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The operation of a low energy Beta ray spectrometer and the measurement of the spectrum of radium D Brown, Harry 1951

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THE OPERATION OF A LOW ENERGY BETA RAY SPECTROMETER AND THE MEASUREMENT OF THE SPECTRUM OF RADIUM D  by H a r r y Brown  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in PHYSICS  W© a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e s t a n d a r d r e q u i r e d from c a n d i d a t e s f o r t h e degree o f DOCTOR OF PHILOSOPHY  Members o f t h e Department o f PHYSICS  THE UNIVERSITY OF BRITISH COLUMBIA September, 1951  ABSTRACT  A semi c i r c u l a r f o c u s s i n g s p e c t r o m e t e r lias been b u i l t t o examine b e t a s p e c t r a i n t h e energy range 100 Kev. plished  below  The d e t e c t i o n o f t h e b e t a p a r t i c l e s i s accom-  by means o f G e i g e r c o u n t e r s f i l l e d w i t h t h e s a t u r -  a t e d vapor o f l i q u i d heptane (C^Hj^) kept i n a b a t h o f . melting i c e .  The windows o f the c o u n t e r s a r e made from  t h i n f i l m s o f zapon about 5 t o 8 micrograms/cm ness.  2  The s o u r c e s a r e mounted on s i m i l a r f i l m s  i m a t e l y 10 micrograms/cm  i n thickapprox-  and have an average t o t a l t h i c k -  ness of t h e o r d e r o f 30 micrograms/cm . The c o m b i n a t i o n o f t h i n s o u r c e and t h i n windows e n a b l e s measurements o f s p e c t r a to be made down t o an energy o f 2 :Kev. An e x a m i n a t i o n o f t h e b e t a spectrum o f RaD (82JPb ) 210  w i t h t h e s p e c t r o m e t e r has been c a r r i e d o u t .  I t consists of  L, M and N c o n v e r s i o n l i n e s o f a 47 Kev gamma r a y , a peak a t about 2 Kev a s s i g n e d t o c o n v e r s i o n o f a 7.7 Kev gamma i n t h e M s h e l l o f t h e atom, and a p r i m a r y b e t a spectrum.  A Kurie  p l o t o f t h e p r i m a r y b e t a spectrum y i e l d s an end p o i n t of 21.7 Kev.  I n a d d i t i o n t h e r e a r e two weak c o n v e r s i o n l i n e s  at 18 and 21 Kev w h i c h a r e t e n t a t i v e l y a s s i g n e d t o t h e L c o n v e r s i o n o f gamma r a y s o f 34 and 37 Kev.  T H E UNIVERSITY OF BRITISH COLUMBIA F A C U L T Y OF G R A D U A T E  STUDIES  P R O G R A M M E O FT H E FINAL ORAL EXAMINATION FOR T H E DEGREE OF D O C T O R  OF PHILOSOPHY  o£  HARRY  BROWN  B . A . (Brit. Col.) 1943 M . A . (Brit. Col.) 1948  TUESDAY, OCTOBER  9th, 1951, A T 2 P.M.  IN R O O M 201, PHYSICS B U I L D I N G  C O M M I T T E E IN CHARGE:  Professor Professor Professor Professor  Dean H . F. Angus, K. C. Mann G. M . Shrum S. A. Jennings J . B. Warren  Chairman Dean Blythe Eagles Professor H . C. Gunning Professor W. A . Bryce Professor Harry Adaskin  THESIS THE  OPERATION  OF A L O W ENERGY  BETA-RAY  SPECTROMETER  A N D T H E M E A S U R E M E N T OP T H E S P E C T R U M OF R A D I U M D  A semi-circular focussing spectrometer has been built to examine beta spectra in the energy range below 100 Kev. The detection of the beta particles is accomplished by means of Geiger counters filled with the saturated vapor of liquid heptane (C H,„) kept in a bath of melting ice. The windows of the counters are made from thin films of zapon about 5 to 8 micrograms/cm in thickness. The sources are mounted on similar films approximately 10 micrograms/cm-, and have an average total thickness of Lire order of 30 micrograms/cm . The combination of thin source and thin windows enables measurements of spectra to be made down to an energy of 2 Kev. 7  2  2  A n examination of the beta spectrum of RaD ( oPb ) with the spectrometer has been carried out. It consists of L , M , and N conversion lines of a 47 Kev gamma ray, a peak at about 3 Kev assigned to conversion of a 7.7 Kev gamma in the M shell of the atom, and a primary beta spectrum. A Kurie plot of the primary beta spectrum yields an end point of 21.7 Kev. In addition, there are two weak conversion lines at 18 and 21 Kev which are tentatively assigned to the L conversion of gamma rays of 34 and 37 Kev. A tentative analysis .of the decay scheme of RaD is given. 210  s  G R A D U A T E STUDIES Field of Study: Physics. Quantum Mechanics—Professor F. J . Bclinfante Spectroscopy—Professor A. M . Crooker X-rays and Crystal Structure—Professor J . B. Warren Electromagnetic Theory—Professor G. L . Pickard Thermodynamics—Professor F. J. Bclinfante Kinetic Theory—Professor A . E . Pfennings Beta-Ray Spectroscopy—Professor K. C. Mann Theory of Measurements—Professor A. M . Crooker Electronics—Professor A. van der Ziel Chemical Physics—Professor A . J. Dekker Radiation Theory—Professor F. A.'Kacinpffer Nuclear Physics—Professor G. M . Volkoff  Other Studies: Theory of Functions of a Complex Variable—Professor W. H . Simons Theory of Functions of a Real Variable—Professor S. A. Jennings and Professor D. C. Murdoch Advanced Calculus—Dean W. H . Gage Tensor Analysis—Dean W. H . Gage Differential Equations—Dean W. H . Cage  ACKNOWLEDGEMENTS  The supported  r e s e a r c h d e s c r i b e d i n t h i s t h e s i s was  by g r a n t s f r o m t h e N a t i o n a l R e s e a r c h C o u n c i l  o f Canada and by a g r a n t from t h e B r i t i s h Columbia Research Council. The  continued  effort  of t h e a u t h o r was made  p o s s i b l e by t h e award o f N a t i o n a l R e s e a r c h C o u n c i l s t u d e n t s h i p s i n 1948-49, 1949-50, o f a B r i t i s h Columbia Telephone Company S c h o l a r s h i p i n 19.50-.51 and o f N a t i o n a l R e s e a r c h C o u n c i l summer s c h o l a r s h i p s i n 1950-and 19.51. I am i n d e b t e d t o Dr. K.C. Mann f o r t h e s u g g e s t i o n o f t h e problem and f o r i n v a l u a b l e a d v i c e , a s s i s t a n c e and encouragement d u r i n g t h e course o f t h e r e s e a r c h . F u r t h e r acknowledgement i s made o f t h e a d v i c e g i v e n by members o f t h e Department o f C h e m i s t r y w i t h r e g a r d t o t h e manufacture o f s o u r c e s  and o f t h e h e l p and  a d v i c e o f Mr. A. F r a s e r and Mr. J". L e e s i n t h e machine work and g l a s s b l o w i n g connected w i t h t h e p r o j e c t .  TABLE.OF CONTENTS Page I II  INTRODUCTION THE SPECTROMETER  I 11  A. P r i m a r y C o n s i d e r a t i o n i n D e s i g n B. The I n n e r S p e c t r o m e t e r C. P r o d u c t i o n o f t h e Magnetic F i e l d D. T e s t i n g t h e U n i f o r m i t y o f t h e M a g n e t i c Field S. M a t h e m a t i c a l Treatment o f a S p e c t r o m e t e r III IV  RESULTS  31  CONCLUSIONS AND RECOMMENDATIONS  48  APPENDIX I  50  The S c a t t e r i n g and A b s o r p t i o n o f Beta-Rays APPENDIX I I  5$  Counter Windows A. P r o d u c t i o n o f Counter Windows B. A t t a c h i n g o f t h e Windows t o t h e C o u n t e r s APPENDIX I I I  58  P r e p a r a t i o n o f Sources APPENDIX I V  62  The Counter F i l l i n g System APPENDIX V  65  A u x i l i a r y E l e c t r o n i c Apparatus A. C u r r e n t R e g u l a t i n g System B. H. T. R e g u l a t i o n C. P u l s e A m p l i f i e r and S c a l a r BIBLIOGRAPHY  6?  TABLE OF ILLUSTRATIONS FIGURE  F a c i n g Page  1  I l l u s t r a t i o n o f Semi C i r c u l a r F o c u s s i n g  2  2  A Normal B e t a Spectrum  2  J>  Energy I t e v e l Diagram f o r N e g a t r o n Decay  6  4  Energy L e v e l Diagram f o r P o s i t r o n Decay  6  5  Energy L e v e l Diagram f o r O r b i t a l E l e c t r o n Capture  6  Energy L e v e l Diagram f o r N e g a t r o n Decay to Two D i f f e r e n t S t a t e s  6  K u r i e P l o t f o r N e g a t r o n Decay t o two D i f f e r e n t States  7  6 7 8  The E f f e c t o f the Coulomb F i e l d on t h e Shape 7  o f the B e t a Spectrum 9 10  I n t e r n a l C o n s t r u c t i o n of the Spectrometer  lj?  F i e l d o f a P l a n e C i r c u l a r C o i l as a F u n c t i o n of the Distance from the Center C o n s t r u c t i o n o f the Magnet  18 19  Observed V a r i a t i o n o f Magnetic F i e l d i n Spectrometer Region  20  13>  Diagram o f E l e c t r o n P a t h s i n the S p e c t rometer  21  14  Theoretical Line P r o f i l e s  27  1.5  Comparison o f V a r i o u s B e t a Ray S p e c t r o m e t e r s  28  16  B e t a Spectrum o f Radium D  17  B e t a Spectrum o f Radium D w i t h JO Kev  11 12  Conversion Line Subtracted  J>5  •  40  18  K u r i e P l o t o f B e t a Spectrum o f Radium D  40  19  L i n e .Widths from one Counter and from Three Counters '  42  II FIGURE  F a c i n g Page  20  Suggested Decay Scheme f o r Radium D  45  21  Range o f E l e c t r o n s i n Muminum and A i r  53  22  L o s s o f Energy o f M o n o e n e r g e t i c E l e c t r o n s i n an Absorber  54  23  P l a t e a u E x h i b i t e d by one Counter F i l l e d W i t h 1.15 cms. o f Heptane Yapor  62  24  Heptane P u r i f i c a t i o n System  63  25  P l a t e a u E x h i b i t e d by Three C o u n t e r s i n P a r a l l e l  63  26  B l o c k Diagram o f C u r r e n t R e g u l a t i n g System  66  27  C i r c u i t Diagram o f C u r r e n t R e g u l a t i n g System  66  28  H. T. R e g u l a t i n g  6b  29  C i r c u i t Diagram o f P u l s e A m p l i f i e r  Circuit  6b  /  I INTRODUCTION  As soon as i t was r e a l i z e d t l i a t r a d i o - a c t i v e s u b s t ances e m i t t e d charged p a r t i c l e s w i t h a wide range o f v e l o c i t y , a t t e m p t s were made t o a n a l y z e the v e l o c i t y d i s t r i b u t i o n u s i n g a magnetic f i e l d .  The s i m p l e s t method, t h a t o f c o l l i m a t i n g a  beam o f p a r t i c l e s by s l i t s and o b s e r v i n g t h e s m a l l d e f l e c t i o n caused by a t r a n s v e r s e f i e l d w i t h p h o t o g r a p h i c quite successful with alpha p a r t i c l e s .  methods, proved  I t was f i r s t used w i t h  a source w h i c h e m i t t e d b e t a p a r t i c l e s by Baeyer and Hahn. Here t h e a n g l e s o f d e f l e c t i o n were l a r g e r , t h a n w i t h a l p h a ticles,  b u t were n o t g r e a t e r t h a n 60°.  The p h o t o g r a p h i c  1  parplate  showed a number o f l i n e s i n d i c a t i n g t h a t t h e e l e c t r o n s d i d not l e a v e t h e s o u r c e w i t h a unique v e l o c i t y but r a t h e r were e m i t t e d i n groups, each w i t h a d i f f e r e n t v e l o c i t y .  Such an a n a l y s i s o f  the v e l o c i t y d i s t r i b u t i o n o f t h e e l e c t r o n s was c a l l e d a , b e t a r a y spectrum. T h i s method o f d e t e r m i n i n g  t h e b e t a - r a y spectrum o f  a s u b s t a n c e was o b v i o u s l y l i m i t e d i n i t s r e s o l v i n g power s i n c e o n l y by i m p r o v i n g t h e c o l l i m a t i o n c o u l d t h e l i n e s be made narrower.  The c o l l i m a t i o n c o u l d o n l y be improved a t t h e ex-  pense o f i n t e n s i t y , n e c e s s i t a t i n g s t r o n g e r s o u r c e s o r l o n g e r exposures t o get u s a b l e r e s u l t s .  The way o u t o f t h e  difficulty  was t o d e v i s e some method o f f o c u s s i n g t h e e l e c t r o n s so t h a t 1.  G. Baeyer and 0. Hahn: Phys. Z e i t . 11,  488, 1910.  2.  the image, on the p l a t e would be s m a l l e r t h a n t h e e x i t s l i t  of  t h e c o l l i m a t i n g system. T h i s was  done by Danysz^ who  p o i n t e d out t h a t i f two  e q u a l c i r c l e s were drawn about two p o i n t s s e p a r a t e d  by a s m a l l  f r a c t i o n o f a r a d i u s the c i r c l e s would i n t e r s e c t a t p o i n t s d i a m e t r i c a l l y opposite.  Then, s i n c e e l e c t r o n p a t h s i n a u n i -  f o r m magnetic f i e l d a r e c i r c l e s whose r a d i i depend on  the  momentum o f t h e p a r t i c l e and t h e s t r e n g t h of the f i e l d ,  focus-  s i n g c o u l d be o b t a i n e d by a l l o w i n g , e l e c t r o n s t o t r a v e l t h r o u g h a s e m i c i r c l e b e f o r e s t r i k i n g the p h o t o g r a p h i c p l a t e .  In F i g . l ,  e l e c t r o n s s t a r t i n g f r o m t h e s o u r c e S a t an a n g l e A w i t h each o t h e r are s e l e c t e d by the b a f f l e and brought t o g e t h e r t o s t r i k e n e a r the same p o i n t o f t h e p l a t e .  Electrons of greater or l e s s  momentum are brought to a f o c u s at f u r t h e r o r n e a r e r p a r t s o f the p l a t e .  I t i s obvious t h a t the f o c u s s i n g i s . n o t p e r f e c t f o r  a finite baffle s l i t .  The  c e n t r a l r a y i n F i g . l w i l l not h i t  the p h o t o g r a p h i c p l a t e a t e x a c t l y t h e same spot as t h e  two  outer rays. This s e m i c i r c u l a r focussing spectrograph  was  used  by many w o r k e r s , n o t a b l y R u t h e r f o r d and R o b i n s o n ^ t o determine t h e momenta o f a number o f l i n e s i n the b e t a - r a y most o f t h e n a t u r a l l y r a d i o - a c t i v e elements.  spectra of  O r d i n a r i l y the  l i n e s are r e f e r r e d to by t h e q u a n t i t y Hr ( i n gauss-cms) f r o m w h i c h the energy can be o b t a i n e d by use of t h e  relativistic  formula 2.  J.  Danysz: Comptes Rendus 153.  339,  1066,  3.  E. R u t h e r f o r d and H. R o b i n s o n : P h i l . M a g .  1911. (6)  26,  717,  3.  ;  Hr = 1 0 / 3 /T(T+1.02) 4  where T i s the energy o f t h e p a r t i c l e s i n Mev i n cm.  and r i s the r a d i u s  of t h e i r o r b i t i n a u n i f o r m f i e l d o f H gauss.  A  non-  r e l a t i v i s t i c a p p r o x i m a t i o n good t o a few p e r c e n t below 50 Kev i s  Hr - 3.37ys" where S i s the energy o f the e l e c t r o n s i n v o l t s . The f i r s t m o d i f i c a t i o n o f t h e method was t h e  sub-  s t i t u t i o n o f an e l e c t r i c a l method o f d e t e c t i o n f o r t h e p h o t o 4 5 g r a p h i c p l a t e . A F a r a d a y cage, an i o n i z a t i o n chamber, o r l a t e r a G e i g e r c o u n t e r was p l a c e d b e h i n d an e x i t s l i t and magnetic  f i e l d was  investigated.  the  v a r i e d t o change t h e energy r e g i o n b e i n g  T h i s s p e c t r o m e t e r was  an improvement s i n c e w i t h  p h o t o g r a p h i c d e t e c t i o n the r e s o l u t i o n , d i s p e r s i o n and f o c u s s i n g changed from one end o f t h e p l a t e to t h e o t h e r . 5  W i t h such a s p e c t r o m e t e r Chadwick  proved t h a t i n  a d d i t i o n to the groups o f e l e c t r o n s o f d i s c r e t e e n e r g i e s t h e r e was a c o n t i n u o u s d i s t r i b u t i o n so t h a t a normal s p e c t r u m as i n F i g . 2 .  Rutherford e t . a l .  appeared  proved t h a t t h e d i s c r e t e groups  were o f secondary o r i g i n by w r a p p i n g  f o i l s of various metals  around the c y l i n d r i c a l s o u r c e i n a b e t a r a y s p e c t r o g r a p h .  When  t h e f o i l s were thick,.enough to s t o p a l l e l e c t r o n s from t h e s o u r c e 4.  E. Gurney? P r o 0 . . Roy.  5.  J . Chadwick: Verh.d.D.Phys.Ges., 16, 383,  S o c , A109,  340,  1925. 1914.  6. E. R u t h e r f o r d , H. Robinson and R a w l i n s o n : P h i l . M a g . , 28_, 281, 1914.  Baffle  FIGURE 2. A NORMAL BETA SPECTRUM  4.  a l i n e spectrum was s t i l l  observed.  From these a n d o t h e r experiments  a comprehensive t h e o r y  o f b e t a - r a y s p e c t r a was b u i l t up. The e l e c t r o n s e m i t t e d d u r i n g t h e d i s i n t e g r a t i o n o f r a d i o - a c t i v e n u c l e i : , had a c o n t i n u o u s t r i b u t i o n o f energy.  dis-  The d a u g h t e r n u c l e i i were u s u a l l y l e f t i n  an e x c i t e d s t a t e and gave up more energy by e m i t t i n g gamma r a y s o r by e j e c t i n g e l e c t r o n s f r o m t h e K, L, e t c , s h e l l s of t h e newly formed atom.  I n Fig.2 i t i s indicated that a strong l i n e i n a  beta-spectrum  i s o f t e n accompanied by a weaker s a t e l l i t e  or l i n e s .  line  I f the b i n d i n g energy o f a K e l e c t r o n o f t h e d a u g h t e r  atom i s added t o t h e energy o f t h e most i n t e n s e l i n e , an L t o t h e n e x t , and so f o r t h , a c o n s t a n t energy v a l u e i s o b t a i n e d which u s u a l l y corresponds The  t o t h e energy o f a known gamma r a y .  gamma r a y i s s a i d t o be p a r t i a l l y i n t e r n a l l y c o n v e r t e d and  the peaks i n the b e t a - r a y s p e c t r a a r e known a s c o n v e r s i o n l i n e s . The  continuous d i s t r i b u t i o n o f t h e d i s i n t e g r a t i o n  e l e c t r o n s presented great d i f f i c u l t i e s i n regard t o t h e conserv a t i o n of energy, p a r t i c u l a r l y when i t was shown t h a t t h e energy a v a i l a b l e corresponded  t o t h e maximum energy of t h e b e t a p a r t i c l e s .  A d e t a i l e d t h e o r y o f b e t a d i s i n t e g r a t i o n was g i v e n by F e r m i ^ i n w h i c h he assumed t h a t a d i s i n t e g r a t i o n was a t h r e e body p r o c e s s w i t h another p a r t i c l e , c a l l e d a n e u t r i n o , being emitted w i t h the electron.  The p r o p e r t i e s o f the n e u t r i n o were assumed t o be such  t h a t i t s d e t e c t i o n was d i f f i c u l t , i f n o t i m p o s s i b l e . was  zero. 7.  The mass was presumed t o be v e r y s m a l l .  S. F e r m i : Z e i t s f u r Phys. 8b, 161, 193A-.  The charge Indeed, on  3  the b a s i s of experiments  0  on t h e b e t a momentum d i s t r i b u t i o n o f  , an upper l i m i t t o t h e mass o f t h e n e u t r i n o has been p l a c e d at  0.002 e l e c t r o n mass. I n t h e s i m p l e s t f o r m o f t h e t h e o r y p l a n e wave f u n c t i o n s  a r e assumed f o r t h e e l e c t r o n and n e u t r i n o w h i c h a r e c r e a t e d a t the moment o f e m i s s i o n . a t e d by combining  The t r a n s i t i o n p r o b a b i l i t y i s c a l c u l -  the value of these f u n c t i o n s a t the nucleus  w i t h a m a t r i x element r e l a t i n g t h e i n i t i a l and f i n a l s t a t e s o f the nucleus.  I n a d d i t i o n t h e r e i s a new u n i v e r s a l c o n s t a n t  called a coupling factor.  The shape of t h e momentum  distri-  b u t i o n o f t h e e m i t t e d b e t a - p a r t i c l e s depends t o a c o n s i d e r a b l e e x t e n t on t h e type o f i n t e r a c t i o n used i n t h e m a t r i x . element. A l s o t h e t o t a l p r o b a b i l i t y o f decay i s a f u n c t i o n o f t h e s p i n change and p a r i t y change between t h e i n i t i a l and f i n a l s t a t e s and t h i s f u n c t i o n i s a l s o i n c l u d e d i n t h e m a t r i x element.  The  most p r o b a b l e t y p e o f t r a n s i t i o n i n v o l v i n g a s p i n v e c t o r change o f 1 and p a r i t y change i s c a l l e d an a l l o w e d t r a n s i t i o n .  A  s i m p l e re-arrangement o f t h e Fermi p r o b a b i l i t y f u n c t i o n enables one t o p l o t a c o m p l i c a t e d f u n c t i o n (which i n c l u d e s N, t h e number i n a s m a l l momentum i n t e r v a l ) a g a i n s t t h e b e t a energy 2 t o g i v e a s t r a i g h t l i n e w i t h a n i n t e r c e p t on t h e energy a x i s c o r r e s p o n d i n g a to t h e d i s i n t e g r a t i o n energy. T h i s i s c a l l e d a " K u r i e p l o t " . In  a b e t a d i s i n t e g r a t i o n t h e mass o f t h e n u c l e u s  8. S.C. C u r r a n , A.L. C o c k c r o f t and C.Insch: P h i l . M a g . . 4 1 . 51.7, 1930. — 9.  F.N.D. K u r i e , J.E. R i c h a r d s o n a n d H.C. P a x t o n : Phys.Rev.,  4?_, 368, 1936.  changes by a s m a l l f r a c t i o n o f t h e mass o f a n e u t r o n o r p r o t o n but t h e atomic number i s changed by one u n i t .  I f a negatron  i s e m i t t e d the n u c l e u s i n c r e a s e s i t s atomic number by one a s i l l u s t r a t e d in.Fig..3. t h e atomic number.  P o s i t r o n e m i s s i o n as i n F i g . 4  F i g . 3 shows t h e case where t h e  reduces  atomic  number i s r e d u c e d by t h e a b s o r p t i o n o f an e x t e r n a l e l e c t r o n i n t o the nucleus.  A s t h e e l e c t r o n absorbed  i s usually  from  the K s h e l l o f t h e atom t h i s p r o c e s s i s known as K c a p t u r e . A f t e r any o f t h e s e t r a n s i t i o n s t h e n u c l e u s may be l e f t i n a n e x c i t e d s t a t e from w h i c h i t r e v e r t s t o t h e ground s t a t e by e m i t t i n g a gamma ray o r a c o n v e r s i o n e l e c t r o n .  Whenever an  atomic e l e c t r o n i s removed, e i t h e r by K c a p t u r e o r c o n v e r s i o n o f a gamma r a y , t h e r e a r e a l s o c h a r a c t e r i s t i c X r a y s o f t h e daughter atom e m i t t e d and i n some cases Auger e l e c t r o n s . Somet i m e s a t r a n s i t i o n by b e t a e m i s s i o n i s p o s s i b l e t o two d i f f e r e n t e x c i t e d s t a t e s o f t h e daughter n u c l e u s , a s i n F i g . 6 .  This i s  most r e a d i l y d e t e c t e d by t h e K u r i e p l o t w h i c h i s no l o n g e r a s i n g l e s t r a i g h t l i n e but r a t h e r t w o . i n t e r s e c t i n g l i n e s .  (Fig.7).  The methods o£ b e t a - r a y s p e c t r o s c o p y have been s u c c e s s f u l i n d e t e r m i n i n g t h e e n e r g i e s o f p a r t i c l e s and photons e m i t t e d by r a d i o - a c t i v e n u c l e i i and thus have p r o v i d e d a knowl e d g e o f n u c l e a r energy l e v e l s .  W h i l e t h e s e e n e r g i e s have  been measured o y e r a l a r g e range w i t h a c o n s i d e r a b l e degree o f accuracy t h e r e are l i m i t a t i o n s .  I n v e r y few i n s t r u m e n t s has a  r e s o l u t i o n o f one p a r t i n a thousand  been a t t a i n e d and a more  u s u a l v a l u e i s one i n t h i r t y t o one i n one hundred.  A standard  s p e c t r o m e t e r may c o v e r t h e range from 0.1 t o 3 Mev, t h e l o w e r  Gamma  FIGURE 3. ENERGY LEVEL DIAGRAM FOR JMEGATRON DECAY  Z-l 2mc' Beta  Emax  Gamma FIGURE 4 . ENERGY LEVEL DIAGRAM FOR POSITRON DECAY  FIGURE 5. ENERGY LEVEL DIAGRAM FOR ORBITAL ELECTRON CAPTURE  Z  Z+l  FIGURE 6. ENERGY LEVEL DIAGRAM FOR NEGATRON DECAY TO TWO DIFFERENT STATES  7.  l i m i t b e i n g an i n s t r u m e n t a l l i m i t , caused by e x c e s s i v e s c a t t e r i n g o f low energy e l e c t r o n s from b a f f l e s and r e s i d u a l gas, by  the  i n c r e a s i n g l y s e r i o u s d e f o c u s s i n g by uncompensated e a r t h ' s  field  components over the l o n g p a t h l e n g t h as t h e energy d e c r e a s e s  and  by a b s o r p t i o n of t h e low energy b e t a p a r t i c l e s i n b o t h t h e s o u r c e and the c o u n t e r window.  The  upper l i m i t i s s e t by  power demands of t h e f o c u s s i n g magnet.  A few  the  spectrometers  have been b u i l t t o measure e n e r g i e s g r e a t e r t h a n 10 Mev  and some  t o e x t e n d the l o w e r l i m i t t o 10 Kev o r l e s s . W h i l e t h i s low energy r e g i o n has been n e g l e c t e d because o f e x p e r i m e n t a l investigation exist. the c o n t i n u o u s  d i f f i c u l t i e s a number o f r e a s o n s f o r i t s  I n t h e s i m p l e d e r i v a t i o n o f the shape of  spectrum i t i s assumed t h a t t h e e l e c t r o n has  p l a n e wave f u n c t i o n a t the n u c l e u s .  a  A c o r r e c t i o n must be made  t o account f o r the p e r t u r b a t i o n o f t h e wave by t h e coulomb field. and  The  amount of the c o r r e c t i o n i n c r e a s e s a t low  i s i n d i f f e r e n t d i r e c t i o n f o r p o s i t r o n s and  energies  negatrons.  Thus t h e r e i s c o n s i d e r a b l e d i f f e r e n c e between t h e shapes of p o s i t r o n and n e g a t r o n s p e c t r a .  (Fig.8)  I f this factor i s  i n c o r p o r a t e d i n t o the t h e o r y a v a l u e of the r a t i o N / N ~ +  can  be  o b t a i n e d f o r n u c l e i i which d i s i n t e g r a t e by e i t h e r n e g a t r o n o r p o s i t r o n emission. c a l c u l a t e d and Backus  1 0  Cu^  4  i s an i s o t o p e f o r w h i c h t h i s can  c o n s i d e r a b l e work has been done on the. q u e s t i o n .  w o r k i n g i n the r e g i o n 5 t o 50 Kev  times greater than expected at the lowest spectrum was  be  found N / N " +  energy.  i n v e s t i g a t e d by Cook and L a n g e r  10.  3". Backus: Phys.Rev., 68,  11.  C.S.  Cook and L.M.  59,  1 1  to be  ten  The e n t i r e  f r o m 10 t o 700  1945.  L a n g e r : Phys.Rev., 22.* 601*  1948.  Kev.  FIGURE 7. .KURIE PLOT FOR NEGATRON DECAY TO TWO DIFFERENT STATES  N(E)  Beta for Z  Beta - f o r Z = 0 0  FIGURE 8. THE EFFECT OF THE COULOMB FIELD ON THE SHAPE OF THE BETA SPECTRUM  8.  Their measurements are i n agreement with Backus and show that 12  NVN"* deviates from theory below lj>0 Kev.  Lewis and Bohm  have attempted to explain the discrepancy by using linear combinations of the f i v e r e l a t i v i s t i c a l l y invariant interactions which are possible i n the matrix element of the t r a n s i t i o n probability.  However Wu and A l b e r t ^ report deviations from 1  theory much less than the above and conclude that any are e n t i r e l y instrumental i n o r i g i n .  remaining  As the techniques used  by these three groups seem to be similar the question warrants further investigation. Cook and Langer"** and other 1  experimenters ^ '^ ^ 1  ,1  ,1  report that i n a number of cases the Kurie plot deviates from 17 18 19 a straight l i n e at low energies.  More recent work  indicates that these results were e n t i r e l y due to the t h i c k ness of the source.  However there i s always the p o s s i b i l i t y that  the curvature of the Kurie plot at the low energy end i s caused by the presence of a low energy beta group. (Fig.7).  Only the  most refined techniques can distinguish between these p o s s i b i l i t i e s . 12. H. Lewis and D. Bohm: Phys.Rev., 69_, 129, 1946.  11  13.  C.S. Wu and R.D.  14.  A.W.  13.  J".L. Lawson: Phys.Rev., ^6,, 131,  16.  A.A.  Townsend: Proc.Roy.Soc., A177.  17.  R.D.  Albert and G.S. Wu:  18.  L. Feldman and C.S. Wu: Phys.Rev., 2£, 697,  798  WO  Ait> t er  :  Phys.Rev., J2> 315>  T y l e r : Phys.Rev., £6, 123,  L a n g e r  ' **' r  W  M  o  t  z  8 1 1 4  1949.  1939. 1939. 337,  1941.  Phys.Rev., 24, 847, 1948. Phys.Rev., 1107, 1949.  H , C  *  P^  0 6  1949.  Phys.Rev.,  9  B e s i d e s t h e low energy b e t a groups t h e r e may be l o w energy c o n v e r s i o n l i n e s .  Even a 0.1 l e v gamma from a n u c l e u s  o f h i g h Z may y i e l d a c o n v e r s i o n l i n e o f a few Kev when conL i n e s a t l e s s t h a n 50 Kev have been  verted i n the K s h e l l .  found i n t h e b e t a s p e c t r a o f almost a l l n a t u r a l l y r a d i o - a c t i v e substances  2 0  and i n some a r t i f i c a l l y p r e p a r e d i s o t o p e s .  2 1  There i s a l s o a p o s s i b i l i t y o f d e t e c t i n g . t h e Auger e l e c t r o n s e j e c t e d f r o m t h e e l e c t r o n i c s h e l l s of an atom a f t e r K c a p t u r e has t a k e n p l a c e .  22  1  I f a n u c l e u s i s i n t h e ground s t a t e on  c a p t u r i n g a K e l e c t r o n t h e s o f t X r a y s and t h e Auger e l e c t r o n s o f f e r t h e o n l y means o f d e t e c t i n g t h e change. Many suggested  decay schemes f o r v a r i o u s n u c l e i based  on t h e measurements o f h i g h - e n e r g y  gamma-rays and c o n v e r s i o n  e l e c t r o n s have energy l e v e l s w i t h i n 50 Kev o r l e s s o f each other.  Most c u r r e n t s p e c t r o m e t e r s  could not detect t r a n s i t i o n s  between such s t a t e s i f t h e y d i d e x i s t .  An i n s t r u m e n t w h i c h  c o u l d do so would be a v a l u a b l e t o o l i n c h e c k i n g t h e proposed s p i n and p a r i t y v a l u e s a s s i g n e d t o these s t a t e s on t h e e v i d e n c e o f t h e h i g h energy t r a n s i t i o n s a l o n e . . Thus t h e e x t e n s i o n o f t h e energy range measured by beta r a y spectrometers  to as l o w a v a l u e as p o s s i b l e i s im-  p o r t a n t i n c h e e k i n g t h e agreement o f experiment w i t h t h e o r y and 20. R a d i a t i o n s f r o m R a d i o - a c t i v e Substances. Chadwick and E l l i s : pp.560-380. 21.  R.D. H i l l : Phys.Rev., 24,  78,  22.  3T. M i l l e r J r . ; Phys.Rev., 62, 309, 1945.  1948.  Rutherford,  i n i n c r e a s i n g our knowledge o f the energy l e v e l s o f n u c l e i i . T h i s i n c r e a s e d knowledge i s e s s e n t i a l t o t h e development o f a theory of nuclear processes.  This research describes the  d e s i g n , c o n s t r u c t i o n and use o f a s p e c t r o m e t e r purpose.  for this  11.  II THE SPECTROMETER  A.  Primary Considerations i n Design. The d e s i g n of a s p e c t r o m e t e r t o be used  primarily  i n t h e energy r e g i o n below 100 Kev r e q u i r e s c a r e f u l c o n s i d e r a t i o n o f a number o f f u n d a m e n t a l l y i m p o r t a n t p o i n t s . (a)  The s c a t t e r i n g o f e l e c t r o n s from a l l p a r t s o f  the i n s t r u m e n t i n c r e a s e s g r e a t l y a t l o w e r e n e r g i e s .  I t has  been shown ^ t h a t a t l o w e n e r g i e s t h e s c a t t e r i n g , v a r i e s i n v e r 2  s e l y a s t h e f i r s t power, a t l e a s t , o f t h e e l e c t r o n energy and d i r e c t l y as t h e a t o m i c number o f t h e s c a t t e r i n g m a t e r i a l . (b)  The d e t e c t i o n of l o w energy b e t a p a r t i c l e s p r e -  s e n t s a g r e a t d e a l of d i f f i c u l t y .  Photographic d e t e c t i o n could  be p o s s i b l e , d e s p i t e t h e o b j e c t i o n s t o a s p e c t r o g r a p h .  How-  e v e r , t h e s e n s i t i v i t y o f even t h e b e s t p l a t e s f a l l s o f f v e r y r a p i d l y as t h e energy o f t h e i m p i n g i n g e l e c t r o n s i s d e c r e a s e d . ^ The s e n s i t i v i t y of t h e c r y s t a l and e l e c t r o n m u l t i p l i e r combina t i o n a l s o decreases tremendously  at l o w e n e r g i e s , and t h e oper-  a t i o n of t h e m u l t i p l i e r i s s e r i o u s l y a f f e c t e d by a magnetic field.  A G e i g e r c o u n t e r seems t o be t h e b e s t method o f d e t e c t i o n  s i n c e i t i s w e l l known t h a t e l e c t r o n s o f almost z e r o energy c a n be d e t e c t e d i n t h i s way p r o v i d i n g they p e n e t r a t e i n t o t h e 23.  Appendix I .  24.  L. Cranberg. a n d J . H a l p e r n : R.S.I., 2p_, 641, 1949.  12.  s e n s i t i v e volume o f t h e c o u n t e r .  The problem i s reduced t o  one o f making t h e window o f t h e c o u n t e r s u f f i c i e n t l y t h i n t o a v o i d a b s o r p t i o n at l o w e n e r g i e s y e t s t r o n g enough t o w i t h s t a n d t h e p r e s s u r e of t h e c o u n t e r g a s . Windows o f n y l o n , zapon, formvar and c o l l o d i o n a s t h i n as a few micrograms/cm  can be made q u i t e r e a d i l y w i t h  t h e method d e s c r i b e d by B a c k u s .  1 0  Windowless c o u n t e r s have  19 been used w i t h s u c c e s s by Langer, Motz and P r i c e w i t h an e q u i v a l e n t window t h i c k n e s s due t o d i f f u s i n g . g a s o f about one p microgram/cm . The problem of t h e c o u n t e r windows has been s o l v e d s a t i s f a c t o r i l y f o r o u r problem. /cm  2  Zapon f i l m s o f 3 t o 5 micrograms  a r e cemented over a c o u n t e r e n t r a n c e s l i t 0.025 cm, w i d e .  The c o m b i n a t i o n o f t h e narrow window,and t h e l o w gas p r e s s u r e used i n t h e c o u n t e r (1.1 cm.Hg.) makes t h e use o f such entirely  films  practicable. (c)  The method by w h i c h t h e r a d i o - a c t i v e s o u r c e i s  p r e p a r e d a n d mounted i s i m p o r t a n t a t e n e r g i e s up to a t l e a s t 0.5 Mev b u t p a r t i c u l a r l y so a t l o w e n e r g i e s . » ^ > 6 , 2 7 rph. t h i c k n e s s o f t h e s u p p o r t a n d of t h e l a y e r o f r a d i o a c t i v e 2  2  e  m a t e r i a l d e p o s i t e d on i t can have a g r e a t i n f l u e n c e on t h e shape o f t h e l o w energy spectrum even when o n l y a few m i c r o / p 19 grams/cm^. T h i s n e c e s s i t a t e s extreme c a r e to ensure t h a t 25.  C u r r a n , Angus & C p c k r o f t : P h i l . M a g . , 4 0 , 53, 1949.  26.  L a n g e r , M o f f a t , & P r i c e : Phys.Rev., ^ 6 , 1725, 1949.  27.  G.2. Owen & G . S . Cook: Phys.Rev., 2i» 1726, 1949.  t h e source i s spread u n i f o r m l y o v e r t h e a c t i v e r e g i o n . The e x t r e m e l y t h i n source mounts r e q u i r e d by t h e s e c o n s i d e r a t i o n s l e a d s to a new d i f f i c u l t y .  Because o f t h e l o w  c o n d u c t i v i t y o f t h e b a c k i n g and t h e s m a l l c a p a c i t y to ground t h e s o u r c e can a c q u i r e a p o t e n t i a l of s e v e r a l thousand 28 s e r i o u s l y d i s t o r t i n g t h e low energy  volts,  spectrum.  To overcome t h e s e d i f f i c u l t i e s , t h e s o u r c e was p r e pared by d e p o s i t i n g an a p p r o x i m a t e l y u n i f o r m s t r i p o f r a d i o a c t i v e m a t e r i a l on a zapon o r LG600 f i l m o f about 10 m i c r o grams/cm . 2  was  The f i l m was s u p p o r t e d ,by a l u c i t e h o l d e r which  c u t away d i r e c t l y behind t h e s o u r c e .  The a c c u m u l a t i o n o f  charge was p r e v e n t e d e i t h e r by e v a p o r a t i n g aluminum onto t h e h o l d e r u n t i l a f i n i t e e l e c t r i c a l r e s i s t a n c e appeared o r by p a i n t i n g t h i n l i n e s o f aquadag t o connect t h e ends o f t h e s o u r c e t o t h e metal o f t h e s p e c t r o m e t e r .  See APPENDIX I I I  for further details. (d)  The d i f f i c u l t i e s o f h a n d l i n g l a r g e amounts o f  a c t i v i t y r e q u i r e t h a t maximum use be made o f the s o u r c e .  A  r e d u c t i o n i n t h e s i z e o f t h e s p e c t r o m e t e r and t h e r e f o r e o f t h e s o u r c e ensures t h a t t h e amount o f a c t i v i t y / c m  2  i s reason-  a b l y l a r g e w h i l e t h e a b s o l u t e amount of a c t i v i t y i s kept s m a l l . T h i s l a s t i s e s s e n t i a l i n a l o w energy s p e c t r o m e t e r s i n c e t h e s o u r c e cannot be covered because of a b s o r p t i o n o f e l e c t r o n s i n the c o v e r i n g m a t e r i a l .  I n addition the f r a g i l i t y of the  b a c k i n g p r o v i d e s a c o n s t a n t danger o f c o n t a m i n a t i o n . ^•-j..  •  With •  28. 0.--H. Braden, G.E. Owen, J . Townsend, O.S. Cook & F.B. S k u l l : Phys.Rev., J4, 1539, 1 9 4 8 .  14. m a t e r i a l s o f low s p e c i f i c a c t i v i t y the s o u r c e s t r e n g t h w i l l  be  l i m i t e d by c o n s i d e r a t i o n s of source t h i c k n e s s . E v i d e n t l y t h e n , a low energy s p e c t r o m e t e r s h o u l d as e f f i c i e n t as p o s s i b l e , t h a t i s , t h e f r a c t i o n d e t e c t e d  be  of a l l  e l e c t r o n s l e a v i n g t h e s o u r c e i n a g i v e n momentum range s h o u l d be as l a r g e as i s c o n s i s t e n t w i t h t h e r e s o l u t i o n r e q u i r e d . w i l l be shown l a t e r t h a t t h i s f r a c t i o n i s a f u n c t i o n of same v a r i a b l e s as i s . the r e s o l u t i o n . w i d t h a t low e n e r g i e s  It  the  However, s i n c e the  line  i s g r e a t l y i n c r e a s e d by s c a t t e r i n g and  s e l f a b s o r p t i o n , t h e r e s o l u t i o n need not be t o o good. (e) v a l u e o f 340  An e l e c t r o n w i t h 10 Kev gauss cms.  o f energy has an  I f i t s radius of curvature  s p e c t r o m e t e r i s to be, say, 10 cms.  Hr  i n the  the f i e l d r e q u i r e d i s 34 gauss.  The  i n f l u e n c e of the e a r t h ' s f i e l d i s c o n s i d e r a b l y g r e a t e r t h a n  one  p e r c e n t of t h i s and  and  o t h e r e l e c t r i c a l equipment, can r a d i a t e f l u c t u a t i n g f i e l d s  e l e c t r i c motors, r e g u l a t i n g  of t h i s order f o r several f e e t .  transformers  The measurement o f a s m a l l  magnetic f i e l d w i t h an a c c u r a c y o f a few p e r c e n t i s d i f f i c u l t . I t i s an advantage to keep the s i z e of t h e s p e c t r o m e t e r down i n o r d e r t h a t f a i r l y l a r g e f i e l d s can be used.  I f the  can be o b t a i n e d w i t h o u t the use of an i r o n c o r e t h e  field  instrument  can be c a l i b r a t e d q u i t e r e a d i l y w i t h o u t t h e measurement o f  small  fields.  B.  The  Inner Spectrometer. The  s e m i - c i r c u l a r f o c u s s i n g type of instrument best  f u l f i l s t h e above c o n d i t i o n s .  The r a d i u s o f c u r v a t u r e  of  d e t e c t e d e l e c t r o n s can be r e d u c e d t o a s m a l l v a l u e , t h e p a t h l e n g t h i s s h o r t and the i n n e r s u r f a c e can be k e p t s m a l l , r e d u c i n g s c a t t e r i n g t o a minimum.  I n o r d e r to have a l a r g e t r a n s -  m i s s i o n t h e s p e c t r o m e t e r was d e s i g n e d t o a c c e p t e l e c t r o n s from the source i n f o u r d i f f e r e n t d i r e c t i o n s .  D e t e c t i o n i s accom-  p l i s h e d by means of G-eiger c o u n t e r s w i t h zapon windows, t h e p r e s s u r e b e i n g k e p t c o n s t a n t by a dynamic f i l l i n g  system.  C o n s t r u c t i o n views of t h e i n n e r s p e c t r o m e t e r are shown i n F i g . 9 .  The dimensions a r e i n i n c h e s because o f the  sizes of materials  available.  The s o u r c e i s i n t h e form o f a l i n e about 0.1 cm. wide and 1.5 cm. h i g h . p microgram/cm  I t i s mounted on a b a c k i n g o f 10  zapon w h i c h i s s u p p o r t e d by a l u c i t e h o l d e r .  The h o l d e r i s a r r a n g e d i n t h e s p e c t r o m e t e r so t h a t t h e m i d d l e l i n e o f t h e s o u r c e passes t h r o u g h t h e c e n t e r o f t h e a p p a r a t u s . The c o u n t e r s a r e s y m m e t r i c a l l y spaced about t h e source on t h e c i r c u m f e r e n c e o f a c i r c l e o f 2.4 i n c h e s r a d i u s (3.05 cm.). The f o u r s e t s o f b a f f l e s a r e a r r a n g e d so t h a t e l e c t r o n s l e a v i n g +  t h e source a t a n g l e s o f 45° - 5 . 7 ° t o t h e p l a n e o f t h e b a c k i n g t r a v e l a c i r c u l a r p a t h o f 3.05 - .03 cm. r a d i u s ( i n t h e c o r r e s p o n d i n g magnetic f i e l d ) t o s t r i k e t h e c o u n t e r windows.  The  b a f f l e s were c u t on a l a t h e t o t h e r e q u i r e d r a d i u s and grooves c u t i n t h e s u r f a c e t o reduce t h e r e f l e c t i o n o f e l e c t r o n s from the b a f f l e s u r f a c e s i n t o t h e c o u n t e r s . Each c o u n t e r ( s e e F i g . 9 ) was made by d r i l l i n g a 0.62$ i n c h d i a m e t e r h o l e t h r o u g h a b l o c k o f b r a s s 1.5 long.  inches  The b r a s s was t h e n trimmed down w i t h a s h a p e r , w i t h  To c o u n t e r system  filling U3  To vacuum system  FIGURE 9. .INTERNAL CONSTRUCTION OF THE SPECTROMETER a b c  Baffles Counters Source h o l d e r  16.  p a r t i c u l a r c a r e t a k e n w i t h t h e f a c e c o n t a i n i n g the window. T h i s f a c e was  c u t a s smooth a s p o s s i b l e , to l e a v e a t h i c k n e s s  o f .030 i n c h e s i n t h e c e n t e r . l o n g i t u d i n a l s l o t about 5/8 was  cut.  The  Through t h e narrowest  i n c h e s l o n g and 0.010  i n s i d e of t h e c o u n t e r was  o u g h l y w i t h emery paper and c r o c u s  part a  i n c h e s wide  then p o l i s h e d t h o r -  cloth.  A n o t h e r h o l e o f about t h e same s i z e was t h r o u g h t h e b r a s s , p a r a l l e l t o the f i r s t ,  drilled  f o r t h e purpose o f  f i l l i n g t h e c o u n t e r , so t h a t about 0.050 i n c h e s o f m e t a l a t e d t h e two.  S m a l l h o l e s (No.48 d r i l l )  were d r i l l e d  separ-  through  t h i s s e p a r a t i n g w a l l to a l l o w t h e f i l l i n g gas t o e n t e r t h e counter proper.  The a u x i l i a r y h o l e was  t h e n plugged  at  one  end w i t h a b r a s s p l a t e and a t t h e o t h e r w i t h a eopper tube to a l l o w c o n n e c t i o n t o the f i l l i n g  system.  The e n t i r e c o u n t e r was t h e n immersed i n b o i l i n g n i t r i c a c i d (0.1  Normal) f o r a few minutes u n t i l the s u r f a c e s  appeared c l e a n . , I t was  t h e n washed, f i r s t  and t h e n i n a b s o l u t e a l c o h o l and d r i e d . w i t h a Kovar s e a l and d e K h o t i n s k y wax.  in distilled  One  end was  water,  closed  the o t h e r w i t h a p y r e x cap s e a l e d w i t h  A .005 i n c h t u n g s t e n w i r e was  used f o r t h e  anode. The a p p a r a t u s 6.5  i s c o n t a i n e d i n a b r a s s c y l i n d e r of  inches i n s i d e diameter.  brass.  The  end p l a t e s a r e o f 5/16  S o f t rubber r i n g s a r e used as vacuum s e a l s .  bottom p l a t e a number of h o l e s a r e d r i l l e d f o r t h e  inch  I n the admission  o f t h e c o u n t e r f i l l i n g gas, the h i g h v o l t a g e l e a d and f o r c o n n e c t i o n t o the vacuum system.  17.  One i n c h above t h e l o w e r end p l a t e i s mounted a 1/8 i n c h b r a s s p l a t e ( h e r e a f t e r c a l l e d t h e base p l a t e ) .  The  base p l a t e was h i g h l y p o l i s h e d and t h e p o s i t i o n o f t h e s o u r c e , the p o s i t i o n o f t h e b a f f l e s and t h e l o c a t i o n s o f t h e entrance s l i t s , o f the c o u n t e r s were marked on i t .  The c o u n t e r s were  a l i g n e d w i t h t h e b a f f l e system <by o b s e r v i n g  that the counter  window, i t s r e f l e c t e d image, and t h e mark on t h e base p l a t e , were i n one s t r a i g h t l i n e .  The e r r o r i n t r o d u c e d was c e r t a i n l y  no more t h a n t h e w i d t h o f t h e s l i t ably l e s s .  (.025 ems.) and was prob-  The c o u n t e r s were c o n n e c t e d t o a f o u r arm g l a s s  tee by l e n g t h s o f Tygon_ t u b i n g t o a l l o w movement d u r i n g alignment. A l l exposed m e t a l s u r f a c e s were c o a t e d w i t h a m a t e r i a l o f low a t o m i c number i n o r d e r to reduce s c a t t e r i n g as much as p o s s i b l e .  This was done by d i s s o l v i n g vacuum wax  ( A p i e z o n W) i n c a r b o n t e t r a c h l o r i d e and a p p l y i n g s e v e r a l  coats  of t h i s paint.  C.  Production  o f t h e Magnetic F i e l d .  I n o r d e r t o e l i m i n a t e t h e n e c e s s i t y o f measuring s m a l l magnetic f i e l d s i t was d e c i d e d t o produce i t w i t h o u t the use o f i r o n .  The f i e l d w o u l d then be p r o p o r t i o n a l to t h e  c u r r e n t used and c a l i b r a t i o n a t one p o i n t on a w e l l known l i n e would g i v e Hr v a l u e s f o r t h e e n t i r e spectrum. From t h e d e s c r i p t i o n o f t h e i n n e r s p e c t r o m e t e r i t i s seen t h a t a u n i f o r m magnetic f i e l d i s r e q u i r e d o v e r a d i s c shaped r e g i o n , 12 cms. i n d i a m e t e r and about 2 cms. t h i c k w i t h  the magnetic v e c t o r p e r p e n d i c u l a r t o the s u r f a c e .  The  usual  method o f p r o v i d i n g a u n i f o r m f i e l d o v e r a c o n s i d e r a b l e volume o f space i s to use Helmholz c o i l s . space, m e c h a n i c a l s t a b i l i t y ,  However, c o n s i d e r a t i o n s o f  the power a v a i l a b l e and t h e amount  o f w i r e r e q u i r e d l e d to a n attempt to p r o v i d e the f i e l d r e quired w i t h a combination  of f l a t  coils.  I f a c u r r e n t I t r a v e l s i n a c i r c u l a r p a t h of r a d i u s a the f i e l d a t any p o i n t P i n s i d e the l o o p and the c i r c l e  i n the plane o f  i s g i v e n by  H  *  =  2a  /  2  Tr(x2-a2)  Ho*  / / l - k 2 in20 S  d#  o where x = the d i s t a n c e o f P f r o m the  center  k = x/a Rq= the f i e l d a t t h e c e n t e r = 27TI 10a  T h i s i s an e l l i p t i c i n t e g r a l and must be o b t a i n e d f r o m t a b l e s . A c u r v e p l o t t i n g H^/Ho  a g a i n s t x/a i s shown i n F i g . 1 0 .  U s i n g e m p i r i c a l methods and t h i s c u r v e i t was mined t h a t t h r e e c o p l a n a r c o i l s , of r a d i u s 1 7 . 5 cms., 11 cms.  one  deter-  o f +14000 ampere t u r n s  a second o f - 2 7 0 0 ampere t u r n s of r a d i u s  and a t h i r d o f +120 ampere t u r n s o f r a d i u s 8.5  would g i v e a f i e l d o f a p p r o x i m a t e l y  cms.  360 gauss a t t h e i r common  c e n t e r , w i t h a maximum inhomogeneity, o f 0.28fo o v e r an a r e a r a d i u s 6 cms.  of  (The minus s i g n on the second c o i l i n d i c a t e s t h a t  t h e c u r r e n t i n t h i s c o i l i s i n the o p p o s i t e sense to the i n the o t h e r two  coils).  current  THE FIELD OF A PLANE CIRCULAR COIL AS A FUNCTION OF THE DISTANCE FROM THE CENTER  19.  These c a l c u l a t i o n s , however, were f o r i d e a l c o i l s and would n o t n e c e s s a r i l y h o l d f o r c o i l s of a f i n i t e c r o s s s e c t i o n such as i s n e c e s s a r y t o c a r r y t h e c u r r e n t r e q u i r e d .  The d e s i g n  f o r the. a c t u a l c o i l w i n d i n g s w i t h f i n i t e c r o s s - s e c t i o n s was c a r r i e d o u t by approximate s o l u t i o n s , whereby each c o i l wasr e p l a c e d by a s e r i e s o f t h i n c o i l s e c t i o n s .  The f i e l d s due to  the i n d i v i d u a l c o i l s were added g r a p h i c a l l y . The c o n s t r u c t i o n o f t h e magnet i s shown i n F i g . 1 1 . The c o i l s were wound f r o m No. 14 w i r e and c a n c a r r y a c u r r e n t o f up t o 10 amps f o r 10 minutes w i t h o u t e x t e r n a l c o o l i n g .  An  approximate c a l c u l a t i o n o f t h e e f f e c t o f t h e f i n i t e s i z e o f the c o i l s showed t h a t t h e r e should  be no change i n t h e d i s t r i -  b u t i o n o f t h e f i e l d but t h a t a s m a l l decrease i n s t r e n g t h c o u l d be e x p e c t e d .  The c a l c u l a t e d v a l u e o f E  Q  f o r 10 amps through  the c o i l was 347 gauss. The c u r r e n t t h r o u g h t h e c o i l i s s e t t o a known v a l u e w i t h an a c c u r a c y of one p a r t i n t e n thousand and i s c o n t r o l l e d by an e l e c t r o n i c c i r c u i t t o somewhat b e t t e r t h a n one p a r t i n a thousand.  A s e t t i n g o f 1.0 v o l t s on the c o n t r o l p o t e n t i o m e t e r  corresponded t o a c u r r e n t o f 9.7 t .03 amps and t h u s t o a f i e l d o f 336 t 1.6  D.  gauss.  T e s t i n g t h e U n i f o r m i t y of the.Magnetic  Field.  The u n i f o r m i t y o f t h e f i e l d was checked by t h e f o l l o w i n g method.  experimentally  Two i d e n t i c a l c o i l s o f No.28  copper  w i r e were wound on b a k e l i t e forms so t h a t t h e i n s i d e d i a m e t e r was 1 cm. and t h e c o i l w i n d i n g c r o s s - s e c t i o n was a square o f 0.5 cm. s i d e .  The two c o i l s were connected i n s e r i e s w i t h a  12 Turns  270 Turns  1400 Turns  5T  1/4 FIGURE 11. CONSTRUCTION OF THE MAGNET  20.  b a l l i s t i c galvanometer.  W i t h a measured c u r r e n t o f 4 amperes  t h r o u g h t h e magnet one c o i l was p l a c e d i n t h e c e n t e r of t h e magnet and t h e o t h e r a t " i n f i n i t y " .  The magnet c i r c u i t was  broken and t h e d e f l e c t i o n o f t h e galvanometer o b s e r v e d . t h e c o i l s were i n t e r c h a n g e d  and t h e p r o c e s s r e p e a t e d  When  t h e ob-  s e r v e d d e f l e c t i o n d i f f e r e d by l e s s t h a n 0*5%' Then one c o i l was f i x e d a t t h e c e n t e r o f t h e magent and t h e o t h e r , i n o p p o s i t e sense t o t h e f i r s t , was p l a c e d a t a p o i n t i n t h e r e g i o n t o be o c c u p i e d  by t h e s p e c t r o m e t e r .  When;  the c u r r e n t was i n t e r r u p t e d t h e o b s e r v e d d e f l e c t i o n o f t h e galvanometer was p r o p o r t i o n a l t o t h e d i f f e r e n c e o f t h e e.m.f.'s i n d u c e d i n t h e c o i l s and t h u s p r o p o r t i o n a l t o t h e d i f f e r e n c e i n t h e f i e l d at t h e two p o i n t s .  By comparing t h e d e f l e c t i o n  to t h a t due t o one c o i l a l o n e t h e percentage v a r i a t i o n o f t h e f i e l d c o u l d be f o u n d .  The r e s u l t s a r e shown i n F i g . 12A.  I t can be seen t h a t t h e maximum v a r i a t i o n over t h e r e g i o n was about 2% and t h a t t h e f i e l d i n c r e a s e d s t e a d i l y w i t h ; t h e d i s t a n c e from t h e c e n t e r . As t h e i n n e r c o i l o f 12 t u r n s i s v e r y c l o s e t o t h e s p e c t r o m e t e r and thus has a f a i r l y l a r g e e f f e c t on t h e f i e l d f o r t h e l a r g e r v a l u e s o f r a t r i a l was made w i t h t h i s disconnected.  coil  The r e s u l t s a r e shown by t h e c u r v e s o f F i g . 12B.  The maximum v a r i a t i o n o v e r a c y l i n d r i c a l r e g i o n 6 cms. i n r a d i u s i and  2 cms. t h i c k i s seen t o be i%.  I t was d e c i d e d t h a t  this  amount o f inhomogeneity would not be s e r i o u s and t h a t f u t u r e measurements would be made w i t h t h e i n n e r c o i l  disconnected.  1.Q2 H  0.99  1.01 B  H_  o  1.005  0.995  2  1  3  4  •  3  o  x(cm) o  FIGURE 12. OBSERVED VARIATION OF MAGNETIC FIELD I N SPECTROMETER REGION A.  Inner e o l l  connected  B.  Inner c o i l disconnected  E.  Mathematical... Treatment of. a Spectrometer.  7  E r e c t a r i g h t handed system o f c o o r d i n a t e s OX, OY, OZ i n a u n i f o r m magnetic  f i e l d so-that the negative d i r e c t i o n o f  the Z a x i s i s i n the d i r e c t i o n o f H.  C o n s i d e r a two dimen-  s i o n a l r a d i o - a c t i v e s o u r c e o c c u p y i n g a r e c t a n g u l a r a r e a i n the ZOX p l a n e , from x • -Q/2 t o +Q/2 and Z = -h/2 t o +h/2. ( F i g . 1 2 ) . An e l e c t r o n l e a v i n g t h e source f r o m a p o i n t PtX©, 0 , Z ) w i l l 0  meet t h e ZOX p l a n e a g a i n a t a p o i n t P^(x,y,z)  whose c o o r d i n a t e s  a r e g i v e n by t h e e q u a t i o n s ? x = x  + 2 r cos A cos B  0  y = 0 z = z  0  + r (1T+2A) s i n B  where? r i s the r a d i u s o f c u r v a t u r e o f t h e e l e c t r i c p a t h i n t h e magnetic  field.  I t i s e q u a l t o t h e momentum of the e l e c t r o n  d i v i d e d by t h e f i e l d H and by t h e e l e c t r o n i c charge i n electromagnetic u n i t s .  expressed  Since i n beta r a y spectroscopy the  momentum always appears d i v i d e d by t h e e l e c t r o n i c charge i t i s u s u a l to r e d e f i n e t h e u n i t s of the momentum so t h a t p = Hr e x p r e s s e d i n gauss-cms. A i s t h e a n g l e between t h e i n i t i a l d i r e c t i o n o f p and the p l a n e YOZ and B i s t h e a n g l e between t h e i n i t i a l  direction  29. T h i s development i s e s s e n t i a l l y t h a t g i v e n by C. G e o f f r i o n : R.S.I., 20, 6?8, 194-9.  FIGURE 1 3 . DIAGRAM OF ELECTRON PATHS I N THE SPECTROMETER  22 o f p and t h e YOX p l a n e .  Note t h a t t h e a n g l e s A and B a r e  measured p o s i t i v e l y f r o m t h e i n i t i a l  d i r e c t i o n o f p to the  respective planes. N o r m a l l y A i s l i m i t e d t o -Ao^A<+Ao by a t l e a s t one b a f f l e opening o f w i d t h 2b p e r p e n d i c u l a r to t h e e l e c t r o n p a t h a t a p o i n t 90° from t h e s o u r c e . A  Q  = fe/r -  Then  - - - - - - - - - - - - - - -  1.  I t i s a l s o u s u a l f o r t h e e x i t s l i t and s o u r c e t o have t h e same h e i g h t h, B i s t h e n r e s t r i c t e d so t h a t -B <B 0  <B  0  with B  0  - h/Orr)  -2.  Under t h e s e c o n d i t i o n s e l e c t r o n s o f a g i v e n momentum w i l l  form  an image o f t h e s o u r c e on t h e ZOX p l a n e w i t h c e r t a i n a b e r r a t i o n s caused by t h e f i n i t e v a l u e s o f A and B.  The s i z e o f t h e image  w i l l be g i v e n by: Width = Q  1  = £+2r(l-cos Ao eos B ) 0  Height = h i = h+2r(7r+2A )sin 0  B ) 0  The r i g h t hand edge o f t h i s image i s l o c a t e d a d i s t a n c e 2 r f r o m t h e r i g h t hand edge o f the s o u r c e .  S i n c e r depends on t h e  momentum o f t h e e l e c t r o n s a number o f images w i l l be formed w i t h d i f f e r e n t v a l u e s o f r f o r d i f f e r e n t v a l u e s of t h e momenta. I f a d e t e c t o r i s p l a c e d behind an e x i t s l i t i n the ZOX p l a n e of h e i g h t h and w i d t h F ( n o r m a l l y l e s s t h a n o r e q u a l t o Qj i t w i l l r e c e i v e e l e c t r o n s w i t h o n l y a c e r t a i n range o f v a l u e s  23,  o f momenta.  The w i d t h o f the e x i t s l i t adds t o t h e e f f e c t i v e  w i d t h o f t h e image o f the s o u r c e so t h a t i t now becomes e q u a l to F + Q + 2r(l-cos I f H i s constant  COS B ) 0  t h e r e i s an u n c e r t a i n t y i n t h e d i a m e t e r o f t h e  e l e c t r o n t r a j e c t o r y o f e x a c t l y t h i s amount o r one h a l f o f t h i s i n the r a d i u s of t h e t r a j e c t o r y . The l i m i t o f r e s o l u t i o n o f a s p e c t r o m e t e r i s d e f i n e d as t h e r a t i o ^ p / p where ^ p  i s t h e range of t h e momenta o f t h o s e  e l e c t r o n s passing through the e x i t s l i t .  Now  since  p = Hr ^p and  = HAr  + rAH  i f H i s constant  A  p  = HZir = H « [ F + Q, + 2 r ( l - c o s A Q c o s B ) £ 0  /2  Now s i n c e p = Hr we have A P = F + Q, + 2 r ( l - c o s AQ COS Bp) P 2r and s i n c e Ao„ and Bo a r e s m a l l t h i s can be s i m p l i f i e d to ZS. p - F + Q, + Ap^ + Bo' p 2r 2 Now i f T i s t h e k i n e t i c energy of t h e p a r t i c l e i n Mev p = Hr = 1 0 / T { T + 1.02) 3• 4  24.  and i t can e a s i l y be d e r i v e d A  p  P  that  = T + .51 T + 1.02  A T T  The l u m i n o s i t y o f a s p e c t r o m e t e r i s a measure of the number of e l e c t r o n s o f a g i v e n momentum range which form an image o f t h e s o u r c e .  I t i s a f u n c t i o n o f t h e source a r e a and  the  s o l i d a n g l e w o f the b a f f l e system where w = 2AoB  0  The l u m i n o s i t y L can be d e f i n e d as  follows  L = KQhw/4 7T where Qh i s the a r e a of the source and K i s the.number o f e l e c t r o n s i n the g i v e n momentum range e m i t t e d by t h e s o u r c e i n a l l d i r e c t i o n s p e r u n i t a r e a per u n i t t i m e .  From p r e v i o u s  e q u a t i o n s i t can be shown t h a t L = K^rAoB§/2. • Thus t h e l u m i n o s i t y i s a f u n c t i o n o f the same v a r i a b l e s as the r e s o l u t i o n A P / P  i . Q » Q,r,Ao.,.Bo. G e o ; f f r i o n ?  has a p p l i e d t h e method o f undetermined  2  c o e f f i c i e n t s t o es-  t a b l i s h t h e optimum r e l a t i o n s h i p s between t h e s e v a r i a b l e s making L a maximum.  They a r e :  % = 2Ao r  4.  2  Bo = A o ( 2 )  1 / 2  5o  25.  Under optimum c o n d i t i o n s t h e n t h e l u m i n o s i t y becomes L = 2Kr Ao^ 2  I t can a l s o be shown t h a t i f F i s t h e w i d t h of the e x i t i t s optimum v a l u e i s F =  slit  The v a l u e chosen f o r F has an e f f e c t  on b o t h t h e r e s o l u t i o n and on t h e l u m i n o s i t y w h i c h now become under optimum c o n d i t i o n s = 7A /2  AP/P  2  and L = 0.725 K r ( ^ p / p ) ^ 2  2  •  -6.  The l i m i t of r e s o l u t i o n g i v e n above i s d e f i n e d f o r complete s e p a r a t i o n o f two l i n e s , ZIP/P  = 3-^/2  7.  g i v e s t h e w i d t h of a l i n e a t h a l f maximum i n t e n s i t y as i s more usual. The s p e c t r o m e t e r d e s c r i b e d i n t h i s r e p o r t has a r a d i u s o f 3 . 0 5 cms. and A Q was chosen as 0 . 1 . v a l u e s o f ^, F, and B  0  are then  Q = 2 x 3.05 x  .01  = .06 cms. F = q = .06 cms. B  0  =  1.4AQ  =  .14  The optimum  26  The w i d t h o f the source c o u l d n o t be made much l e s s t h a n 1 mm. because o f the d i f f i c u l t i e s i n h a n d l i n g , s m a l l  drops  o f r a d i o - a c t i v e s o l u t i o n s . - - However t h i s i s m u l t i p l i e d by the f a c t o r . 7 0 7 s i n c e t h e s o u r c e i s a t an a n g l e o f 4 5 ° t o the p l a n e o f the source and e x i t s l i t .  (See F i g . 9 ) .  The a c t u a l v a l u e  o f % i s p r o b a b l y w i t h i n 1Q7» o f t h e optimum v a l u e g i v e n above. The h e i g h t o f t h e s o u r c e and e x i t s l i t a r e about 1 . 5 cms.  This gives B  0  = h/Trr - .156  about 10> h i g h e r t h a n the optimum v a l u e . The w i d t h of the e x i t s l i t  ( w i d t h o f c o u n t e r window)  i s about . 0 2 5 cms. because i t was f e a r e d t h a t a w i d e r window would not s t a n d t h e p r e s s u r e .  T h i s was not checked, however,  and i t might be i n t e r e s t i n g to c o n s t r u c t a c o u n t e r w i t h optimum window w i d t h .  T h i s s h o u l d improve t h e performance o f t h e  spectrometer. The r e s o l u t i o n o f t h e s p e c t r o m e t e r 1.7% (3)  s h o u l d be about  a t h a l f maximum i n t e n s i t y u s i n g e q u a t i o n ( 7 ) . using t h e a c t u a l values of  comes out t o be about 1.$%. t o t h e s m a l l v a l u e o f F.  F, A Q and B  0  From e q u a t i o n  the r e s o l u t i o n  The d i f f e r e n c e i s due almost  This small value o f F should  the l u m i n o s i t y o f t h e s p e c t r o m e t e r  entirely  reduce  by F/Q. Assuming K to be  unity t h i s gives L • . 1 4 6 x 10~2 cms  2  and a d d i n g t h e l u m i n o s i t y f o r t h e f o u r s e c t i o n s o f t h e s p e c t r o m e t e r  27.  gives L = .58 x 1 0 - 5 cm  2  G e o f f r i o n ( i b i d ) shows a c u r v e o f t h e i n t e n s i t y t o be e x p e c t e d under optimum c o n d i t i o n s u s i n g an e x i t s l i t o f i n f i n i t e s i m a l w i d t h ( t h i s i s t h e case i n p h o t o g r a p h i c d e t e c t i o n ) .  The  t h e o r e t i c a l l i n e p r o f i l e f o r an e x i t s l i t o f a g i v e n w i d t h F can be o b t a i n e d f r o m t h i s c u r v e by i n t e g r a t i o n .  F i g . 1 4 shows  the p r o f i l e s o b t a i n e d from t h e dimensions o f our s p e c t r o m e t e r f o r - F = .025 cms. and F = . 0 6 cms.  Note t h a t t h e p r o f i l e i s  not s y m m e t r i c a l , the l o w e r energy s i d e extends f u r t h e r t h a n t h e h i g h energy s i d e . of  T h i s tendency i s exaggerated by the e f f e c t  a t h i c k source as can be seen from t h e 50 Kev l i n e  spectrum o f RaD ( F i g . l 6 ) .  i n the  Other e x p e r i m e n t e r s have r e p o r t e d  e n t i r e l y s i m i l a r results.^° P e r s i c o and G e o f f r i o n ^  1  have made an a n a l y s i s o f the  v a r i o u s b e t a r a y s p e c t r o g r a p h s and s p e c t r o m e t e r s mentioned i n the l i t e r a t u r e and c o m p i l e d t h e i r r e s u l t s i n t h e f o r m o f a table.  T h i s i s r e p r o d u c e d i n p a r t i n T a b l e I f o r comparison  w i t h t h e r e s u l t s f o r t h e s p e c t r o m e t e r d e s c r i b e d by t h i s  report.  They a l s o g i v e a s c a t t e r diagram o f t h e v a r i o u s i n s t r u m e n t s , p l o t t i n g r e s o l u t i o n a g a i n s t what t h e y c a l l the e f f i c i e n c y . eff.  = 107L/r  2  30.  G.E. Owen and H. P r i m a k o f f : Phys.Rev., 2 1 , 1 4 0 6 , 1 9 4 8 .  31.  E. P e r s i c o and C. G e o f f r i o n : R.S.T., 2 1 , 9 4 5 , 1 9 5 0 .  «-2%  • FIGURE 14. THEORETICAL LINE PROFILES A  Counter s l i t 0.025 om wide  B  Counter s l i t 0.06 wide  28.  T h i s i s p r o p o r t i o n a l t o the l u m i n o s i t y d i v i d e d by t h e c r o s s s e c t i o n a l a r e a o f t h e magnetic  field.  The diagram i s r e p r o d u c e d  i n part i n Fig.15• The  q u a n t i t i e s compared.in T a b l e I a r e s e l f - e x p l a n -  a t o r y w i t h t h e e x c e p t i o n o f W, C and D w h i c h a r e d e f i n e d as follows W = w/4-T  . The l u m i n o s i t y and s o l i d angle o f t h e s e  spectrometers  cannot be compared d i r e c t l y s i n c e they a r e i n f l u e n c e d by the r e s o l u t i o n s of t h e instruments.  However, t h e q u a n t i t i e s C and  t  D p r o v i d e a means o f comparison which e l i m i n a t e s the d i f f e r e n t resolutions.  The v a l u e of C c a l c u l a t e d f o r t h i s  instrument  ( 0 . 3 4 ) i s c o n s i d e r a b l y h i g h e r t h a n any o f t h e o t h e r s a n d , i n f a c t , i s almost o n e - h a l f o f t h e optimum v a l u e ( 0 . 7 2 5 ) .  I t c o u l d be  i n c r e a s e d by making the c o u n t e r e n t r a n c e s l i t t h e same w i d t h as t h e s o u r c e .  ;  D r e p r e s e n t i n g t h e r a t i o o f t h e s o l i d a n g l e to  t h e r e s o l u t i o n has d i f f e r e n t v a l u e s depending f o u r c o u n t e r s a r e used. D = 0.60.  ;  on whether one o r  W i t h one c o u n t e r D = 0 . 1 5 and w i t h f o u r  No 9 i n t h e t a b l e i s t h e s p e c t r o m e t e r d e s c r i b e d i n  t h i s r e p o r t , (a) i s the d a t a f o r one c o u n t e r o n l y and (b) i s t h e data f o r four counters.  The v a l u e s of t h e r e s o l u t i o n and l u m i n - i  o s i t y i n 9 ( b ) a r e c a l c u l a t e d on t h e b a s i s t h a t the e x i t s l i t s a r e a l l l i n e d up e x a c t l y w i t h t h e e l e c t r o n t r a j e c t o r i e s .  This  !  FIGURE 15. 'COMPARISON OF VARIOUS BETA RAY SPECTROMETERS (The numbers on the p o i n t s r e f e r t o the c o r r e s p o n d i n g i n s t r u m e n t s i n TABLE I ) A  Optimum v a l u e s f o r t h e u s u a l semi c i r c u l a r spectrometer  focussing,  B  Optimum v a l u e s f o r h i g h s o u r c e type o f semi c i r c u l a r f o c u s s i n g spectrometer  29.  i s almost t r u e as w i l l be shown l a t e r .  4 ( a ) and 4(b) a r e  c o n d i t i o n s o f o p e r a t i o n o f t h e same i n s t r u m e n t .  two  •No  Authors  Year  •Ref.  Type  TABLE I Emax I r o n Mev r  1  Li  1937  ?2  Spg.  7  2  Arnould  1939  33  Spg.  n  0.26  3 - .Lawson and T y l e r  1939  34  Spm.  y  3.1  4  1940  Spm.  y  Neary  a  MM  b  p  W%  LxlO^ cm2  CxlO  0.63  0.0067  0.020  18  0.2  0.011  0.00022  12  1.6  0.10  0.50  11  6.3  7  1.0  0.041  0.052  11  4.1  1.26  0.041  0.052  0.10  0.38  cm. 6  MM  8  1.6  11.4  0.2  12  0.17  0.029  0.00073  4.2  0.20  7.3  1941  w.  Spm.  y  6  P l e s s e t , Harnw e l l and S e i d l  1942  37  Spg.  y  7  S e i gbahn  1944  ?8  Spm.  y  8  L a n g e r , Motz and P r i c e  1950  19  Spm.  n  0.23  2.6  0.10  Brown  1951  Spm.  n  0.10. ? . 0 5 1 . 7  .25  a  10 MM-  0.10  b  2.8  10  Townsend  ?  0.74  MM  5  164, 1937*  ?.05 1.7  1.0  2  19  Dxl02 1.1 5.5  3.3 6.3  17 3.9  0.146  34  15  0.58  34  60  32.  K.T. K i : Proc.Camb.Phil.Soc.,  36.' A.A. Townsend: Proc.Roy.Soc. 177.358,1940.  33.  R . A r n o u l d : Ann.de Phys: S e r i e 11,to 12., 241, 1939.  37.  P l e s s e t , Harmwell & S e i d l : R.S.I., 11, 351, 1942.  34.  J.L. Lawson & A.W.Tyler: R.S.I.,11,6,1940.  38.  35.  G-.J. N e a r y : Proc.Roy.Soc., 175,71.1940.  K, Siegbahn: A r k i v . M a t . A s t r o m . F y s . B d . , 30A, (No20) 1944. T ©  Ill RESULTS  Radium D /  Pb  )  The p r i m a r y b e t a spectrum has l o n g been known t o c o n s i s t of continuous d i s t r i b u t i o n s of e l e c t r o n s , conversion e l e c t r o n s and Auger e l e c t r o n s a l l i n t h e energy r e g i o n below 50 Kev.  The v e r y r e a l e x p e r i m e n t a l t r o u b l e s a t t e n d a n t upon a  d e t a i l e d a n a l y s i s of t h e s e r a d i a t i o n s have l e d t o l a r g e d i s c r e p a n c i e s among and u n c e r t a i n t i e s i n t h e r e p o r t e d f i n d i n g The b u l k o f t h e work has been done w i t h c l o u d chambers and a b s o r p t i o n t e c h n i q u e s which have grave l i m i t a t i o n s i n r e s o l u t i o n and s t a t i s t i c a l a c c u r a c y .  Because o f t h e low  energy  o f any gamma-rays, t h e r e are many c o n v e r s i o n e l e c t r o n s f r o m t h e L , M and N s h e l l s superimposed  upon t h e p r i m a r y b e t a d i s -  t r i b u t i o n w h i c h makes i t d i f f i c u l t t o l o c a t e the e n d - p o i n t accurately. beta  The Auger e l e c t r o n l i n e s f u r t h e r obscure the  spectrum. In  s p i t e of these obvious problems, i t was  felt  t h a t t h i s n u c l e u s would p r o v i d e a good t e s t o f the p e r f o r mance o f the s p e c t r o m e t e r under v e r y u n f a v o r a b l e c o n d i t i o n s . A l s o , i f s u c c e s s f u l , t h e experiment would p r o v i d e u s e f u l i n f o r m a t i o n t h a t might h e l p i n e l i m i n a t i n g some o f the r e p o r t e d i n c o n s i s t e n c i e s i n the decay o f The b e t a spectrum was  RaD.  s t u d i e d e x t e n s i v e l y by e a r l y  e x p e r i m e n t e r s w i t h p h o t o g r a p h i c methods.  I t appeared  t o be  v e r y s i m p l e , c o n s i s t i n g o f a group o f c o n v e r s i o n l i n e s a l l a t t r i b u t a b l e t o t h e a c t i o n of one gamma r a y .  Rutherford,  Chadwick and E l l i s r e p o r t t h e f o l l o w i n g v a l u e s .  TABLE I I Number of l i n e  Hr  Intensity  Energy i n Kev  1  50  600  30.9  2  2  606  31.5  3  0.5  628  33.8  4  20  714  43.3  P  10  738  46.1  which are analyzed as f o l l o w s TABLE I I I Number of l i n e -  Origin  Energy + a b s o r p t i o n energy i n Kev  Energy o f Gamma i n Kev  1  Li  30.9+16.3  47.2  2  I'll  31.5+15.7  47.2  3  L  33.8+13.4  47.2  III  4  Mj  43.3+ 4.0  47.3  5  Nj  46.1+ 1.0  47.1  G. v o n D r o s t e ^ u s i n g a W i l s o n c l o u d chamber a n d magnetic a n a l y s i s o b t a i n e d most o f t h e above c o n v e r s i o n l i n e s and a g r e e s r o u g h l y on t h e energy o f t h e p r i m a r y gamma. 39.  G. v o n D r o s t e : Z e i t s . f u r Phys., 84, 1 7 , 1 9 3 3 .  He also  33.  o b s e r v e d a l a r g e number of t r a c k s c o r r e s p o n d i n g t o t h e x - r a y spectrum o f t h e i n n e r s h e l l e l e c t r o n s o f atoms o f a t o m i c number 8 3 .  R i c h a r d s o n and L e i g h - S m i t h  4 0  d i s t r i b u t e d Radium  D as a gas i n t h e f o r m o f t e t r a - m e t h y l l e a d t h r o u g h o u t a c l o u d chamber.  The b e t a s p e c t r u m was c a l c u l a t e d from e l -  e c t r o n p a t h l e n g t h s and range-energy measurements.  In  a d d i t i o n to the usual conversion l i n e s they report a large number o f e l e c t r o n s o f v e r y l o w energy.  T h e i r r e s u l t s were  based on a s m a l l number of o b s e r v a t i o n s and thus have poor statistics. A K u r i e p l o t of t h e r e s u l t s g i v e s an end p o i n t , 4.1 of 16 Kev. Lee and L i b b y used a b s o r p t i o n t e c h n i q u e s t o s t u d y t h e gammas from RaD and a s c r e e n w a l l c o u n t e r w i t h magn e t i c d e f l e c t i o n to o b s e r v e t h e p r i m a r y b e t a d i s t r i b u t i o n . They r e p o r t a n end p o i n t o f 2 5 . 5 - .1 Kev.  The c o n t i n u o u s 42  d i s t r i b u t i o n has a l s o been observed by Saha  who g i v e s t h e  end p o i n t as 29 Kev. A g r e a t d e a l of work has been done on t h e a n a l y s i s o f t h e gamma r a y s o f RaD by T s i e n S a n - T s i a n g , F r i l l e y e t a l . ^ 4  By a number o f methods such a s a bent c r y s t a l s p e c t r o m e t e r , 160,  40.  H.O.W. R i c h a r d s o n and A . L e i g h - S m i t h :  41.  D.D. Lee and W.F. L i b b y : Phys.Rev.  42.  A.K. Saha: P r o c . N a t . I n s t . S c i . I n d i a , 1 2 , N o . 3 , 1 9 4 6 .  454, 1937.  43.  Proc.Roy.Soc. 252, 1939.  T s i e n S a n - T s i a n g : Comples Rendus, 2 1 6 . 7 6 5 , 1 9 4 3 . Ouang TeTchao: J". Surugue, T s i e n S a n - T s i a n g : Comptes Rendus, 2 1 2 , 5 3 5 , 1 9 4 3 . T s i e n S a n - T s i a n g : Comptes-Rendus, 2 1 8 . 5 0 3 , 1 9 4 4 . M. " F r i l l e y : Comptes Rendus 2 1 8 , 5 0 5 , 1 9 4 4 . T s i e n S a n - T s i a n g and C.Marty: Comptes R e n d u s , 2 2 0 . 6 8 8 . 1 9 4 5 . • T s i e n S a n - T s i a n g and C.Marty: Comptes Rendus,221,177,1945. T s i e n S a n - T s i a n g : Phys.Rev., 6 £ , 3 8 , 1 9 4 6 . —  34.  measurement o f p a t h l e n g t h s i n a c l o u d chamber, magnetic d e f l e c t i o n i n a c l o u d chamber, a b s o r p t i o n measurements t h e y show the e x i s t e n c e of t h e f o l l o w i n g n u c l e a r gamma r a y s .  TABLE I V Number of l i n e  Energy i n Kev  Quanta/100 dis int egrations < 0.2  1  65*5  2  46.7-0.1  2.8  3  43*0.  0.2  4  37*1  0.2  5  32*1  0.4  6  23 ..2*0..6  1.0  7  7.3*0.7  —10  More r e c e n t l y Gurran e t a l .  have i n v e s t i g a t e d t h e  gamma r a y s o f RaD by means of a p r o p o r t i o n a l c o u n t e r .  The b e t a  p a r t i c l e s from t h e i r s o u r c e were d e f l e c t e d m a g n e t i c a l l y and t h e gammas e n t e r e d t h e c o u n t e r t h r o u g h a t h i n m i c a window.  They  r e p o r t t h e f o l l o w i n g gamma r a y s  TABLE V Intensity  Energy  7.3  7.7 Kev  0.4  2 5 . 8 Kev  3.0  4 6 . 6 Kev  44. S.C. C u r r a n , J . Angus a n d A.L. C o c k e r o f t : P h i l . M a i 40, 3 6 , 1949.  35  and i n a d d i t i o n s t r o n g L x - r a y l i n e s i n the 1 0 - 1 5 Kev r e g i o n T h e i r r e s u l t s appear t o be t h e most r e l i a b l e t o d a t e . Another  i n v e s t i g a t i o n of" RaD has been done by Cranberg'  u s i n g t h i n s o u r c e s (average t h i c k n e s s about 43 micrograms/cm ) 2  and a s e m i c i r c u l a r f o c u s s i n g s p e c t r o g r a p h .  H i s p l a t e s show t h e  Lj, L j x i > M and N c o n v e r s i o n l i n e s f r o m t h e 47 Kev gamma r a y . There i s a l s o some e v i d e n c e o f a l i n e a t 19 K e v ( 4 7 0 gauss cm. ). The  s e n s i t i v i t y of t h e e m u l s i o n i s e v i d e n t l y v e r y poor below  1 5 Kev.  F i g . l 6 shows the r e s u l t s o b t a i n e d here w i t h a s o u r c e o f about 30 micrograms/cm . ' The r e a d i n g s have been r e p e a t e d a number o f t i m e s w i t h d i f f e r e n t s o u r c e s t r e n g t h s w i t h o u t any a p p r e c i a b l e change i n the spectrum.  The L j , L i n y M, and N  c o n v e r s i o n l i n e s o f the 4 7 Kev gamma l i n e a r e i n d i c a t e d .  The  broad peak a t about 3 0 0 gauss-cms i s p r o b a b l y due t o t h e cont i n u o u s spectrum  o f nuclear beta p a r t i c l e s .  The l o w energy peak  a t about 1 5 0 gauss-cms i s h a r d to i d e n t i f y because o f i t s w i d t h . The most p r o b a b l e l o s s of energy o f an e l e c t r o n o f 3 Kev energy i s about 50 e l e c t r o n v o l t s p e r mierogram/cm . 2  weighs 3 0 micrograms/cm  2  Since the source  the w i d t h o f t h e l i n e can r e a d i l y be  e x p l a i n e d i n terms o f a b s o r p t i o n i n s o u r c e . I f t h i s i s t h e cause o f t h e l i n e w i d t h t h e n the a c t u a l energy o f t h e e l e c t r o n s must be a t t h e h i g h energy end o f t h e l i n e , about 200 gauss-cms, c o r r e s p o n d i n g t o 3.7; Kev.  Thus t h e  l i n e may be due t o an I s h e l l c o n v e r s i o n o f the 7 . 7 Kev gamma r e p o r t e d above. 45.  L. Cranberg: Phys.Rev., 2 1 , 1 5 5 , 1 9 5 0 .  _l8oo  600  1400 Hr(Gauss-cms) JL200 1Q2.5 0J9 ^J.000  800 CO .O o 600  J-00  200  205.0  307.5  410.0  3J  8  14.6  5X2  Energy (Kev)  (The a r r o w s i n d i c a t e t h e l i n e s as d e s c r i b e d by t h e c o r r e s p o n d i n g numbers i n TABLE V I I I )  36.  On t h e o t h e r hand t h e l i n e may be due w h o l l y o r i n p a r t t o Auger t r a n s i t i o n s i n t h e e l e c t r o n i c s h e l l s o f t h e daughter B i atoms.  S i n c e the 4 6 Kev gamma i s most h i g h l y  converted i n the  l e v e l i t i s to be expected t h a t most Auger  t r a n s i t i o n s would s t a r t f r o m h e r e . as f o l l o w s . electron.  The p r o c e s s c a n be p i c t u r e d  The atom i s s i n g l y i o n i z e d , h a v i n g l o s t an L j T h i s vacancy c a n be f i l l e d by an e l e c t r o n from any  h i g h e r energy s t a t e L J X V . III» I» L  M  N  I  a n o t h e r e l e c t r o n i s e j e c t e d from t h e atom.  and s i m u l t a n e o u s l y F o r an energy  b a l a n c e , t h e k i n e t i c energy o f t h e e j e c t e d e l e c t r o n p l u s i t s b i n d i n g energy must be e q u a l t o t h e energy g i v e n up by t h e reversionto the L j state.  Note t h a t s i n c e t h e r e i s a vacancy  i n t h e 1 s h e l l t h e b i n d i n g e n e r g i e s o f t h e M and N are i n c r e a s e d ,  electrons  and must be c a l c u l a t e d on t h e b a s i s o f an i n -  crease of u n i t y i n the nuclear  charge.  As a n example, c o n s i d e r  t r a n s i t i o n ; from an atom  s i n g l y i o n i z e d by l a c k of an L i e l e c t r o n t o doubly i o n i z e d by l a c k o f L J J J and Mjy  I-I-  The  electrons.  )  L  III IV M  k i n e t i c energy o f t h e e j e c t e d e l e c t r o n i s g i v e n by:  E(Kin) = E ( L l ) z - E ( L l I l ) z - S(Miv)  z+1  Table vT 6 l i s t s t h e binding energies of the L 4  46. These v a l u e s were o b t a i n e d from Compton and A l l i s o n : X r a y s i n Theory and E x p e r i m e n t , and from t h e I n t e r n a t i o n a l C r i t i c a l Tables.  37  e l e c t r o n i n b i s m u t h and some o f t h e M and N e l e c t r o n s i n p o l o n i u m and T a b l e V I I g i v e s some of t h e p o s s i b l e  transitions  t o g e t h e r w i t h the k i n e t i c energy o f t h e e j e c t e d e l e c t r o n s . R i c h t m e y e r and Kennard "^ s t a t e t h a t t h e t r a n s i t i o n s 4  Lj  ^  L  I I X  M , IV  y  a r e o f t e n o b s e r v e d i n X r a y work f o r Z>75.  However, t h e excess  energy i n t h i s case i s t o o s m a l l f o r d e t e c t i o n .  TABLB V I L  M  N  I  16.400  4.000  900  II  15.700  3,700  boo  III  13.400  3.200  700  IV  2,700  500  V  2,600  400  Thus t h e r e a r e a number o f t r a n s i t i o n s t h a t  could  y i e l d e l e c t r o n s i n t h e energy range o c c u p i e d by t h i s l i n e . have d i f f e r e n t e n e r g i e s occurring.  They  and d i f f e r e n t degrees o f p r o b a b i l i t y o f  I t i s l i k e l y t h a t t h e l i n e i s a c t u a l l y composed o f  e l e c t r o n s r e s u l t i n g f r o m s e v e r a l Auger t r a n s i t i o n s and t h e M conversion  o f t h e 7 Kev gamma w i t h i t s s t r u c t u r e t o t a l l y o b s c u r e d  by a b s o r p t i o n i n t h e s o u r c e , w i t h f u r t h e r c o n f u s i o n  due t o t h e  v a r i a t i o n o f t r a n s m i s s i o n of the c o u n t e r windows i n t h i s r e g i o n . 47. R i c h t m e y e r & Kennard: I n t r o d u c t i o n t o Modern Phys., 3rd E d i t i o n , p.548.  38.  TABLE V I I No  . Transition  1  Li—» ^ I I I I V  300  i—* m v  400  M  2  L  3  L l ^  4  i»i—:> L i l i a n  3  L  6  Energy i n e.v.  L  M  2100  I I I %  L  2200  i—> nAn  2300  L  I»l-^1"III%V  2500  I—> III V  2700  7  L  8  Hj—^NJNJJ  L  N  2200 2400;  9 10  M  I—> I IV  2600  11  M i — > NjNy  2800  N  N  W i t h one source w h i c h was made t h i n n e r t h a n u s u a l (of t h e o r d e r o f 10 micrograms/cm ) some s t r u c t u r e was n o t i c e d 2  but b e f o r e r e l i a b l e s t a t i s t i c s c o u l d be o b t a i n e d an a c c i d e n t o c c u r r e d i n w h i c h t h e s o u r c e became damaged.  I f a source c o u l d  be made l e s s t h a n 5 micrograms/cm more i n f o r m a t i o n c o u l d be 2  o b t a i n e d about t h i s  line.  There i s some evidence o f a v e r y weak peak a t 450 gauss-cm (18 K e v ) .  I f t h i s corresponds  t o M-shell conversion  then t h e energy o f t h e t r a n s i t i o n i s about 22 Kev and a n Ls h e l l peak s h o u l d o c c u r n e a r 5.5 Kev. this.  There i s no e v i d e n c e o f  Therefore should t h i s t r a n s i t i o n a c t u a l l y e x i s t , the  t r a n s i t i o n energy i s about 34 Kev and t h e c o n v e r s i o n t a k e s p l a c e  39.  in  this L shell.  There i s a s i m i l a r l y d o u b t f u l peak a t 500 an  gauss-cm (21 Kev) w h i c h by t h e same arguments would  be^L-shell  c o n v e r s i o n o f a 37*5 Kev t r a n s i t i o n . T a b l e T i l l l i s t s t h e r e s u l t s o f t h i s experiment to determine t h e c o n v e r s i o n t r a n s i t i o n s product.  o f t h e RaE daughter  The e n e r g i e s were d e t e r m i n e d by use o f t h e t h e o r e t i c a l  value of the f i e l d .  No. o f line  (See page 1 9 ) . TJ (U3LI  Origin  VIII. Conv.line + Shell Binding  Transition Energy 7.7 Kev  1*  M  3.7-1.0+4.0  2  Li  3*.0 l.0+16.4  47.4  3  L I I I 34.3 1.0+13.4  47.7  4  M  43.4+1.0+4.0  47.4  5  N  48.0*1.5+1.0  49.0  6**  LI,.  18.3-1+16.4  34.7**  21.5*1+16.4  37.9**  +  +  ft C o r r e c t e d f o r s o u r c e a b s o r p t i o n . &k D o u b t f u l .  The P r i m a r y B e t a Spectrum The low-energy t a i l on t h e L i c o n v e r s i o n l i n e o f t h e 47 Kev gamma i s u n f o r t u n a t e i n t h a t i t tends t o obscure t h e d i s t r i b u t i o n of the disintegration version l i n e s i n this region.  e l e c t r o n s and any weak eon-  The l e a d i n g edge o f t h e l i n e  c o r r e s p o n d s w e l l w i t h t h e expected h a l f maximum i n t e n s i t y u t i o n o f 1.7%.  resol-  The l o w energy t a i l appears to be caused by the  40.  spectrometer  r a t h e r t h a n by source a b s o r p t i o n s i n c e d i f f e r e n t  t h i c k n e s s e s o f sources d i d not make much d i f f e r e n c e .  Owen and  P r i m a k o f f " ^ have r e p o r t e d almost i d e n t i c a l l i n e p r o f i l e s f r o m 4  t h e i r small s e m i c i r c u l a r l y f o c u s s i n g spectrometer.  They d e s c r i b e  t h e f i t t i n g of. t h e t r a i l i n g edge o f t h e l i n e by means o f an exponential  curve  N(H) = C o n s t a n t X e x p ^ - Po~P j  where p  0  i s t h e Hr v a l u e o f t h e l e a d i n g edge o f t h e l i n e and  a i s the average w i d t h o f t h e l i n e i n gauss-ems. T h i s has been done w i t h t h e L j c o n v e r s i o n peak ( t h e s o l i d l i n e i n F i g . l 6 ) and t h e c a l c u l a t e d v a l u e s s u b t r a c t e d f r o m t h e o b s e r v e d d i s t r i b u t i o n , r e s u l t i n g i n t h e p l o t shown i n F i g . 1 7 . I n s p e c t i o n o f t h i s curve g i v e s a b e t a r a y end p o i n t o f 22.4 Kev, a v a l u e w h i c h i s s t r o n g l y i n f l u e n c e d by t h e f i t t i n g o f an e x p o n e n t i a l curve t o t h e 46 Kev ILj c o n v e r s i o n  line.  The K u r i e p l o t o f t h e b e t a spectrum i s shown i n F i g . l 8 . I n t h e c a l c u l a t i o n o f t h e curve the f o l l o w i n g p r o c e d u r e was used. The Fermi r e l a t i o n i s g i v e n by  N  1/2  X  1  where  ~ **max"" jt  s  -y •» t h e momentum o f t h e e l e c t r o n s i n u n i t s o f M G . 0  N = t h e number o f e l e c t r o n s i n t h e momentum i n t e r v a l ^ to + dl^ 48.  See r e f e r e n c e  No.30.  •FIGURE 17. •BETA SPECTRUM OF RADIUM D WITH 30 KEV CONVERSION LINE SUBTRACTED  ENERGY (Kev)  •FIGURE 1 8 . •KURIE PLOT OF BETA SPECTRUM OF RADIUM D  41.  and f ( Z , ^ ) -  ^ 2S  Q  7ry  P t l  S - ^/i-(z/i37)  + S +l y )  - 1  :  y = zyr+T " 2  137 y S i n c e t h e r e a r e no complete t a b l e s o f the complex gamma f u n c t i o n a v a i l a b l e i t was approximated by means o f a T a y l o r e x p a n s i o n t o t h e f i r s t power o n l y o f S.  Neglecting  h i g h e r terms we get 2  Ptl+S+iy)  _  Try  •ainh it y  l  +  Sr {l+U) l  s  ( /^ll+iy)  -  /^il-ly) /"* ( 1 - i y ) 1  The e x p r e s s i o n i n ^ j was f u r t h e r expanded i n a s e r i e s u s i n g a w e l l known e x p a n s i o n f o r f 1  s e r i e s i n v o l v e d o f t h e form  ri(n +y ) 2  2  n = 1 was approximated by  h(n +y ) 2  whence  2  \Z)Jp{Z).  The  42.  Try J 1+2S V+S I n ( 1 + y ) t iinh.7ry [ 2  with  ^ = E u l e r c o n s t a n t « 0.5772  The f i n a l r e s u l t i s t h a t  f(z,7 ) = 7  2 S  ' .  I  7ry e^y sinli;7ry (  fi+zsY+s  m  (l+y ) J 2  t  A s t r a i g h t l i n e was f i t t e d to t h e p o i n t s from 7 Kev \  t o 15 Kev by means o f t h e l e a s t squares, p r o c e d u r e y i e l d i n g an end p o i n t o f 2 1 . 7 - 1 Kev Below 7 Kev t h e curve d e v i a t e s from a s t r a i g h t l i n e due to a b s o r p t i o n i n t h e s o u r c e .  The p o i n t a t 1 8 . 5 Kev was n e g l e c t e d  i n t h e d e t e r m i n a t i o n o f t h e l i n e s i n c e i t i s so s t r o n g l y i n f l u e n c e d by t h e two s m a l l peaks i n t h a t r e g i o n and by t h e t a i l of the I i j conversion l i n e . Most o f the r e a d i n g s on RaD were t a k e n w i t h o n l y t h r e e o f t h e f o u r c o u n t e r s o p e r a t i n g as one c o u n t e r was found to be u n r e l i a b l e and c o u l d n o t be made t o o p e r a t e p r o p e r l y .  A r u n was  t a k e n on t h e $00) gauss-cm l i n e u s i n g o n l y one c o u n t e r , as a check on t h e a l i g n m e n t  of t h e spectrometer.  The comparison i s shown  i n E i g . 1 9 , t h e d i f f e r e n c e i n r e s o l u t i o n i s v e r y s m a l l and o f t h e o r d e r o f magnitude t o be expected f r o m t h e alignment  procedure.  FIGURE 19. . LINE WIDTHS FROM ONE COUNTER AND FROM THREE COUNTERS Solid  line  Dashed l i n e  One c o u n t e r Three' c o u n t e r s  43.  D i s c u s s i o n o f t h e R e s u l t s on RaD There seems to be no doubt b u t t h a t t h e decay RaD—>RaE t a k e s p l a c e w i t h a n e g a t r o n decay t o an e x c i t e d s t a t e o f RaE.  The predominant gamma-ray and t h e c o n v e r s i o n  e l e c t r o n s correspond o f 7.7  Kev.  t o a t r a n s i t i o n energy o f 4?. Kev a n d one  The maximum energy of t h e beta-spectrum  f r o m t h e Kuriae p l o t i s 21.7  as t a k e n  Kiev.  I n a d d i t i o n t o t h e s e two major t r a n s i t i o n s t h e r e i s c o n f l i c t i n g evidence o f o t h e r v e r y weak t r a n s i t i o n s w i t h v e r y l i t t l e c o r r e l a t i o n between t h e d i f f e r e n t r e p o r t e d f i g u r e s . Examination  o f t h e e x p e r i m e n t a l e v i d e n c e i n each case l e a d s  one to c o n c l u d e t h a t t h e e v i d e n c e i s not very s t r o n g i n most cases. 7.7  A l l q u a n t i t a t i v e experiments  quote t h e 47 Kev and the  Kev t r a n s i t i o n s , and i t appears t h a t t h e s e a r e t h e o n l y  t r a n s i t i o n s upon which much r e l i a n c e c a n be p l a c e d . Now i t i s i m p o s s i b l e t o p o s t u l a t e a decay scheme f o r a n u c l e u s when the r a d i a t i o n s c o n s i s t o f one beta-group and two major gamma-rays, u n l e s s one assumes t h e gamma-rays a r e i n cascade.  We c a n make t h i s p o s t u l a t e and t r y t o f i t t h e known  d a t a t o such a scheme t o see i f such d a t a a r e c o n s i s t e n t or not'.  I f a cascade gamma scheme i s c o r r e c t then t h e r e s h o u l d be  !  e q u a l numbers o f t r a n s i t i o n s c o r r e s p o n d i n g t o the 47 Kev and t h e 7.7  Kev l i n e s .  That i s , t h e sum o f t h e c o n v e r s i o n e l e c t r o n s  p l u s t h e gamma-rays s h o u l d be t h e same i n b o t h c a s e s . The r e l a t i v e numbers o f c o n v e r s i o n e l e c t r o n s f o r the two t r a n s i t i o n s may be r o u g h l y e s t i m a t e d f o r t h e f i r s t time f r o m the r e s u l t s o f the p r e s e n t i n v e s t i g a t i o n i f we make t h e some-  44  what d r a s t i c assumption  t h a t t h e t r u e h e i g h t o f t h e 7«7 Kev  peak i s t h a t o f a peak whose a r e a i s e q u a l t o t h e measured peak and whose h a l f - w i d t h i s about 1.5% i n momentum. to a c o r r e c t e d peak h e i g h t o f 1200 counts/minute.  This  corresponds  This estimate  w i l l p r o b a b l y e r r on t h e l o w s i d e because a t t h e e n e r g i e s i n v o l v e d , we may expect s c a t t e r e d and absorbed rons t h a t would not reach t h e counter.  conversion e l e c t -  The t o t a l number o f  47 Kev c o n v e r s i o n e l e c t r o n s w i l l o f course be p r o p o r t i o n a l t o t h e sum o f a l l t h e c o n v e r s i o n peak h e i g h t s c o r r e s p o n d i n g t o t h i s t r a n s i t i o n — i . e . 1800 + 800 + 300 - — o r ^ - 3 0 0 0 counts p e r minute.  Hence  (N ) . E  7  7  \  W^huT '  1200  = 0.4  1.  3000  The work o f C u r r a n and c o l l a b o r a t o r s on t h e gammar a y s o f RaD g i v e s t h e r a t i o o f 7«7 Kev gammas t o 47 Kev gammas as about 2.4. San-Tsiang r a t i o a t 3.6.  and co-workers  p u t t h e v a l u e o f the  T a k i n g t h e mean v a l u e , we a c c e p t  (N  r>7..7 ^  3.0  F i n a l l y on t h e b a s i s of h i s measurements, San-Tsiang  2.  concludes  t h a t t h e r e a r e a p p r o x i m a t e l y 10 quanta o f 7.7 Kev energy e m i t t e d f o r each 100 d i s i n t e g r a t i o n s . To summarize t h e n , f o r each 100 d i s i n t e g r a t i o n s , t h e r e w i l l be 10 - 7.7 Kev quanta and 90 c o n v e r s i o n e l e c t r o n s  45  (2)  f o r t h i s energy.. On t h e cascade p i c t u r e , u s i n g e q u a t i o n t h e r e a r e a p p r o x i m a t e l y 3 - 47, Kev q u a n t a and 97 conversion electrons.  corresponding  T h i s would p r e d i c t  i£ej_7.7  = 29.  or^o.9  whereas o u r rough e s t i m a t e s p u t t h e v a l u e as g r e a t e r t h a n 0 . 4 from ( 1 ) .  C o n s i d e r i n g the data a v a i l a b l e , then there i s nothing  i n c o n s i s t e n t i n t h e a s s u m p t i o n o f a cascade gamma system.  This  would then l e a d to a decay scheme as i l l u s t r a t e d i n F i g u r e 2 0 . T h i s scheme c o u l d be t e s t e d by t h e use o f c o i n c i d e n c e t e c h n i q u e s except f o r t h e presence  o f Auger e l e c t r o n s and X-ray3  i n t h e 7«7 Kev energy r e g i o n w h i c h a r e c o i n c i d e n t w i t h the 47. Kev transition.  I t i s l i k e l y t h a t t h e e x p e r i m e n t a l d i f f i c u l t i e s would  p r e c l u d e t h i s check. From o u r p r e v i o u s f i g u r e s , we c a n e s t i m a t e t h e o r d e r o f magnitude o f t h e c o n v e r s i o n c o e f f i c i e n t s s i n c e by d e f i n i t i o n  « Hence < X  M  - N  r  f o r t h e 7 . 7 Kev t r a n s i t i o n has t h e v a l u e 9 w h i l e  °(= ^ I ^ + ^ M + ^ N  F  O  R  t  h  e  4  7 Kev t r a n s i t i o n i s a p p r o x i m a t e l y 30 o r  0£ x, a l o n e has the v a l u e 1 8 .  U n f o r t u n a t e l y t h e r e i s no a v a i l a b l e  c a l Q u l a t i o n o f values of M-conversion  c o e f f i c i e n t s , the l i t e r -  a t u r e a t p r e s e n t b e i n g l i m i t e d t o K- and L - c o n v e r s i o n . Nelson 49.  4 9  Hebb and  l i s t v a l u e s o f L - c o n v e r s i o n c o e f f i c i e n t s f r o m w h i c h we M.H. Hebb and S. N e l s o n , Phys. Rev., j>8, 4 8 8 , 1 9 4 0 .  '  21.7 Kev 7.7 Kev  4 7 . 4 Kev  21.7 Kev  4 7 „ 4 Kev  7.7 Kev  FIGURE 2 0 . SUGGESTED DECAY SCHEME FOR RADIUM D  would expect a v a l u e o f $f L = 0 . 5 f o r t h e 47 Kev t r a n s i t i o n if  the s p i n change i s 1 ( E l e c t r i c D i p o l e ) and cxl-^ = 38 i f t h e  s p i n change i s 2 ( E l e c t r i c q u a d r u p o l e ) . Our c.ascade-gamma h y p o t h e s i s t h e n would i d e n t i f y t h e 47 Kev r a d i a t i o n as e l e c t r i c quadrupole i f a c h o i c e has t o be made.  Now an e s t i m a t e o f t h e  mean l i f e - t i m e o f t h i s s t a t e may be had ( t o one o r two o r d e r s o f magnitude) by u s i n g t h e r e l a t i o n o f Segre and H e l m h o l z ^  0  where  V  f~  (fJ  £(2l-i)ry  2  f  (  -3 l / 3 R b e i n g t h e n u c l e a r r a d i u s w h i c h we c a n t a k e a s 1,5 x 10 From t h i s , £y = 3 x 1 0 " seconds f o r A = 2.  1 0  A' .  seconds f o r 1 = 1 and £J, = 6 x 1 0 "  These o f c o u r s e a r e l i f e t i m e s  3  by gamma  e m i s s i o n o n l y and hence the t o t a l l i f e t i m e s a r e probably.much l e s s t h a n t h i s s i n c e c o n v e r s i o n i s t h e predominant decay method on o u r b a s i c assumption.  I t i s i m p r o b a b l e t h a t X i s 'greater t h a n  2 s i n c e t h i s would mean a l o n g l i f e t i m e , i . e . an i s o m e r i c s t a t e and would have been, o b s e r v e d .  T h e r e f o r e , quadrupole r a d i a t i o n  i s n o t an u n r e a s o n a b l e assignment f o r t h e 47 Kev t r a n s i t i o n . U n f o r t u n a t e l y , f o r t h e r e a s o n s g i v e n above, no such guess may be made f o r t h e 7.7 Kev t r a n s i t i o n o t h e r t h a n t o suggest t h a t because o f i t s low energy even an assignment o f ^ =  2 would  p r o b a b l y produce a m e t a s t a b l e s t a t e t h a t i s o b s e r v a b l e . This 50. E. Segre and A.C. Helmholz; Rev.Mod.Phys., 2 1 , 280, 1949.  i s o f course p o s s i b l e and perhaps s h o u l d energy might make i t s o b s e r v a t i o n  i t e x i s t , i t s low  difficult.  I n a l l t h e above, w h i c h must be c l a s s e d as s p e c u l a t i o n based upon what e v i d e n c e t h e r e i s , we have been d i s c u s s i n g t h e major t r a n s i t i o n s . can be s a i d .  Of o t h e r weak o r d o u b t f u l t r a n s i t i o n s ,  little  I f t h e y e x i s t , t h e y may be due t o a l t e r n a t e branch  t r a n s i t i o n s from t h e h i g h energy e x c i t e d s t a t e t h r o u g h i n t e r mediate l e v e l s t o the ground s t a t e . a w a i t more p r e c i s e and r e p r o d u c i b l e  F u r t h e r d i s c u s s i o n must experimental  results.  48, IV CONCLUSIONS AND RECOMMENDATIONS  The experiment has shown t h a t i t i s f e a s i b l e t o b u i l d a s p e c t r o m e t e r t o s t u d y b e t a and gamma s p e c t r a i n the low r e g i o n down to 2 Kev or l e s s .  energy  The r e s o l u t i o n as t a k e n f r o m h i g h  energy s i d e o f t h e 30 Kev peak i n RaD  i s v e r y c l o s e to the v a l u e  c a l c u l a t e d from the d e s i g n of the s p e c t r o m e t e r .  I t i s unprofit-  a b l e t o t r y t o i n c r e a s e t h e r e s o l u t i o n o f t h e instrument, because o f t h e l i n e w i d t h produced  by a b s o r p t i o n i n t h e s o u r c e .  I n add-  i t i o n t h e r e s o l u t i o n i s l i m i t e d under p r e s e n t c o n d i t i o n s , m a i n l y by t h e w i d t h of the s o u r c e , and i t would be d i f f i c u l t i f n o t i m p o s s i b l e to make s o u r c e s much narrower t h a n 1  mm.  A number o f improvements t o i n c r e a s e the r e l i a b i l i t y ease o f o p e r a t i o n o f t h e i n s t r u m e n t can be suggested.  F i r s t the  b a f f l e s i n the s p e c t r o m e t e r s h o u l d be redesigned, so t h a t  new  windows can be a t t a c h e d w i t h o u t removing t h e b a f f l e s and  source  from t h e i n s t r u m e n t .  Secondly the c o u n t e r s s h o u l d be  and  connected  t o g e t h e r o u t s i d e o f the a p p a r a t u s so t h a t they c o u l d be  checked  i n d i v i d u a l l y a t any time and any f a u l t y one o r ones d i s c o n n e c t e d . F i n a l l y t h e 6AS7 r e g u l a t o r t u b e s s h o u l d be m o n i t o r e d w i t h a wattmeter  i n o r d e r to p r e v e n t o v e r l o a d i n g them. W i t h t h e method o f a t t a c h i n g t h e c o u n t e r windows  now  used i t might be p o s s i b l e to make the e n t r a n c e s l i t s w i d e r , say t o 0.05  cms.  T h i s would i n c r e a s e t h e l u m i n o s i t y w i t h o u t changing  the r e s o l u t i o n a p p r e c i a b l y .  The problem o f e v a p o r a t i n g l i n e  sources on the b a c k i n g s h o u l d be i n v e s t i g a t e d .  T h i s might be done  49  from a c r u c i b l e o f some s o r t as w e l l as from a f i l a m e n t .  Finally  t h e problem o f e x t e r n a l quenching o f the c o u n t e r s s h o u l d be i n v e s t i g a t e d more f u l l y .  P o s s i b l y w i t h g r e a t e r quench v o l t a g e  and l o n g e r p u l s e s an improvement i n performance might be obtained.  50.  APPENDIX I THE SCATTERING. AND. ABSORPTION 01 BETA-RAYS  The b e t a spectrum o f r a d i o - a c t i v e s u b s t a n c e s a s measured w i t h t h e s p e c t r o m e t e r , c a n be d i s t o r t e d i n many ways by the s c a t t e r i n g and a b s o r p t i o n o f e l e c t r o n s .  I f the spectrometer  i s s e t t o observe a c e r t a i n energy range the number o f e l e c t r o n s counted may be r e d u c e d by some o f them l o s i n g energy i n p a s s i n g t h r o u g h t h e m a t e r i a l of t h e source and s o u r c e b a c k i n g , by s c a t t e r i n g from m o l e c u l e s o f t h e r e s i d u a l g a s , by r e f l e c t i o n  (scattering  t h r o u g h more t h a n 90?) from t h e window o f t h e c o u n t e r and by a b s o r p t i o n i n t h e window.  I f the c o u n t e r i s o f t h e end window  t y p e an e l e c t r o n may be absorbed i n t h e c o u n t e r gas between the window and t h e s e n s i t i v e volume of t h e c o u n t e r w i t h o u t b e i n g recorded.  However, i t has been shown^  1  t h a t w i t h a s i d e window  c o u n t e r t h e s e n s i t i v e volume extends as f a r as t h e window.  An  i n c r e a s e i n the number o f e l e c t r o n s counted can be caused by e l e c t r o n s o f h i g h e r energy l o s i n g energy i n t h e s o u r c e and b a c k i n g and by r e f l e c t i o n from t h e s o u r c e s u p p o r t s , b a f f l e s and • a l l o t h e r s u r f a c e s i n the s p e c t r o m e t e r . A knowledge of t h e t h e o r e t i c a l e s t i m a t e s o f t h e magn i t u d e o f s c a t t e r i n g and a b s o r p t i o n e f f e c t s and o f t h e e x p e r i m e n t a l work on t h e s u b j e c t i s u s e f u l i n d e s i g n i n g a low energy s p e c t rometer s i n c e i t i s i n the low energy r e g i o n t h a t t h e d i s t o r t i o n becomes most t r o u b l e s o m e . An e l e c t r o n may be s c a t t e r e d by an atom i n e i t h e r o f two ways: i t may be d e f l e c t e d t h r o u g h a l a r g e a n g l e by t h e n u c l e u s 51.  S.C. Brown: Phys.Rev.,  9^4, 1941.  51  w i t h o u t l o s s o f energy  ( e l a s t i c s c a t t e r i n g ) o r i t may be d e f l e c t e d  t h r o u g h a s m a l l a n g l e by an e l e c t r o n .  For energies greater than  1000 e.v. and f o r low Z t h e second i s always accompanied by a l o s s o f energy and i s c a l l e d i n e l a s t i c s c a t t e r i n g .  I t can be  shown t h a t f o r e l a s t i c s c a t t e r i n g t h e p r o b a b i l i t y v a r i e s as (1 -  v2/o ) 2  Thus t h e p r o b a b i l i t y o f an e l e c t r o n b e i n g s c a t t e r e d , i s 10  times  t h e p r o b a b i l i t y o f an a l p h a p a r t i c l e of the same v e l o c i t y . The t h i c k n e s s o f c o u n t e r windows used i s such t h a t a ' s i n g l e s c a t t e r i n g ' t h e o r y can be a p p l i e d , a t l e a s t f o r e n e r g i e s g r e a t e r t h a n 50 Kev.  The r e f l e c t i o n o f e l e c t r o n s from the windows  i s due almost e n t i r e l y t o e l a s t i c s c a t t e r i n g and i n c r e a s e s as t h e energy d e c r e a s e s .  W h i l e t h i s t h e o r y cannot be e x t r a p o l a t e d t o  lower energies the ' p l u r a l s c a t t e r i n g ' theory y i e l d s  similar  results. The r e f l e c t i o n o f h i g h energy e l e c t r o n s from t h e w a l l s of t h e s p e c t r o m e t e r can t a k e p l a c e t h r o u g h a l a r g e number o f small angle d e f l e c t i o n .  Thus a ' m u l t i p l e s c a t t e r i n g ' t h e o r y can  52  be a p p l i e d .  Fermi  s t a t e s t h a t t h e r o o t mean square a n g l e of  d e f l e c t i o n o f an e l e c t r o n a f t e r p a s s i n g t h r o u g h a g i v e n t h i c k n e s s o f m a t t e r o f atomic number Z i s a p p r o x i m a t e l y e q u a l t o Z d i v i d e d by t h e k i n e t i c energy o f t h e e l e c t r o n . Thus i n any c i r c u m s t a n c e t h e s c a t t e r i n g i n c r e a s e s as t h e energy o f t h e e l e c t r o n s d e c r e a s e s and as t h e atomic 52.  E. F e r m i , N u c l e a r P h y s i c s , p.57.  number  52  of the s c a t t e r i n g m a t e r i a l i n c r e a s e s . An e l e c t r o n l o s e s energy b y . i n e l a s t i c s c a t t e r i n g , t h a t 53 i s , by i o n i z a t i o n o f the atoms i t e n c o u n t e r s . give the f o l l o w i n g n o n - r e l a t i v i s t i c formula  Mott and M a s s e y "  for the r a t e o f l o s s of  energy.  Where  T x e m v N Z E  I s t h e k i n e t i c energy o f t h e e l e c t r o n , i s the distance, i s t h e e l e c t r o n i c charge, i s t h e e l e c t r o n i c mass, i s t h e v e l o c i t y of t h e e l e c t r o n . i s t h e number of atoms per c c . of a b s o r b e r . i s t h e atomic number o f t h e a b s o r b e r . i s t h e mean i o n i z a t i o n p o t e n t i a l o f t h e a b s o r b e r .  This formula  i s good f o r e l e c t r o n e n e r g i e s  from 1 Kev t o 50 Kev.  I n t e g r a t i o n o f t h i s s h o u l d y i e l d a v a l u e f o r t h e range o f e l e c t r o n s o f a g i v e n energy, b u t because o f t h e t o r t u o u s  paths  f o l l o w e d by e l e c t r o n s i t would be s l i g h t l y g r e a t e r t h a n t h e maximum e x p e r i m e n t a l  range.  The most e x t e n s i v e e x p e r i m e n t a l and  work on t h e a b s o r p t i o n  s c a t t e r i n g o f e l e c t r o n s i s t h a t o f Schpnland-* ". 4  With h i s  a p p a r a t u s he c o u l d measure t h e number o f e l e c t r o n s , r e f l e c t e d , absorbed, o r t r a n s m i t t e d by f o i l s o f a number o f m e t a l s and o f d i f f e r e n t thicknesses.  He found t h e amount r e f l e c t e d to be l j f ,  f o r A l , 2 9 % f o r Cu, 391» f o r Ag and 507* f o r Au. 53-  N.F. Mott and H.S.W. Massey, The Theory o f Atomic C o l l i s i o n s  54.  B.E.J. S c h o n l a n d ; Proc.Roy.Soc. A104. 235, 1923. AIOF, 187, 1925.  53.  F o r a g i v e n energy o f e l e c t r o n s , a v a l u e o f the  thick-  n e s s o f f o i l n e c e s s a r y to s t o p a l l but a few p e r c e n t o f the e l e c t r o n s , c o u l d be o b t a i n e d f r o m h i s c u r v e s .  This value  he  c a l l e d t h e range and found t h a t i t v a r i e d o n l y s l i g h t l y w i t h the atomic number o f the m a t e r i a l o f the f o i l .  At t w i c e t h e energy  c o r r e s p o n d i n g to a g i v e n range a p p r o x i m a t e l y 50% of the e l e c t r o n s were t r a n s m i t t e d .  A c u r v e o f range v e r s u s energy p l o t t e d from  h i s r e s u l t s i s shown i n F i g . In  21.  the r e g i o n below 10 Kev t h e r e a r e v e r y few  exper-  i m e n t a l v a l u e s of the range o f e l e c t r o n s . A paper by T s i e n  San-  T s i a n g - ^ e t a l , g i v e s the r a n g e of photo e l e c t r o n s e j e c t e d by weak X - r a y s i n a low p r e s s u r e c l o u d chamber from 1 Kev t o 40 Key.  They  d e f i n e l e p a r c o u r s " as t h e p a t h l e n g t h — t h e t o t a l d i s t a n c e an M  e l e c t r o n t r a v e l s i n i t s meanderings and " l a p o r t e e " as t h e  range—  the d i s t a n c e i n a s t r a i g h t l i n e between the b e g i n n i n g and end o f the t r a c k .  There appeared t o be a - c o n s t a n t  r a t i o of 0.67  between  the r.m.si. v a l u e s o f the range and t h e p a t h l e n g t h s . The average p a t h l e n g t h s were f o u n d t o be v e r y c l o s e to t h e v a l u e s o b t a i n e d by i n t e g r a t i o n o f the f o r m u l a f o r energy l o s s mentioned above.  The c u r v e o b t a i n e d by i n t e g r a t i o n o f t h i s  formula i s - p l o t t e d i n Fig.21.  I t w i l l be n o t i c e d t h a t between  10 and 100 Kev t h e range as g i v e n by Schonland  f a l l s between t h i s  c u r v e and a n o t h e r o b t a i n e d by m u l t i p l y i n g the o r d i n a t e s by  O.67.  Hence i t seems r e a s o n a b l e to t a k e t h e w o r s t of the v a l u e s as the range o f e l e c t r o n s o f a g i v e n energy. 55. et Had.,  T s i e n San-Tsiang, 8., ( S e r . 8 ) , 269,  On t h i s b a s i s t h e range  C. M a r t y and B. D r e y f u s : Jour.de 1947.  Phys.  A  200  400  800  1000  2000  4000  8000  10000  20000  B  2  4  8  10  20  40  80  100  200  MICROGRAMS/CM  2  •FIGURE 21. RANGE OF ELECTRONS I N ALUMINUM AND I N AIR Dashed l i n e  Schonland v a l u e s  Solid lines  San-Tsiang v a l u e s  5<  o f a 1 Kev e l e c t r o n i s about 5 micrograms/cm  and a window o f  2  t h i s t h i c k n e s s s h o u l d t r a n s m i t 50% o f e l e c t r o n s o f 2 Kev energy, w i t h some a b s o r p t i o n t o 5 Kev. The l o s s o f energy by e l e c t r o n s i n an a b s o r b e r i s a s t a t i s t i c a l process. amount, o t h e r s l e s s . 56 ' Millington  Some w i l l l o s e more energy t h a n t h e average F i g . 2 2 , t a k e n from t h e work o f White and v  shows the s p r e a d i n energy o f an o r i g i n a l l y mono-  chromatic beam o f e l e c t r o n s a f t e r p a s s i n g t h r o u g h v a r i o u s t h i c k nesses o f absorbing m a t e r i a l . g r e a t importance  T h i s s p r e a d i n energy i s o f no  i n the d e t e r m i n a t i o n o f the t h i c k n e s s o f counter  window r e q u i r e d but must be t a k e n i n t o account f a c t u r e of the s o u r c e and s o u r c e  i n t h e manu-  backing.  Both t h e o r e t i c a l and e x p e r i m e n t a l s t u d i e s o f a b s o r p t i o n and s c a t t e r i n g i n d i c a t e t h a t t h e r e i s no easy way over t h e difficulty.  A l l p o s s i b l e s c a t t e r i n g s u r f a c e s must be o f as l o w  an atomic number as i s p o s s i b l e and c a r e must be t a k e n i n t h e d e s i g n o f t h e b a f f l e s and s u p p o r t s t o ensure t h a t an e l e c t r o n must be s c a t t e r e d a t l e a s t t w i c e b e f o r e e n t e r i n g the c o u n t e r . The source b a c k i n g and the c o u n t e r window must be o f l o w atomic number and as t h i n as p o s s i b l e .  i 56.  P. White and G. M i l l i n g t o n : Proc.Roy.Soc., A120.701.1928.  205  200  195  190  185  180  175  ENERGY (Kev) FIGURE 2 2 . LOSS OV ENERGY OF MONOENERGETIC ELECTRONS I N AN ABSORBER A  Energy o f i n c i d e n t e l e c t r o n s  B  L i n e p r o f i l e a f t e r e l e c t r o n s pass through 2.25 m i l l i g r a m s / e r a o f mica absorber 2  C  L i n e p r o f i l e a f t e r 2.65  milligrams/cm p  D  Line p r o f i l e a f t e r 3.95  milligrams/cm  E  L i n e p r o f i l e a f t e r 5.72  milligrams/cm  2  2  APPENDIX I I COUNTER WINDOWS  A.  P r o d u c t i o n o f Counter Windows s  The windows a r e produced by t h e method f i r s t  published  57 by Backus  .  A few drops of a s o l u t i o n o f zapon l a c q u e r i n amy!  a c e t a t e a r e dropped on t h e c l e a n s u r f a c e o f d i s t i l l e d w a t e r .  The  s o l u t i o n spreads out o v e r the s u r f a c e o f t h e water and the amyl a c e t a t e e v a p o r a t e s l e a v i n g a t h i n f i l m of zapon on the s u r f a c e . T h i s i s p i c k e d up by means of a r e c t a n g u l a r w i r e frame so t h a t the f i l m f a l l s on b o t h s i d e s of i t making a double l a y e r . appears to be a c e r t a i n amount of a r t to p i c k i n g up v e r y  There thin  f i l m s — a s l i g h t s i d e w i s e m o t i o n w h i l e l i f t i n g seems to h e l p . A t t e m p t s were made to remove the human element from t h i s p r o c e s s by l i f t i n g the f i l m s v e r y s l o w l y w i t h m e c h a n i c a l d e v i c e o r by h o l d i n g the w i r e frame underneath t h e f i l m and a l l o w i n g the water to  r u n out v e r y s l o w l y .  These a t t e m p t s were not s u c c e s s f u l s i n c e  f i l m s about 1/4 as t h i c k c o u l d be l i f t e d  by hand.  The s o l u t i o n used i s one p a r t o f zapon t o two p a r t s o f amyl a c e t a t e .  When 20 m i c r o l i t e r s of t h i s s o l u t i o n i s dropped  on  the water from a h e i g h t o f about 1 cm. i t spreads o v e r a c i r c l e about 30 cms. i n d i a m e t e r .  The f i l m can be c u t i n s e c t i o n s by  moving a t h i n w i r e r a p i d l y t h r o u g h i t w i t h an up and down m o t i o n . The s e c t i o n s a r e t h e n p i c k e d up on t h e frames and hung on a r a c k ! to  dry. I t was n o t e d t h a t some o f the f i l m s produced had s m a l l 51.  See r e f e r e n c e No.10.  56.  s t r e a k s i n them; these were e v i d e n t l y due t o breaks o r c r e a s e s i n one l a y e r of the f i l m and appear t o be due to s t r a i n s s e t up by t h e f i l m c o l l a p s i n g around the end of t h e frame.  The number of  t h e s e s t r e a k s c o u l d be reduced by e x t e n d i n g t h e t o p of the frame i n b o t h d i r e c t i o n s i n o r d e r to p r o v i d e a s u p p o r t .  The q u a l i t y o f  the f i l m s produced i s a l s o i n c r e a s e d by not u s i n g s o l u t i o n s more t h a n a week o l d and by u s i n g f r e s h d i s t i l l e d water.  The zapon  t a k e s a t l e a s t h a l f an hour to d i s s o l v e i n t h e amyl a c e t a t e and the p r o c e s s s h o u l d be a s s i s t e d by a c e r t a i n amount o f a g i t a t i o n . The w e i g h t o f the windows was o b t a i n e d by w e i g h i n g a microscope s l i d e t h e n p l a c i n g s e v e r a l t h i c k n e s s e s of f i l m on i t and w e i g h i n g a g a i n .  From t h e a r e a of t h e s l i d e , the number o f  f i l m s , and t h e d i f f e r e n c e i n w e i g h t , t h e number o f gms/cm o f a 2  s i n g l e f i l m c o u l d be c a l c u l a t e d .  T h i s was  checked by d e p o s i t i n g  20 d r o p s , each o f the u s u a l s i z e , on a p r e v i o u s l y weighed g l a s s plate.  A f t e r t h e amyl a c e t a t e had e v a p o r a t e d a n o t h e r weighing  determined t h e amount o f s o l i d m a t e r i a l i n t h e d r o p s .  From the  a r e a of t h e c i r c l e w h i c h one drop formed on t h e s u r f a c e o f t h e w a t e r , t h e average t h i c k n e s s o f the f i l m c o u l d be d e t e r m i n e d . The maximum d i f f e r e n c e i n w e i g h t s determined by t h e s e two methods was 50%.  The t h i n n e s t f i l m s t h a t c o u l d be produced were p  about 3 micrograms/cm  but i t was found e a s i e r t o work w i t h t h o s e  o f 5 t o 8 micrograms/cm . 2  B.  A t t a c h i n g of t h e Windows to t h e Counters About a dozen f i l m s o f a p p r o x i m a t e l y t h e same t h i c k -  ness a r e made and are hung on t h e r a c k t o dry f o r an hour o r so.  f  57. A s o l u t i o n o f one p a r t v i n y l i t e r e s i n t o one p a r t o f acetone has been p r e v i o u s l y made and t o one p a r t o f t h i s s o l u t i o n i s now added two p a r t s o f amyl a c e t a t e .  The o l d windows a r e s t r i p p e d  o f f t h e c o u n t e r s w i t h s c o t c h tape and t h e s u r f a c e s c l e a n e d amyl a c e t a t e i f n e c e s s a r y .  with  About 10 m i c r o l i t e r s o f t h e v i n y l i t e  s o l u t i o n i s dropped on a s u r f a c e o f w a t e r and p i c k e d up w i t h a w i r e frame i n a s i m i l a r manner t o t h e zapon windows.  The f i l m  formed i s v e r y e l a s t i c and the frame has to be manoeuvered so t h a t t h e l o o s e ends wrap around t h e h a n d l e o f t h e frame.  Immed-  i a t e l y t h i s v i n y l i t e f i l m i s p i c k e d up i t i s t a k e n to t h e spectrometer  and p l a c e d on the f a c e o f t h e c o u n t e r .  The entrance  s l i t t o t h e c o u n t e r i s c l e a n e d out w i t h a sharp c o r n e r o f a p i e c e o f paper.  As soon as p o s s i b l e a zapon f i l m w i t h no c r e a s e s i s  s e l e c t e d f r o m t h e r a c k and p l a c e d o v e r t h e v i n y l i t e . the windows a r e on, t h e p r e s s u r e i n s i d e t h e c o u n t e r s  When a l l ' i s reduced  by about 1 cm. f o r a minute o r two t o h e l p cement t h e windows i n place.  They a r e l e f t to d r y f o r h a l f an hour and t h e n checked  by b l o w i n g  i n to t h e c o u n t e r s w h i l e a s m a l l gas flame about 1/4  o f an i n c h l o n g i s passed i n f r o n t of t h e windows.. Most p i n h o l e s i n t h e f i l m c a n be r e a d i l y d e t e c t e d by t h e d e f l e c t i o n o f t h e gas flame.  58. APPENDIX I I I PREPARATION OF SOURCES  The source h o l d e r i s made f r o m a p i e c e o f 3/16 i n c h l u c i t e 2 inches s q u a r e .  A r e c t a n g u l a r s l o t 2 cms. l o n g by . 0 5 cms.  wide i s m i l l e d t h r o u g h the l u c i t e w i t h t h e back c u t away a t an a n g l e o f 4 5 ° , l e a v i n g a narrow edge around t h e s l o t .  A hole i s  d r i l l e d i n t h e l u c i t e f o r mounting on t h e base p l a t e o f the spectrometer  and a l i n e s c r i b e d a b r o s s t h e m i d d l e o f t h e s l o t t o  i n d i c a t e the p o s i t i o n o f the source. 58 The source b a c k i n g s  a r e made o f L C 6 0 0 r e s i n  s i m i l a r manner t o t h e zapon windows.  i na  A t f i r s t t h e r e s i n was  d i s s o l v e d i n L C 6 0 0 t h i n n e r b u t i t was found o u t t h a t t h i n n e r and more u n i f o r m f i l m s c o u l d be made i f i t was d i s s o l v e d i n amyl a c e t a t e . The f i l m i s p i c k e d up on a frame made o f 1/16 i n c h l u c i t e and l a i d on t h e source h o l d e r w h i l e s t i l l wet. 58  A s o l u t i o n o f one p a r t o f z i n c i n s u l i n ^  t o eight  p a r t s o f d i s t i l l e d w a t e r i s made and about 1/4 o f a micro  liter  d e p o s i t e d w i t h a p i p e t t e a t each end o f t h e f i l m i n l i n e w i t h t h e mark on t h e h o l d e r .  The p i p e t t e i s made from a . 2 5 mm  capillary  t u b i n g w i t h t h e end p u l l e d down to about 1 mm o u t s i d e d i a m e t e r and t h e h o l e t o about 0 . 1 mms.  The s o l u t i o n i s brought up i n t o  the_ p i p e t t e and t h e end w i p e d c l e a n w i t h a paper t o w e l .  Careful  b l o w i n g i n t o t h e p i p e t t e makes t h e l i q u i d bulge o u t o f t h e end of t h e c a p i l l a r y w i t h o u t f o r m i n g a drop.  T h i s i s touched t o t h e  f i l m and l e a v e s a spot somewhat l e s s t h a n 1 mm. i n d i a m e t e r . 58.  L.M. L a n g e r , R.S.I., 2 0 , 2 1 6 , 1 9 4 9 .  The source h o l d e r i s now p l a c e d on a f l a t s u r f a c e w i t h one edge a l o n g a r u l e r .  A r e f i l l from, a b a l l p o i n t pen ( i n k  removed) i s lowered v e r y s l o w l y by means o f a j i g u n t i l t h e p o i n t j u s t touched one of t h e drops o f i n s u l i n s o l u t i o n .  The  h o l d e r i s moved back and f o r t h a l o n g t h e r u l e r u n t i l a l i n e o f i n s u l i n i s formed.  I f a l i n e does n o t form t h e pen i s l o w e r e d  a s m a l l amount and t h e p r o c e s s r e p e a t e d u n t i l a l i n e forms o r t h e f i l m breaks.  I f the i n s u l i n s o l u t i o n i s s u f f i c i e n t l y concentrated  a l i n e c a n be drawn e v e r y time w i t h o u t b r e a k i n g t h e f i l m . When t h e source b a c k i n g i s completed  the r a d i o a c t i v e  m a t e r i a l i s dropped on i t i n t h e f o r m o f a water o r weak a c i d s o l u t i o n ( c o n c e n t r a t e d h y d r o c h l o r i c a c i d does n o t appear t o harm t h e LC600 f i l m s but c o n c e n t r a t e d n i t r i c a c i d w i l l burn h o l e s i n them i n about 10 minutes t i m e ) .  The r a d i o - a c t i v e s o l u t i o n i s  d e p o s i t e d w i t h a s i m i l a r p i p e t t e to t h e one used f o r i n s u l i n . T h i s p i p e t t e i s connected by r u b b e r t u b i n g t o a b a l l o o n i n a b o t t l e i n order to i s o l a t e the a c t i v e s o l u t i o n .  Another  piece  o f r u b b e r t u b i n g connects t h e b o t t l e t o a mouthpiece which i s f a s t e n e d t o a w i r e frame and hung on a hook so t h a t i t i s never l a i d on t h e bench o r touched w i t h t h e hands.  The a c t i v e s o l u t i o n  i s d e p o s i t e d on t h e source b a c k i n g i n t h e same f a s h i o n as t h e insulin.  When v e r y s m a l l drops o f about 1/4 m i c r o l i t e r a r e p l a c e d  on t h e b a c k i n g the s o l u t i o n c o v e r s t h e a r e a c o a t e d w i t h i n s u l i n but does n o t spread onto t h e remainder  of the f i l m .  made were about 1.5 cms l o n g by 0 . 1 cms wide. s l o w l y d r i e d under an i n f r a r e d lamp.  The s o u r c e s  The s o u r c e i s  The a p p l i c a t i o n o f t o o  much heat causes t h e b a c k i n g t o w r i n k l e and t h e h o l d e r t o warp.  60.  Two methods o f g r o u n d i n g t h e s o u r c e were used.  The  f i r s t was t o p u t drops of aquadag on t h e h o l d e r and l e a d i t a l o n g w i t h a f i n e p o i n t e d b r u s h u n t i l i t touched l i n e on t h e b a c k i n g .  t h e end o f t h e i n s u l i n  The aquadag t h e n r a n a l o n g t h e l i n e o f  i n s u l i n u n t i l i t touched  the source.  I t i s not c e r t a i n that this  method i s r e l i a b l e , some s o u r c e s checked gave a r e s i s t a n c e o f about 1000 megohms between ends w h i l e o t h e r s gave no d e t e c t a b l e conduction. The second method o f g r o u n d i n g t h e source i s t o evaporate a t h i n l a y e r o f aluminum onto i t . Aluminum l a y e r s were made w h i c h were about 9 0 % t r a n s p a r e n t and had a r e s i s t a n c e o f 10,000 ohms over a d i s t a n c e o f one i n c h p r o v i d e d a l a r g e a r e a o f c o n t a c t was used. films  A t t e m p t s were made to w e i g h t h e s e aluminum  but a l l t h a t c o u l d be d e t e r m i n e d  than 5 micrograms/cm . 59  was t h a t they were l e s s  T h i s t h i c k n e s s checks w i t h t h e v a l u e s  given i n Strong. The aluminum i s e v a p o r a t e d f r o m a f i l a m e n t made o f t h r e e .015 i n c h t u n g s t e n w i r e s .  Two o f t h e w i r e s a r e t w i s t e d t o g e t h e r  w i t h about 1 t u r n p e r c e n t i m e t e r and t h e t h i r d t w i s t e d around t h e o t h e r two w i t h about f i v e t u r n s p e r c e n t i m e t e r .  About 10 m i l l i g r a m s  o f al.uminum i s hung on t h e f i l a m e n t i n t h e f o r m o f s t r i p s and p r e heated i n a vacuum to i n s u r e c o n t a c t . this preheating i n illuminating  An attempt  was made t o do  gas b u t t h i s proved u n s u c c e s s f u l .  Two s m a l l areas about 1/2 i n c h a p a r t on a l u c i t e p l a t e were p a i n t e d w i t h aquadag and these a r e a s connected 59*  J . Strong. Procedures  t o an ohmmeter  i n Experimental Physics. p . l 8 6 .  o u t s i d e t h e vacuum system.  The l u c i t e p l a t e i s p l a c e d near t h e  s o u r c e h o l d e r and as e v a p o r a t i o n proceeds t h e r e s i s t a n c e o f the aluminum l a y e r can be checked.. By use o f t h i s method,evaporated l a y e r s have been made to any d e s i r e d t h i c k n e s s w i t h q u i t e r e produceable r e s u l t s . A g r e a t d e a l of t r o u b l e was encountered w h i l e aluminum onto v e r y t h i n f i l m s .  This was m i n i m i z e d  evaporating  by p r o t e c t i n g  the f i l m w i t h a b a f f l e u n t i l t h e f i l a m e n t h e a t e d up and e v a p o r a t i o n started.  The b a f f l e was t h e n moved, by means o f a magnet h e l d -  o u t s i d e the vacuum system.  I t was a l s o v e r y n e c e s s a r y  t o l e t the  a i r i n v e r y s l o w l y and to handle t h e h o l d e r w i t h t h e utmost c a r e .  62.  ' APPENDIX I V THE COUNTER FILLING SYSTEM  The c o u n t e r s a t f i r s t were f i l l e d w i t h a l c o h o l vapor and argon i n t h e u s u a l m i x t u r e .  However, t h e c h a r a c t e r i s t i c s of  the c o u n t e r s changed r a p i d l y and t h i s was found t o be t h e r e s u l t of t h e p r e s s u r e c h a n g i n g due to gas s l o w l y d i f f u s i n g t h r o u g h t h e zapon windows.  A n attempt was made t o keep t h e p r e s s u r e r e a s o n a b l y  c o n s t a n t by means o f b a l l a s t f L a s k b u t t h i s was u n s u c c e s s f u l besides being  uneconomical.  An o b v i o u s method o f k e e p i n g t h e p r e s s u r e i n t h e c o u n t e r s c o n s t a n t i s to use t h e s a t u r a t e d vapor o f a l i q u i d h e l d at  a c o n s t a n t temperature  temperature  for a f i l l i n g .  U s i n g t h i s method t h e  o f the l i q u i d has to be l o w e r t h a n room t e m p e r a t u r e  s i n c e o t h e r w i s e the l i q u i d would be d i s t i l l e d to o t h e r p a r t s o f the apparatus.  The c o n s t a n t temperature  t h a t c a n be a t t a i n e d most  c o n v e n i e n t l y i s t h a t o f m e l t i n g i c e . A s e a r c h was made f o r l i q u i d s whose vapor p r e s s u r e a t 0°C was 1 t o 5 cms o f mercury. The f i r s t vapor t r i e d as a c o u n t e r f i l l i n g gas was t h a t of  pure e t h y l a l c o h o l a t 1.2 cms p r e s s u r e .  T h i s d i d n o t . g i v e any  p l a t e a u and t h e c o u n t i n g r a t e s were v e r y u n r e l i a b l e .  A number o f  o t h e r v a p o r s such a s m e t h y l a l c o h o l , benzene, and acetone were t r i e d without success.  I n v i e w of Farmer and Brown's^  0  experiments  w i t h methane i t was d e c i d e d t h a t hydro c a r b o n compounds o f f e r e d t h e best chance o f s u c c e s s . of  1.15  Heptane (C7H16) has a vapor  cms a t 0°C and a c o u n t e r f i l l e d w i t h i t s vapor gave a s h o r t  but u s e f u l p l a t e a u shown i n F i g . 2 3 . 60.  pressure  I t s e f f i c i e n c y f o r gammas and  E.C. Farmer and S.C. Brown: Phys.Rev., 74,902.1948.  600  1—400  >h-200  1200  12^0  1300  1550  VOLTAGE  FIGURE 2 3 . PLATEAU EXHIBITED BY ONE COUNTER FILLED WITH 1.15 CMS OF HEPTANE VAPOR  63. for  h i g h energy b e t a s was t h e same a s w i t h an a l c o h o l and a r g o n  filling. The c o u n t e r e x h i b i t e d a r a t h e r l o n g p r o p o r t i o n a l region.  I t s t a r t e d c o u n t i n g w i t h about 8007 on t h e anode g i v i n g  v e r y s m a l l p u l s e s , l e s s t h a n .01V.  As the v o l t a g e on t h e c o u n t e r s  was i n c r e a s e d t h e maximum p u l s e s i n c r e a s e d i n s i z e but were accompanied by l a r g e numbers o f s m a l l e r p u l s e s .  A t a counter  v o l t a g e o f about 1250 v o l t s the p u l s e s were o f a u n i f o r m s i z e , about t h r e e o r f o u r v o l t s peak a m p l i t u d e w i t h a r i s e t i m e l e s s t h a n one m i c r o s e c o n d and a l e n g t h o f about 50 m i c r o s e c o n d s .  The  G e i g e r r e g i o n s t a r t e d here and extends t o almost 1350 v o l t s .  The  b e s t p l a t e a u s o b t a i n e d were w i t h . 0 0 5 i n c h t u n g s t e n w i r e as anode. The c o u n t e r s i n t h e s p e c t r o m e t e r were t h e n f i l l e d  from  a f l a s k of heptane p u r i f i e d as f o l l o w s : f l a s k A i n F i g . 2 4 was almost f i l l e d w i t h heptane and t h e n c o n n e c t e d t o t h e vacuum system. About 1/10 o f t h e l i q u i d i n A was c a r e f u l l y pumped away.  I t was  t h e n c o o l e d to d r y i c e t e m p e r a t u r e s by means o f an e x t e r n a l b a t h i and e v a c u a t i o n c o n t i n u e d f o r about h a l f an hour.  A t t h i s p o i n t (the  s t o p c o c k was c l o s e d , i s o l a t i n g f l a s k s A and B from t h e vacuum system and t h e c o l d b a t h moved to f l a s k B.  I  The heptane vapor  e v o l v i n g from t h e l i q u i d i n A passed t h r o u g h a d r y i n g agent and condensed i n f l a s k B.  When about 1/10 o f the heptane remained i n  A t h e p r o c e s s was stopped. F l a s k B was t h e n surrounded by a b a t h o f m e l t i n g i c e and connected t o t h e c o u n t e r s .  The c o u n t e r s were checked i n -  d i v i d u a l l y and as one o f them was u n r e l i a b l e , t h e other:'three were used i n p a r a l l e l ; a p l a t e a u i s shown i n F i g u r e 2 5 .  To c o u n t e r s and vacuum system  Flask B  FIGURE 24. 'HEPTANE PURIFICATION SYSTEM (The heptane remains i n F l a s k B, and i n o p e r a t i o n i s surrounded by a b a t h o f melting ice.)  Flask A  1150  1200  12^0  1500  VOLTAGE  FIGURE 2 5 . PLATEAU EXHIBITED BY THREE COUNTERS I N PARALLEL  64.  The c o u n t e r s worked v e r y w e l l a t f i r s t but t h e p l a t e a u grew worse a f t e r a few months o f use. gave o c c a s i o n a l b u r s t s o f 50 t o 100 b e f o r e the c o u n t e r s r e c o v e r e d .  Intermittent discharges  counts i n a second o r  two  This appeared t o happen most o f t e n  i n the l a s t JO seconds o f a t e n minute c o u n t . An attempt was  made to improve the performance o f the  c o u n t e r s by the use o f e x t e r n a l "quenching c i r c u i t s .  A number of  t h e s e c i r c u i t s were t r i e d , some w i t h quenching p u l s e s o f 200 a m p l i t u d e and 400 microseconds d u r a t i o n , w i t h o u t the l e a s t The use o f e x t e r n a l quenching was  abandoned and i t was  r e p l a c i n g the anode o f the c o u n t e r s and  7  success.  found t h a t  t h o r o u g h l y c l e a n i n g the  cathodes w i t h benzene and a b s o l u t e a l c o h o l r e s t o r e d them to t h e i r original condition.  APPENDIX 7 AUXILIARY ELECTRONIC APPARATUS  A.  C u r r e n t R e g u l a t i n g System, I n o r d e r t o observe a b e t a o r gamma spectrum w i t h  the s p e c t r o m e t e r i t i s e s s e n t i a l t h a t t h e magnetic f i e l d  should  not change o f i t s e l f d u r i n g the course o f a s i n g l e r e a d i n g , and to r e a l i z e the advantages o f b u i l d i n g t h e i n s t r u m e n t w i t h o u t i r o n , means must be p r o v i d e d to s e t the c u r r e n t , and t h e r e f o r e the magnetic f i e l d , a t any d e s i r e d v a l u e .  Since the r e s o l u t i o n  of t h e i n s t r u m e n t i s of the .order o f 1%, t h e magnetic f i e l d s h o u l d be r e g u l a t e d to a t l e a s t one p a r t i n a thousand  and t h e  c a l i b r a t i o n s h o u l d be b e t t e r t h a n t h i s . The c o n t r o l system i s . q u i t e s t r a i g h t f o r w a r d , the c u r r e n t through t h e magnet a l s o passes t h r o u g h a ' s t a n d a r d i  resistor  1  o f about 0.1 ohms, made o f 10 f e e t o f 1 i n . manganin  strip.  T h i s r e s i s t o r can c a r r y the l a r g e s t c u r r e n t s used  w i t h a temperature  i n c r e a s e o f l e s s t h a n 1°C, c o n s e q u e n t l y i t s  r e s i s t a n c e w i l l s t a y c o n s t a n t to' almost 1 i n 10-^.  The v o l t a g e  developed a c r o s s t h e s t a n d a r d r e s i s t a n c e i s compared t o a v o l t age determined  by t h e s e t t i n g o f a S t u d e n t ' s P o t e n t i o m e t e r and t h e  d i f f e r e n c e a m p l i f i e d 100 db. by a two c h a n n e l a m p l i f i e r .  One  channel a m p l i f i e s t h e f r e q u e n c y r a n g e ofO-10 c y c l e s p e r second, t h e o t h e r 5-1000 c y c l e s p e r second.  The two s i g n a l s a r e r e -  u n i t e d a t t h e g r i d of a 6L6 w h i c h i n t u r n d r i v e s t h e g r i d s o f a bank o f e i g h t 6AS7's i n s e r i e s w i t h the magnet and t h e s t a n d a r d resistor.  A t low f i e l d s t h e 6AS7's c a r r y t h e f u l l magnet c u r r e n t  but f o r h i g h e r s e t t i n g s they must be shunted by e x t e r n a l resistors. the  These r e s i s t o r s were c a l c u l a t e d on t h e b a s i s that'  power d i s s i p a t i o n i n the r e g u l a t o r t u b e s s h o u l d n o t exceed  t h e i r r a t e d c a p a c i t y o f 168 w a t t s .  A s e r i e s r e s i s t o r was a l s o  i n c l u d e d i n the c i r c u i t so t h a t low c u r r e n t s c o u l d be drawn s a f e l y f r o m t h e 2J?0 watt D.C. mains.  I f a current o f l e s s than  4 amperes i s conducted t h r o u g h the t u b e s from a s u p p l y o f more t h a n 150 v o l t s , s e r i o u s damage w i l l c e r t a i n l y  result.  The c a l i b r a t i o n o f the p o t e n t i o m e t e r i s checked p e r i o d i c a l l y by comparison w i t h a s t a n d a r d c e l l .  The magnet c u r r e n t  i s b r o k e n by t h r o w i n g t h e main s w i t c h , t h e galvanometer s e n s i t i v i t y s w i t c h t u r n e d p a s t 2 megohms to open t h e c i r c u i t and the  ' v o l t a g e check' s w i t c h d e p r e s s e d .  The p o t e n t i o m e t e r i s  a d j u s t e d to t h e v o l t a g e o f t h e s t a n d a r d c e l l and t h e s e n s i t i v i t y o f t h e galvanometer i n c r e a s e d . to  The galvanometer i s brought back  z e r o by m a n i p u l a t i n g t h e ' v o l t a g e a d j u s t '  controls.  A b l o c k diagram o f the r e g u l a t i n g system i s shown i n F i g . 2 6 and a c i r c u i t diagram i n F i g . 2 7 . The p o t e n t i o m e t e r o u t p u t v o l t a g e can be made t o 4 agree w i t h t h e s e t t i n g t o j? p a r t s i n 10 and t h e v o l t a g e a c r o s s the s t a n d a r d r e s i s t o r i s h e l d e q u a l to t h i s w i t h i n one p a r t 4  i n 10 . Any d e v i a t i o n s o f l o w f r e q u e n c y c a n be observed by the  a c t i o n o f t h e a m p l i f i e r ' m e t e r s o r by t h e galvanometer.  D u r i n g .the o r i g i n a l adjustment o f t h e system a measurement was made o f t h e amount o f h i g h f r e q u e n c y ( g r e a t e r than J>0 c y c l e s p e r second) A.C. p a s s i n g t h r o u g h t h e c o i l .  I t was •  found t o be about 1 m.a. o v e r t h e range o f D.C. c u r r e n t s and  AC Amplifier DC Amplifier  Calibration Galvanometer Calibration Battery  6L6 Driver  Student Potentiometer  Standard  'FIGURE 2 6 . BLOCK DIAGRAM OF CURRENT REGULATING SYSTEM  Cell  FIGURE 2 7 . CIRCUIT DIAGRAM OF CURRENT REGULATING SYSTEM  67.  COMPONENTS Off FIGURE 27 Tubes VI V2 V3 V4  8-6AS7's i n parallel 6SJ7 6SJ7 6V6  V5 V6 V7 V8 V9  VR105 VR130  V10 VI1 VI2 VI3  6H6 1N34 6SJ7 6SJ7 SY3G  3T3G 6L6  Meters 100 microamperes f u l l s c a l e . 1 milliampere, center reading. 150 microamperes f u l l s c a l e .  Ml Mg Mj5  Trans f o r m e r s and Chokes Ti Hammond 276 To " 270 C h j and C h Hammond 10-100x  T3 T 4  Hammond 337 51 11  2  R e s i s t o r s ( A l l 1/2 w a t t u n l e s s o t h e r w i s e s t a t e d ) Rl R2 R3 R4 R5 R$  R7 R8 R9 RIO Rll R12 R13 R14 R15 R16 R17  S t . r . a b o u t O.lohm 1000 ohms 12.8 " 1200 w. 30.1 ? 230 w. 30.3 ? 210 w. 40.4 » 200 w. 50.7 " 200 w. 8.0 " 200 w. 11.5 190 w. 30 K » 20 K » 30 K » 20 K » 1 M 9 3 K « 2 M » 500 K 9 11  R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28 R29 R30 R31 R32 R33 R34  1.5 3 2 500 500 250 5 5 150 50 50 100 100 25 50 5 2  M ohms K n M 11 K 11 K a" ? 2 w. K "10 w. K •?10 w. K IJ K tt K u K 11 K 11 K 11 K 11 K 11 M 11  R35 R36 R37 R38 R39 R40 R41 R42 R43 R44 R45 R46 R47 R48 R49 R50 R51 R52  3 500 1 2 150 2.5 1 30 40 30 40 100 10 18 7.5 2 100 100  K ohms K n M 11 M a  mf mf mf mf mf mf mf mf mf mf mf mf  450 450 500 500 500 450 450 450 450 450 400 400  v. v. v. v. V. V. V. V. V. V. V. V.  K K  11 »» 2 w. u 11 tt 11 9 1 w. K K 'ao w. K 9 5 w. K ? 2 w. M 11 ohm-pot. K ohm p o t . K K K K K  Condensers G l 0.1 C2 . 0 0 5 C3 0.1 G4 0.1 C5 . 0 0 5 C6 .006 C7 0.1 C8 100 C9 16 CIO 1.0 C l l 2.0  mf mf mf mf mf mf mf mf mf mf mf  400 500 500 500 500 500 500 50 450 500 500  v. V. V. V. V. V. V. V. V. V. V.  C12 C13 C14 C15 CI 6 C17 018 C19 C20 021 C22 C23  16 16 1.0 1.0 0.1 30 30 30 30 30 1.0 1.0  a  68.  thus i s o n l y 0.1% i n t h e w o r s t oase.  B.  H.T. R e g u l a t i o n . S i n c e t h e p l a t e a u i n t h e c o u n t i n g r a t e curve o f Hep-  tane f i l l e d c o u n t e r s had c o n s i d e r a b l e s l o p e i t was n e c e s s a r y to p r o v i d e a v e r y s t a b l e h i g h v o l t a g e s u p p l y .  Fig.28 i s a  c i r c u i t d i a g r a m o f the r e g u l a t i n g system f i n a l l y  developed.  The p l a t e v o l t a g e o f the a m p l i f i e r tube (72) i s t a k e n f r o m t h e r e g u l a t e d s i d e o f 71 i n s t e a d o f t h e u n r e g u l a t e d s i d e . T h i s r e s u l t s i n c o n s i d e r a b l y improved performance.  The e r r o r  s i g n a l f e d i n t o t h e g r i d of the a m p l i f i e r tube i s t a k e n f r o m t h e imput v o l t a g e and p a r t l y from the o u t p u t .  partly  By a d j u s t -  ment o f R l 8 and R19 t h e c i r c u i t c a n be made t o under-compensate, over-compensate o r r e g u l a t e p e r f e c t l y .  R17 c o n t r o l s t h e s c r e e n  v o l t a g e o f 72 a n d t h u s t h e g r i d b i a s on 7 1 . The adjustment was made i n i t i a l l y by f e e d i n g 6.3 A.C.  i n s e r i e s w i t h R l and R2.  volts  The c o n t r o l s were s e t f o r a  r i p p l e i n t h e output o f l e s s than 1 m i l l i v o l t .  With the c i r c u i t  i n o p e r a t i n g c o n d i t i o n t h e r e was no o b s e r v a b l e r i p p l e i n t h e output.  The o u t p u t v o l t a g e d r i f t e d about 3 v o l t s p e r hour f o r  4 hours a f t e r t h e s u p p l y was t u r n e d on, a f t e r t h i s any changes were o f t h e o r d e r o f 1 v o l t .  C.  P u l s e A m p l i f i e r and S c a l a r . A c i r c u i t o f t h e p u l s e a m p l i f i e r i s shown i n F i g . 2 9 .  The o u t p u t o f t h i s c i r c u i t was f e d i n t o an Atomic Company s c a l e o f 64 s c a l a r .  Instrument  +  A/ •  Rl  16507  2500 V  FIGURE 28. H. T. REGULATING CIRCUIT L i s t o f Components 71 —  6J5  R l , R2 — 100 K ohm R3-R13 — 5 0 0 K ohm R14-R16 1 M ohm A l l r e s i s t o r s 2 watts 01, C3  C2  1 i f 3000 v o l t s .01 mf 3 0 0 0 v o l t s  Bl B2  90 v o l t b a t t e r y 300 v o l t battery  72 — R17  6SJ7 —  Rl8 — R19 — R20 —  5 0 0 K ohm 100 K p o t . 500 K p o t . 500 K p o t .  -vwv Rio  CC  « < 7  n  C8  >  C?  FIGURE 29. CIRCUIT DIAGRAM OF PULSE AMPLIFIER  Rl R2 R3 R4 R5  1 M ohm 50 ohm  330 K ohm 10 K ohm 50 K ohm  50 K ohm R6 ohm R7 200 5 K ohm R8 60 K ohm R9 RIO 10 K ohm  Rll R12 R13  R14 R15  1 K ohm 1 K ohm  100 K ohm 200 ohm 60 K ohm  A l l r e s i s t r o s 1/2 w a t t 71  6J6  CI .001 mf 25007 02 .002 mf 4007 C3 .0001 mf 4007  72  6AK5  . 1 mf 4007 C4 .01 mf 4007 C5 C6 .0001 mf 4007  73  6AC7  °2 C8  .001 mf 4007 . 1 mf 4007 .001 mf 4007  C9  BIBLIOGRAPHY H.A.  Bethe, E l e m e n t a r y N u c l e a r Theory, John W i l e y & Sons, I n c . New Y o r k , 1947,  A.H.  Compton & S.K. A l l i s o n , X-Rays i n Theory and E x p e r i m e n t . D. Van N o s t r a n d Co., I n c . , New Y o r k , Second ed. 1935.  E. F e r m i , N u c l e a r P h y s i o s , The U n i v e r s i t y o f Chicago P r e s s , R e v i s e d ed. 1950. D.J.X. Montgomery, Cosmic Ray P h y s i c s , P r i n c e t o n U n i v e r s i t y P r e s s , 1949. N.F.  Mott and H.S.W. Massey, The Theory of Atomic O x f o r d a t t h e C l a r e n d o n P r e s s , 1933.  Collisions,  F. R a s e t t i , Elements o f N u c l e a r P h y s i o s , P r e n t i c e - H a l l , I n c . New Y o r k , 1936. F.Z. R i c h t m e y e r & E.H. Kennard, I n t r o d u c t i o n t o Modern P h y s i c s , 3 r d E d i t i o n , 1942. S i r E. R u t h e r f o r d , J . Chadwick, C D . E l l i s , R a d i a t i o n s from R a d i o a c t i v e S u b s t a n c e s , Cambridge a t the U n i v e r s i t y P r e s s , 1930, John S t r o n g , P r o c e d u r e s i n E x p e r i m e n t a l P h y s i c s , P r e n t i c e - H a l l , I n c . , New Y o r k , 1938. V.K.  Z w o r y k i n , e t a l , E l e c t r o n O p t i c s and t h e E l e c t r o n M i c r o scope, John W i l e y & Sons, I n c . , New Y o r k , 1945.  

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