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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 Harry Brown A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n PHYSICS W© accept t h i s t h e s i s as conforming to the standard r e q u i r e d from candidates f o r the degree of DOCTOR OF PHILOSOPHY Members of the Department of PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA September, 1951 ABSTRACT A semi c i r c u l a r focussing spectrometer lias been b u i l t to examine beta s p e c t r a i n the energy range below 100 Kev. The d e t e c t i o n of the beta p a r t i c l e s i s accom-p l i s h e d by means of Geiger counters f i l l e d w i t h the s a t u r -ated vapor o f l i q u i d heptane (C^Hj^) kept i n a bath o f . mel t i n g i c e . The windows of the counters are made from t h i n f i l m s of zapon about 5 to 8 micrograms/cm 2 i n t h i c k -ness. The sources are mounted on s i m i l a r f i l m s approx-imately 10 micrograms/cm and have an average t o t a l t h i c k -ness of the order of 30 micrograms/cm . The combination of t h i n source and t h i n windows enables measurements of s p e c t r a to be made down to an energy o f 2 :Kev. An examination of the beta spectrum of RaD (82JPb 2 1 0 ) w i t h the spectrometer has been c a r r i e d out. I t c o n s i s t s of L, M and N conversion l i n e s o f a 47 Kev gamma ra y , a peak at about 2 Kev assigned to conversion of a 7.7 Kev gamma i n the M s h e l l of the atom, and a primary beta spectrum. A K u r i e p l o t of the primary beta spectrum y i e l d s an end point of 21.7 Kev. I n a d d i t i o n there are two weak conversion l i n e s at 18 and 21 Kev which are t e n t a t i v e l y assigned t o the L conversion of gamma rays of 34 and 37 Kev. T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 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 F T H E F I N A L O R A L E X A M I N A T I O N F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y H A R R Y B R O W N B.A. (Brit. Col.) 1943 M . A . (Brit. Col.) 1948 TUESDAY, O C T O B E R 9th, 1951, A T 2 P.M. IN R O O M 201, PHYSICS BUILDING o£ C O M M I T T E E IN CHARGE: Dean H . F. Angus, Chairman Professor K. C. Mann Professor G. M. Shrum Professor S. A. Jennings Professor J. B. Warren Dean Blythe Eagles Professor H . C. Gunning Professor W. A. Bryce Professor Harry Adaskin T H E S I S T H E O P E R A T I O N OF A L O W E N E R G Y B E T A - R A Y S P E C T R O M E T E R 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 (C7H,„) kept in a bath of melting ice. The windows of the counters are made from thin films of zapon about 5 to 8 micrograms/cm2 in thickness. The sources are mounted on similar films approximately 10 micro-grams/cm-, and have an average total thickness of Lire order of 30 micrograms/cm2. The combination of thin source and thin windows enables measurements of spectra to be made down to an energy of 2 Kev. An examination of the beta spectrum of RaD (soPb210) 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. 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 research described i n t h i s t h e s i s was supported by grants from t h e N a t i o n a l Research C o u n c i l of Canada and by a grant from the B r i t i s h Columbia Re-search C o u n c i l . The continued e f f o r t of the author was made p o s s i b l e by the award of N a t i o n a l Research C o u n c i l studentships 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 of N a t i o n a l Research 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 indebted to Dr. K.C. Mann f o r the suggestion o f the problem and f o r i n v a l u a b l e advice, a s s i s t a n c e and encouragement d u r i n g the course of the research. Further acknowledgement i s made of the advice given by members of the Department of Chemistry w i t h regard to the manufacture of sources and of the help and advice o f Mr. A. Fra s e r and Mr. J". Lees i n the machine work and glass blowing connected w i t h the p r o j e c t . TABLE.OF CONTENTS Page I INTRODUCTION I I I THE SPECTROMETER 11 A. Primary C o n s i d e r a t i o n i n Design B. The Inner Spectrometer C. Production of the Magnetic F i e l d D. T e s t i n g the U n i f o r m i t y of the Magnetic F i e l d S. Mathematical Treatment of a Spectrometer I I I RESULTS 31 IV CONCLUSIONS AND RECOMMENDATIONS 48 APPENDIX I 50 The S c a t t e r i n g and Absorption o f Beta-Rays APPENDIX I I 5$ Counter Windows A. Production of Counter Windows B. A t t a c h i n g of the Windows to the Counters APPENDIX I I I 58 P r e p a r a t i o n o f Sources APPENDIX IV 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. Current Regulating System B. H. T. Reg u l a t i o n C. Pulse A m p l i f i e r and S c a l a r BIBLIOGRAPHY 6? TABLE OF ILLUSTRATIONS FIGURE Facing Page 1 I l l u s t r a t i o n of Semi C i r c u l a r Focussing 2 2 A Normal Beta Spectrum 2 J> Energy Itevel Diagram f o r Negatron 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 6 Energy L e v e l Diagram f o r Negatron Decay to Two D i f f e r e n t States 6 7 K u r i e P l o t f o r Negatron Decay to two D i f f e r e n t States 7 8 The E f f e c t of the Coulomb F i e l d on the Shape of the Beta Spectrum 7 9 I n t e r n a l C o n s t r u c t i o n of the Spectrometer lj? 10 F i e l d of a Plane C i r c u l a r C o i l as a Function of the Distance from the Center 18 11 C o n s t r u c t i o n o f the Magnet 19 12 Observed V a r i a t i o n of Magnetic F i e l d i n Spectrometer Region 20 13> Diagram of E l e c t r o n Paths i n the Spect-rometer 21 14 T h e o r e t i c a l L i n e P r o f i l e s 27 1.5 Comparison of Various Beta Ray Spectrometers 28 16 Beta Spectrum o f Radium D J>5 17 Beta Spectrum of Radium D w i t h JO Kev Conversion Lin e Subtracted • 40 18 K u r i e P l o t of Beta Spectrum of Radium D 40 19 L i n e .Widths from one Counter and from Three Counters ' 42 I I FIGURE Facing 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 Loss of Energy of Monoenergetic 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 With 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 Counters i n P a r a l l e l 63 26 Block Diagram of Current R e g u l a t i n g System 66 27 C i r c u i t Diagram of Current Regulating System 66 28 H. T. Regulating C i r c u i t 6b 29 C i r c u i t Diagram of Pulse A m p l i f i e r 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 subst-ances emitted 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 , attempts were made to analyze the v e l o c i t y d i s t r i b u t i o n using a magnetic f i e l d . The simplest method, th a t of c o l l i m a t i n g a beam of p a r t i c l e s by s l i t s and observing the s m a l l d e f l e c t i o n caused by a transverse f i e l d w i t h photographic methods, proved q u i t e s u c c e s s f u l w i t h alpha p a r t i c l e s . I t was f i r s t used w i t h a source which emitted beta p a r t i c l e s by Baeyer and Hahn. 1 Here the angles o f d e f l e c t i o n were larger, than w i t h alpha par-t i c l e s , but were not greater than 60°. The photographic p l a t e showed a number of l i n e s i n d i c a t i n g that the e l e c t r o n s d i d not leave the source w i t h a unique v e l o c i t y but r a t h e r were emitted 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 of the v e l o c i t y d i s t r i b u t i o n of the e l e c t r o n s was c a l l e d a,beta-ray spectrum. This method of determining the beta-ray spectrum o f a substance 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 only by improving the c o l l i m a t i o n could the l i n e s be made narrower. The c o l l i m a t i o n could only be improved at the ex-pense of i n t e n s i t y , n e c e s s i t a t i n g stronger sources or longer exposures to get usable r e s u l t s . The way out of the d i f f i c u l t y was t o devise some method o f f o c u s s i n g the 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 than the e x i t s l i t of the c o l l i m a t i n g system. This was done by Danysz^ who pointed out that i f two equal c i r c l e s were drawn about two p o i n t s separated by a small f r a c t i o n of 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 at 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 paths i n a u n i -form magnetic f i e l d are c i r c l e s whose r a d i i depend on the momentum of the p a r t i c l e and the s t r e n g t h of the f i e l d , focus-s i n g could be obtained by a l l o w i n g , e l e c t r o n s to t r a v e l through a s e m i c i r c l e before s t r i k i n g the photographic p l a t e . I n F i g . l , e l e c t r o n s s t a r t i n g from the source S at an angle A w i t h each other are s e l e c t e d by the b a f f l e and brought together to s t r i k e near the same po i n t o f the p l a t e . E l e c t r o n s of greater or l e s s momentum are brought to a focus at f u r t h e r or nearer p a r t s of 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 f i n i t e b a f f l e s l i t . The c e n t r a l ray i n F i g . l w i l l not h i t the photographic p l a t e at e x a c t l y the same spot as the two outer r a y s . This s e m i c i r c u l a r f o c u s s i n g spectrograph was used by many workers, notably Rutherford and Robinson^ to determine the momenta o f a number of l i n e s i n the beta-ray s p e c t r a of most of the n a t u r a l l y r a d i o - a c t i v e elements. 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 the q u a n t i t y Hr ( i n gauss-cms) from which the energy can be obtained by use of the r e l a t i v i s t i c formula 2. J . Danysz: Comptes Rendus 153. 339, 1066, 1911. 3. E. Rutherford and H. Robinson: Phil.Mag. (6) 26, 717, 3. ; Hr = 10 4/3 /T(T+1.02) where T i s the energy of the p a r t i c l e s i n Mev and r i s the r a d i u s i n cm. of t h e i r o r b i t i n a uniform f i e l d o f H gauss. A non-r e l a t i v i s t i c approximation good to a few percent below 50 Kev i s Hr - 3.37ys" where S i s the energy of 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 of the method was the sub-s t i t u t i o n o f an e l e c t r i c a l method of d e t e c t i o n f o r the photo-4 5 graphic p l a t e . A Faraday cage, an i o n i z a t i o n chamber, or l a t e r a Geiger counter was placed behind an e x i t s l i t and the magnetic f i e l d was v a r i e d to change the energy r e g i o n being i n v e s t i g a t e d . This spectrometer was an improvement s i n c e with photographic 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 of the p l a t e to the other. 5 With such a spectrometer Chadwick proved t h a t i n a d d i t i o n to the groups of e l e c t r o n s of d i s c r e t e energies there was a continuous d i s t r i b u t i o n so t h a t a normal spectrum appeared as i n F i g . 2 . Rutherford e t . a l . proved that the d i s c r e t e groups were of secondary o r i g i n by wrapping f o i l s of v a r i o u s metals around the c y l i n d r i c a l source i n a beta ray spectrograph. When the f o i l s were thick,.enough to stop a l l e l e c t r o n s from the source 4. E. Gurney? Pro0 . . Roy. S o c , A109, 340, 1925. 5. J . Chadwick: Verh.d.D.Phys.Ges., 16, 383, 1914. 6. E. Rutherford, H. Robinson and Rawlinson: Phil.Mag., 28_, 281, 1914. B a f f l e FIGURE 2. A NORMAL BETA SPECTRUM 4. a l i n e spectrum was s t i l l observed. From these and other experiments a comprehensive theory of beta-ray s p e c t r a was b u i l t up. The e l e c t r o n s emitted during the 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 nuclei:, had a continuous d i s -t r i b u t i o n of energy. The daughter 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 rays or by e j e c t i n g e l e c t r o n s from the K, L, e t c , s h e l l s of the newly formed atom. I n Fig.2 i t i s i n d i c a t e d t h a t 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 l i n e o r l i n e s . I f the binding energy of a K e l e c t r o n of the daughter atom i s added to the energy of the most intense l i n e , an L to the next, and so f o r t h , a constant energy value i s obtained which u s u a l l y corresponds to the energy of a known gamma ray. The gamma ray i s s a i d to be p a r t i a l l y i n t e r n a l l y converted and the peaks i n the beta-ray s p e c t r a are known as conversion l i n e s . The continuous d i s t r i b u t i o n of the 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 the conser-v 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 the energy a v a i l a b l e corresponded to the maximum energy of the beta p a r t i c l e s . A d e t a i l e d theory of beta d i s i n t e g r a t i o n was given by Fermi^ i n which he assumed that a d i s i n t e g r a t i o n was a three body process 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 e l e c t r o n . The p r o p e r t i e s of the neutrino were assumed t o be such that i t s d e t e c t i o n was d i f f i c u l t , i f not impossible. The charge was zero. The mass was presumed to be very s m a l l . Indeed, on 7. S. Fermi: Z e i t s f u r Phys. 8b, 161, 193A-. 3 the b a s i s of experiments 0 on the beta momentum d i s t r i b u t i o n of , an upper l i m i t to the mass of the neutrino has been placed at 0.002 e l e c t r o n mass. In the simplest form of the theory plane wave f u n c t i o n s are assumed f o r the e l e c t r o n and neutrino which are created at the moment of emission. 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 -ated by combining the value of these f u n c t i o n s at the nucleus w i t h a matrix element r e l a t i n g the i n i t i a l and f i n a l s t a t e s of the nucleus. I n a d d i t i o n there i s a new u n i v e r s a l constant c a l l e d a co u p l i n g f a c t o r . The shape of the momentum d i s t r i -b u t i o n of the emitted b e t a - p a r t i c l e s depends to a considerable extent on the type of i n t e r a c t i o n used i n the matrix . element. A l s o the t o t a l p r o b a b i l i t y of decay i s a f u n c t i o n of the s p i n change and p a r i t y change between the 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 included i n the ma t r i x element. The most probable type of 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 of 1 and p a r i t y change i s c a l l e d an allowed t r a n s i t i o n . A simple re-arrangement of the 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 complicated f u n c t i o n (which i n c l u d e s N, the number i n a s m a l l momentum i n t e r v a l ) against the beta energy 2 to give a s t r a i g h t l i n e w i t h an i n t e r c e p t on the energy a x i s corresponding a to the d i s i n t e g r a t i o n energy. This i s c a l l e d a "Kurie p l o t " . In a beta d i s i n t e g r a t i o n the mass of the nucleus 8. S.C. Curran, A.L. Cockcroft and C.Insch: Phil.Mag.. 41. 51.7, 1930. — 9. F.N.D. K u r i e , J.E. Richardson and H.C. Paxton: Phys.Rev., 4?_, 368, 1936. changes by a small f r a c t i o n of the mass o f a neutron or proton but the atomic number i s changed by one u n i t . I f a negatron i s emitted the nucleus increases i t s atomic number by one as i l l u s t r a t e d in.Fig..3 . P o s i t r o n emission as i n Fig.4 reduces the atomic number. F i g . 3 shows the case where the atomic number i s reduced by the a b s o r p t i o n of an e x t e r n a l e l e c t r o n i n t o the nucleus. As the e l e c t r o n absorbed i s u s u a l l y from the K s h e l l of the atom t h i s process i s known as K capture. A f t e r any of these t r a n s i t i o n s the nucleus may be l e f t i n an e x c i t e d s t a t e from which i t r e v e r t s to the ground s t a t e by em i t t i n g a gamma ray or a conversion 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 capture or conversion of a gamma ray, there are a l s o c h a r a c t e r i s t i c X rays of the daughter atom emitted and i n some cases Auger e l e c t r o n s . Some-times a t r a n s i t i o n by beta emission i s p o s s i b l e to two d i f f e r e n t e x c i t e d s t a t e s of the daughter nucleus, as i n F i g . 6 . This i s most r e a d i l y detected by the K u r i e p l o t which i s no longer 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 . ( F i g . 7 ) . The methods o£ beta-ray spectroscopy have been s u c c e s s f u l i n determining the energies of p a r t i c l e s and photons emitted by r a d i o - a c t i v e n u c l e i i and thus have provided a know-ledge of nuc l e a r energy l e v e l s . While these energies have been measured oyer a l a r g e range w i t h a considerable degree o f accuracy there are l i m i t a t i o n s . I n very few instruments has a r e s o l u t i o n of one part i n a thousand been a t t a i n e d and a more usual value i s one i n t h i r t y to one i n one hundred. A standard spectrometer may cover the range from 0.1 to 3 Mev, the lower 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 being an i n s t r u m e n t a l l i m i t , caused by excessive 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 defocussing by uncompensated earth's f i e l d components over the l o n g path l e n g t h as the energy decreases and by a b s o r p t i o n of the low energy beta p a r t i c l e s i n both the source and the counter window. The upper l i m i t i s set by the power demands of the f o c u s s i n g magnet. A few spectrometers have been b u i l t to measure energies greater than 10 Mev and some to extend the lower l i m i t to 10 Kev or l e s s . While t h i s low energy r e g i o n has been neglected because of experimental d i f f i c u l t i e s a number of reasons f o r i t s i n v e s t i g a t i o n e x i s t . I n the simple d e r i v a t i o n of the shape of the continuous spectrum i t i s assumed that the e l e c t r o n has a plane wave f u n c t i o n a t the nucleus. A c o r r e c t i o n must be made to account f o r the p e r t u r b a t i o n of the wave by the coulomb f i e l d . The amount of the c o r r e c t i o n increases at low energies and 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 negatrons. Thus there i s considerable d i f f e r e n c e between the shapes of p o s i t r o n and negatron s p e c t r a . (Fig.8 ) I f t h i s f a c t o r i s incorporated i n t o the theory a value of the r a t i o N +/N~ can be obtained 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 negatron or p o s i t r o n emission. Cu^ 4 i s an isotope f o r which t h i s can be c a l c u l a t e d and considerable work has been done on the. question. B a c k u s 1 0 working i n the r e g i o n 5 to 50 Kev found N +/N" to be ten times greater than expected at the lowest energy. The e n t i r e spectrum was i n v e s t i g a t e d by Cook and L a n g e r 1 1 from 10 to 700 Kev. 10. 3". Backus: Phys.Rev., 68, 59, 1945. 11. C.S. Cook and L.M. Langer: Phys.Rev., 22.* 601* 1948. FIGURE 7. .KURIE PLOT FOR NEGATRON DECAY TO TWO DIFFERENT STATES N(E) Beta - f o r Z = 0 Beta f o r Z 0 FIGURE 8. THE EFFECT OF THE COULOMB FIELD ON THE SHAPE OF THE BETA SPECTRUM 8. Their measurements are in 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 com-binations of the five r e l a t i v i s t i c a l l y invariant interactions which are possible in the matrix element of the transition probability. However Wu and Albert 1^ report deviations from theory much less than the above and conclude that any remaining are entirely instrumental in origin. As the techniques used by these three groups seem to be similar the question warrants further investigation. Cook and Langer"**1 and other experimenters 1^ , 1'^ , 1^ report that i n a number of cases the Kurie plot deviates from 17 18 19 a straight line at low energies. More recent work indicates that these results were entirely due to the thick-ness of the source. However there is always the possibility 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. 13. C.S. Wu and R.D. Ait> e rt : Phys.Rev., J2> 315> 1949. 14. A.W. Tyler: Phys.Rev., £6, 123, 1939. 13. J".L. Lawson: Phys.Rev., ^6,, 131, 1939. 16. A.A. Townsend: Proc.Roy.Soc., A177. 337, 1941. 17. R.D. Albert and G.S. Wu: Phys.Rev., 24, 847, 1948. Phys.Rev., 1107, 1949. 18. L. Feldman and C.S. Wu: Phys.Rev., 2£, 697, 1949. 11 798 WO L a n g e r ' *r*W' M o t z 8 1 1 4 H , C * P ^ 0 6 Phys.Rev., 9 Besides the low energy beta groups there may be low energy conversion l i n e s . Even a 0.1 l e v gamma from a nucleus of h i g h Z may y i e l d a conversion l i n e of a few Kev when con-v e r t e d i n the K s h e l l . L i n e s at l e s s than 50 Kev have been found i n the beta s p e c t r a of almost a l l n a t u r a l l y r a d i o - a c t i v e s u b s t a n c e s 2 0 and i n some a r t i f i c a l l y prepared i s o t o p e s . 2 1 There i s also a p o s s i b i l i t y of detecting.the Auger e l e c t r o n s e j e c t e d from the 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 capture 22 1 has taken p l a c e . I f a nucleus i s i n the ground s t a t e on ca p t u r i n g a K e l e c t r o n the s o f t X rays and the Auger electrons o f f e r the only means of d e t e c t i n g the change. Many suggested decay schemes f o r var i o u s n u c l e i based on the measurements of high-energy gamma-rays and conversion 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 or l e s s of each other. Most current spectrometers could not detect t r a n s i t i o n s between such s t a t e s i f they d i d e x i s t . An instrument which could do so would be a v a l u a b l e t o o l i n checking the proposed s p i n and p a r i t y values assigned to these s t a t e s on the evidence of the h i g h energy t r a n s i t i o n s alone. . Thus the extension of the energy range measured by beta ray spectrometers to as low a value as p o s s i b l e i s im-portant i n cheeking the agreement of experiment w i t h theory and 20. R a d i a t i o n s from Radio-active Substances. Rutherford, Chadwick and E l l i s : pp.560-380. 21. R.D. H i l l : Phys.Rev., 24, 78, 1948. 22. 3T. M i l l e r J r . ; Phys.Rev., 62, 309, 1945. i n i n c r e a s i n g our knowledge of the energy l e v e l s of n u c l e i i . This increased knowledge i s e s s e n t i a l to the development of a theory of nuclear processes. This research describes the design, c o n s t r u c t i o n and use of a spectrometer f o r t h i s purpose. 11. I I THE SPECTROMETER A. Primary Considerations i n Design. The design of a spectrometer to be used p r i m a r i l y i n the 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 consider-a t i o n of a number of fundamentally important p o i n t s . (a) The s c a t t e r i n g of e l e c t r o n s from a l l p a r t s of the instrument increases g r e a t l y at lower energies. I t has been shown 2^ t h a t at low energies the s c a t t e r i n g , v a r i e s i n v e r -s e l y as the f i r s t power, at l e a s t , of the e l e c t r o n energy and d i r e c t l y as the atomic number of the 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 low energy beta p a r t i c l e s pre-sents a great 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 ite the o b j e c t i o n s to a spectrograph. How-ever, the s e n s i t i v i t y of even the best p l a t e s f a l l s o f f very r a p i d l y as the energy of the impinging e l e c t r o n s i s decreased. ^ The s e n s i t i v i t y of the 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 combin-a t i o n also decreases tremendously at low energies, and the oper-a t i o n of the 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 f i e l d . A Geiger counter seems to be the best method of d e t e c t i o n si n c e i t i s w e l l known that e l e c t r o n s of almost zero energy can be detected i n t h i s way p r o v i d i n g they penetrate i n t o the 2 3 . Appendix I . 24. L. Cranberg. and J . Halpern: R.S.I., 2p_, 641, 1949. 12. s e n s i t i v e volume of the counter. The problem i s reduced to one of making the window of the counter s u f f i c i e n t l y t h i n to avoid a b s o r p t i o n at low energies yet stro n g enough t o w i t h -stand the pressure of the counter gas. Windows of nylon, zapon, formvar and c o l l o d i o n as 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 the method described by B a c k u s . 1 0 Windowless counters have 19 been used w i t h success by Langer, Motz and P r i c e w i t h an equivalent window t h i c k n e s s due to d i f f u s i n g . g a s of about one p microgram/cm . The problem of the counter windows has been solved s a t i s f a c t o r i l y f o r our problem. Zapon f i l m s of 3 to 5 micrograms /cm 2 are cemented over a counter entrance s l i t 0.025 cm, wide. The combination of the narrow window,and the low gas pressure used i n the counter (1.1 cm.Hg.) makes the use of such f i l m s e n t i r e l y p r a c t i c a b l e . (c) The method by which the r a d i o - a c t i v e source i s prepared and mounted i s important at energies up to at l e a s t 0.5 Mev but p a r t i c u l a r l y so at low e n e r g i e s . » 2 ^ > 2 6 , 2 7 rph.e t h i c k n e s s of the support and of the l a y e r of r a d i o a c t i v e m a t e r i a l deposited on i t can have a great i n f l u e n c e on the shape of the low energy spectrum even when only a few micro-/ p 19 grams/cm^. This n e c e s s i t a t e s extreme care to ensure t h a t 25. Curran, Angus & Cpckroft: Phil.Mag., 40, 53, 1949. 26. Langer, Moffat, & P r i c e : Phys.Rev., ^6, 1725, 1949. 27. G.2. Owen & G.S. Cook: Phys.Rev., 2i» 1726, 1949. the source i s spread uniformly over the a c t i v e r e g i o n . The extremely t h i n source mounts r e q u i r e d by these c o n s i d e r a t i o n s leads to a new d i f f i c u l t y . Because of the low c o n d u c t i v i t y of the backing and the small c a p a c i t y to ground the source can acquire a p o t e n t i a l of s e v e r a l thousand v o l t s , 28 s e r i o u s l y d i s t o r t i n g the low energy spectrum. To overcome these d i f f i c u l t i e s , the source was pre-pared by d e p o s i t i n g an approximately uniform s t r i p of r a d i o -a c t i v e m a t e r i a l on a zapon or LG600 f i l m of about 10 micro-grams/cm 2. The f i l m was supported ,by a l u c i t e holder which was cut away d i r e c t l y behind the source. The accumulation of charge was prevented e i t h e r by evaporating aluminum onto the holder 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 or by p a i n t i n g t h i n l i n e s of aquadag to connect the ends of the source to the metal of the spectrometer. See APPENDIX I I I f o r f u r t h e r d e t a i l s . (d) The d i f f i c u l t i e s of hand l i n g l a r g e amounts of a c t i v i t y r e q u i r e t h a t maximum use be made of the source. A re d u c t i o n i n the s i z e of the spectrometer and t h e r e f o r e of the source ensures t h a t the amount of 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 the absolute amount of a c t i v i t y i s kept s m a l l . This l a s t i s e s s e n t i a l i n a low energy spectrometer s i n c e the source cannot be covered because of a b s o r p t i o n of e l e c t r o n s i n the covering m a t e r i a l . I n a d d i t i o n the f r a g i l i t y of the backing provides a constant danger of contamination. With ^•-j.. • • 2 8 . 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 of low s p e c i f i c a c t i v i t y the source 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 then, a low energy spectrometer should be as e f f i c i e n t as p o s s i b l e , that i s , the f r a c t i o n detected of a l l e l e c t r o n s l e a v i n g the source i n a given momentum range should be as l a r g e as i s c o n s i s t e n t w i t h the r e s o l u t i o n r e q u i r e d . I t 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 the same v a r i a b l e s as i s . the r e s o l u t i o n . However, since the l i n e w idth a t low energies i s g r e a t l y increased by s c a t t e r i n g and s e l f a b s o r ption, the r e s o l u t i o n need not be too good. (e) An e l e c t r o n w i t h 10 Kev of energy has an Hr value of 340 gauss cms. I f i t s r a d i u s o f curvature i n the spectrometer i s to be, say, 10 cms. 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 earth's f i e l d i s c o n s i d e r a b l y greater than one percent of t h i s and e l e c t r i c motors, r e g u l a t i n g transformers and other 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 o f t h i s order f o r s e v e r a l f e e t . The measurement of a small magnetic f i e l d w i t h an accuracy of a few percent 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 the spectrometer down i n order 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 f i e l d can be obtained without the use of an i r o n core the 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 without the measurement of small f i e l d s . 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 the above c o n d i t i o n s . The r a d i u s o f curvature of detected e l e c t r o n s can be reduced to a small value, the path l e n g t h i s sh o r t and the inner surface can be kept s m a l l , r e -ducing s c a t t e r i n g to a minimum. I n order to have a l a r g e t r a n s -m i s s i o n the spectrometer was designed t o accept e l e c t r o n s from the source i n four 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 counters w i t h zapon windows, the pressure being kept constant 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 the inner spectrometer are shown i n F i g . 9 . The dimensions are i n inches because of the s i z e s of m a t e r i a l s a v a i l a b l e . The source i s i n the form o f a l i n e about 0.1 cm. wide and 1.5 cm. high. I t i s mounted on a backing of 10 p microgram/cm zapon which i s supported by a l u c i t e holder. The holder i s arranged i n the spectrometer so that the middle l i n e of the source passes through the center of the apparatus. The counters are symmetrically spaced about the source on the circumference of a c i r c l e o f 2.4 inches 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 are arranged so that e l e c t r o n s l e a v i n g + the source at angles of 45° - 5 . 7 ° t o the plane of the backing t r a v e l a c i r c u l a r path o f 3.05 - .03 cm. ra d i u s ( i n the c o r r e s -ponding magnetic f i e l d ) to s t r i k e the counter windows. The b a f f l e s were cut on a l a t h e to the r e q u i r e d r a d i u s and grooves cut i n the surface to reduce the r e f l e c t i o n of e l e c t r o n s from the b a f f l e surfaces i n t o the counters. Each counter (see Fig.9) was made by d r i l l i n g a 0.62$ i n c h diameter hole through a block of brass 1.5 inches l o n g . The brass was then trimmed down w i t h a shaper, w i t h To counter f i l l i n g system To vacuum system U 3 FIGURE 9. .INTERNAL CONSTRUCTION OF THE SPECTROMETER a B a f f l e s b Counters c Source holder 16. p a r t i c u l a r care taken w i t h the face c o n t a i n i n g the window. This face was cut as smooth as p o s s i b l e , to leave a thickness of .030 inches i n the center. Through the narrowest p a r t a l o n g i t u d i n a l s l o t about 5/8 inches l o n g and 0.010 inches wide was cut. The i n s i d e of the counter was then p o l i s h e d t h o r -oughly w i t h emery paper and crocus c l o t h . Another hole of about the same s i z e was d r i l l e d through the b r a s s , p a r a l l e l to the f i r s t , f o r the purpose of f i l l i n g the counter, so that about 0.050 inches of metal separ-ated the two. Small holes (No.48 d r i l l ) were d r i l l e d 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 the f i l l i n g gas to enter the counter proper. The a u x i l i a r y hole was then plugged at one end w i t h a brass p l a t e and a t the other w i t h a eopper tube to a l l o w connection to the f i l l i n g system. The e n t i r e counter was then 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 surfaces appeared c l e a n . , I t was then washed, f i r s t i n d i s t i l l e d water, and then i n absolute a l c o h o l and d r i e d . One end was c l o s e d w i t h a Kovar s e a l and the other w i t h a pyrex cap sealed w i t h deKhotinsky wax. A .005 i n c h tungsten w i r e was used f o r the anode. The apparatus i s contained i n a brass c y l i n d e r of 6.5 inches i n s i d e diameter. The end p l a t e s are of 5/16 i n c h brass. S o f t rubber r i n g s are used as vacuum s e a l s . I n the bottom p l a t e a number of holes are d r i l l e d f o r the admission of the counter f i l l i n g gas, the high voltage l e a d and f o r connection to the vacuum system. 17. One inc h above the lower end p l a t e i s mounted a 1/8 inch brass p l a t e ( h e r e a f t e r c a l l e d the 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 the p o s i t i o n of the source, the p o s i t i o n of the b a f f l e s and the l o c a t i o n s of the entrance s l i t s , of the counters were marked on i t . The counters were a l i g n e d w i t h the b a f f l e system <by observing that the counter window, i t s r e f l e c t e d image, and the mark on the 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 introduced was c e r t a i n l y no more than the width of the s l i t (.025 ems.) and was prob-ably l e s s . The counters were connected to a f o u r arm g l a s s tee by lengths of Tygon_ t u b i n g to a l l o w movement d u r i n g alignment. A l l exposed metal surfaces were coated w i t h a m a t e r i a l of low atomic number i n order 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 (Apiezon W) i n carbon 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 o f t h i s p a i n t . C. Production o f the Magnetic F i e l d . I n order to e l i m i n a t e the n e c e s s i t y of measuring small magnetic f i e l d s i t was decided to produce i t without the use of i r o n . The f i e l d would then be p r o p o r t i o n a l to the current used and c a l i b r a t i o n at one poin t on a w e l l known l i n e would give Hr values f o r the e n t i r e spectrum. From the d e s c r i p t i o n of the inner spectrometer i t i s seen t h a t a uniform magnetic f i e l d i s r e q u i r e d over a d i s c -shaped r e g i o n , 12 cms. i n diameter and about 2 cms. t h i c k w i t h the magnetic v e c t o r perpendicular to the s u r f a c e . The u s u a l method of p r o v i d i n g a uniform f i e l d over a considerable volume of space i s to use Helmholz c o i l s . However, co n s i d e r a t i o n s of space, mechanical s t a b i l i t y , the power a v a i l a b l e and the amount of wire r e q u i r e d l e d to an attempt to provide the f i e l d r e -quired w i t h a combination of f l a t c o i l s . I f a current I t r a v e l s i n a c i r c u l a r path of r a d i u s a the f i e l d at any point P i n s i d e the loop and i n the plane of the c i r c l e i s given by H * = 2 a 2 / Ho* Tr (x2-a2) / / l - k 2 S i n 2 0 d# o where x = the d i s t a n c e of P from the center k = x/a Rq= the f i e l d at the center = 27TI 1 0 a This i s an e l l i p t i c i n t e g r a l and must be obtained from t a b l e s . A curve p l o t t i n g H^/Ho against x/a i s shown i n Fig.10 . Using e m p i r i c a l methods and t h i s curve i t was deter-mined that three coplanar c o i l s , one of +14000 ampere turns of r a d i u s 17 .5 cms., a second of - 2 7 0 0 ampere t u r n s of r a d i u s 11 cms. and a t h i r d of +120 ampere turns of r a d i u s 8.5 cms. would give a f i e l d of approximately 360 gauss at t h e i r common center, w i t h a maximum inhomogeneity, of 0.28fo over an area of r a d i u s 6 cms. (The minus s i g n on the second c o i l i n d i c a t e s that the current i n t h i s c o i l i s i n the opposite sense to the current i n the other two c o i l s ) . 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 not n e c e s s a r i l y hold f o r c o i l s of a f i n i t e cross s e c t i o n such as i s necessary to c a r r y the current r e q u i r e d . The design f o r the. a c t u a l c o i l windings 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 out by approximate s o l u t i o n s , whereby each c o i l was-replaced by a s e r i e s of 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 of the magnet i s shown i n Fig.1 1 . The c o i l s were wound from No. 14 wire and can c a r r y a current of up to 10 amps f o r 10 minutes without 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 the e f f e c t of the f i n i t e s i z e of the c o i l s showed that there should be no change i n the d i s t r i -b u tion of the f i e l d but that a sm a l l decrease i n streng t h could be expected. The c a l c u l a t e d value of EQ f o r 10 amps through the c o i l was 347 gauss. The current through the c o i l i s set t o a known value w i t h an accuracy of one part i n ten 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 to somewhat b e t t e r than one part i n a thousand. A s e t t i n g of 1.0 v o l t s on the c o n t r o l potentiometer corresponded to a current of 9.7 t .03 amps and thus to a f i e l d of 336 t 1.6 gauss. D. Te s t i n g the U n i f o r m i t y of the.Magnetic F i e l d . The u n i f o r m i t y o f the f i e l d was checked experimentally by the f o l l o w i n g method. Two i d e n t i c a l c o i l s of No.28 copper wire were wound on b a k e l i t e forms so that the i n s i d e diameter was 1 cm. and the c o i l winding 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 270 12 Turns Turns 1400 Turns 5T 1/4 FIGURE 11. CONSTRUCTION OF THE MAGNET 20. b a l l i s t i c galvanometer. With a measured current of 4 amperes through the magnet one c o i l was placed i n the center of the magnet and the other a t " i n f i n i t y " . The magnet c i r c u i t was broken and the d e f l e c t i o n of the galvanometer observed. When the c o i l s were interchanged and the process repeated the ob-served d e f l e c t i o n d i f f e r e d by l e s s than 0*5%' Then one c o i l was f i x e d at the center of the magent and the other, i n opposite sense to the f i r s t , was placed at a po i n t i n the r e g i o n to be occupied by the spectrometer. When; the current was i n t e r r u p t e d the observed d e f l e c t i o n of the galvanometer was p r o p o r t i o n a l to the d i f f e r e n c e of the e.m.f.'s induced i n the c o i l s and thus p r o p o r t i o n a l to the d i f f e r e n c e i n the f i e l d at the two p o i n t s . By comparing the d e f l e c t i o n to t h a t due to one c o i l alone the percentage v a r i a t i o n of the f i e l d could be found. The r e s u l t s are shown i n F i g . 12A. I t can be seen t h a t the maximum v a r i a t i o n over t h e re g i o n was about 2% and t h a t the f i e l d increased s t e a d i l y with; the d i s t a n c e from the center. As the i n n e r c o i l of 12 turns i s very c l o s e to the spectrometer and thus has a f a i r l y l a r g e e f f e c t on the f i e l d f o r the l a r g e r values of r a t r i a l was made w i t h t h i s c o i l disconnected. The r e s u l t s are shown by the curves of F i g . 12B. The maximum v a r i a t i o n over 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 to be i%. I t was decided t h a t t h i s amount o f inhomogeneity would not be s e r i o u s and that f u t u r e measurements would be made w i t h the inner c o i l disconnected. 1.Q2 H 0.99 1.01 H_ B o o 1.005 0.995 3 x(cm) o 1 2 3 4 • FIGURE 12. OBSERVED VARIATION OF MAGNETIC FIELD IN SPECTROMETER REGION A. Inner e o l l connected B. Inner c o i l disconnected E. Mathematical... Treatment of. a Spectrometer. 7 Erect a r i g h t handed system o f coordinates OX, OY, OZ i n a uniform magnetic f i e l d so-that the negative d i r e c t i o n of the Z a x i s i s i n the d i r e c t i o n o f H. Consider a two dimen-s i o n a l r a d i o - a c t i v e source occupying a r e c t a n g u l a r area i n the ZOX plane, from x • -Q/2 to +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 the source from a point PtX©, 0 , Z 0) w i l l meet the ZOX plane again at a point P^(x,y,z) whose coordinates are given by the equations? x = x 0 + 2r cos A cos B 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 curvature o f the e l e c t r i c path i n the magnetic f i e l d . I t i s equal t o the momentum of the e l e c t r o n d i v i d e d by the f i e l d H and by the e l e c t r o n i c charge expressed i n electromagnetic u n i t s . Since i n beta r a y spectroscopy the momentum always appears d i v i d e d by the e l e c t r o n i c charge i t i s usual to r e d e f i n e the u n i t s of the momentum so tha t p = Hr expressed i n gauss-cms. A i s the angle between the i n i t i a l d i r e c t i o n o f p and the plane YOZ and B i s the angle between the i n i t i a l d i r e c t i o n 29. This development i s e s s e n t i a l l y t h a t given by C. G e o f f r i o n : R.S.I., 20, 6?8, 194-9. FIGURE 13. DIAGRAM OF ELECTRON PATHS IN THE SPECTROMETER 22 of p and the YOX plane. Note t h a t the angles A and B are measured p o s i t i v e l y from the i n i t i a l d i r e c t i o n o f p to the re s p e c t i v e planes. Normally A i s l i m i t e d to -Ao^ A<+Ao by a t l e a s t one b a f f l e opening of width 2b perpendicular to the e l e c t r o n path at a point 90° from the source. Then A Q = fe/r - - - - - - - - - - - - - - - - 1. I t i s also usual for the e x i t s l i t and source to have the same height h, B i s then r e s t r i c t e d so t h a t -B0<B <B 0 w i t h B 0 - h / O r r ) - 2 . Under these c o n d i t i o n s e l e c t r o n s of a given momentum w i l l form an image of the source on the ZOX plane w i t h c e r t a i n aberrations caused by the f i n i t e values of A and B. The s i z e of the image w i l l be given by: Width = Q 1 = £+2r(l-cos Ao eos B 0) Height = h i = h+2r(7r+2A 0)sin 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 distance 2r from the r i g h t hand edge o f the source. Since r depends on the momentum of the el e c t r o n s a number of images w i l l be formed w i t h d i f f e r e n t values of r f o r d i f f e r e n t v a l u e s of the momenta. I f a d e t e c t o r i s placed behind an e x i t s l i t i n the ZOX plane of height h and width F (normally l e s s than or equal to 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 only a c e r t a i n range of values 23, of momenta. The w i d t h of the e x i t s l i t adds to the e f f e c t i v e width of the image o f the source so that i t now becomes equal to F + Q + 2 r ( l - c o s COS B 0) I f H i s constant there i s an u n c e r t a i n t y i n the diameter of the e l e c t r o n t r a j e c t o r y of e x a c t l y t h i s amount or one h a l f of t h i s i n the radius of the t r a j e c t o r y . The l i m i t of r e s o l u t i o n of a spectrometer i s defined as the r a t i o ^ p / p where ^ p i s the range of the momenta of those 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 = H A r + r A H and i f H i s constant A p = H Z i r = H « [ F + Q, + 2 r ( l - c o s A Q cos 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 are small 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 the k i n e t i c energy of the p a r t i c l e i n Mev p = Hr = 1 0 4 /T{T + 1.02) 3 • 24. and i t can e a s i l y be de r i v e d t h a t A P = T + .51 A T p T + 1.02 T The l u m i n o s i t y o f a spectrometer i s a measure of the number of e l e c t r o n s of a given momentum range which form an image of the source. I t i s a f u n c t i o n of the source area and the s o l i d angle w of 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 define d as f o l l o w s L = KQhw/4 7T where Qh i s the area of the source and K i s the.number of e l e c t r o n s i n the given momentum range emitted by the source i n a l l d i r e c t i o n s per u n i t area per u n i t time. From previous equations i t can be shown t h a t L = K^rAoB§/2. • Thus the l u m i n o s i t y i s a f u n c t i o n of 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. Geo;ffrion 2? has a p p l i e d the method of undetermined c o e f f i c i e n t s t o es-t a b l i s h the optimum r e l a t i o n s h i p s between these v a r i a b l e s making L a maximum. They a r e : % = 2Ao 2r 4. Bo = A o ( 2 ) 1 / 2 5o 2 5 . Under optimum c o n d i t i o n s then the l u m i n o s i t y becomes L = 2Kr 2Ao^ I t can a l s o be shown t h a t i f F i s the wi d t h of the e x i t s l i t i t s optimum value i s F = The value chosen f o r F has an e f f e c t on both the r e s o l u t i o n and on the l u m i n o s i t y which now become under optimum c o n d i t i o n s A P / P = 7 A 2 / 2 and L = 0 . 7 2 5 K r 2 ( ^ p / p ) ^ 2 • - 6 . The l i m i t of r e s o l u t i o n given above i s d e f i n e d f o r complete sepa r a t i o n of two l i n e s , Z I P / P = 3 -^/2 7 . gives the w i d t h of a l i n e at h a l f maximum i n t e n s i t y as i s more us u a l . The spectrometer described i n t h i s r e p o r t has a ra d i u s of 3 . 0 5 cms. and AQ was chosen as 0 . 1 . The optimum values of ^, F, and B 0 are then Q = 2 x 3 . 0 5 x . 0 1 = .06 cms. F = q = .06 cms. B 0 = 1 . 4 A Q = . 1 4 26 The wi d t h of the source could not be made much l e s s than 1 mm. because of the d i f f i c u l t i e s i n handling, small drops of r a d i o - a c t i v e solutions.- - 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 . 707 since the source i s at an angle of 4 5 ° t o the plane of the source and e x i t s l i t . (See F i g . 9 ) . The a c t u a l value of % i s probably w i t h i n 1Q7» of the optimum value g i v e n above. The height o f the source 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> higher than the optimum va l u e . The width of the e x i t s l i t (width of counter window) i s about . 0 2 5 cms. because i t was feared that a wider window would not stand the pressure. This 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 counter w i t h optimum window width. This should improve the performance of the spectrometer. The r e s o l u t i o n of the spectrometer should be about 1.7% at h a l f maximum i n t e n s i t y using equation ( 7 ) . From equation (3) using the a c t u a l values of F, AQ and B 0 the r e s o l u t i o n comes out to be about 1.$%. The d i f f e r e n c e i s due almost e n t i r e l y to the small value of F. This small value of F should reduce the l u m i n o s i t y of the spectrometer by F/Q. Assuming K to be u n i t y t h i s gives L • . 146 x 10~2 cms 2 and adding the l u m i n o s i t y for the f o u r s e c t i o n s of the spectrometer 27. gives L = .58 x 10-5 cm 2 G e o f f r i o n ( i b i d ) shows a curve o f the i n t e n s i t y to be expected 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 -esimal width ( t h i s i s the case i n photographic 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 given w i d t h F can be obtained from t h i s curve by i n t e g r a t i o n . Fig.14 shows the p r o f i l e s obtained from the dimensions of our spectrometer f o r - F = .025 cms. and F = .06 cms. Note th a t the p r o f i l e i s not symmetrical, the lower energy s i d e extends f u r t h e r than the high energy s i d e . This tendency i s exaggerated by the e f f e c t of a t h i c k source as can be seen from the 50 Kev l i n e i n the spectrum of RaD ( F i g . l 6 ) . Other experimenters have report e d e n t i r e l y s i m i l a r results.^° Pe 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 of the var i o u s beta ray spectrographs and spectrometers mentioned i n the l i t e r a t u r e and compiled t h e i r r e s u l t s i n the form of a t a b l e . This i s reproduced i n p a r t i n Table I f o r comparison w i t h the r e s u l t s f o r the spectrometer described by t h i s report. They also g i v e a s c a t t e r diagram o f the v a r i o u s instruments, p l o t t i n g r e s o l u t i o n against what they c a l l the e f f i c i e n c y . e f f . = 1 0 7 L / r 2 3 0 . G.E. Owen and H. Primakoff: Phys.Rev., 21, 1 4 0 6 , 1 9 4 8 . 3 1 . 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 2 8 . This i s p r o p o r t i o n a l to the l u m i n o s i t y d i v i d e d by the c r o s s -s e c t i o n a l area of the magnetic f i e l d . The diagram i s reproduced i n p a r t i n Fig. 1 5 • The q u a n t i t i e s compared.in Table I are s e l f - e x p l a n -atory w i t h the exception o f W, C and D which are defined as f o l l o w s W = w/4-T . The l u m i n o s i t y and s o l i d angle of these spectrometers cannot be compared d i r e c t l y s i n c e they are i n f l u e n c e d by the r e s o l u t i o n s of the instruments. However, the q u a n t i t i e s C and tD provide a means of comparison which e l i m i n a t e s the d i f f e r e n t r e s o l u t i o n s . The value 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 considerably higher than any of the others and,in f a c t , i s almost one-half of the optimum value ( 0 . 7 2 5 ) . I t co u l d be ; increased by making the counter entrance s l i t the same width ; as the source. D r e p r e s e n t i n g the r a t i o of the s o l i d angle to the r e s o l u t i o n has d i f f e r e n t values depending on whether one or four counters are used. With one counter D = 0 . 1 5 and w i t h f o u r D = 0 . 6 0 . No 9 i n the t a b l e i s the spectrometer 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 data f o r one counter only and (b) i s the data f o r four counters. The values of the r e s o l u t i o n and lumin - i o s i t y i n 9(b) are c a l c u l a t e d on the b a s i s that the e x i t s l i t s ! are a l l l i n e d up e x a c t l y w i t h the 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 po i n t s r e f e r to the corresponding instruments i n TABLE I ) A Optimum values f o r the usual semi c i r c u l a r f o c u s s i n g , spectrometer B Optimum values f o r high source 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 true as w i l l be shown l a t e r . 4(a) and 4(b) are two c o n d i t i o n s of o p e r a t i o n of the same instrument. TABLE I •No Authors Year •Ref. Type Iron Emax Mev r cm. p W% LxlO^ cm2 C x l O 2 Dxl02 1 L i 1937 ?2 Spg. 7 MM 6 0 .63 0 .0067 0.020 18 1 . 1 2 Arnould 1939 33 Spg. n 0.26 0.2 0.011 0.00022 0.74 5.5 3 - .Lawson and T y l e r 1939 34 Spm. y 3.1 12 1 . 6 0.10 0 .50 11 6.3 4 Neary a 1940 Spm. y 7 1.0 0.041 0.052 11 4.1 b MM 10 1 .26 0.041 0.052 2 .8 3 .3 5 Townsend 1941 w. Spm. y MM 8 1 . 6 0.10 0 .38 19 6.3 6 P l e s s e t , Harn-w e l l and S e i d l 1942 37 Spg. y 10 11.4 0.2 7 Sei gbahn 1944 ?8 Spm. y MM- 12 0.17 0.029 0.00073 4.2 17 8 Langer, Motz and P r i c e 1950 19 Spm. n 0.23 2 . 6 0.10 0.20 7.3 3 .9 ? Brown a 1951 Spm. n 0.10. ? . 0 5 1 . 7 .25 0.146 34 15 b 0.10 ? . 0 5 1 . 7 1.0 0.58 34 60 32. K.T. K i : Proc.Camb.Phil.Soc., 164, 1937* 36.' A.A. Townsend: Proc.Roy.Soc. 177.358,1940. 33. R.Arnould: Ann.de Phys: S e r i e 11,to 12., 241, 1939. 34. J.L. Lawson & A.W.Tyler: R.S.I.,11,6,1940. 35. G-.J. Neary: Proc.Roy.Soc., 175,71.1940. 37. P l e s s e t , Harmwell & S e i d l : R.S.I., 11, 351, 1942. 38. K, Siegbahn: Arkiv.Mat.Astrom.Fys.Bd., 30A, (No20) 1944. T © I l l RESULTS Radium D / Pb ) The primary beta spectrum has long been known to 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 the energy r e g i o n below 50 Kev. The very r e a l experimental t r o u b l e s attendant upon a d e t a i l e d a n a l y s i s of these r a d i a t i o n s have l e d to 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 the reported f i n d i n g The bulk of the work has been done w i t h cloud chambers and absorption techniques 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 accuracy. Because of the low energy of any gamma-rays, t h e r e are many conversion e l e c t r o n s from theL, M and N s h e l l s superimposed upon the primary beta d i s -t r i b u t i o n which makes i t d i f f i c u l t t o l o c a t e the end-point a c c u r a t e l y . The Auger e l e c t r o n l i n e s f u r t h e r obscure the beta spectrum. In s p i t e of these obvious problems, i t was f e l t that t h i s nucleus would provide a good t e s t of the p e r f o r -mance of the spectrometer under very unfavorable 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 , the experiment would provide u s e f u l i n f o r m a t i o n that might help i n e l i m i n a t i n g some of the r e -ported i n c o n s i s t e n c i e s i n the decay of RaD. The beta spectrum was s t u d i e d e x t e n s i v e l y by e a r l y experimenters w i t h photographic methods. I t appeared to be very simple, c o n s i s t i n g of a group of conversion l i n e s a l l a t t r i b u t a b l e to the a c t i o n of one gamma ray. Rutherford, Chadwick and E l l i s r eport the f o l l o w i n g v a l u e s . TABLE I I Number of l i n e I n t e n s i t y Hr Energy i n Kev 1 50 600 30.9 2 2 606 31 . 5 3 0 . 5 628 3 3 . 8 4 20 714 4 3 . 3 P 10 738 4 6 . 1 which are analyzed as f o l l o w s TABLE I I I Number of l i n e - O r i g i n Energy + abso r p t i o n energy i n Kev Energy of Gamma i n Kev 1 L i 30.9+16.3 47.2 2 I ' l l 31.5+15.7 47.2 3 L I I I 33.8+13.4 47.2 4 Mj 43.3+ 4.0 47.3 5 N j 46.1+ 1.0 47.1 G. von D r o s t e ^ using a Wilson cloud chamber and magnetic a n a l y s i s obtained most of the above conversion l i n e s and agrees roughly on the energy of the primary gamma. He also 3 9 . G. von Droste: Z e i t s . f u r Phys., 84, 1 7 , 1 9 3 3 . 3 3 . observed a l a r g e number of t r a c k s corresponding to the x-ray spectrum of the inner s h e l l e l e c t r o n s of atoms of atomic number 8 3 . Richardson 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 the form o f tetra-methyl l e a d throughout a cloud chamber. The beta spectrum was c a l c u l a t e d from e l -ec t r o n path lengths and range-energy measurements. I n a d d i t i o n to the usual conversion l i n e s they report a l a r g e number of e l e c t r o n s of very low energy. Their r e s u l t s were based on a sm a l l number of observations and thus have poor s t a t i s t i c s . A K u r i e p l o t of the r e s u l t s gives an end point , 4.1 of 16 Kev. Lee and Lib b y used a b s o r p t i o n techniques to study the gammas from RaD and a screen w a l l counter w i t h mag-n e t i c d e f l e c t i o n to observe the primary beta d i s t r i b u t i o n . They r e p o r t an end p o i n t of 2 5 . 5 - .1 Kev. The continuous 4 2 d i s t r i b u t i o n has a l s o been observed by Saha who gives the end point as 29 Kev. A great deal of work has been done on the a n a l y s i s of the gamma rays of RaD by Tsien San-Tsiang, F r i l l e y et a l . 4 ^ By a number o f methods such as a bent c r y s t a l spectrometer, 40. H.O.W. Richardson and A.Leigh-Smith: Proc.Roy.Soc. 1 6 0 , 4 5 4 , 1 9 3 7 . 41. D.D. Lee and W.F. Libby: Phys.Rev. 2 5 2 , 1 9 3 9 . 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 , No.3, 1 9 4 6 . 4 3 . T s i e n San-Tsiang: Comples Rendus, 216 . 7 6 5 , 1 9 4 3 . Ouang TeTchao: J". Surugue, Tsien San-Tsiang: Comptes Rendus, 2 1 2 , 5 3 5 , 1 9 4 3 . Tsien San-Tsiang: 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 . Tsien San-Tsiang and C.Marty: Comptes Rendus,220.688.1945. • Tsi e n San-Tsiang and C.Marty: Comptes Rendus,2 2 1 , 1 7 7 , 1 9 4 5 . Tsien San-Tsiang: Phys.Rev., 6£, 3 8 , 1 9 4 6 . — 34. measurement of path lengths i n a cloud chamber, magnetic def-l e c t i o n i n a cloud chamber, abs o r p t i o n measurements they show the existence of the f o l l o w i n g nuclear gamma r a y s . TABLE IV Number of l i n e Energy i n Kev Quanta/100 d i s i n t e grations 1 65*5 < 0.2 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 et a l . have i n v e s t i g a t e d the gamma rays of RaD by means of a p r o p o r t i o n a l counter. The beta p a r t i c l e s from t h e i r source were d e f l e c t e d m a g n e t i c a l l y and the gammas entered the counter through a t h i n mica window. They repo r t the f o l l o w i n g gamma r a y s TABLE V I n t e n s i t y Energy 7.3 7.7 Kev 0.4 2 5 . 8 Kev 3.0 46 . 6 Kev 44. S.C. Curran, J . Angus and A.L. Cockeroft: Phil.Mai 40, 36, 1949. 35 and i n a d d i t i o n strong L x-ray 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 to be the most r e l i a b l e t o date. 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 sources (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 spectrograph. His p l a t e s show the Lj, L j x i > M and N conversion l i n e s from the 47 Kev gamma ray. There i s a l s o some evidence of a l i n e at 19 Kev (470 gauss cm. ). The s e n s i t i v i t y of the emulsion i s e v i d e n t l y very poor below 15 Kev. F i g . l 6 shows the r e s u l t s obtained here w i t h a source o f about 30 micrograms/cm . ' The readings have been repeated a number of times w i t h d i f f e r e n t source strengths without any appreciable change i n the spectrum. The L j , Liny M, and N conversion l i n e s of the 47 Kev gamma l i n e are i n d i c a t e d . The broad peak at about 300 gauss-cms i s probably due to the con-tinuous spectrum of nuclear beta p a r t i c l e s . The low energy peak at about 150 gauss-cms i s hard to i d e n t i f y because of i t s w i d t h . The most probable l o s s of energy of an e l e c t r o n of 3 Kev energy i s about 50 e l e c t r o n v o l t s per mierogram/cm 2. Since the source weighs 30 micrograms/cm 2 the width of the l i n e can r e a d i l y be explained i n terms of a b s o r p t i o n i n source. I f t h i s i s the cause of the l i n e width then the a c t u a l energy of the e l e c t r o n s must be at the h i g h energy end of the l i n e , about 200 gauss-cms, corresponding to 3.7; Kev. Thus the l i n e may be due to an I s h e l l conversion of the 7 . 7 Kev gamma reported above. 4 5 . L. Cranberg: Phys.Rev., 21, 1 5 5 , 1 9 5 0 . _l8oo JL200 1Q2.5 205 .0 307.5 410.0 5X2 ^J.000 CO .O o 600 1400 Hr(Gauss-cms) 0J9 3J 8 14.6 Energy (Kev) 800 600 (The arrows i n d i c a t e the l i n e s as des c r i b e d by the corresponding numbers i n TABLE V I I I ) J-00 200 3 6 . On the other hand the l i n e may be due wholly or i n part t o Auger t r a n s i t i o n s i n the e l e c t r o n i c s h e l l s of the daughter B i atoms. Since 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 from here. The process can be p i c t u r e d as f o l l o w s . The atom i s s i n g l y i o n i z e d , having l o s t an L j e l e c t r o n . This vacancy can be f i l l e d by an e l e c t r o n from any higher energy s t a t e LJXV. LIII» MI» N I and simultaneously another e l e c t r o n i s e j e c t e d from the atom. For an energy balance, the k i n e t i c energy of the eje c t e d e l e c t r o n plus i t s b i n d i n g energy must be equal to the energy given up by the re v e r s i o n t o the L j s t a t e . Note t h a t s i n c e there i s a vacancy i n the 1 s h e l l the b i n d i n g energies of the M and N e l e c t r o n s are increased, and must be c a l c u l a t e d on the b a s i s of an i n -crease of u n i t y i n the nuclear charge. As an example, consider 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 to doubly i o n i z e d by l a c k o f L J J J and Mjy e l e c t r o n s . I-I- ) L I I I M I V The k i n e t i c energy of the ejected e l e c t r o n i s given by: E(Kin) = E ( L l ) z - E ( L l I l ) z - S(Miv) z + 1 Table vT 4 6 l i s t s the bi n d i n g energies of the L 4 6 . These values were obtained from Compton and A l l i s o n : X rays i n Theory and Experiment, and from the 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 bismuth and some of the M and N e l e c t r o n s i n polonium and Table V I I gives some of the p o s s i b l e t r a n s i t i o n s together w i t h the k i n e t i c energy of the ejected e l e c t r o n s . Richtmeyer and Kennard 4"^ s t a t e t h a t the t r a n s i t i o n s Lj ^ L I I X M I V, y are o f t e n observed i n X ray work f o r Z>75. However, the excess energy i n t h i s case i s too small f o r d e t e c t i o n . TABLB VI L M N I 16.400 4.000 900 I I 15.700 3,700 boo 700 I I I 13.400 3.200 IV 2,700 500 V 2,600 400 Thus there are a number of t r a n s i t i o n s that could y i e l d e l e c t r o n s i n the energy range occupied by t h i s l i n e . They have d i f f e r e n t energies and d i f f e r e n t degrees o f p r o b a b i l i t y of o c c u r r i n g . I t i s l i k e l y that the l i n e i s a c t u a l l y composed of el e c t r o n s r e s u l t i n g from s e v e r a l Auger t r a n s i t i o n s and the M conversion of the 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 obscured by a b s o r p t i o n i n the source, w i t h f u r t h e r confusion due to the v a r i a t i o n of t r a n s m i s s i o n of the counter windows i n t h i s r e g i o n . 4 7 . Richtmeyer & Kennard: I n t r o d u c t i o n to Modern Phys., 3 r d E d i t i o n , p.548. 38. TABLE V I I No . T r a n s i t i o n Energy i n e.v. 1 L i — » ^ I I I M I V 300 2 L i — * L m M v 400 3 L l ^ L I I I % 2100 4 i»i—:> L i l i a n 2200 3 Li—> LnAn 2300 6 I»l-^1"III%V 2500 7 L I — > L I I I N V 2700 8 H j — ^ N J N J J 2200 9 2400; 10 M I — > N I N I V 2600 11 Mi—> NjNy 2800 With one source which was made thi n n e r than usual (of the order of 10 micrograms/cm 2) some s t r u c t u r e was n o t i c e d but before r e l i a b l e s t a t i s t i c s could be obtained an accident occurred i n which the source became damaged. I f a source could be made l e s s than 5 micrograms/cm 2 more i n f o r m a t i o n could be obtained about t h i s l i n e . There i s some evidence of a very weak peak a t 450 gauss-cm (18 Kev). I f t h i s corresponds to M- s h e l l conversion then the energy of the t r a n s i t i o n i s about 22 Kev and an L-s h e l l peak should occur near 5.5 Kev. There i s no evidence of t h i s . 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 the conversion takes place 3 9 . i n t h i s L s h e l l . There i s a s i m i l a r l y d o u b t f u l peak at 500 an gauss-cm (21 Kev) which by the same arguments would b e ^ L - s h e l l conversion o f a 37*5 Kev t r a n s i t i o n . Table T i l l l i s t s the r e s u l t s o f t h i s experiment to determine the conversion t r a n s i t i o n s of the RaE daughter product. The energies were determined by use of the t h e o r e t i c a l value of the f i e l d . (See page 19). TJ (U3LI V I I I . No. o f l i n e O r i g i n Conv.line + S h e l l B i n d i n g T r a n s i t i o n Energy 1* M 3.7-1.0+4 .0 7.7 Kev 2 L i 3*.0 +l.0+16.4 47.4 3 L I I I 34.3 +1.0+13.4 47.7 47.4 4 M 43.4+1.0+4.0 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 Corrected f o r source a b s o r p t i o n . &k Doubtful. The Primary Beta Spectrum The low-energy t a i l on the L i conversion l i n e of the 47 Kev gamma i s unfortunate i n t h a t i t tends to obscure the d i s t r i b u t i o n of the d i s i n t e g r a t i o n e l e c t r o n s and any weak eon-v e r s i o n l i n e s i n t h i s r e g i o n . The leading edge o f the l i n e corresponds w e l l w i t h the expected h a l f maximum i n t e n s i t y r e s o l -u t i o n o f 1.7%. The low energy t a i l appears to be caused by the 40. spectrometer r a t h e r than by source absorption since d i f f e r e n t thicknesses of sources d i d not make much d i f f e r e n c e . Owen and Primakoff 4"^ have reported almost i d e n t i c a l l i n e p r o f i l e s from t h e i r s m all 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 describe the f i t t i n g of. the t r a i l i n g edge of the l i n e by means of an exponential curve N(H) = Constant X e x p ^ - Po~P j where p 0 i s the Hr value o f the l e a d i n g edge of the l i n e and a i s the average wi d t h of the l i n e i n gauss-ems. This has been done w i t h the L j conversion peak (the s o l i d l i n e i n F i g . l 6 ) and the c a l c u l a t e d values subtracted from the observed d i s t r i b u t i o n , r e s u l t i n g i n the p l o t shown i n F i g . 1 7 . I n s p e c t i o n of t h i s curve g i v e s a beta ray end po i n t of 22.4 Kev, a value which i s s t r o n g l y i n f l u e n c e d by the f i t t i n g of an exponential curve to the 46 Kev ILj conversion l i n e . The K u r i e p l o t of the beta spectrum i s shown i n F i g . l 8 . I n the c a l c u l a t i o n of the curve the f o l l o w i n g procedure was used. The Fermi r e l a t i o n i s given by N X1 1/2 ~ jt**max""s where -y •» the momentum of the e l e c t r o n s i n u n i t s of M 0 G . N = the number of el e c t r o n s i n the momentum i n t e r v a l ^ to + dl^ 48. See reference No.30. •FIGURE 17. •BETA SPECTRUM OF RADIUM D WITH 30 KEV CONVERSION LINE SUBTRACTED ENERGY (Kev) •FIGURE 18. •KURIE PLOT OF BETA SPECTRUM OF RADIUM D 41. and f ( Z , ^ ) - ^ 2S Q 7 r y P t l + S + l y ) S - ^ /i-(z/i37): - 1 y = zyr+T2" 137 y Since t h e r e are no complete t a b l e s of 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 of a Taylor expansion t o the f i r s t power only of S. N e g l e c t i n g higher terms we get P t l + S + i y ) 2 _ Try •ainh it y l + s Srl{l+U) - / ^ i l - l y ) 1 ( / ^ l l + i y ) /"* ( 1 - i y ) The expression i n ^  j was f u r t h e r expanded i n a s e r i e s using a w e l l known expansion f o r f1- \Z)Jp{Z). The s e r i e s i n v o l v e d of the form ri(n2+y2) n = 1 was approximated by h(n 2+y 2) whence 42. Try J 1+2S V+S I n (1+y 2) t iinh.7ry [ -w i t h ^ = E u l e r constant « 0.5772 The f i n a l r e s u l t i s that f(z,7 ) = 7 2 S 7 r y e ^ y fi+zsY+s m ( l + y 2 ) t ' . I sinli;7ry ( J A s t r a i g h t l i n e was f i t t e d to the p o i n t s from 7 Kev \ t o 15 Kev by means of the l e a s t squares, procedure y i e l d i n g an end p o i n t of 21 .7 - 1 Kev Below 7 Kev the curve deviates 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 the source. The po i n t at 18.5 Kev was neglected i n the determination of the l i n e s i n c e i t i s so s t r o n g l y i n -fluenced by the two sm a l l peaks i n t h a t r e g i o n and by the t a i l o f the I i j conversion l i n e . Most of the readings on RaD were taken w i t h only three of the fo u r counters o p e r a t i n g as one counter was found to be u n r e l i a b l e and could not be made to operate p r o p e r l y . A run was taken on the $00) gauss-cm l i n e using only one counter, as a check on the alignment of the spectrometer. The comparison i s shown i n Eig.19, the d i f f e r e n c e i n r e s o l u t i o n i s very s m a l l and of the order of magnitude to be expected from the alignment procedure. FIGURE 19. . LINE WIDTHS FROM ONE COUNTER AND FROM THREE COUNTERS S o l i d l i n e Dashed l i n e One counter Three' counters 43. D i s c u s s i o n of the R e s u l t s on RaD There seems to be no doubt but t h a t the decay RaD—>RaE takes place w i t h a negatron decay to an e x c i t e d s t a t e of RaE. The predominant gamma-ray and the conversion e l e c t r o n s correspond to a t r a n s i t i o n energy of 4?. Kev and one of 7.7 Kev. The maximum energy of the beta-spectrum as taken from the Kuriae p l o t i s 21.7 Kiev. In a d d i t i o n to these 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 of other very weak t r a n s i t i o n s w i t h very l i t t l e c o r r e l a t i o n between the d i f f e r e n t reported f i g u r e s . Examination o f the experimental evidence i n each case leads one to conclude t h a t the evidence i s not very strong i n most cases. A l l q u a n t i t a t i v e experiments quote the 47 Kev and the 7.7 Kev t r a n s i t i o n s , and i t appears t h a t these are the only t r a n s i t i o n s upon which much r e l i a n c e can be placed. Now i t i s impossible to p o s t u l a t e a decay scheme for a nucleus when the r a d i a t i o n s c o n s i s t of one beta-group and two major gamma-rays, unless one assumes the gamma-rays are i n cascade. We can make t h i s p o s t u l a t e and t r y to f i t the known data to such a scheme to see i f such data are 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 there should be! equal numbers of t r a n s i t i o n s corresponding to the 47 Kev and the 7.7 Kev l i n e s . That i s , the sum o f the conversion e l e c t r o n s plus the gamma-rays should be the same i n both cases. The r e l a t i v e numbers of conversion 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 roughly estimated f o r the f i r s t time from the r e s u l t s o f the present i n v e s t i g a t i o n i f we make the some-44 what d r a s t i c assumption that the t r u e height of the 7«7 Kev peak i s that of a peak whose area i s equal to the measured peak and whose h a l f - w i d t h i s about 1.5% i n momentum. This corresponds to a c o r r e c t e d peak height of 1200 counts/minute. This estimate w i l l probably e r r on the low s i d e because at the energies i n -volved, we may expect s c a t t e r e d and absorbed conversion e l e c t -rons t h a t would not reach the counter. The t o t a l number of 47 Kev conversion e l e c t r o n s w i l l of course be p r o p o r t i o n a l to the sum o f a l l the conversion peak heights corresponding to 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 per minute. Hence ( N E ) 7 . 7 \ 1200 = 0 . 4 1. W^huT ' 3000 The work o f Curran and c o l l a b o r a t o r s on the gamma-rays of RaD gives the r a t i o of 7«7 Kev gammas to 47 Kev gammas as about 2.4. San-Tsiang and co-workers put the value of the r a t i o at 3.6. Taking the mean v a l u e , we accept ( Nr> 7 . . 7 ^ 3.0 2. F i n a l l y on the basis of h i s measurements, San-Tsiang concludes that there are approximately 10 quanta of 7.7 Kev energy emitted f o r each 100 d i s i n t e g r a t i o n s . To summarize then, f o r each 100 d i s i n t e g r a t i o n s , there w i l l be 10 - 7.7 Kev quanta and 90 conversion e l e c t r o n s 45 f o r t h i s energy.. On the cascade p i c t u r e , using equation (2) there are approximately 3 - 47, Kev quanta and 97 corresponding conversion e l e c t r o n s . This would p r e d i c t i£ej_7.7 = 29. o r ^ o . 9 whereas our rough estimates put the value as greater than 0 . 4 from ( 1 ) . Considering 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 the assumption o f a cascade gamma system. This would then lead to a decay scheme as i l l u s t r a t e d i n Figure 2 0 . This scheme could be t e s t e d by the use of coincidence techniques except f o r the presence of Auger e l e c t r o n s and X-ray3 i n the 7«7 Kev energy r e g i o n which are c o i n c i d e n t w i t h the 47. Kev t r a n s i t i o n . I t i s l i k e l y that the experimental d i f f i c u l t i e s would preclude t h i s check. From our previous f i g u r e s , we can estimate the order of magnitude of the conversion c o e f f i c i e n t s since by d e f i n i t i o n « - N r Hence <X M f o r the 7 . 7 Kev t r a n s i t i o n has the value 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 approximately 30 or 0£ x, alone has the value 1 8 . Unfortunately there i s no a v a i l a b l e c a l Q u l a t i o n of values of M-conversion c o e f f i c i e n t s , the l i t e r -ature at present being l i m i t e d to K- and L-conversion. Hebb and N e l s o n 4 9 l i s t values of L-conversion c o e f f i c i e n t s from which we 4 9 . M.H. Hebb and S. Nelson, Phys. Rev., j>8, 4 8 8 , 1 9 4 0 . ' 21.7 Kev 7.7 Kev 4 7 . 4 Kev 21.7 Kev 47„4 Kev 7.7 Kev FIGURE 20. SUGGESTED DECAY SCHEME FOR RADIUM D would expect a value of $f L = 0 .5 f o r the 47 Kev t r a n s i t i o n i f the s p i n change i s 1 ( E l e c t r i c Dipole) and cxl-^ = 38 i f the s p i n change i s 2 ( E l e c t r i c quadrupole). Our c.ascade-gamma hypothesis then would i d e n t i f y the 47 Kev r a d i a t i o n as e l e c t r i c quadrupole i f a choice has t o be made. Now an estimate of the mean l i f e - t i m e of t h i s s t a t e may be had (to one or two orders of magnitude) by using the r e l a t i o n o f Segre and Helmholz^ 0 where V f ~ ( f J £ ( 2 l - i ) r y 2 f( -3 l / 3 R being the nuclear r a d i u s which we can take as 1,5 x 10 A ' . From t h i s , £y = 3 x 1 0 " 1 0 seconds f o r 1 = 1 and £J, = 6 x 1 0 " 3 seconds f o r A = 2. These of course are l i f e t i m e s by gamma emission only and hence the t o t a l l i f e t i m e s are probably.much l e s s than t h i s s i n c e conversion i s the predominant decay method on our basic assumption. I t i s improbable t h a t X i s 'greater than 2 s i n c e t h i s would mean a long l i f e t i m e , i . e . an isomeric s t a t e and would have been, observed. Therefore, quadrupole r a d i a t i o n i s not an unreasonable assignment for the 47 Kev t r a n s i t i o n . U nfortunately, f o r the reasons given above, no such guess may be made for the 7.7 Kev t r a n s i t i o n other than t o suggest t h a t because of i t s low energy even an assignment o f ^ = 2 would probably produce a metastable s t a t e t h a t i s observable. This 50. E. Segre and A.C. Helmholz; Rev.Mod.Phys., 21 , 280, 1949. i s of course p o s s i b l e and perhaps should i t e x i s t , i t s low energy might make i t s observation d i f f i c u l t . I n a l l the above, which must be c l a s s e d as s p e c u l a t i o n based upon what evidence there i s , we have been d i s c u s s i n g the major t r a n s i t i o n s . Of other weak or d o u b t f u l t r a n s i t i o n s , l i t t l e can be s a i d . I f they e x i s t , they may be due to a l t e r n a t e branch t r a n s i t i o n s from the high energy e x c i t e d s t a t e through i n t e r -mediate l e v e l s to the ground s t a t e . Further d i s c u s s i o n must await more p r e c i s e and re p r o d u c i b l e experimental r e s u l t s . 48, IV CONCLUSIONS AND RECOMMENDATIONS The experiment has shown that i t i s f e a s i b l e t o b u i l d a spectrometer to study beta and gamma sp e c t r a i n the low energy r e g i o n down to 2 Kev or l e s s . The r e s o l u t i o n as taken from high energy s i d e of the 30 Kev peak i n RaD i s very c l o s e to the value c a l c u l a t e d from the design of the spectrometer. I t i s u n p r o f i t -able to t r y to increase the r e s o l u t i o n of the instrument, because of the l i n e w i d t h produced by a b s o r p t i o n i n the source. I n add-i t i o n the r e s o l u t i o n i s l i m i t e d under present c o n d i t i o n s , mainly by the width of the source, and i t would be d i f f i c u l t i f not impossible to make sources much narrower than 1 mm. A number of improvements to increase the r e l i a b i l i t y and ease of operation of the instrument can be suggested. F i r s t the b a f f l e s i n the spectrometer should be redesigned, so t h a t new windows can be attached without removing the b a f f l e s and source from the instrument. Secondly the counters should be connected together outside of the apparatus so that they could be checked i n d i v i d u a l l y at any time and any f a u l t y one or ones disconnected. F i n a l l y the 6AS7 r e g u l a t o r tubes should be monitored w i t h a wattmeter i n order to prevent overloading them. With the method o f a t t a c h i n g the counter windows now used i t might be p o s s i b l e to make the entrance s l i t s wider, say to 0.05 cms. This would increase the l u m i n o s i t y without 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 evaporating l i n e sources on the backing should be i n v e s t i g a t e d . This might be done 4 9 from a c r u c i b l e of some s o r t as w e l l as from a f i l a m e n t . F i n a l l y the problem of e x t e r n a l quenching of the counters should 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 voltage and longer pulses an improvement i n performance might be ob-tain e d . 50. APPENDIX I THE SCATTERING. AND. ABSORPTION 01 BETA-RAYS The beta spectrum of r a d i o - a c t i v e substances as measured w i t h the spectrometer, can 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 et to observe a c e r t a i n energy range the number of e l e c t r o n s counted may be reduced by some of them l o s i n g energy i n passing through the m a t e r i a l of the source and source backing, by s c a t t e r -i n g from molecules of the r e s i d u a l gas, by r e f l e c t i o n ( s c a t t e r i n g through more than 90?) from the window of the counter and by absorption i n the window. I f the counter i s of the end window type an e l e c t r o n may be absorbed i n the counter gas between the window and the s e n s i t i v e volume of the counter without being recorded. However, i t has been shown^ 1 that w i t h a s i d e window counter the s e n s i t i v e volume extends as f a r as the window. An increase i n the number of e l e c t r o n s counted can be caused by e l e c t r o n s of higher energy l o s i n g energy i n the source and backing and by r e f l e c t i o n from the source supports, b a f f l e s and • a l l other surfaces i n the spectrometer. A knowledge of the t h e o r e t i c a l estimates of the mag-nitude of s c a t t e r i n g and absorption e f f e c t s and of the experimental work on the subject i s u s e f u l i n designing a low energy spect-rometer since i t i s i n the low energy r e g i o n t h a t the d i s t o r t i o n becomes most troublesome. 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 through a l a r g e angle by the nucleus 51. S.C. Brown: Phys.Rev., 9^4, 1941. 51 without l o s s of energy ( e l a s t i c s c a t t e r i n g ) or i t may be d e f l e c t e d through a small angle by an e l e c t r o n . For energies greater than 1000 e.v. and f o r low Z the second i s always accompanied by a l o s s of 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 th a t f o r e l a s t i c s c a t t e r i n g the p r o b a b i l i t y v a r i e s as (1 - v 2/o 2) Thus the p r o b a b i l i t y of an e l e c t r o n being scattered, i s 10 times the p r o b a b i l i t y of an alpha p a r t i c l e of the same v e l o c i t y . The thi c k n e s s of counter 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 ' theory can be a p p l i e d , at l e a s t f o r energies greater than 50 Kev. The r e f l e c t i o n of 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 increases as the energy decreases. While t h i s theory cannot be extrapolated to 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 s i m i l a r r e s u l t s . The r e f l e c t i o n of high energy e l e c t r o n s from the w a l l s of the spectrometer can take place through a l a r g e number of 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 ' theory can 52 be a p p l i e d . Fermi s t a t e s that the root mean square angle of d e f l e c t i o n of an e l e c t r o n a f t e r passing through a given t h i c k n e s s of matter of atomic number Z i s approximately equal to Z d i v i d e d by the k i n e t i c energy o f the e l e c t r o n . Thus i n any circumstance the s c a t t e r i n g increases as the energy of the e l e c t r o n s decreases and as the atomic number 52. E. Fermi, Nuclear P h y s i c s , p.57. 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 , that 53 i s , by i o n i z a t i o n of the atoms i t encounters. Mott and Massey" 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 f o r the r a t e of l o s s of energy. Where T Is the k i n e t i c energy of the e l e c t r o n , x i s the d i s t a n c e , e i s the e l e c t r o n i c charge, m i s the e l e c t r o n i c mass, v i s the v e l o c i t y of the e l e c t r o n . N i s the number of atoms per cc. of absorber. Z i s the atomic number of the absorber. E i s the mean i o n i z a t i o n p o t e n t i a l of the absorber. This formula i s good f o r e l e c t r o n energies from 1 Kev t o 50 Kev. I n t e g r a t i o n of t h i s should y i e l d a value f o r the range of e l e c t r o n s of a given energy, but because of the tortuous paths followed by e l e c t r o n s i t would be s l i g h t l y greater than the maximum experimental range. The most extensive experimental work on the ab s o r p t i o n and s c a t t e r i n g o f el e c t r o n s i s that of Schpnland-*4". With h i s apparatus he could measure the number o f e l e c t r o n s , r e f l e c t e d , absorbed, or tr a n s m i t t e d by f o i l s of a number of metals and of d i f f e r e n t t hicknesses. He found the amount r e f l e c t e d to be l j f , f o r A l , 29% f o r Cu, 391» for Ag and 507* f o r Au. 53- N.F. Mott and H.S.W. Massey, The Theory of Atomic C o l l i s i o n s 54. B.E.J. Schonland; Proc.Roy.Soc. A104. 235, 1923. AIOF, 187, 1925. 53. For a given energy of e l e c t r o n s , a value of the t h i c k -ness of f o i l necessary to stop a l l but a few percent of the e l e c t r o n s , could be obtained from h i s curves. This value he c a l l e d the range and found t h a t i t v a r i e d only s l i g h t l y w i t h the atomic number of the m a t e r i a l of the f o i l . At t w i c e the energy corresponding to a given range approximately 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 curve o f range versus 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 . 21 . In the r e g i o n below 10 Kev there are very few exper-imental values of the range of e l e c t r o n s . A paper by Tsien San-Tsiang-^ et a l , gives the range of photo e l e c t r o n s ejected by weak X-rays i n a low pressure cloud chamber from 1 Kev t o 40 Key. They de f i n e M l e parcours" as the path l e n g t h — t h e t o t a l d i s t a n c e an e l e c t r o n t r a v e l s i n i t s meanderings and " l a portee" as the r a n g e — 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 beginning and end of the t r a c k . There appeared to be a-constant r a t i o of 0.67 between the r.m.si. values of the range and the path l e n g t h s . The average path lengths were found to be very c l o s e to the values obtained by i n t e g r a t i o n o f the formula f o r energy l o s s mentioned above. The curve obtained by i n t e g r a t i o n of t h i s formula i s - p l o t t e d i n Fig. 2 1 . I t w i l l be n o t i c e d t h a t between 10 and 100 Kev the range as given by Schonland f a l l s between t h i s curve and another obtained by m u l t i p l y i n g the ordinates by O .67. Hence i t seems reasonable to take the worst of the values as the range of e l e c t r o n s of a given energy. On t h i s b a s i s the range 55. Tsien San-Tsiang, C. Marty and B. Dreyfus: Jour.de Phys. et Had., 8., (Ser.8), 269, 1947. A 200 400 800 1000 2000 4000 8000 10000 20000 B 2 4 8 10 20 40 80 100 200 MICROGRAMS/CM2 •FIGURE 21. RANGE OF ELECTRONS IN ALUMINUM AND IN AIR Dashed l i n e Schonland values S o l i d l i n e s San-Tsiang values 5< of a 1 Kev e l e c t r o n i s about 5 micrograms/cm 2 and a window of t h i s thickness should transmit 50% of 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 absorber i s a s t a t i s t i c a l process. Some w i l l l o s e more energy than the average amount, others l e s s . Fig.22, taken from the work of White and 56 ' v M i l l i n g t o n shows the spread i n energy o f an o r i g i n a l l y mono-chromatic beam of e l e c t r o n s a f t e r passing through various t h i c k -nesses o f absorbing m a t e r i a l . This spread i n energy i s o f no great importance i n the determination o f the th i c k n e s s of counter window r e q u i r e d but must be taken i n t o account i n the manu-f a c t u r e of the source and source backing. Both t h e o r e t i c a l and experimental s t u d i e s of absorption and s c a t t e r i n g i n d i c a t e t h a t there i s no easy way over the d i f f i c u l t y . A l l p o s s i b l e s c a t t e r i n g surfaces must be o f as low an atomic number as i s p o s s i b l e and care must be taken i n the design of the b a f f l e s and supports to 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 at l e a s t twice before e n t e r i n g the counter. The source backing and the counter window must be of low 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 22. LOSS OV ENERGY OF MONOENERGETIC ELECTRONS IN AN ABSORBER A Energy of i n c i d e n t e l e c t r o n s B Line 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 milligrams/era 2 o f mica absorber C L i n e p r o f i l e a f t e r 2.65 milligrams/cm 2 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 APPENDIX I I COUNTER WINDOWS A. Production of Counter Windows s The windows are produced by the method f i r s t published 57 by Backus . A few drops of a s o l u t i o n of zapon lacquer i n amy! acetate are dropped on the c l e a n s u r f a c e of d i s t i l l e d water. The s o l u t i o n spreads out over the surface o f the water and the amyl acetate evaporates l e a v i n g a t h i n f i l m of zapon on the surf a c e . This i s picked up by means of a r e c t a n g u l a r wire frame so that the f i l m f a l l s on both sides of i t making a double l a y e r . There 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 very t h i n f i l m s — a s l i g h t sidewise motion w h i l e l i f t i n g seems to help. Attempts were made to remove the human element from t h i s process by l i f t i n g the f i l m s very s l o w l y w i t h mechanical device or by h o l d i n g the wire frame underneath the f i l m and a l l o w i n g the water to run out very slowly. These attempts 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 part of zapon t o two p a r t s of 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 height o f about 1 cm. i t spreads over a c i r c l e about 30 cms. i n diameter. The f i l m can be cut i n s e c t i o n s by moving a t h i n wire r a p i d l y through i t w i t h an up and down motion. The s e c t i o n s are then picked up on the frames and hung on a rack ! to dry. I t was noted that some of the f i l m s produced had small 51. See reference No.10. 56. streaks i n them; these were e v i d e n t l y due to breaks or creases i n one l a y e r of the f i l m and appear to be due to s t r a i n s set up by the f i l m c o l l a p s i n g around the end of the frame. The number of these s t r e a k s could be reduced by extending the top of the frame i n both d i r e c t i o n s i n order to provide a support. The q u a l i t y of the f i l m s produced i s also increased by not u s i n g s o l u t i o n s more than 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 takes at l e a s t h a l f an hour to d i s s o l v e i n the amyl acetate and the process should be a s s i s t e d by a c e r t a i n amount of a g i t a t i o n . The weight of the windows was obtained by weighing a microscope s l i d e then 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 weighing again. From the area of the s l i d e , the number of f i l m s , and the d i f f e r e n c e i n weight, the number of gms/cm2 of a s i n g l e f i l m could be c a l c u l a t e d . This was checked by d e p o s i t i n g 20 drops, each of the usual s i z e , on a p r e v i o u s l y weighed g l a s s p l a t e . A f t e r the amyl acetate had evaporated another weighing determined the amount of s o l i d m a t e r i a l i n the drops. From the area of the c i r c l e which one drop formed on the surface o f the water, the average t h i c k n e s s of the f i l m c o uld be determined. The maximum d i f f e r e n c e i n weights determined by these two methods was 50%. The t h i n n e s t f i l m s that could 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 those of 5 t o 8 micrograms/cm 2. B. A t t a c h i n g of the Windows to the Counters About a dozen f i l m s of approximately the same t h i c k -ness are made and are hung on the rack to dry f o r an hour or so. f 57. A s o l u t i o n of one part v i n y l i t e r e s i n to one part o f acetone has been p r e v i o u s l y made and to one part of t h i s s o l u t i o n i s now added two p a r t s of amyl acetate. The o l d windows are s t r i p p e d o f f the counters w i t h s c o t c h tape and the surfaces cleaned w i t h amyl acetate i f necessary. About 10 m i c r o l i t e r s of the v i n y l i t e s o l u t i o n i s dropped on a surface of water and picked up w i t h a wire frame i n a s i m i l a r manner to the zapon windows. The f i l m formed i s very e l a s t i c and the frame has to be manoeuvered so that the loose ends wrap around the handle of the 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 picked up i t i s taken to the spectrometer and placed on the face of the counter. The entrance s l i t to the counter i s cleaned out w i t h a sharp corner of a p i e c e of paper. As soon as p o s s i b l e a zapon f i l m w i t h no creases i s s e l e c t e d from the rack and placed over the v i n y l i t e . When a l l ' the windows are on, the pressure i n s i d e the counters i s reduced by about 1 cm. f o r a minute or two to help cement the windows i n p l a c e . They are l e f t to dry for h a l f an hour and then checked by blowing i n to the counters while a small gas flame about 1/4 of an i n c h long i s passed i n f r o n t of the windows.. Most pinholes i n the f i l m can be r e a d i l y detected by the d e f l e c t i o n o f the gas flame. 58. APPENDIX I I I PREPARATION OF SOURCES The source holder i s made from a piece of 3/16 i n c h l u c i t e 2 inches square. A r e c t a n g u l a r s l o t 2 cms. long by . 0 5 cms. wide i s m i l l e d through the l u c i t e w i t h the back cut away at an angle of 4 5 ° , l e a v i n g a narrow edge around the s l o t . A hole i s d r i l l e d i n the l u c i t e f o r mounting on the base p l a t e of the spectrometer and a l i n e s c r i b e d abross the middle of the s l o t to i n d i c a t e the p o s i t i o n o f the source. 58 The source backings are made of L C 6 0 0 r e s i n i n a s i m i l a r manner t o the zapon windows. At f i r s t the 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 but i t was found out that t h i n n e r and more uniform f i l m s c ould be made i f i t was d i s s o l v e d i n amyl acetate. The f i l m i s picked up on a frame made of 1/16 i n c h l u c i t e and l a i d on the source holder w h i l e s t i l l wet. 58 A s o l u t i o n of one pa r t of z i n c i n s u l i n ^ to eight parts of d i s t i l l e d water i s made and about 1/4 of a micro l i t e r deposited w i t h a p i p e t t e at each end of the f i l m i n l i n e w i t h the mark on the holder. The p i p e t t e i s made from a . 2 5 mm c a p i l l a r y t u b i ng w i t h the end p u l l e d down to about 1 mm outside diameter and the hole to 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 the end wiped clean w i t h a paper towel. C a r e f u l blowing i n t o the p i p e t t e makes the l i q u i d bulge out of the end of the c a p i l l a r y without forming a drop. This i s touched to the f i l m and leaves a spot somewhat l e s s than 1 mm. i n diameter. 5 8 . L.M. Langer, R.S.I., 2 0 , 2 1 6 , 1 9 4 9 . The source holder i s now placed on a f l a t surface w i t h one edge along a r u l e r . A r e f i l l from, a b a l l point pen ( i n k removed) i s lowered very s l o w l y by means of a j i g u n t i l the point j u s t touched one of the drops of i n s u l i n s o l u t i o n . The holder i s moved back and f o r t h along the r u l e r u n t i l a l i n e of i n s u l i n i s formed. I f a l i n e does not form the pen i s lowered a small amount and the process repeated u n t i l a l i n e forms or the 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 can be drawn every time without breaking the f i l m . When the source backing 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 the form o f a water o r weak a c i d s o l u t i o n (concentrated h y d r o c h l o r i c a c i d does not appear t o harm the LC600 f i l m s but concentrated n i t r i c a c i d w i l l burn holes i n them i n about 10 minutes ti m e ) . The r a d i o - a c t i v e s o l u t i o n i s deposited w i t h a s i m i l a r p i p e t t e to the one used f o r i n s u l i n . This p i p e t t e i s connected by rubber t u b i n g to 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 of rubber t u b i n g connects the b o t t l e to a mouthpiece which i s fastened to a wire frame and hung on a hook so that i t i s never l a i d on the bench or touched w i t h the hands. The a c t i v e s o l u t i o n i s deposited on the source backing i n the same f a s h i o n as the i n s u l i n . When very s m a l l drops of about 1/4 m i c r o l i t e r are placed on the backing the s o l u t i o n covers the area coated w i t h i n s u l i n but does not spread onto the remainder of the f i l m . The sources made were about 1.5 cms l o n g by 0 .1 cms wide. The source i s slo w l y d r i e d under an i n f r a red lamp. The a p p l i c a t i o n of too much heat causes the backing to w r i n k l e and the holder to warp. 60. Two methods of grounding the source were used. The f i r s t was to put drops of aquadag on the hol d e r and le a d i t along w i t h a f i n e pointed brush u n t i l i t touched the end of the i n s u l i n l i n e on the backing. The aquadag then ran along the l i n e of 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 t h a t t h i s method i s r e l i a b l e , some sources checked gave a r e s i s t a n c e of about 1000 megohms between ends while others gave no detectable conduction. The second method of grounding the source i s to evaporate a t h i n l a y e r of aluminum onto i t . Aluminum l a y e r s were made which were about 90% transparent and had a r e s i s t a n c e of 10,000 ohms over a d i s t a n c e of one i n c h provided a l a r g e area of contact was used. Attempts were made to weigh these aluminum f i l m s but a l l that could be determined was t h a t they were l e s s than 5 micrograms/cm . This thickness checks w i t h the values 59 given i n Strong. The aluminum i s evaporated from a filament made of three .015 i n c h tungsten w i r e s . Two of the wires are t w i s t e d together w i t h about 1 t u r n per centimeter and the t h i r d t w i s t e d around the other two w i t h about f i v e t urns per centimeter. About 10 mil l i g r a m s of al.uminum i s hung on the filament i n the form of s t r i p s and pre-heated i n a vacuum to i n s u r e contact. An attempt was made to do t h i s preheating i n i l l u m i n a t i n g gas but t h i s proved unsuccessful. Two small areas about 1/2 i n c h apart on a l u c i t e p l a t e were painte d w i t h aquadag and these areas connected to an ohmmeter 59* J . Strong. Procedures i n Experimental P h y s i c s . p . l 8 6 . outside the vacuum system. The l u c i t e p l a t e i s placed near the source holder and as evaporation proceeds the r e s i s t a n c e of 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 thickness w i t h quite r e -produceable r e s u l t s . A great deal of t r o u b l e was encountered w h i l e evaporating aluminum onto very t h i n f i l m s . This was minimized 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 the f i l a m e n t heated up and evaporation s t a r t e d . The b a f f l e was then moved, by means o f a magnet held-o u t s i d e the vacuum system. I t was also very necessary to l e t the a i r i n very s l o w l y and to handle the ho l d e r w i t h the utmost care. 62. ' APPENDIX IV THE COUNTER FILLING SYSTEM The counters at 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 the usual mixture. However, the c h a r a c t e r i s t i c s of the counters changed r a p i d l y and t h i s was found to be the r e s u l t of the pressure changing due to gas slowly d i f f u s i n g through the zapon windows. An attempt was made to keep the pressure reasonably constant by means o f b a l l a s t fLask but t h i s was unsuccessful besides being uneconomical. An obvious method of keeping the pressure i n the counters constant i s to use the sat u r a t e d vapor of a l i q u i d h e l d at a constant temperature f o r a f i l l i n g . Using t h i s method the temperature of the l i q u i d has to be lower than room temperature s i n c e otherwise the l i q u i d would be d i s t i l l e d to other p a r t s o f the apparatus. The constant temperature that can be a t t a i n e d most conveniently i s t h a t of me l t i n g i c e . A search was made f o r l i q u i d s whose vapor pressure at 0°C was 1 to 5 cms of mercury. The f i r s t vapor t r i e d as a counter f i l l i n g gas was that of pure e t h y l a l c o h o l at 1.2 cms pressure. This d i d not.give any pl a t e a u and the counting r a t e s were very u n r e l i a b l e . A number of other vapors such as methyl a l c o h o l , benzene, and acetone were t r i e d without success. I n view of Farmer and Brown's^ 0 experiments w i t h methane i t was decided that hydro carbon compounds o f f e r e d the best chance of success. Heptane (C7H16) has a vapor pressure of 1.15 cms at 0°C and a counter f i l l e d w i t h i t s vapor gave a short but u s e f u l p l a t e a u shown i n Fig. 2 3 . I t s e f f i c i e n c y f o r gammas and 60. E.C. Farmer and S.C. Brown: Phys.Rev., 74,902.1948. 600 1—400 >h-200 1200 12^0 1300 1550 VOLTAGE FIGURE 23 . PLATEAU EXHIBITED BY ONE COUNTER FILLED WITH 1.15 CMS OF HEPTANE VAPOR 63. f o r high energy betas was the same as w i t h an a l c o h o l and argon f i l l i n g . The counter 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 r e g i o n . I t s t a r t e d counting w i t h about 8007 on the anode g i v i n g very s m a l l pulses, l e s s than .01V. As the v o l t a g e on the counters was increased the maximum pulses increased i n s i z e but were accompanied by l a r g e numbers o f sm a l l e r pulses. At a counter v o l t a g e o f about 1250 v o l t s the pulses were o f a uniform s i z e , about three or four v o l t s peak amplitude w i t h a r i s e time l e s s than one microsecond and a l e n g t h of about 50 microseconds. The Geiger r e g i o n s t a r t e d here and extends to almost 1350 v o l t s . The best plateaus obtained were w i t h . 0 0 5 i n c h tungsten w i r e as anode. The counters i n the spectrometer were then 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 Fig.24 was almost f i l l e d w i t h heptane and then connected to the vacuum system. About 1/10 o f the l i q u i d i n A was c a r e f u l l y pumped away. I t was then cooled to dry i c e temperatures by means of an external bath i and evacuation continued f o r about h a l f an hour. At t h i s point (the stopcock was cl o s e d , i s o l a t i n g f l a s k s A and B from the vacuum I system and the c o l d bath moved to f l a s k B. The heptane vapor e v o l v i n g from the l i q u i d i n A passed through a d r y i n g agent and condensed i n f l a s k B. When about 1/10 of the heptane remained i n A the process was stopped. F l a s k B was then surrounded by a bath of m e l t i n g i c e and connected to the counters. The counters were checked i n -d i v i d u a l l y and as one of them was u n r e l i a b l e , the other:'three were used i n p a r a l l e l ; a plateau i s shown i n Figure 2 5 . To counters and vacuum system F l a s k B F l a s k A FIGURE 24. 'HEPTANE PURIFICATION SYSTEM (The heptane remains i n F l a s k B, and i n opera t i o n i s surrounded by a bath of me l t i n g i c e . ) 1150 1200 12^0 1500 VOLTAGE FIGURE 25. PLATEAU EXHIBITED BY THREE COUNTERS IN PARALLEL 64. The counters worked very w e l l at f i r s t but the plateau grew worse a f t e r a few months o f use. I n t e r m i t t e n t discharges gave o c c a s i o n a l bursts o f 50 to 100 counts i n a second or two before the counters recovered. This appeared to happen most o f t e n i n the l a s t JO seconds of a ten minute count. An attempt was made to improve the performance of the counters by the use of e x t e r n a l "quenching c i r c u i t s . A number of these c i r c u i t s were t r i e d , some w i t h quenching pulses of 200 7 amplitude and 400 microseconds d u r a t i o n , without the l e a s t success. The use of e x t e r n a l quenching was abandoned and i t was found that r e p l a c i n g the anode of the counters and thoroughly c l e a n i n g the cathodes w i t h benzene and absolute a l c o h o l r e s t o r e d them to t h e i r o r i g i n a l c o n d i t i o n . APPENDIX 7 AUXILIARY ELECTRONIC APPARATUS A. Current Regulating System, In order to observe a beta or gamma spectrum w i t h the spectrometer i t i s e s s e n t i a l t h a t the magnetic f i e l d should not change of i t s e l f d u r i n g the course of a s i n g l e reading, and to r e a l i z e the advantages of b u i l d i n g the instrument without i r o n , means must be provided to set 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 , at any d e s i r e d value. Since the r e s o l u t i o n of the instrument i s of the .order of 1%, the magnetic f i e l d should be regulated to at l e a s t one part i n a thousand and the c a l i b r a t i o n should be b e t t e r than 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 forward, the cu r r e n t through the magnet also passes through a 'standard i r e s i s t o r 1 of about 0.1 ohms, made of 10 fe e t of 1 i n . manganin s t r i p . This r e s i s t o r can carry the l a r g e s t currents used w i t h a temperature i n c r e a s e of l e s s than 1°C, consequently i t s r e s i s t a n c e w i l l stay constant to' almost 1 i n 10-^. The vol t a g e developed across the standard r e s i s t a n c e i s compared to a v o l t -age determined by the s e t t i n g of a Student's Potentiometer and the d i f f e r e n c e a m p l i f i e d 100 db. by a two channel a m p l i f i e r . One channel a m p l i f i e s the frequency range ofO-10 c y c l e s per second, the other 5-1000 c y c l e s per second. The two s i g n a l s are r e -uni t e d at the g r i d of a 6L6 which i n t u r n d r i v e s the g r i d s of a bank of eig h t 6AS7's i n s e r i e s w i t h the magnet and the standard r e s i s t o r . At low f i e l d s the 6AS7's c a r r y the f u l l magnet current but f o r higher s e t t i n g s they must be shunted by e x t e r n a l r e s i s t o r s . These r e s i s t o r s were c a l c u l a t e d on the basis that' the power d i s s i p a t i o n i n the r e g u l a t o r tubes should not exceed t h e i r r a t e d capacity of 168 watts. A s e r i e s r e s i s t o r was also i n c l u d e d i n the c i r c u i t so t h a t low currents could be drawn s a f e l y from the 2J?0 watt D.C. mains. I f a current of l e s s than 4 amperes i s conducted through the tubes from a supply of more than 150 v o l t s , serious damage w i l l c e r t a i n l y r e s u l t . The c a l i b r a t i o n of the potentiometer i s checked p e r i o d -i c a l l y by comparison w i t h a standard c e l l . The magnet current i s broken by throwing the main sw i t c h , the galvanometer sen-s i t i v i t y s w i t c h turned past 2 megohms to open the c i r c u i t and the 'voltage check' s w i t c h depressed. The potentiometer i s adjusted to the vo l t a g e of the standard c e l l and the s e n s i t i v i t y o f the galvanometer increased. The galvanometer i s brought back to zero by manipulating the 'voltage a d j u s t ' c o n t r o l s . A block diagram of the r e g u l a t i n g system i s shown i n Fig.2 6 and a c i r c u i t diagram i n Fig. 2 7 . The potentiometer output v o l t a g e can be made to 4 agree w i t h the s e t t i n g t o j? p a r t s i n 10 and the volt a g e across the standard r e s i s t o r i s h e l d equal to t h i s w i t h i n one part 4 i n 10 . Any d e v i a t i o n s o f low frequency can be observed by the a c t i o n of the amplifier'meters or by the galvanometer. During .the o r i g i n a l adjustment o f the system a measurement was made of the amount of h i g h frequency (greater than J>0 c y c l e s per second) A.C. passing through the c o i l . I t was • found t o be about 1 m.a. over the range of D.C. currents and C a l i b r a t i o n Galvanometer C a l i b r a t i o n B a t t e r y AC A m p l i f i e r 6L6 D r i v e r DC A m p l i f i e r Student Potentiometer Standard C e l l 'FIGURE 26 . BLOCK DIAGRAM OF CURRENT REGULATING SYSTEM FIGURE 27 . CIRCUIT DIAGRAM OF CURRENT REGULATING SYSTEM 67. COMPONENTS Off FIGURE 27 Tubes VI 8-6AS7's i n p a r a l l e l V2 6SJ7 V3 6SJ7 V4 6V6 V5 6H6 V10 VR105 V6 1N34 VI1 VR130 V7 6SJ7 VI2 3T3G V8 6SJ7 VI3 6L6 V9 SY3G Meters Ml 100 microamperes f u l l s c a l e . Mg 1 m i l l i a m p e r e , center reading. Mj5 150 microamperes f u l l s c a l e . Trans formers and Chokes T i Hammond 276 T3 Hammond 337 To " 270 T 4 11 51 Chj and Ch 2 Hammond 10-100x R e s i s t o r s ( A l l 1/2 watt unless otherwise stated) R l St.r.about O.lohm R18 1 . 5 M ohms R35 3 K ohms R2 1000 ohms R19 3 K n R36 500 K n R3 12.8 " 1200 w. R20 2 M 11 R37 1 M 11 R4 30.1 ? 230 w. R21 500 K 11 R38 2 M a R5 3 0 . 3 ? 210 w. R22 500 K a" R39 150 K a R$ 40.4 » 200 w. R23 250 ? 2 w. R40 2 . 5 K 11 R7 50 . 7 " 200 w. R24 5 K "10 w. R41 1 K »» 2 w. R8 8.0 " 200 w. R25 5 K •?10 w. R42 30 K u R9 11 . 5 11 190 w. R26 150 K IJ R43 40 K 11 RIO 30 K » R27 50 K tt R44 30 K tt R l l 20 K » R28 50 K u R45 40 K 11 R12 30 K » R29 100 K 11 R46 100 K 9 1 w. R13 20 K » R30 100 K 11 R47 10 K 'ao w. R14 1 M 9 R31 25 K 11 R48 18 K 9 5 w. R15 3 K « R32 50 K 11 R49 7.5 K ? 2 w. R16 2 M » R33 5 K 11 R50 2 M 11 R17 500 K 9 R34 2 M 11 R51 100 ohm-pot. R52 100 K ohm pot. Condensers Gl 0.1 mf 400 v. C12 16 mf 450 v. C2 .005 mf 500 V. C13 16 mf 450 v. C3 0.1 mf 500 V. C14 1.0 mf 500 v. G4 0.1 mf 500 V. C15 1.0 mf 500 v. C5 .005 mf 500 V. CI 6 0.1 mf 500 V. C6 .006 mf 500 V. C17 30 mf 450 V. C7 0.1 mf 500 V. 018 30 mf 450 V. C8 100 mf 50 V. C19 30 mf 450 V. C9 16 mf 450 V. C20 30 mf 450 V. CIO 1.0 mf 500 V. 021 30 mf 450 V. C l l 2.0 mf 500 V. C22 1.0 mf 400 V. C23 1.0 mf 400 V. 68. thus i s only 0.1% i n the worst oase. B. H.T. Regulation. Since the plateau i n the counting r a t e curve of Hep-tane f i l l e d counters had considerable slope i t was necessary to provide a very stable high voltage supply. Fig.28 i s a c i r c u i t diagram 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 of the a m p l i f i e r tube (72) i s taken from the r e g u l a t e d side o f 71 i n s t e a d o f the unregulated s i d e . This 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 ed i n t o the g r i d of the a m p l i f i e r tube i s taken p a r t l y from the imput voltage and p a r t l y from the output. By a d j u s t -ment of Rl8 and R19 the c i r c u i t can be made to under-compensate, over-compensate or re g u l a t e p e r f e c t l y . R17 c o n t r o l s the screen v o l t a g e of 72 and thus the g r i d bias on 71. The adjustment was made i n i t i a l l y by feeding 6.3 v o l t s A.C. i n s e r i e s w i t h R l and R2. The c o n t r o l s were se t f o r a r i p p l e i n the output of 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 observable r i p p l e i n the output. The output voltage d r i f t e d about 3 v o l t s per hour f o r 4 hours a f t e r the supply was turned on, a f t e r t h i s any changes were of the order of 1 v o l t . C. Pulse A m p l i f i e r and S c a l a r . A c i r c u i t of the pulse a m p l i f i e r i s shown i n Fig.29. The output of t h i s c i r c u i t was fed i n t o an Atomic Instrument Company s c a l e o f 64 s c a l a r . + A/ • Rl 2500 V 1 6 5 0 7 FIGURE 28. H. T. REGULATING CIRCUIT L i s t of Components 71 — 6 J 5 R l , R2 — 100 K ohm R3-R13 — 500 K ohm R14-R16 - 1 M ohm A l l r e s i s t o r s 2 watts 01, C2 1 i f 3000 v o l t s C3 .01 mf 3000 v o l t s 72 — 6SJ7 R17 — 500 K ohm Rl8 — 100 K pot. R19 — 500 K pot. R20 — 500 K pot. B l 90 v o l t b a t t e r y B2 300 v o l t b a t t e r y -vwv Rio CC n « 7 < C8 > C? FIGURE 29. CIRCUIT DIAGRAM OF PULSE AMPLIFIER R l 1 M ohm R6 50 K ohm R l l 1 K ohm R2 50 ohm R7 200 ohm R12 1 K ohm R3 330 K ohm R8 5 K ohm R13 100 K ohm R4 10 K ohm R9 60 K ohm R14 200 ohm R5 50 K ohm RIO 10 K ohm R15 60 K ohm A l l r e s i s t r o s 1/2 watt 71 6J6 72 6AK5 73 6AC7 CI .001 mf 25007 C4 . 1 mf 4007 °2 .001 mf 4007 02 .002 mf 4007 C5 .01 mf 4007 C8 . 1 mf 4007 C3 .0001 mf 4007 C6 .0001 mf 4007 C9 .001 mf 4007 BIBLIOGRAPHY H.A. Bethe, Elementary Nuclear Theory, John Wiley & Sons, Inc. New York, 1947, A.H. Compton & S.K. A l l i s o n , X-Rays i n Theory and Experiment. D. Van Nostrand Co., Inc., New York, Second ed. 1935. E. Fermi, Nuclear P h y s i o s , The U n i v e r s i t y of Chicago Press, Revised 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 C o l l i s i o n s , Oxford at the Clarendon Press, 1933. F. R a s e t t i , Elements of Nuclear Physios, P r e n t i c e - H a l l , Inc. New York, 1936. F.Z. Richtmeyer & E.H. Kennard, I n t r o d u c t i o n to Modern  P h y s i c s , 3rd E d i t i o n , 1942. S i r E. Rutherford, 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 Substances, Cambridge a t the U n i v e r s i t y P r e s s , 1930, John Strong, Procedures i n Experimental P h y s i c s , P r e n t i c e - H a l l , Inc., New York, 1938. V.K. Zworykin, et a l , E l e c t r o n Optics and the E l e c t r o n Micro- scope, John Wiley & Sons, Inc., New York, 1945. 

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