due t o the presence  and other gas i m p u r i t i e s .  of  They estimate t h a t the  e r r o r i n j u d g i n g the number of b l o b s per cm. produced b y f a s t  -  e l e c t r o n s i s I n s i g n i f i c a n t compared to the e r r o r of the f i r s t  two  causes.  F o r slow e l e c t r o n s the method i s v e r y i n a c c u r a t e be  cause of the s c a t t e r i n g .  be-  They f i n d the v a r i a t i o n of P.S.I, w i t h  v e l o c i t y can be g i v e n b y - \.S  P.S.I. a 5.2 /B P.S.I.  22 /?~ *"*  =  M±  tO.T-  f o r hydrogen. f o r oxygen.  T h e i r r e s u l t s show t h a t e q u a t i o n ( i ) p r e d i c t s the c o r r e c t order of magnitude f o r lower than  P.S.I, b u t t h e o r e t i c a l v a l u e s are s i x times  experimental.  E . J . W i l l i a m s ^ f o u n d t h a t equation ( i i ) gave v a l u e s w i t h i n 10/£ of the experimental v a l u e s f o r e l e c t r o n s h a v i n g and  p a 0.50,  0.75  0.96. Kunze d i d not f i n d the expected  i n c r e a s e of P.S.I, w i t h  T e l o c i t y a t e n e r g i e s g r e a t e r than 2 H e v « , nor d i d Anderson?' who  ob-  t a i n e d a v a l u e of 31 i o n p a i r s per cm. f o r e n e r g i e s g r e a t e r than  1 0 ' ev.  As BrodeVint's out. t u .  may be due to an error in the  o p e r a t i o n of the c l o u d chamber, g i v i n g a r e s u l t which i s too low a f a c t o r of 2.  T h i s same mistake was made b y Corson and E r o d e  and  i s due t o the f a c t t h a t they were o b s e r v i n g condensation on posi t i v e i o n s alone, i n s t e a d of on i o n p a i r s . Hazen quotes a p r o b a b l e e r r o r of 1.6% li7/£ f o r mesons.  f o r e l e c t r o n s and  T h i s c o v e r s an e s t i m a t i o n of the percentages  a l c o h o l and water vapor p r e s e n t i n the chamber.  by  of  13.  Skramstad and Loughridge  estimate t h a t the r e s o l v i n g  power of t h e observer*s eye l i m i t s the accuracy to 10-15# f o r Bfg. and 7-10^  for B ,  depending  e  on the v e l o c i t y of the e l e c t r o n .  They d i d not f i n d an i n c r e a s e of P.S.I, w i t h r e l a t i v i s t i c v e l o c ities. ... '  T h e i r 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 a l s o observed a few t r a c k s i n oxygen, two  or t h r e e of w h i c h  were d e f i n i t e l y due t o p o s i t r o n s and o t h e r s to e l e c t r o n s .  The r e -  s u l t s were i n d i s t i n g u i s h a b l e i n t h e two cases, and agreed w i t h the v a l u e s of W i l l i a m s and  Terroux.  The r e s u l t s of D a n f o r t h and Ramsey, Cosyns and H e r e f o r d , u s i n g the counter t e c h n i q u e , a l l g i v e a v a l u e f o r the P.S.I, of a p a r t i c l e of E/mc * 20, where E i s the t o t a l energy of t h e p a r t i c l e , 2  which i s an e l e c t r o n i n the case of H e r e f o r d and a cosmic r a y p a r t i c l e i n the other c a s e s . F o r low e n e r g i e s , H e r e f o r d * s r e s u l t s f o l l o w 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 t h e r e are t h r e e experimental p o i n t s to i n d i c a t e t h a t the P.S.I, does i n c r e a s e a t r e l a t i v i s t i c v e l o c i t i e s . ed i n the September 1948  Hereford*s r e s u l t s  appear-  i s s u e of The P h y s i c a l Review, sometime  a f t e r the p r e s e n t experiment had begun and he used an e x p e r i m e n t a l set up v e r y s i m i l a r t o the one used by the author, b u t  Hereford.has  used c y l i n d r i c a l g l a s s envelope counters w i t h g r a p h i t e cathodes. The m a j o r i t y of the r e s u l t s quoted i n the l i t e r a t u r e a r e not i n p a r t i c u l a r accord, w h i c h would suggest t h a t the p r e c i s i o n of the c l o u d chamber has been o v e r e s t i m a t e d .  The t h e o r y has been  checked  14  and v e r i f i e d most c l o s e l y i n the r e g i o n of the minimum of the ionization-energy curve.  IV.  A)  E x p e r i m e n t a l Arrangement.  G e n e r a l Scheme. I n t h i s r e s e a r c h the primary s p e c i f i c i o n i z a t i o n of  negatrons and p o s i t r o n s i s o b t a i n e d by measurement of the i n e f f i c i e n c y of a Geiger counter o p e r a t i n g a t a low p r e s s u r e of the gas under i n 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 t o g i v e a d i r e c t comparison  of the primary s p e c i f i c  i z a t i o n of /3 and .p~ of v a r i o u s v e l o c i t i e s . f  s m a l l magnetic ft*  ion-  F o r t h i s purpose  a  a n a l y s e r has been s e t up, the s e l e c t i o n of e i t h e r  or p>~ b e i n g 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 w h i l e a l l  other experimental c o n d i t i o n s remain unchanged. T h i s method o b v i o u s l y can be a p p l i e d t o study the v a r i a t i o n of P.S.I, w i t h the energy of the bombarding p a r t i c l e and w i t h the n a t u r e of the gas through which the p a r t i c l e p a s s e s .  The gases i t  i s proposed t o study i n c l u d e argon, helium, c h l o r i n e , hydrogen, neon, and quenching vapors such as a l c o h o l , methane and  methyl  c h l o r i d e , w h i l e the energy range a v a i l a b l e f o r i n v e s t i g a t i o n i s from 200 Kev. t o 1.5 Mev.,  the lower l i m i t b e i n g s e t b y the  energy  spread i n t o r d u c e d by the m i c a windows, and the upper l i m i t b y sources a t p r e s e n t o b t a i n a b l e .  the  15.  B)  Design of the fs -ray Energy Analyser. The magnet used i s a l/& scale model of the d e f l e c t i o n  magnet designed f o r the If .B.C. Van de Graaf generator, hut with d i f f e r e n t pole pieces to provide a3/4 i n . gap and wedge shaped field.  I t 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. D e t a i l s of the design and performance  are given i n Appendices 2 and 3.  In add-  i t i o n to i t s s i m p l i c i t y , the main v i r t u e of wedge refocussing i s that i t enables the v e l o c i t i e s of the electrons to be analysed without the d e f l e c t i n g magnetic f i e l d straying over into the regions i n which the electrons originate and where they are detected.  Further, the yoke provides some shielding of the detector  and the geometry and distances are such that excellent shielding from gamma rays and a n n i h i l a t i o n r a d i a t i o n from the source can be achieved by use of lead blocks, while s t i l l maintaining a reasonable s o l i d angle and counting r a t e .  The spread, or departure from  perfect focus i s given by S •  a#c sine 2  (See Appendix 4 ) .  where, f o r the wedge used, a  30 cms. - distance from wedge apex to source.  =  O a 21° • z whence,  5° = S  =  one h a l f the wedge angle, one h a l f the c o l l e c t i o n angle, 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 l e s s than the counter window width. The dispersion, or the a b i l i t y to separate two d i f f e r e n t v e l o c i t i e s , as measured by the distance between the points at which  16*  central rays corresponding to the two v e l o c i t i e s would focus, i s shown to be  -  D s 2a s i n e AjI f we take then  D  s  (See Appendix 4 ) .  - 0 6 cms. = window width, #  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 d i s t r i b u t e d i n v e l o c i t y up to the maximum v e l o c i t y of electrons from the source, the magnet should select a l l those i n a 6% band, i . e . , 6 i n 100 p a r t i c l e s •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 t i n . i n 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 i n one end plate.  A 1/2 i n . diameter mica window i n the other end plate  serves as exit s l i t f o r tiie electron beam.  A lead b a f f l e placed  next to the exit flange serves to cut down the amount of scattered r a d i a t i o n i n the beam a r i s i n g from Compton and photo-electrons ejected from the walls of the vacuum box by gamma rays from the source and from a n n i h i l a t i o n r a d i a t i o n from positrons stopped i n the w a l l s .  Lead blocks are set up to prevent d i r e c t gamma rays  from the source entering the counters.  The general layout of t h i s  apparatus i s shown i n F i g . 3 and Plate 1.  17.  C)  Choice of Sources. RaE, with an Emax of 1.17 Mev. and h a l f 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 n i c k e l surface after removal of RaF by a similar electrochemical deposition on s i l v e r , 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 t h i s experiment the alpha emission from  RaF and sof b e t a emission from RaD i t s e l f are not harmful. Reasonably t h i n sources were used, which were deposited on an area of about 1 cm. diameter, and thick backings. The choice of a positron emitter f o r these experiments was a d i f f i c u l t one, since there are r e l a t i v e l y few positron emitters with Emax. greater "than 1 Mev., s t i l l fewer of these have an adequate h a l f l i f e to be u s e f u l f o r these experiments In Vancouver.  Further owing to the ready a v a i l a b i l i t y of sources  from the Chalk River P i l e i t was preferable that the source should be producable by a neutron reaction i n r e l a t i v e l y high s p e c i f i c activity. One of the positron emitters producable i n a p i l e Cu64. from C u ( n » y ) C u 6S  64  l i f e of 12.8 hours.  reaotion, has Emax. of 0.66 Mev. and a h a l f A considerable f r a c t i o n of the active n u c l e i  decay v i a f emission but the main objection to using t h i s 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 Z n 4 ( , y ) z n 6  n  6 5  reaction,  "but on taking an absorption curve i t was evident that the r a t i o of Zn t» n u c l e i which decayed by emitting a positron to those which 6  18.  decayed "by K capture and emitted a 1 Mev. * r a y was i n the region of 1 i n 2 0 0 .  This source only provides positrons of Emax. of  0 . 4 Mev., hut the h a l f l i f e of 2 5 0 days would have been very s u i t able.  Owing to the high r a t i o of gamma rays to positrons t h i s  source was not used. Consideration was then given to sources which could be prepared with the a i d of a cyclotron.  Of these the f o l l o w i n g  were considered: £ o  ix r t e  r  Pre p& rist 'i •  T  0.77  H&V  4,5" <Aivjs  72 3.1  w  s  WrS.  Mev.  O.S8' Y[ev.  1.0  0 5  E »HI\X  G o o J. Ty^_ " t o o s k o r t  Lrf>UJ  E rwjxy  ^eV.  |.0  Co  Low  |V  It  W'  AN^S  was chosen as the positron emitter.  Emix ^ d  l  i  ]  y  U  u  K  Through the kind-  ness of Dr.Hamilton, who i s i n charge of the 6 0 i n . cyclotron used at Berkeley f o r trace preparation, a m t l l i c u r i e of C o prepared f o r use i n t h i s experiment.  5 6  has been  Sinoe the range of the 2 5 Mev.  deuturons from the Berkeley 6 0 i n . cyclotron used f o r the bombardment of the i r o n i s small, the C o surface layer of the target d i s c , the atoms decay by K-capture.  5 6  w i l l be concentrated i n a t h i n i t has been shown that l/z of  The fi* spectrum 1B b e l i e v e d to be  simple, and therefore the momentum-number d i s t r i b u t i o n can be  19. g i v e n b y a Fermi  plot:  i . e . , the p r o b a b i l i t y cj(6,I t It where £ = E E l e c t r o n / m c , 2  0  )-=Kf(£'--lK(£ -£ ) e  <> Eniax/ni o  £  a  2  0  From t h i s , t h e average energy can b e shown t o be a p p r o x i m a t e l y 650 Kev. D)  Intensity Considerations.  ,  The wedge magnet i n use h a s t h e c o l l e c t i o n angle i n one plane of 2 / l l r a d i a n .  I n the other p l a n e the angle, as l i m i t e d  by the e x i t window which i s 1/2 i n . a t a d i s t a n c e o f 28 i n . , i s approximately l / 5 6 r a d i a n .  Thus the o v e r a l l s o l i d a n g l e  sub-  tended b y t h e counter a t t h e source i s (1/4TT)  (1/56) (2/11) = 1/3872  Hence a m i l l i c u r i e source of C o (3.7)  5 6  can b e expected t o g i v e  ( 1 0 ) (1/3872) (6/100) ( l / 3 ) (1/3) = 50 c o u n t s / s e c , 7  where the f a c t o r s of 1/3 a r e allowances f o r K-capture and s e l f a b s o r p t i o n i n the source, w h i l e a m i l l i c u r i e source of RaE would be expected t o g i v e s l i g h t l y l e s s than 450 c o u n t s / s e c , on the t h i c k n e s s . RaE  depending  I n f a c t w i t h approximately 1/2 m i l l i c u r i e of  t h e c o u n t i n g r a t e a t the optimum v a l u e o f  was found t o b e  170 c o u n t s / s e c . E)  Counter  Design.  I n order t o a p p l y t h e e q u a t i o n f o r e f f i c i e n c y i t i s n e c e s s a r y t o determine p r e c i s e l y  the value of  the path length  through t h e c o u n t e r , or t o e v a l u a t e t h e o r e t i c a l l y t h e average v a l u e of l %  ment.  1  pertaining to the p a r t i c u l a r  e x p e r i m e n t a l arrange-  W i t h the wedge a n a l y s e r d e s c r i b e d , t h e d i r e c t i o n o f t h e  e l e c t r o n s l e a v i n g t h e e x i t window are w i t h i n the window,  5° t o t h e normal t o  i n order t o d e f i n e w i t h some e x a c t i t u d e the p a t h  20.  l e n g t h through the i n e f f i c i e n t counter i t was d e c i d e d t o use a r e c t a n g u l a r envelope, and t h e whole counter d e s i g n was based oh use of 3 cm* wave guide b r a s s t u b i n g f o r t h i s envelope* has t h e obvious advantage  This  over a c y l i n d r i c a l counter t h a t n o t o n l y  i s t h e d i s t a n c e between the windows known q u i t e c l o s e l y b u t t h a t t h i s d i s t a n c e can b e made q u i t e s m a l l - 1 cm* - so t h a t  relatively  l a r g e v a l u e s o f P.S.I, can b e measured w i t h a n o t too low f i l l i n g p r e s s u r e , such as occur w i t h gases l i k e argon*  Too low a p r e s s -  u r e i s r a t h e r u n d e s i r a b l e as t h e s t a b i l i t y o f counter  performance  over a p e r i o d 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 o f t h e counter i s low. Again i t i s r e l a t i v e ly  easy t o i n s e r t windows o f 1/2 i n . b y 1 i n . i n m i c a o f t h i c k -  ness as low as 2 m i l l i g r a m s / s q . cm. on a f l a t b r a s s s u r f a c e b u t almost i m p o s s i b l e t o do so over a c y l i n d r i c a l s u r f a c e .  Finally  a c l o s e l y packed c o i n c i d e n c e arrangement i s e a s i l y s e t up w i t h such r e c t a n g u l a r envelopes, and so enable a l a r g e r s o l i d angle t o be subtended a t t h e source f o r t h e same counter volume than i s p o s s i b l e w i t h c y l i n d r i c a l geometry. Curran and R e i d have i n v e s t i g a t e d some of t h e p r o p e r t i e s o f rectangular counters.  U s i n g a c o l l i m a t e d source they found t h a t  the e f f e c t i v e c o u n t i n g volume o f t h e counter c o i n c i d e d w i t h i t s g e o m e t r i c a l volume.  Because of the reduced l e n g t h s of paths a-  l o n g which t h e p o s i t i v e i o n s pro duced i n a d i s c h a r g e t r a v e l t o the cathode, i t was expected t o observe s h o r t e r dead times than found i n c y l i n d r i c a l c o u n t e r s of comparable c r o s s s e c t i o n a l a r e a , 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 t o the r a t i o of t h e l e n g t h of the w a l l s o f a r e c t a n g u l a r counter which i s imposed b y t h e f a c t  that  21.  the f i e l d must not be too h i g h i n the s h o r t d i r e c t i o n t o p r o duce o v e r s h o o t i n g and y e t the f i e l d i n the l o n g d i r e c t i o n must b e s u f f i c i e n t f o r an avalanche t o o c c u r .  Curran and R e i d p o i n t  out t h a t the r a t i o of maximum t o minimum f i e l d s t r e n g t h s e f f e c t ive  i n a r e c t a n g u l a r counter i s g i v e n by  -(my* ) + p *  where  0  1  f>- 3 w i r e r a d i u s * d i s t a n c e a t which m u l t i p l i c a t i o n process begins is  l e n g t h of s h o r t w a l l .  F o r the counters, used i n the p r e s e n t i • 1  cm.  f> = 0.01905 hence M » One  experiment  cm.  1.002  can t h e r e f o r e conclude t h a t tiieee counters s h o u l d operate  c o m p a r a t i v e l y as w e l l as c y l i n d r i c a l . were of t h e order of 60 V o l t s .  The p l a t e a u l e n g t h s found  T h i s i s more than adequate f o r  a c c u r a t e c o u n t i n g when the counter v o l t a g e can be d e r i v e d wrom a w e l l s t a b i l i z e d v o l t a g e supply.  The power u n i t c o n s t r u c t e d 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 v o l t a g e s , and a f t e r 15 minutes  warming up p e r i o d 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 s e c t i o n b r a s s c o u n t e r s , one w i t h 3/8  i n . square  m i c a windows and one w i t h o u t , have a l s o been b u i l t , p a r t l y f o r comparison w i t h the r e c t a n g u l a r shaped envelope,  and show r a t h e r  b e t t e r p l a t e a u 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 p a r a graph  " R e s u l t s " ) . O r d i n a r y b e l l type c o u n t e r s have been used f o r  22. t h e second 100$ e f f i c i e n t c o u n t e r . F u r t h e r , as an a l t e r n a t i v e scheme f o r d e t e r m i n i n g P.S.I*» a t r i p l e segmented c o u n t e r ( 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 a l o n g t h e l i n e s suggested by Ramsey.  T h i s has been op-  e r a t e d s u c c e s s f u l l y as t h r e e c o u n t e r s i n one.  I n o r d e r t o be u s e d  f o r a c t u a l measurement of P . S . I . , i t s t i l l needs t o 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 t h e r a t h e r s m a l l s o l i d of e l e c t r o n s i t w i l l F)  angle  accept.  Counter C o n s t r u c t i o n and F i l l i n g  Techniques.  S c a l e diagrams of t h e c o u n t e r s u s e d a r e g i v e n i n F i g 5. The r e c t a n g u l a r wave g u i d e has t h e 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 K o v a r s e a l s and f i l l e r tube a r e t h e n s o f t  dered w i t h a c i d c o r e s o l d e r and a hand t o r c h (gas and  sol-  oxygen).  Care i s t a k e n t o keep t h e s o l d e r c l e a n b y w i p i n g i t w i t h a wet b e f o r e and a f t e r t h e s e a l s a r e i n s e r t e d .  rag  The c e n t r a l w i r e o f  0.005 i n . d i a m e t e r t u n g s t e n , s p o t w e l d e d 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 , being 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 c o u n t e r i s now  i n g i t i n a h o t s o l u t i o n of 1, IT. HNO^.  c l e a n e d by  plac-  G l y p t a l i s f i r s t coated  on  t o p of t h e s o f t s o l d e r t o p r e v e n t i t b e i n g c o r r o d e d b y 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 t o a water b a t h , where i t i s t h o r o u g h l y r i n s e d .  F i n a l l y the  c o u n t e r 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 a l l o w e d t o d r y i n a vacuum dessicator. counter.  The n e x t p r o c e d u r e  i s t o s e a l m i c a windows onto  the  B e s t Ruby m i c a i s u s e d w h i c h has been s p l i t under warm  water b y a v e r y sharp t u n g s t e n n e e d l e .  The t h i n s h e e t s of m i c a a r e  examined under p o l a r i z e d l i g h t t o s e l e c t t h o s e of u n i f o r m t h i c k n e s s . The s e a l u s e d i s G e l v a V-7,  a V i n y l Acetate Resin,  Fill«r TuLe Tungst en- <J l*cs$ Silver  solder  Gkss  Sleeve.  O.0O5"  Tungsten.  S  0 0 1 5 " Tungsten  Spring Cowto^cts  Glctss Beads Tjrex Envelope. cLiam.. Cu coXkodes.  Silver  Solder.  stu »k.ff . F  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 ->$tuptkl(off Rect  t^ncj u.  1 evr -  E n v e l o p e s : \ x \ **+ brass Wave  Wihct-OWS  Sc&l  cjaide  tu.bi«<j  -* O.oos" T u n g s t e n  \"X M\co.or M  2. S ^ u ^ r e . Envelopes:\*%  U~fr.ss  t u b i n g  W i rvdows - Vj >• 'y H  11 a  -» Window -RoundedL Ed^es Cknd Corners.  •^o.oi Advance  23.  which i s mixed i n acetone.  A t h i n 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 a i r bubbles "by heating at 150° C. f o r 1/2 hour. After t h i s , the window i s placed on the counter and weighted i n p o s i t i o n while the Gelaa i s baked to hardness at 150° C. f o r 3/4 hogr.  F i n a l l y the mica i s trimmed down and a coat of g l y p t a l  applied to the edges.  The heating process causes the solder to  soften and the wire to p u l l i n and hence to require resoldering. The c y l i n d r i c a l counters having Cu cylinders are cleaned "by a chromic acid p a s s i v i z i n g process.  The mica window i s 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 t e s t i n g apparatus i s shown i n Plate 2. Taper j o i n t s 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 a i d of the mercury d i f f u s i o n pump, and the wires are glowed to burn o f f sharp points or d i r t p a r t i c l e s adhering to t h e i r surfaces.  They are then f i l l e d i n the usual way  by allowing the organic vapor 1/2 hour to d i f f u s e before adding the main Inorganic component.  Several hours are l e f t f o r d i f f u s i o n and  absorption by the counter surfaces to be complete before t e s t i n g 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 b e t t e r plateau, etc., after t h i s time than shortly after f i l l i n g .  The operating voltage  does not noticeably a l t e r during t h i s time. The counter operation i s tested before i t i s removed from the f i l l i n g system.  24.  G)  E l e c t r o n i c Equipment. The electronic equipment used f o r t e s t i n g , as shown i n  Plate 2, includes a h e a d amplifier, s t a b i l i z e d power supply, a scaling u n i t 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 s i z e .  It consists  of a single 6AC7 amplifying stage with a low anode load to f o l l o w a r a p i d pulse r i s e , important  i n 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  i s a 6AG7 cathode follower adequate to drive a long cable capaci 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 o f p o t e n t i a l on the counter wire. pected amplifier voltage gain of U  Measurements confirm the exand maximum output pulse s i z e  p f Ztf v o l t s , and also that the r i s e time with 6 f t . of cable i s l e s s than 1/2 microsec. The  •Triggered* time base enables the start of the time  base to be coincident with the a r r i v a l of the pulse, so that on the screen with a high counting rate the appearance i s as shown i n P l a t e 3t  A delay time of l/4 micro sec. i n the s i g n a l lead en-  ables the time base to be started ahead of the v e r t i c a l displacement of the beam so the r a t e of r i s e 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 d i f f e r e n t heights, and i n f a c t of deducing most of the  25.  troubles which a r i s e i n the counter* The electronic equipment used i n the main experiment i s shown schematically i n F i g . %, and a photograph i s shown i n - P l a t e 4.  The head amplifier and s t a b i l i z e d power u n i t 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 s p e c i a l adjustment  of the coincidence mix-  er, the r e s o l v i n g time was found to be 0.8 m i c r o s e c , 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  B 0  Z&x^gff the r e s o l v i n g time ~T was deduced.  V.  Results.  Graphs of observed counting rates f o r t y p i c a l specimen ~ counters against voltage are given i n F i g . $ . The b e l l type of r  counter and the rectangular and square gamma counters have u s e f u l plateaus, while the rectangular and square b e t a counters show very poor •plateaus'. One rectangular gamma counter was tested at reduced pressures and even with a t o t a l pressure of only slope of n % over a range of 100 v o l t s .  1 cms. had a plateau  A square /J-counter of  \.< cms. t o t a l pressure showed a slope of  over ioo v o l t s .  Although our value of M as previously calculated was 1.002 f o r the rectangular ^-counters and hence, on the b a s i s of Curran and Reid*s report, should have operated successfully, i t can be seen by the graph that t h i s was not the case*  The rectangular  ^-oounters having windows of either A l or mica*when operated i n  Fig  (p.  Schematic  Electronic  ftrr^emerv  Counter 1 Unit  1  Ml  Stabilized! H.I  Counter Z  Double BeM*| Oscilloscope  Coincidence Miver  3  Fig. *7 (co»x,t3  26.  their  'Geiger* r e g i o n , gave p u l s e s o f two d i s t i n c t h e i g h t s  analogous t o t h e e f f e c t o f a head a t t h e c e n t r e o f the w i r e , as was checked "by p l o t t i n g c o u n t i n g r a t e a g a i n s t s c a l a r criminator setting.  dis-  T h i s e f f e c t was o n l y p a r t i a l l y improved when  t h e m i c a was made c o n d u c t i n g on the o u t s i d e b y c o a t i n g i t w i t h g r a p h i t e , which seems t o i n d i c a t e , c o n t r a r y t o the u s u a l t h e o r y , t h a t a cathode mechanism such as t h e e j e c t i o n o f e l e c t r o n s from the cathode b y quanta emitted i n the i n i t i a l avalanche, ed i n the spread o f t h e d i s c h a r g e .  To check t h i s l a s t  i s involvhypothesis  a p o i n t 43 source was p l a c e d a g a i n s t the window c e n t r e and t h e counting  r a t e noted, then t h e source was moved t o the window's edge and  the c o u n t i n g r a t e a g a i n r e c o r d e d . E f f i c i e n c y a t Edge E f f i c i e n c y a t Centre  The v a l u e o f the r a t i o  was 1.54 f o r a g r a p h i t e covered m i c a window,  and was 1.91 f o r t h e same window without g r a p h i t e .  The e f f i c i e n c y  r a t i o s were found t o b e t h e same when c o u n t i n g o n l y l a r g e p u l s e s and when c o u n t i n g b o t h l a r g e and s m a l l p u l s e s and a l s o f o r a gamma source.  Thus i t would appear t h a t t h e e f f i c i e n c y o f t h e counter  i n the c e n t r a l r e g i o n where the windows a r e i s v e r y low,  even when  t h e f i e l d d i s t r i b u t i o n i n t h i s r e g i o n i s made u n i f o r m . A f u r t h e r check was made b y moving a p o i n t gamma source along the narrow edge o f t h e counter and a g a i n the e f f i c i e n c y was found t o drop i n t h e c e n t r a l r e g i o n .  T e s t s made w i t h o o l l i m a t e d  b e t a sources d i d not show any s i g n i f i c a n t change i n l a r g e t o s m a l l p u l s e s i z e as the r e g i o n i n t o which the b e t a s 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 t o b e l i e v e t h a t t h e cathode mechanism and not m e r e l y t h e f i e l d d i s t o r t i o n p r e v e n t s t h e c e n t r a l r e g i o n  27.  from having  t h e same G e i g e r  the counter. these  N a t u r a l l y t h i s r e s u l t s i n very poor plateaus f o r .  beta counters An  o p e r a t i n g v o l t a g e as t h e r e s t o f  so f a rt e s t e d .  a t t e m p t was made t o m e a s u r e t h e r e a l  a counter  e f f i c i e n c y o f such  by p l o t t i n g t h e 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 t h e r e c t a n g u l a r counter, 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 ious counts is  raised  until  of i t s slope.  which a r i s e i n the rectangular counter  should not a f f e c t  t h e s t a t e o f almost  N w i t h N2 = 5 0 c o u n t s 50 counts  thebell  the coincidence rate  continuous  The s p u r -  as the voltage  significantly  i s reached, f o r  = 2 NxN t , 2  c  p e r s e c . and hence N  c  = (1/2-HlO)  p e r s e c , and w i t h = 10^ counts  5  discharge  counter  s h o u l d a l s o be a b o u t D  s e c , N-^ c a n be  p e r s e c . b e f o r e t h e chance  12)150)11/2)110 >-«• 'spurious' The  c o i n c i d e n c e r a t e amounts t o 1 0 % o f t h e r e a l results  t a b u l a t e d below bear t h i s  t h a t even a t t h e h i g h e s t v o l t a g e s reached in  the counter  rate.  o u t and i n d i c a t e  before  discharge  sets  e f f i c i e n c y was o n l y 96foiLinstead o f t h e c o m p u t e d  f i g u r e o f 100%mfor t h e f i l l i n g .  118 L  :  coit  B V t k cj roav\d 20 C u.irr«rvt  (Amps)  0.1  Counts Eff  »v»im  i cJcRcy=  my  K  .i Con.  11  *,  *.  *  1*  ft  «  O./S'  D.I  OAST  I38-& IS5-I  A  1%  2  S-7f-  COO-KTS/ 1 i H i n -  N  in  n^s  %  28.  I t was obvious a t t h i s stage t h a t f u r t h e r work was needed t o improve t h e b e h a v i o u r o f t h e r e c t a n g u l a r b e t a c o u n t e r s . F i r s t l y i t i s i n t e n d e d t o s p u t t e r copper onto t h e m i c a i n an attempt  t o e q u a l i z e t h e work f u n c t i o n s of t h e cathode m a t e r i a l s  and hence make t h e counter 100^ e f f i c i e n t , and secondly t o use a "quench u n i t " t o reduce v o l t a g e on counter b y 250 v o l t s once d i s charge has o c c u r r e d and keep i t a t t h i s  'below G e i g e r t h r e s h o l d '  l e v e l f o r 300 m i c r o s e c . t o e l i m i n a t e m u l t i p l e p u l s e s and so f l a t t e n the p l a t e a u and so b e sure t h a t b o t h c o u n t e r s w i l l f i r e once o n l y 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 t o t h e c i r c u i t shown and appears t o work satisfactorily.  STABILIZED  POWER U N I T  -  T.RE.  H F S I ^  HEAD  A M P L I F I E R  32.  APPENDIX 1. THE 1) C o l l i s i o n  ENERGY TRANSFER RELATIONS.  Equations.  >_  C o n s e r v a t i o n o f momentum r e q u i r e s &)  M V'  b)  MV  hence  2  2  2  cos 0>  - m u  2  2  2  sin <(> 2 2  =  2  c ) MV* = m u 2  c o s © - 2MVmu c o s e + M V  2  2  2  2  2  2  - 2 MVmu c o s e + M V  2  2  m u sin e 2  Conservation o f Energy r e q u i r e s d)  that  1/2 MV"' = 1/2 M V 2  that  - 1/2 m u  2  2  2  C o m b i n i n g C) a n d d ) we g e t , e)  M V'  f)  (Mm + m ) u  2  2  = M Y 2  2  2  therefore or  2  - Mmu  = 2M7'mu c o s  u = *^ cos © Q, = e n e r g y t r a n s f e r r e d = l/2mu =  2)  2  = ^ ^ 0  2  _^U0  L  /  2  MV2  I m p a c t P a r a m e t e r i n Coulomb The p a r t i c l e  will  with a force of z e / r 2  2  t o the second p a r t i c l e ,  cos e  Z  2  c o s  2  e  Field.  be a t t r a c t e d t o w a r d s t h e  and w i l l  describe  a s shown b e l o w :  electrons  a h y p e r b o l a w i t h respab t  In this  sketch q = closest distance of  approach.  p = impact parameter = c l o s e s t d i s t a n c e of if k  p a r t i c l e were not d e f l e c t e d .  = distance of focus  of hyperbola  origin.  of d e f l e c t i o n of i n c i d e n t p a r t i c l e .  & = angle  of d e f l e c t i o n of e l e c t r o n w i t h respect  to  incident direction.  energy r e l a t i o n s h i p a t the c l o s e s t d i s t a n c e of approach i s 1/2  mv  = 1/2  2  mv  2  +  ze /q 2  where  v = v e l o c i t y o f p a r t i c l e a t an  and  v  0  = v e l o c i t y of p a r t i c l e at  Let K = ze /mv  2  hence  2  2  v /v 2  mvp  = 1 -  0  =  whence  2  = l-2K/q  2  From h y p e r b o l a  p/q  2  geometry  q = e ( l + cos e ) e =  have  - mv q 2  p /q  origin.  2K/q  therefore v / v 2  infinite  -~  F r o m a n g u l a r momentum c o n s i d e r a t i o n s we  and  from  cj> = a n g l e  • the The  approach  p/sine  t h e r e f o r e q = p(l+cos£ ) / ( s i n e )  (A)  distance  34. and  P /q 2  By s u b s t i t u t i n g  = (1-oos  2  © )/(l+cos © )  2  = ( 1 - c o s e ) (1+cos e;)  2  i n ( A ) a n d m u l t i p l y i n g b y ( 1 + c o s © ) we g e t  ( 1 - c o s e) = 1 + c o s e -  (2k/p)(sine)  hence  2k/p = 2  and  p/k = t a n ©  now  t a n © = s i n 0 / c o s 0 = ( 1 - c o s e )/cos ©  therefore  1 = cos .e ( l + p / K )  therefore  c o s 0 = 1/(1+  5)  cos©/sine  2  2  2  2  2  2  2  2  2  E v a l u a t i o n o f t h e P a r a m e t e r p. Q=4mM/(M-m)  hence  m p v /z e  and  p  2  2  2  4  2  4  = (4T'/Q  2  .2„  „_„/,„,_,2  T c o s 9 =4mM/(M-m) 2  =( (4mMT/© (M+m) -  - I )  2  e/4T'  2  2  -1))  m  //,.  ™*p*_ + ,  T/(l+  v  )  35-  APPENDIX 2. MAGNET DESIGN. The 1 / 6 model o f t h e magnet d e s i g n e d f o r t h e U . B . C . Van de G r a a f f g e n e r a t o r has been m o d i f i e d t o have an a i r gap o f 3 / 4 i n . Not shown i n t h e diagram F i g . t f ) a r e t h e c o i l s w h i c h have been wound w i t h  woo t u r n s o f N o . 1 3 gauge formex  copper  w i r e and p r o v i d e d w i t h a w a t e r c o o l i n g l a y e r s u c h t h a t a maximum c u r r e n t o f I t amps, can be passed t h r o u g h w i t h o u t s e r i o u s overheating. Hence  N  Therefore  *max  =  '7,£t>o amp. t u r n s  M.M.F.j^^. = 4 T T N I / 1 0 = 12, (ot g i l b e r t s =  ^air !air  Assuming a maxumum v a l u e f o r H j _  +  r o n  H  iron ^ r o n  o f 4 0 Oersteads t o correspond  t o 1 0 , 0 0 0 l i n e s / s q . c m . i n t h e i r o n y o l k used w h i c h i s made o f l a m i n a t e d low c a r b o n s t e e l , t h e n M.M.F. Therefore  ^ a i r-  maX  =22, 10k  =  (11) ( 2 . 3 4 ) + ( 4 0 ) 1 7 2 ) lb 6  (2.34)  " Kilog^uss  W i t h t h e model as used, s a t u r a t i o n would a b v i o u s l y o c c u r 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 e n l a r g e d a i r gap, c l e a r l y t h e l i m i t a t i o n l i e s n o t i n i r o n s a t u r a t i o n but t n t h e c u r r e n t w h i c h can be passed t h r o u g h t h e c o i l s . APPENDIX 3. MAGNET. PERFORMANCE. T h i s magnet.'s performance i s g i v e n i n t h e f o l l o w i n g g r a p h s , as found by a b a l l i s t i c galvanometer and s e a r c h c o i l .  On t h e  n e x t d i a g r a m f o r comparison i s shown t h e performance o f t h e magnet when m o d i f i e d t o have wedge shaped p o l e p i e c e s o f a p p r o x i m a t e l y t h e same t o t a l a r e a as t h e square t i p s .  APPENDIX 4 . MAGNETIC REFOCUSSING OF ELECTRON PATHS. WEDGE MAGNETS.  11  3  The  e l e c t r o n p a t h s i n t h e wedge a r e a r c s o f c i r c l e s  which a r e tangent exit  a t t h e edges o f t h e f i e l d  t o the entrance  and  directions.. Consider  a homogeneous beam o f e l e c t r o n s o f v e l o c i t y  e n t e r i n g the entrance  v  s l i t A making t h e angle © w i t h , t h e base  l i n e and e n t e r i n g t h e 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 fthe  f i e l d H i s s e t t o t u r n t h e beam i n t o a n a r c o f r a d i u s R w h e r e R « a sin © where  = OP = OW  HR = mv/e  then the centre of curvature o f the a r c w i l l 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" a n d  e n t e r t h e c o l l e c t o r a t B on t h e a x i s . AQJ,  A l l o t h e r beams e . g .  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  be r e f o c u s s e d  so a s t o c r o s s v e r y c l o s e t o B.  best refocussing f o r a divergent p e n c i l where The  be 0 , a n d t h e e x i t  departure  b = a  -*  t o AP w i l l  That i s , the  from A occurs  a t B,  sine/sin^  from p e r f e c t focus - the Spread S = UB s i n K, w h e r e UB i s t h e s p r e a d  along the  37, b a s e l i n e due t o beams m a k i n g 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. If  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 A P , its  radius of curvature w i l l  l a r g e r and i t w i l l b a s e l i n e a t C.  intersect the  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 is  be  u  velocities  B  called the dispersion - D D = BC  sin*  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 t h e r a y p a t h as t h e s l i t  of the collector w i l l  d i c u l a r t o the path.  n o r m a l l y be p l a c e d  perpen-  The r a t i o D/S g i v e s a m e a s u r e 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 t h e x - a x i s a n d A Y t h e y - a x i s .  Consider the .  p a t h AQ,vTJ o f t h e beam a t + «*° t o t h e n o r m a l beam.. C o o r d i n a t e s o f Q,: X]_  = a c o s © c o s (© + «<)/cos*  2v  C o o r d i n a t e s o f T: x  2  = a ( ( c o s © c o s (© +°<)/eos»<  y  2  = a( ( c o s 6 s i n ( 0 +  )/eos°<  + s i n © sin( e - s i n o cos( ©+<><)))  C o o r d i n a t e s o f V: X3  = +2(x *y 2  cot* +  2  9  -4 c o s e c ^ Y  2 (X2  a c o t.2 ^tf ) + 4 ( x + y 2  2  +y  2  + 2ay  2  cot y +  a c o t ^ jr )'  2 P ? 2 cot X + a cot^jr - a ^ s i n e)  2 cosec'y y^  2  :  = ( x ^ - a) cot 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 a b o u t T: o  p  2 . 2 .  sr. and  second  edge o f w e d g e :  Coordinates of U:  x  4  = 2:3 +'  y  4  = 0  y = (cotY)x - a cotY  {where i n t e r s e c t s A O )  ly -y )/U^-z ) 5  Hence S - >s» s i n . V =  2  2  (a+b-x^jsinY  - a l s i n if * . s i n e ) - s i n t ( ( z j + y ( y - y ' ) / ( x - x ) -)') • ' 3  On e x p a n d i n g  5  i n p o w e r s o f << a n d d r o p p i n g t e r m s  S • a <</2 ((sin ©/sin y 2  2  When  3 = * , S = a * sin©  When  © « V = 90° ,  +  2  5  i n *3f  2  e  t  c  <  sin y/sine)) 2  2  S =• a *  2  t h e u s u a l 180° f o c u s s i n g c a s e .  Derivation of Equation f o r P i Increase of if  H i s kept  AV i n v i n c r e a s e s R b y  A R / R =AV/V  fixed.  If this  i s d r a w n i n , one c a n f i n d a.new p o s i t i o n a n d 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 ZOB.  A R where  (Same p r o c e d u r e  as b e f o r e ) .  a n d . i t s i n t e r c e p t on  Expanding  gives:  D = a s i n © / s i n V -av/v ( s i n © + s i n y ) Whan  G = y,  When 0 = y= Resolving  D = 2a 90°,  sine-Av/v  D = 2a A V / V .  Power:  D/S i s p l o t t e d a s a f u n c t i o n o f (2A )(AV/V). 2  2sin y  © arid y i n u n i t s o f  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 = s i n © , g i v i n g t h e r a t i o D/S = 1-1/3  t h a t f o r 180° c a s e o f  0 = 43°,  Y=  43° c a s e .  times .  BIBLIOGRAPHY, (1) A n d e r s o n , C. D., P h y s . R e v . 44, 406,  1933.  (2) A n d e r s o n , C. D., P h y s . R e v . 30, 263,  1936.  (3) B a r n o t h y ,  P h y s . Rev.. 74, 844,  1948.  (4) B e t h e H., H a n d b u c h d e r P h y s i k , V o l . 24, 1, p 323, (3) B r o d e , R. D., R e v . Mod. P h y s . 11, 222,  1933.  1939-  (6) C o r s o n , D. R. a n d B r o d e , R. "D., P h y s . R e v . 33, 733, (7) C o s y n s , M.,  Bull.  T e c h . A s s . I n g . B r u x . , 173-263,  (8) S u r r a n , S. C. a n d R e i d , J . M.,  N a t u r e 160, 866,  1938.  1936.  1947.  (9) C u r r a n , S. C. a n d R e i d , J . M., R e v . S c . I n s t . 19,  67,  1948.  (10) D a n f o r t h , W. E . , a n d Ramsey, W. E . , P h y s . R e v . 49, 834, (11) , G r a y , I i . H., P r o c . Camb. P h i l . (12) G u r n e y , R. W.,  S o c . 40, 7.2, 1944.  P r o c . R o y . S o c . A 107, 332,  (13) H a z e n , W. E . , P h y s . R e v . 63, 107,  1943.  (14) H a z e n , W. E . , P h y s . R e v . 63, 239,  1944.  (13) H e r e f o r d , . F. L . , P h y s . R e v . 74, 374, (16) K u n z e , P., Z e i t s . (17) L i v i n g s t o n ,  f . P h y s i k , 83, 1,  1923.  1948. 1933.  Kev- r W . ?kys., J u l ^ , 1137. p.AtS"  (18) N i c o d e m u s , D. B., PhD. T h e s i s , S t a n f o r d , (19) Ramsey, W.  1936.  E., P h y s . R e v . , 6 l , 97,  1946.  1942.  (20) S c h n i e d e r , K., A n n . d e r P h y s i k , 33, 443,  1939.  (21) S k r a m s t a d , H. K. a n d L o u g h r i d g e , D. H., P h y s .  Rev.30,677, 36. 1  (22) S t e p h e n s , W. E . , P h y s . K e v . 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., P h y s . R e v . (23) W i l l i a m s , E. J . , P r o c . R o y . S o c . A 133, 108, (26) W i l l i a m s , E. J . , a n d T e r r o u x , F.R.,  1931.  Proc.Roy.Soc.A126,289,1929  (27) Z a h n , C.T. a n d S p e e s , A.H.,. P h y s . R e v . , 38, .861,  1940.  

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