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Axial alignment in a ring-collection beta-ray spectrometer 1960

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AXIAL ALIGNMENT IN A RING-COLLECTION BETA-RAY SPECTROMETER by ERIC DAVIS EARLE .Sc., Memorial University of Newfoundland, 19 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1960 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the 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 , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d . w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada. ABSTRACT A thin-leas beta-ray spectrometer using ring-focus c o l l e c t i o n was modified. These modifications consisted of; 1) a centering mechanism enabling the source-detector axis to be aligned with the magnetic axis; 2) an extension of the vacuum chamber placing the detector further from the magnet c o i l s . The l a t t e r considerably decreased the magnetic s h i e l d - ing requirements for the detector. A misalignment of 0.25 mm. fox- p a r a l l e l axes and of 0°09' for int e r s e c t i n g axes produced noticeably poorer performance. Using a gathering power of .70%, a resolving power of .94% was obtained for the 661.6 Kev. K-conversion peak of Cs . i i i i TABLE OF CONTENTS PAGE INTRODUCTION A. Nuclear Spectroscopy 1 B. Basic Ideas on Beta- and Gamma-Decay 3 C. Early Spectrometers and t h e i r C h a r a c t e r i s t i c s 13 II THE DEVELOPMENT OF THE THIN-LENS SPECTROMETER 21 I I I PRESENT INVESTIGATION A. Instrumentation 27 B. Experimental Tests 34 C. Conclusions 41 BIBLIOGRAPHY 45 i v TABLE OF ILLUSTRATIONS Figure Following Page lb') T y P i c a l Decay Schemes 4 2. Typical Beta-Ray Spectrum 4 3. H e l i c a l Spectrometer Electron T r a j e c t o r i e s 16 4. Unmodified Thin-Lens Spectrometer 16 5. Detector Assembly of Mann and Payne 22 6. Modified Thin-Lens Spectrometer 23 7. Spectrometer Assembly 27 8. The Source Assembly 27 9. The Detector Assembly 28 10. Sample Entrance B a f f l e 30 11. Chamber Support 31 12. V a r i a t i o n of Peak Shape with Chamber Positi o n 38 13. Some Sample Conversion Peaks 40 V ACKNOWLEDGEMENTS The work described i n t h i s thesis was supported by a Fund-in-Aid-of-Research to Dr. K.C. Mann by the National Research Council of Canada. The author wishes to thank Dr. K.C. Mann for h i s able guidance and assistance throughout the course of t h i s work. Also the author thanks the National Research Council of Canada for awarding him a Bursary and Studentship for the period June 1958 to August 1960. He wishes to express h i s appreciation to H.R. Schneider and F.A. Payne f o r he l p f u l suggestions and c r i t i c i s m s and to F.J. Morgan f o r his assistance i n the experimental work. I. INTRODUCTION A. NUCLEAR SPECTROSCOPY It has been experimentally evident f o r some time that matter i s composed of atoms. These atoms are minute p a r t i c l e s and consist of a combination of a number of other, more funda- mental p a r t i c l e s . The number and arrangement of these funda- mental p a r t i c l e s determine the properties of any p a r t i c u l a r atom and, generally, make i t distinguishable from other atoms with a d i f f e r e n t number and/or arrangement of fundamental p a r t i c l e s . B a s i c a l l y , atoms consist of a heavy, p o s i t i v e l y charged core, c a l l e d the nucleus, around which negatively charged p a r t i c l e s , c a l l e d electrons, " o r b i t " . Nuclear physics i s the study of the c h a r a c t e r i s t i c s of the nucleus. The purpose of nuclear spectroscopy i s to e s t a b l i s h some of these c h a r a c t e r i s t i c s . To a f i r s t approximation, the nucleus i s composed of two kinds of p a r t i c l e s c a l l e d nucleons, a p o s i t i v e l y charged p a r t i c l e c a l l e d the proton and a neutral p a r t i c l e , the neutron. The number of protons, Z, the number of neutrons, N, t h e i r motions and interactions determine the nuclear c h a r a c t e r i s t i c s . Nuclei may be stable or unstable. The unstable ones are termed radioactive and decay to states of lower energy usually through the emission of r a d i a t i o n of some kind. A p a r t i c u l a r nucleus may exi s t i n any one of several nucleonic configurations, l -2- each with i t s c h a r a c t e r i s t i c energy. The lowest energy l e v e l i s c a l l e d the ground state and any nucleus i n a higher energy state may decay to t h i s ground state by the emission of energy i n the form of electromagnetic r a d i a t i o n (photons or gamma- rays). A radioactive nucleus may also decay by p a r t i c l e emission, where energy i s removed k i n e t i c a l l y . Generally, during p a r t i c l e emission, the number of neutrons or the number of protons i n the o r i g i n a l or parent nucleus changes, thereby producing a new or daughter nucleus. In the low energy region the predominant modes of radioactive decay are gamma-ray emission and beta-particle emission. The beta-particles may be negatively charged (the negatron, experimentally i d e n t i c a l with the atomic e l e c t r o n 1 ) or p o s i t i v e l y charged (the positron). The function of the nuclear spectrometer i s to study the energy of the beta-particles and gamma-rays emitted during radioactive decay i n the low energy region and to use the ex- perimental data obtained to give information concerning the angular momentum (spin), the energy l e v e l s and the p a r i t y * of the nuclear states involved i n the decay. I t i s hoped that t h i s data with data c o l l e c t e d i n other branches of nuclear physics w i l l enable p h y s i c i s t s to construct a theory capable of explaining and predicting nuclear phenomena. * P a r i t y arises from the wave mechanical considerations of the r e f l e c t i o n properties of the s p a c i a l part of solutions of the wave equation. -3- B. BASIC IDEAS ON BETA- AND GAMMA-DECAY A b r i e f summary of present nuclear theory, i n p a r t i c u l a r beta-decay and " i n t e r n a l conversion" theory, consistent with the experimental evidence c o l l e c t e d to date i s given below. The types of decay of p a r t i c u l a r i n t e r e s t are: 1) Beta-particle decay; an unstable nucleus emits a negatron or positron. The parent nucleus containing Z protons and N neutrons decays to a daughter nucleus containing Z + 1 protons and N "f 1 neutrons. The nucleus may also reach a lower energy state by the capture of an o r b i t a l electron, leading to the formation of the same nucleus as i s reached by positron decay. This i s c a l l e d o r b i t a l electron capture. 2) Gamma-ray emission; an unstable or excited nucleus spontaneously emits electromagnetic r a d i a t i o n and drops to a lower energy state of the same nucleus. The energy (hV) of the gamma-ray equals the energy difference of the states involved. (h - Plank's universal constant. V - the frequency of the emitted gamma-ray.) The lower energy state may or may not be the ground state of the nucleus. In the event that i t i s not, subsequent decays w i l l occur u n t i l t h i s state i s reached. An alternative method of de-excitation may occur when the e x c i t a t i o n energy i s transferred to an o r b i t a l electron. The o r b i t a l electron escapes from the atom with an energy equal to hy - E b where i s the binding energy of the atomic electron to the nucleus. This l a s t mode of decay i s c a l l e d -4- "Internal Conversion". In general, a decay scheme consists of a combination of these modes of decay and often may be quite complex. Two decay schemes are shown in Figure 1. Here and ft<£ represent beta-particle emission and y represents electromagnetic r a d i - ation which may or may not be accompanied by i n t e r n a l con- version. Beta-decay. Nuclei with the same mass number, i.e. A = N + Z, are c a l l e d isobars. Members of an is o b a r i c group d i f f e r i n Z (and N) and i n th e i r actual nuclear masses. A l l beta-decays occur between members of the same isob a r i c group; i n negatron emission the nuclear charge i s increased by one p o s i t i v e unit; i n positron emission or o r b i t a l electron capture the nuclear charge i s decreased by one p o s i t i v e unit. To decide i f some mode of p a r t i c l e decay i s e n e r g e t i c a l l y possible one must consider the masses of parent, daughter and emitted p a r t i c l e . Let "a" represent a parent nucleus, "b" and "c" represent the product of i t s decay. Then decay w i l l occur only i f M(a) > M(b) + M(c) where M(x) represents the nuclear mass of the x p a r t i c l e . The excess mass m = M(a) - 13(b) - M(c) i s accounted f o r by the extra k i n e t i c energy of the two product 2 p a r t i c l e s , using Einstein's energy equation E = m c . Considering the atomic mass M a^,(Z, A) as d i s t i n c t from the nuclear mass M(Z, A) we see that the above types of decay are energ e t i c a l l y possible i f : P A R E N T DAUGHTER Z p r o t o n s Z f l p r o t o n s PARENT DAUGHTER N n e u t r o n s N - l n e u t r o n s Figs, l a & lb. Typical Decay Schemes c _ =» O k. > Momentum F i g . 2. Typical Beta-Ray Spectrum -5- > M A T (Z -h 1, A) f o r negatron decay > M a t . ( Z - 1, A) + 2 MQ for positron decay > M A T > ( Z - 1, A) for o r b i t a l electron capture where M Q i s the rest mass of the electron. O r b i t a l electron capture produces the same daughter nucleus as positron emission. It usually occurs i n decays where positron emission i s present and, because the mass re- quirements are not so severe, i t sometimes occurs where positron emission i s impossible. For any group of is o b a r i c nuclei the higher mass members always tend to decay to those of lower mass. For iso b a r i c groups of odd A there e x i s t s only one stable member which i s the end product to which a l l other is o b a r i c members decay. However, for even A nuclei there may exis t two or more stable nuclei i n the same iso b a r i c group. This i s because the mass of even Z, even N nuclei i s often less than the mass of either of i t s two odd-odd neighbours and so, i f a lower mass state e x i s t s , the even-even nuclei can only reach i t by double beta- decay. Ingrahm and Reynolds showed that the half l i f e period for double beta-decay of T e 1 3 0 i s 1.2 x 1 0 2 1 years, so that i f t h i s process occurs, i t i s very infrequent. The decay scheme (Fig. 1) suggests that the beta-particles are emitted with discrete energies. One would expect, i f number of beta-particles emitted per unit time were plotted H A T . ( Z , A) M A T . ( Z , A) M a t (Z, A) -6- as a function of energy (oz* momentum), that only at ce r t a i n energies would beta-particles be observed and these would correspond to the energy differences between the i n i t i a l and f i n a l states. Such i s not the case, however. Experimental evidence shows that the beta-energy spectrum i s a continuous d i s t r i b u t i o n , up to some end point energy (referred to as E m a x ). Frequently, spectral " l i n e s " or peaks (Fig. 2) are superimposed on the continuum. These peaks are due to the inte r n a l conversion electrons. The continuous energy d i s - t r i b u t i o n , on the other hand, poses a dilemma, not e a s i l y resolved i f one accepts the assumption that nuclear energy states are fi x e d , since f i x e d energy states would suggest a " l i n e " structure for the primary beta-decay as well. The law of conservation of energy appears to be viola t e d . From a consideration of the angular momenta involved i n the decay, i . e . the spins of the i n i t i a l and f i n a l states and of the electron, i t appears that the law of conservation of angular momentum i s also violated. F i n a l l y , i t may be shown that " s t a t i s t i c s " are not conserved i f only the beta- p a r t i c l e i s involved in the decay. These three d i f f i c u l t i e s , i . e . the energy continuum, angular momentum and s t a t i s t i c s , may a l l be overcome i f one accepts Pauli's suggestion that the beta-decay process i n - volves the simultaneous emission of two p a r t i c l e s — the electron and the neutrino. The neutrino i s postulated to be a new fundamental p a r t i c l e with no charge, very small mass -7- (probably zero), spin equal to ^ f t and which obeys Fermi- Dirac s t a t i s t i c s . The existence of the neutrino now seems to be confirmed, experimentally. In t h i s concept the energy of the decay i s shared between the two p a r t i c l e s . According to the theory of the process worked out by Fermi, the beta-particle's energy d i s t r i b u t i o n may be expressed by P(E)dE a F ( Z , E ) p 2 ( E m a x - E) 2dE (1) where P(E)dE i s the f r a c t i o n of disintegrations which emit beta-particles with energy between E and E + dE Ejjjĝ jj. i s the maximum energy observed in the spectrum E i s the energy of the beta-particle p i s the momentum of the be t a - p a r t i c l e F(Z,E) i s a complicated function which describes the e f f e c t of the Coulomb f i e l d of the nucleus on the emitted beta-particles. From Equation (1) we see that /£iPJ. a ( E ^ ^ - E) where P 2 F N(p) i s the number of beta-particles emitted with momentum p. Hence, i f we plot / a s a function of E we get a straight V P 2F l i n e i n t e r s e c t i n g the energy axis at E^,,. This i s c a l l e d a Fermi p l o t . If other independent beta-groups are present i n the spectrum then the end point energies of these groups may j be obtained by subtracting successive contributions from the -8- composite Fermi plot. Equation (1) i s based on the assumption that the spin change ( A I) i s _fl,0 and that there i s no pa r i t y change. This i s the most probable mode of beta-decay and i s c a l l e d an "allowed" t r a n s i t i o n . A l l other t r a n s i t i o n s are c a l l e d "forbidden", the degree ox forbiddenness depending on the value of A I and the presence or absence of p a r i t y change. Equation (1) gives a straight l i n e plot only during allowed t r a n s i t i o n s . For forbidden t r a n s i t i o n s , involving higher spin changes and possible p a r i t y changes, the "constant" i n equation (1) becomes energy dependent and so gives a non-linear Fermi plot. Certain correction terms have been worked out and by applying these, i t i s possible to determine the degree of forbiddenness of the decay i n question. If P(E)dE represents the p r o b a b i l i t y of beta-emission i n the energy i n t e r v a l (E,E dE) then the pr o b a b i l i t y , A , that the nucleus w i l l decay by the emission of an electron i n a pa r t i c u l a r beta group i s ; This A may be said to equal af where "a" i s a constant and " f " i s some function of Z and E. This t o t a l decay proba. b i l i t y , A , has dimensions disintegrations/time. Hence 1/^ i s the mean l i f e ( T ) of the excited p a r t i c l e . It can be shown that the mean l i f e , f , a n d the half l i f e , T i , are re- o -9- lated by ! ^ T i 1 1 r- —- = _ = — . In 2 \ af The quantity f T ^ i s c a l l e d the comparative h a l f - l i f e of the t r a n s i t i o n . The logarithm of £T| has been found convenient to work with i n the comparison of beta-decay groups and i s a useful way of in d i c a t i n g the degree of forbiddenness and hence spin and p a r i t y changes of the decay. , Gamma-decay. As has been stated, a nucleus i n an excited state may decay spontaneously to a lower state of the same nucleus by the emission of a gamma-ray. The energy of t h i s gamma-ray i s given by: where Eg, E^ are the energies of the upper and lower energy states. The nucleus may also decay to t h i s lower energy state by giving t h i s energy to an electron i n the K,L, -shell of the same atom. The electron i s then ejected with energy hV - Eg, hV - Ej^, ... where Ej*, E^, ... are the binding energies of the o r b i t a l electrons. This l a s t de-excitation process i s c a l l e d i n t e r n a l con- version and the ejected electrons, conversion electrons. -10- These conversion electrons are emitted at discrete energies and w i l l appear i n a beta-energy spectrum as sharp peaks or conversion l i n e s (Fig. 2). Those electrons i n the innermost s h e l l w i l l have the greatest interaction p r o b a b i l i t y with the nucleus. Thus the Reconversion l i n e , usually, w i l l be more intense than the L l i n e , and so on. The t o t a l p r o b a b i l i t y , A, that an excited nucleus w i l l decay depends on the p r o b a b i l i t y of gamma-emission, Ay, and the p r o b a b i l i t y of int e r n a l conversion, A e . The p r o b a b i l i t y of i n t e r n a l conversion may be broken down into p r o b a b i l i t i e s of K conversion, L conversion, etc. Thus * = \ + *e " \ + *K + A L + • ' * The r a t i o of the number of decays by i n t e r n a l conversion to the number of decays by gamma-emission i s c a l l e d the con- version c o e f f i c i e n t and i s given by A e AK A L T 7 7 where a^, a^, ... are K, L, ... conversion c o e f f i c i e n t s . To determine these c o e f f i c i e n t s experimentally, i t i s necessary to compare the r e l a t i v e i n t e n s i t i e s of the d i f f e r e n t modes of decay. i While the i n t e n s i t y of i n t e r n a l l y converted gamma-rays can be measured by the use of a beta-ray spectrometer, the i n t e n s i t y of gamma-rays cannot be measured d i r e c t l y . However, i f the gamma-rays are allowed to s t r i k e a f o i l , of high Z material, placed near the source, they w i l l undergo a process c a l l e d external conversion or a photoelectric process. In t h i s process the energy of the gamma-ray i s transferred to an o r b i t a l electron in the f o i l (or target) and the electron i s then ejected with an energy equal to that of the gamma-ray less the binding energy of the o r b i t a l electron. Electrons ejected i n t h i s manner are c a l l e d photo-electrons and may be analysed i n the spectrometer. The f o i l , as a source of photo- electrons, becomes the source as seen by the spectrometer. One might thus expect that a comparison of i n t e n s i t y measurements on i n t e r n a l l y and externally converted electrons would give s u f f i c i e n t information to determine experimentally the conversion c o e f f i c i e n t s . As theory predicts that these c o e f f i c i e n t s are functions of cer t a i n nuclear c h a r a c t e r i s t i c s , the experimental evaluation of these c o e f f i c i e n t s would give valuable information on the spins and p a r i t i e s of the nuclear energy states. Unfortunately, because of the lack of detailed knowledge of the photo-electric cross-section of the target i n the low energy region where the i n t e r n a l conversion process pre- dominates and because of the v a r i a t i o n of the angle of emission of the photo-electrons with energy, one cannot use the external conversion spectrum for r e l i a b l e comparison with the i n t e r n a l conversion spectrum. A l l one can do i s compare photo-electron i n t e n s i t i e s of gamma-rays whose energies are -12- not too d i f f e r e n t . However, the spectrometer may be used for a comparison of K, L, M, ... int e r n a l conversion i n t e n s i t i e s for any one t r a n s i t i o n . Values of these r a t i o s , f[K, £[K, . .., for various Z values, have been tabulated . A comparison of measured and t h e o r e t i c a l values of these r a t i o s may give information con- cerning the nuclear states involved. As i l l u s t r a t e d i n Figure l a , nuclear states may decay by the emission of a gamma-ray or conversion electron. Frequently, many energy states are involved and the nucleus may emit multiple beta- and gamma-rays (Fig. l b ) . In the majority of cases,excited nuclear states decay to lower states very quickly, for a l l p r a c t i c a l purposes instantaneously. Re- l a t i v e l y few nuclear states have l i f e t i m e s greater than lO"" 1^ 3 4 sees. Such states are c a l l e d isomeric states ' and t h i s designation merely means that the l i f e t i m e can be measured with techniques now available. These "cascade" decays are referred to as gamma-gamma-coincident decays. Analysis of these cascade decays, of beta-gamma-decays and of the angular c o r r e l a t i o n between the beta- and gamma- rays or between two gamma-rays in cascade are useful i n de- termining spin and p a r i t y changes and sometimes these analyses are performed with the aid of a spectrometer. -13- C. EARLY SPECTROMETERS AND THEIR CHARACTERISTICS As we have shown, measurements on nuclear t r a n s i t i o n s are important i n the development of a' consistent nuclear theory. These measurements may be obtained by the use of various instruments. In p a r t i c u l a r , spectrometers are used for measurements on int e r n a l and external conversion electrons, primary beta-particles and f o r coincidence and angular corre- l a t i o n work. These processes can only be studied properly i f reasonably accurate energy and in t e n s i t y measurements of the conversion electron l i n e s and of the primary beta-groups can be obtained. This i s the function of the beta-ray spectrometer. Beta-ray spectrometers may employ e l e c t r o s t a t i c or magnetic focussing. The e l e c t r o s t a t i c spectrometer i s energy s e l e c t i v e while the, more generally used, magnetic spectrometer i s momentum s e l e c t i v e . :. The electron t r a j e c t o r i e s in the magnetic spectrometers are determined by the momentum of the electron and the magnetic f i e l d such that B e v = where B i s the component of the magnetic f i e l d normal to the p a r t i c l e ' s d i r e c t i o n of motion e,m,v are the electron's charge, r e l a t i v i s t i c mass and ve l o c i t y f i s the radius of curvature of the electron's path. -14- The m a g n e t i c s t i f f n e s s , Bp , i s n o r m a l l y u s e d as t h e a b s c i s s a i n p l o t t i n g an e l e c t r o n s p e c t r u m and i s p r o p o r t i o n a l t o t h e e l e c t r o n momentum (mv). A s p e c t r o m e t e r ' s two most i m p o r t a n t c h a r a c t e r i s t i c s a r e i t s t r a n s m i s s i o n (% c o l l e c t e d ) and i t s r e s o l v i n g power. T h e s e w i l l be d i s c u s s e d i n more d e t a i l l a t e r . I n p r a c t i c e , t h e ob- t a i n i n g o f i d e a l t r a n s m i s s i o n a n d r e s o l v i n g power i s l i m i t e d by e l e c t r o n o p t i c a l a b e r r a t i o n s , s o u r c e s i z e , d e t e c t o r b a c k - g r o u n d , f i e l d f o r m , power c o n s u m p t i o n and c o o l i n g , f l e x i b i l i t y and economy, a c c u r a t e a d j u s t m e n t s ( e . g . a l i g n m e n t ) , e t c . A v a r i e t y o f s p e c t r o m e t e r s have b e e n d e s i g n e d t o m i n i m i z e d i f f e r e n t c o m b i n a t i o n s o f t h e s e l i m i t a t i o n s a n d o f t e n a r e d e s i g n e d f o r a n a l y s i s i n e i t h e r t h e low e n e r g y o r h i g h e n e r g y r e g i o n s . F o r example, e l e c t r o s t a t i c s p e c t r o m e t e r s c a n e c o - n o m i c a l l y and p r a c t i c a l l y be u s e d o n l y i n t h e low e n e r g y r e g i o n , a f i e l d o f 300,000 v o l t s / c m . p r o d u c i n g t h e same r a d i u s o f c u r v a t u r e a s a f i e l d o f 1000 g a u s s . M a g n e t i c s p e c t r o m e t e r s may be d i v i d e d i n t o two g r o u p s , f l a t and h e l i c a l . I n t h e f l a t s p e c t r o m e t e r s t h e m a g n e t i c l i n e s o f f o r c e a r e m a i n l y i n a d i r e c t i o n n o r m a l t o t h e e l e c t r o n ' s p a t h w h i l e i n t h e h e l i c a l s p e c t r o m e t e r s t h e l i n e s o f f o r c e a r e m a i n l y i n t h e d i r e c t i o n o f t h e e l e c t r o n ' s p a t h . The f i r s t d e t e r m i n a t i o n s o f b e t a - p a r t i c l e e n e r g y by t h e i r d e f l e c t i o n i n a m a g n e t i c f i e l d were c a r r i e d o u t by v o n B a e y e r 5 and Hahn by t h e " d i r e c t d e f l e c t i o n method". B e t a - r a y s e m i t t e d f r o m a r a d i o a c t i v e s o u r c e were a l l o w e d t o p a s s t h r o u g h a n a r r o w s l i t and then, after t r a v e l l i n g an a r b i t r a r y distance through a magnetic f i e l d , were recorded on a photographic plate. Only crude measurements of i n t e n s i t y were possible since no attempt was made to focus the beta-rays. The f i r s t magnetic focussing device, the semi-circular focussing spectrometer, soon followed, aft e r a suggestion by Danysz . It i s based on the geometric fa c t that i f two c i r c l e s with the same radius are drav/n with t h e i r centres separated by a small distance with respect to the radius then they intersect at approximately diametrically opposite points. The chief disadvantage of the semi-circular focussing p r i n c i p l e i s that there i s only one-dimensional focussing, i.e. in the plane of the c i r c l e s . In 1946 a device was developed which combined many of the advantages of the one- dimensional focussing with those of the two-dimensional h e l i c a l or lens focussing. This was the double focussing spectrometer^. Another f l a t spectrometer developed was the t h i r d order focussing spectrometer which corrected for the spherical aberration c h a r a c t e r i s t i c s of the homogeneous magnetic f i e l d 8 9 used i n semi-circular focussing by shaping the magnetic f i e l d S t i l l others include those arranging a focussing "prism" f i e l d where the source and detector are outside the magnetic f i e l d or a sector f i e l d with inhomogeneous f i e l d s and shaped pole pieces The h e l i c a l or lens-type spectrometer was f i r s t suggested -16- by Kapitza in 1924 (referred to by Tricker in reference 12), the electron focussing properties of short and long c o i l s having been known for some time. Busch*^ was the f i r s t to point out the close analogy between l i g h t and electron optics i f one replaces the o p t i c a l lens by a magnetic "lens". I f electrons are emitted from a source, placed on the axis of an a x i a l symmetric f i e l d , at some angle (other than 0° or 90°) with respect to t h i s axis, they w i l l follow h e l i c a l t r a j e c t o r i e s and return to the axis at some point P. (Fig. 3) Of course, the angle of emission cannot be so great as to carry the electron out of the influence of the magnetic f i e l d . Due to spherical aberration the maximum convergence of these t r a j e c t o r i e s occurs, not on the axis, at P, but at some r i n g of points concentric with the axis, i . e . at the "r i n g focus",F. This i s t y p i c a l of a l l lens-type spectrometers whether the f i e l d i s homogeneous (solenoidal spectrometers) or inhomo- geneous (long and thin lens spectrometers). The f i r s t attempts to use a magnetic lens for beta-ray 12 spectroscopy were made by Tricker who used a long uniform 13 f i e l d , i . e . a solenoidal spectrometer, and Klemperer who used a short f i e l d . These early instruments could not compare with the performance of the f l a t spectrometers because no serious e f f o r t s were made to improve their performance. The p o t e n t i a l i t i e s of these h e l i c a l instruments v/ere not f u l l y r e a l i z e d u n t i l the early f o r t i e s when Witcher developed the solenoidal spectrometer and Deutsch et a l . ' , the short F i g . 3. H e l i c a l Spectrometer Electron Trajectories F i g . 4. Unmodified Thin-Lens Spectrometer l e n s s p e c t r o m e t e r . The s h o r t l e n s u s e d by D e u t s c h p l a y e d t h e p r e d o m i n a n t r o l e i n t h e a c c u m u l a t i o n o f d a t a w h i c h f o l l o w e d t h e s u c c e s s f u l i n t r o d u c t i o n o f t h e l e n s method. T h i s i s n o t meant t o i m p l y t h a t t h e s h o r t o r t h i n l e n s g i v e s t h e b e s t p e r f o r m a n c e . I t i s f l e x i b l e i n i t s p e r f o r m a n c e and e a s y t o c o n s t r u c t w i t h s o u r c e and d e t e c t o r o u t o f t h e m a g n e t i c f i e l d , an i m p o r t a n t f e a t u r e i n a n g u l a r c o r r e l a t i o n work and i n d e t e c t o r s h i e l d i n g . A l s o i t i s r e l a t i v e l y i n e x p e n s i v e t o c o n s t r u c t and r e q u i r e s l e s s e l e c t r i c power t o o p e r a t e t h a n do most o t h e r m a g n e t i c s p e c t r o m e t e r s . However, i t has i n - h e r e n t l y l a r g e s p h e r i c a l a b e r r a t i o n . The c h a r a c t e r i s t i c s o f o t h e r h e l i c a l s p e c t r o m e t e r s may be m e n t i o n e d . The s o l e n o i d a l s p e c t r o m e t e r had t h e a d v a n t a g e s o f a u n i f o r m m a g n e t i c f i e l d , so t h a t e l e c t r o n t r a j e c t o r i e s may be c a l c u l a t e d r i g o r o u s l y , o f e a s y a d j u s t m e n t and o f r e l a t i v e l y low s e n s i t i v i t y t o o u t s i d e f i e l d s . However, t h e y have l a r g e power r e q u i r e m e n t s . S t i l l b e t t e r p e r f o r m a n c e i s o b t a i n a b l e by f i e l d f o r m i n g . T h i s t e c h n i q u e i s e m p l o y e d i n t h e " i n t e r m e d i a t e image" s p e c t r o m e t e r where t h e e l e c t r o n s p a s s t h r o u g h two a d j a c e n t l e n s f i e l d s , t h e f i r s t f o c u s s i n g i n t h e n o r m a l way t o a r i n g f o c u s and t h e s e c o n d r e v e r s i n g t h e p r o c e s s by h a v i n g a f i e l d t h e m i r r o r image o f t h e f i r s t . T hus t h e f i n a l r e s u l t i s an a x i a l image. A n o t h e r example i s t h e lone; l e n s s p e c t r o m e t e r w h i c h t h e o r e t i c a l l y has s i g n i f i - c a n t l y l e s s s p h e r i c a l a b e r r a t i o n t h a n t h e t h i n l e n s s p e c t r o m e t e r . The c h i e f a d v a n t a g e s and d i s a d v a n t a g e s o f t h e t h i n l e n s -18- spectrometer have already been mentioned and i t i s t h i s type of spectrometer which i s i n use in t h i s laboratory. A simple diagram i s shown i n Figure 4. Its operation i s clear from the previous discussion. The gamma-baffle i s to protect the counter from dir e c t r a d i a t i o n and the other b a f f l e s are for electron selection. Only those electrons which pass through the entrance and exit b a f f l e s are counted. Since the path of the electron depends on the magnetic f i e l d and electron momentum, one may, by keeping the radius of curvature constant and varying B, determine the r e l a t i v e i n t e n s i t y d i s t r i b u t i o n of the momentum of the electrons being emitted by the source and c o l l e c t e d by the detector. Some important spectrometer parameters. It i s convenient i n the discussion of a spectrometer's performance and for comparison with other spectrometers to define the two parameters already mentioned, transmission and resolving power, and several others in precise mathematical terms. Transmission: The transmission, T, i s a measure of the c o l l e c t i n g power of the spectrometer and i s expressed as a percentage. T i s the percentage of electrons emitted by the source that reach the detector and are counted when the instrument i s adjusted to focus these electrons, i . e . the f r a c t i o n of the s o l i d angle at the source "seen" by the detector. Related to T i s the gathering power, u?, defined - 1 9 - as the r a t i o of the solid-acceptance angle, -TL , to the t o t a l s o l i d angle. I t i s defined by the entrance b a f f l e s . = of course, T ^ u> Resolution: The resolution, R, i s a measure of the s e l e c t i v e power of the detector system. I f monoenergic electrons are emitted by the source, as i n the case of con- version electrons, they w i l l not appear i n the spectrum as l i n e s but rather as peaks of f i n i t e width. This i s caused by scattex*ing, f i n i t e source and b a f f l e s i z e and the inherent spherical aberration of the focussing f i e l d , a l l of which prohibit a "point" (or r i n g of points) focus which i s required for true spectrum l i n e s . The resolution, R, i s defined as a percentage by the equation: R - A (B / ° ) B f where B p i s the magnetic s t i f f n e s s of the focussed electrons A ( B p ) i s the peak width at half i n t e n s i t y . Dispersion: Dispersion, D, as the name implies, i s a measure of the a b i l i t y of the instrument to separate adjacent energies. Thus we see f o r an instrument to be of any value the dispersion or l i n e separation must be greater than the l i n e or peak width. It i s defined as „ dx D = d ( B f ) -20- where x i s the co-ordinate of the focus. A consideration of the two parameters, transmission and resolution, shows that they are, to a c e r t a i n extent, mutually c o n f l i c t i n g . If one improves the transmission by increasing the source s i z e or by opening the entrance s l o t , the resolving power decreases. The r a t i o of trans- T mission to resolution, — , i s a good measure of the quality R of a spectrometer and i s used extensively i n the comparison of spectrometers. It i s referred to as "the Figure of Merit". -21- II. THE DEVELOPMENT OF THE THIN-LENS SPECTROMETER The f i r s t major contributions to the theory and con- s t r u c t i o n of thin-lens spectrometers were made by Deutsch et a l . . They calculated the electron t r a j e c t o r i e s using the procedure of Busch 1* and analysed the spherical aber- r a t i o n e f f e c t t h e o r e t i c a l l y and experimentally. With source and detector on the axis of the magnetic f i e l d they varied parameters such as source s i z e , emergent angles, etc. They used a b a f f l i n g system to define the electron path, thus determining the re s o l u t i o n and transmission of the spectrome- ter. Other b a f f l e s were used to stop d i r e c t gamma-rays from reaching the counter and to reduce counts due to secondary electrons scattered from b a f f l e s and from the vacuum chamber walls. Also by using a s p i r a l b a f f l e they were able to d i s t i n g u i s h between positrons and negatrons. It i s important to note that c o l l e c t i o n by means of a geiger counter was made on the axis. This li m i t e d the p r a c t i c a l transmission to small values, since only i n these circumstances was the a x i a l "image" small enough to be handled conveniently. They also observed that good alignment of the magnetic axis and source- detector axis was necessary f o r optimum focussing and thus for best f i g u r e of merit. As can be seen from Figure 3, a c a l c u l a t i o n of the electron t r a j e c t o r i e s shows that the envelope of mono- energetic electrons emitted by the entrance b a f f l e has, after -22- passing through the f i e l d , i t s point of maximum convergence not on the axis but on a r i n g of points circumscribing the axis. This fact led several w o r k e r s 1 7 * 1 8 * 1 9 * 2 0 to introduce an annular s l i t at the r i n g focus. This improved the Figure of Merit by a factor of 2. Due to the divergence of the electron envelope past the r i n g focus, an a x i a l detector must be f a i r l y large to c o l l e c t a l l the electrons and hence i s subject to large background noise or i f i t i s made smaller to operate at lower background i t causes a loss i n trans- mission. A r e a l i z a t i o n of t h i s fact led J.A.L. Thompson (unpublished) of t h i s laboratory to investigate the c o l l e c t i o n of electrons at the r i n g focus. Thompson's detector consisted of a r i n g of anthracene s c i n t i l l a t i o n c r y s t a l s "cemented" with high v i s c o s i t y s i l i - cone o i l into a groove on the open l i p of a l u c i t e " l i g h t - cone". The l i g h t cone was o p t i c a l l y coupled, using the same o i l , to a photomultiplier tube. Various detector systems were t r i e d with a view to ob- taining the best signal-to-noise r a t i o possible. The system 21 described by K.C. Mann and F.A. Payne and shown in Figure 5 being one of the most recent. It i s t h i s detector system, with some minor a l t e r a t i o n s , which i s i n use i n t h i s labo- ratory at the present time. The present detector system w i l l be described i n d e t a i l i n a l a t e r section. 21 While the detector used by Mann and Payne was con- siderably further away from the magnet c o i l s than the source Fig. 5. Detector Assembly of Mann and Payne -23- i t s t i l l lay within a r e s i d u a l megnetic f i e l d , which affected the performance of the photo-tube at high magnet currents. The photo-tube was shielded from these f i e l d s by placing the entire detector system ( l u c i t e and a l l ) in a Conetic s h i e l d and by placing a Mu-metal s h i e l d around the photo-tube i t s e l f . It was found that t h i s arrangement gave s u f f i c i e n t protection to leave the photo-tube output unaffected by the magnetic f i e l d for electron momenta less than 4,000 gauss-cm. However, above t h i s momentum i t was found that the greater focussing f i e l d began to reduce the photomultiplier output pulse. Figure 6 shows the r e l a t i v e positions of source, magnet and detector, of the entrance and e x i t b a f f l e s and of the 2 1 source centering controls used by Mann and Payne . The entrance b a f f l i n g system was mounted r i g i d l y to the source holder which was mounted on a centering mechanism capable of moving the source to any desired p o s i t i o n i n a plane perpen- dicular to the magnetic f i e l d axis. This was found to be absolutely necessary, p a r t i c u l a r l y when the b a f f l e s were chosen for optimum resolution, since otherwise the c i r c u l a r r i n g focus of the electron beam was not necessarily concentric with the annular e x i t s l o t . Before centering the source, the spectrometer was aligned i n the center of the magnet as well as possible by v i s u a l observation. Even after source center- ing i t was u n l i k e l y that the source-detector and magnetic axes were coincident, since the centering mechanism did not give the required number of degrees of freedom. F i g . 6. Modified Thin-Lens Spectrometer -24- They investigated the performance of t h i s instrument using a constant source-detector distance of 59.7 cm.; entrance b a f f l e s giving gathering powers of 0.7, 1.1 to 1.6%, the tangent of the mean angle of each trajectory envelope being .4, .385 or .352; r i n g focus detection by means of a 5.15 cm.mean radius c i r c l e of anthracene s c i n t i l l a t i o n c r y s t a l s and a Cs source mounted on a thi n aluminum backing. For each gathering power they obtained an optimum source to magnet-coil-center distance, S, by i n s t a l l i n g a 137 large e x i t s l o t and observing the p r o f i l e of the Cs con- version peak for d i f f e r e n t S positions. The optimum value of S was considered to be the one of the set which gave a peak p r o f i l e having maximum transmission and best resolution. (The two occurred simultaneously.) They then matched the annular e x i t s l o t with the annular entrance s l o t by reducing the e x i t s l o t width u n t i l the transmission started to drop. Each reduction i n e x i t s l o t v/idth before the transmission started to decline improved the resolution. Any further reduction did not improve the res o l u t i o n but did cut down the transmission. The b a f f l e s were matched when maximum transmission and minimum resolution were obtained. A comparison of the performance of some h e l i c a l spectrome- ters was tabulated and that table i s reprinted here: -25- TABLE I Comparison of some high-performance h e l i c a l spectrometers. Type Iron (%) 1 R(%) (JfL) x 100 R Solenoidal No 2 0.4 500 Intermediate image No 4.5 1.6 280 Long lens Yes 6.3 2.4 262 Solenoidal Yes 3 1.2 250 Long lens Intermediate Yes 2.7 1.3 208 image Yes 8 4 200 Intermediate image Yes 10 5.5 180 Long lens No 11 9 122 Thin lens No 1.6 1.37 118 x 100 represents a rough f i g u r e of merit. R The modified spectrometer described above has c e r t a i n l i m i t a t i o n s . 1) Magnetic Shielding. The source-detector distance i s small enough to cause the detector assembly to l i e i n a r e s i d u a l focussing f i e l d . At s u f f i c i e n t l y high magnet currents, t h i s f i e l d adversely a f f e c t s the photomultiplier output. Calculations show that an increase of 20 cm. in the magnet- detector distance would p r a c t i c a l l y eliminate the s h i e l d i n g problem. 2) Centering and Alignment. It has been found that source centering i s very c r i t i c a l . There i s evidence that centering by source movement only, produces an "optimum" for any r e l a t i v e p o s i t i o n of source-detector and magnetic axes. However, i f these two axes are not coincident, t h i s "optimum" may not be the best attainable. This condition conceivably -26- could be improved i f a method of bringing the two axes into coincidence were adopted. 3) Source Position. In the modified spectrometer the source i s placed 11.6 cms. inside the end of the vacuum chamber. The walls of the chamber and the source centering mechanism behind the source pr o h i b i t one from modifying the end plate f o r angular c o r r e l a t i o n v/ork. A simpler source holder which places the source at the end of the chamber would permit the possible use of the spectrometer f o r angular c o r r e l a t i o n work. 4) A minor inconvenience i s the necessity of disturbing the source to reach the detector. III. PRESENT INVESTIGATION A. INSTRUMENTATION The present investigation was ca r r i e d out on a spectrome- ter s i m i l a r to the one used by Mann and Payne. The major differences i n the two spectrometers are: 1) The magnetic f i e l d i s formed by three sets of windings instead of four. (The innermost but one winding had, sometime before, shorted to the case.) Thus the f i e l d strength i s correspondingly smaller f o r a given magnet current. 2) The vacuum chamber has been extended by a cylinder of brass 38 cms. i n length and of the same diameter as the o r i g i n a l chamber. This extension, shown i n Figure 7, houses the detector assembly. 3) The end of the chamber which housed the source now holds the detector and vice versa. Also the source assembly has been constructed so that the source l i e s i n the plane of the end of the chamber (Fig. 8). 4) A centering mechanism has been introduced so that accurate a x i a l alignment can be made. The source holder, the entrance b a f f l e and t h e i r means of attachment to the chamber are shown i n Figure 8. The entrance b a f f l e i s attached i n a f i x e d p o s i t i o n to a plate which i n turn i s f i x e d to the end of the chamber. The source i s attached to t h i s plate so that i t can be positioned on the F i g . 7. Spectrometer Assembly i L o w E n e r g y - B a f f l e E n t r a n c e B a f f l e ~ E n t r a n c e B a f f l e S u p p o r t s n - S o u r c e S o u r c e H o l d e r V a c u u m " C a p C h a m b e r F i g . 8. The Source Assembly central axis of the entrance b a f f l e . In t h i s way, the source or entrance b a f f l e may be replaced without materially disturbing the assembly alignment. Also t h i s assembly allows the source to be removed e a s i l y and exposes i t for possible angular c o r r e l a t i o n work. In addition, Figure 8 shows a "low energy" b a f f l e . This b a f f l e protects the detector from any low energy electrons which might otherwise pass outside the entrance b a f f l e and be focussed. The end of the chamber containing the detector assembly i s shown in Figure 9. The electrons, after t r a v e l l i n g through the annular s l o t in the face of the Conetic s h i e l d , pass through the e x i t b a f f l e and impinge upon anthracene c r y s t a l s placed immediately behind. The exit b a f f l e defines the r i n g focus which has a mean radius of 5.15 cms. The s c i n t i l l a t i o n c r y s t a l s are embedded in the face of a l u c i t e cone with the aid of a s i l i c o n e gel and the cone i s coupled to the photo- sensi t i v e face of a photomultiplier tube by s i l i c o n e o i l . This cone, and hence the c r y s t a l s , i s kept in place by a bakelite r i n g and a screw. The bakelite r i n g surrounds the base of the cone and i s cemented to the photo-tube face. The screw passes through the face of the Conetic s h i e l d and screws through the e x i t b a f f l e . The screw, by pushing against the face of the l u c i t e cone, forces the cone against the photo-tube and forces the photo-tube into the base of the Mu-metal shi e l d . Since the Mu-metal s h i e l d i s f i x e d with respect to the Conetic s h i e l d and since the e x i t b a f f l e i s Chamber Extension" B a k e i i t e A l u m i n i u m | S u p p o r t F o i l F i g . 9 . The Detector Assembly -29- attached to the face of the Conetic s h i e l d by a mild s t e e l cap, the whole assembly i s fix e d with respect to the Conetic s h i e l d . The c r y s t a l s therefore are always immediately behind the exit annular s l o t . F i n a l l y , by means of r i n g supports on the inside of the chamber and on the outside of the Conetic s h i e l d , the Conetic s h i e l d i s placed i n a fi x e d p o s i t i o n with respect to the chamber. This p o s i t i o n i s approximately i n the center of the chamber1 and i s always reproducible. The Conetic s h i e l d was obtained from Perfection Mica Company, Chicago, 111. Inside t h i s s h i e l d and sttrrounding the photo-tube i s a Mu-metal s h i e l d used to diminish the ef f e c t of low f i e l d s which penetrate the Conetic cores. The photomultiplier tube used i s a Dumont 6364 which has a 5 " diameter photosensitive cathode. It was selected from the three tubes available because i t had the best signal-to- c noise r a t i o . Normalizing the signal-to-noise r a t i o of the photo-tube used to 1, the corresponding signal-to-noise r a t i o s of the two remaining photo-tubes were found to be .74 and . 5 5 . F i n a l l y , the sides of the l u c i t e cone are short and were machined i n the form of a section of a logarithmic s p i r a l . The sides and front face (except for the c r y s t a l area) are covered with aluminum f o i l so as to minimize photon loss through the sides and end of the cone. Each b a f f l i n g system consists of tv/o b a f f l e s , an inner and an outer. The inner b a f f l e i s attached by means of "spider" legs (as shown i n Fig. 10) to the outer b a f f l e which i s attached to a support f i x e d with respect to the vacuum chamber. These spider legs and b a f f l e s were care- f u l l y machined so that they f i t t e d together exactly and so that d i f f e r e n t permutations of b a f f l e s could be made without requiring adjustments to the system. Entrance b a f f l e s were machined to give gathering powers of 1.5%, 1.1% and 0.7% at each of three mean admission angles. The tangents of these angles are .400, .388 and .353. Sets of exit b a f f l e s were machined to provide v a r i a t i o n of the ex i t s l o t width by .25mm. steps from 2.25 mm. to 4 mm. With t h i s design one may remove the source holder or detector assembly separately, so as to change b a f f l e s , source, c r y s t a l s , etc., and replace the source holder or detector assembly with a minimum amount of readjustment. Because of the additional chamber length and the removal of the bulky source centering mechanism, the source-detector distance has been increased from 69.7 cms. as used by Mann and Payne to 100 cms. The aim of the new centering technique i s to obtain coincidence of the magnetic axis and the source-detector axis. The magnetic axis i s f i x e d by the position of the magnet c o i l s . The source-detector axis i s fixed with respect to the vacuum chamber. Therefore, to obtain a x i a l alignment and c o i n c i - dence, i t i s necessary to be able to control the orientation of the chamber axis with respect to the magnetic axis, i . e . to F i g . 10. Sample Entrance B a f f l e -31- ; be able to move the chamber l a t e r a l l y to any two dimensional g r i d p o s i t i o n and to rotate i t with respect to the fi x e d magnetic axis. The range of motion i s , of course, limited by the siz e of the magnet c o i l opening. F i n a l l y , since the source-magnet distance i s a parameter which cannot be constant, one must also be able to move the chamber l o n g i t u d i n a l l y along i t s own axis. To achieve t h i s , the entire chamber i s supported on two id e n t i c a l stands which were constructed to permit the required freedom of motion. An i l l u s t r a t i o n of the stands used i s shown in Figure 11. The two stands are placed on the spec- trometer table in l i n e v/ith the magnet c o i l opening. The vacuum chamber rests on the corrugated r o l l e r s which permit motion of the chamber perpendicular to the magnet ( i . e . a var i a t i o n of S ) . As can be seen from Figure 11, one can move the chamber ho r i z o n t a l l y by turning d i a l A, or v e r t i c a l l y by turning d i a l 3. 1 The circumference of the centering d i a l s i s divided into 10 div i s i o n s so that the r e l a t i v e motion of the chamber may be observed and so that the chamber may be returned to any set position. The motion of the chamber i s determined by the motion of the screw threads attached to these d i a l s . Since these screws have 25 threads to the inch, a rot a t i o n of one tenth of a revolution on the d i a l moves the chamber approximately .1 mm. The axis of the magnet i s placed p a r a l l e l to the h o r i - F i g . 11 Chamber Support A -32- zontal component o f the earth's magnetic f i e l d so that un- favourable defocussing effects due to the horizontal com- ponent o f the earth's f i e l d are minimized. The v e r t i c a l com- ponent i s minimized by passing a d i r e c t current of 1.1 amperes through two compensating c o i l s , contained i n two horizontal planes above and below the spectrometer. They are 1.1 meters b y 1.5 meters and the planes containing them are separated by 1 meter. The vacuum chamber l i e s midway between these two c o i l s . A current of 1.1 amperes in these c o i l s creates at the mid-point of the electron envelope, a magnetic f i e l d equal in magnitude but opposite in d i r e c t i o n to that of the v e r t i c a l component of the earth's f i e l d . The d.c. magnet current i s obtained from a 110 v o l t d.c. l i n e . The current i s regulated as follows. The current passes through the magnet c o l l s , a bank of 6AS7 triodes and a standard 0. 03-n-resistor. The voltage developed across the standard r e s i s t o r i s balanced by a control chassis against the output o f a potentiometer. Any error si g n a l between these two provides a compensating voltage to the grids of the 6AS7's. Regulation in current to 1 part in 10 i s achieved. By varying the potentiometer s o t t i n g , the magnet current can be varied from 0 to 10 amperes (H - 0 to 5,000 gauss-cm.). The photomultiplier H.T. i s obtained by tapping the desired voltage from a bank of voltage reference tubes placed across the output o f a regulated H.T. supply. Photomultiplier pulses pass through a cathode follower c i r c u i t mounted on the jo- vacuum chamber (see F i g . 9) i n t o a commercial a m p l i f i e r and b i a s d i s c r i m i n a t o r whose constant height output pulses are counted by a s c a l a r . i. -34- B. EXPERIMENTAL TESTS The chief purpose of the present investigation was to study the e f f e c t of the centering mechanism on the per- formance of the spectrometer. As has been stated, i t i s believed that f o r best performance the source-detector axis (fixed with respect to the vacuum chamber) should coincide with the axis of the magnetic f i e l d . Since the magnetic axis i s f i x e d , the vacuum chamber must have s u f f i c i e n t freedom of motion to permit t h i s a x i a l alignment. It i s necessary that the supports allow one to move the chamber axis anywhere within a small s o l i d cone which has i t s apex at the magnet center and i t s axis along the magnetic axis. Also the supports must allow one to move the chamber axis onto the magnet center. It has been shown that the chamber supports permit t h i s motion. To c a l i b r a t e the instrument, the p r o f i l e and height of 1 "37 the 661.6 Kev. K-conversion peak of Cs was examined at various chamber positions. The optimum pos i t i o n for any set of entrance and e x i t b a f f l e s i s that position giving minimum l "37 peak half-width and maximum peak height. Two Cs sources were studied. One had a source diameter of 2.4 mm., the other 1.6 mm. These were the tv/o sources used by Mann and Payne i n the c a l i b r a t i o n of their spectrometer thus permitting us to compare the performance of the two instruments. A variety of methods of moving the chamber were considered with a view to obtaining a procedure whereby a x i a l alignment could be r e a d i l y obtained. It i s reasonable to assume that the magnetic axis i s approximately normal to the magnet c o i l and that the source-detector axis i s approximately coincident v/ith the c y l i n d r i c a l axis of the vacuum chamber. Hence v i s u a l alignment of the chamber perpendicular to the magnet and v i s u a l centering of the chamber i n the hole of the magnet c o i l should be a f i r s t approximation to a x i a l alignment. Of course, af t e r v i s u a l alignment the two axes are not l i k e l y to coincide exactly or even to l i e i n the same plane. Assuming that the axes do not l i e i n the same plane after v i s u a l alignment and considering the o p t i c a l analogy of a simple converging lens, an improved focussing condition should ari s e when the magnetic axis and the source-detector axis intersect at the magnet (lens) center. Presumably, t h i s " i n t e r s e c t i o n of axes" condition may be reached from an a r b i - t r a r i l y located source position by ro t a t i n g the chamber, and hence the source-detector axis, about the pos i t i o n of the source u n t i l the best peak i s obtained. This i s not the ide a l focus- sing condition since neither "object"nor "image" are located on the "optic" axis. After obtaining the optimum by ro t a t i o n about the source, i d e a l a x i a l alignment should then be reached i f the chamber i s rotated about the magnet center. A possible a l t e r n a t i v e procedure would be to use a trans- l a t i o n a l motion of the chamber to obtain an int e r s e c t i o n of the two axes at the magnet center, as evidenced by maximum transmission and resolving power. Then, the f i n a l r o tation about t h i s i n t e r s e c t i o n point should put the axes in c o i n c i - dence. It i s probable that a l l motions are interconnected, e.g. the optimum reached on a horizontal rotation may depend some- what on the v e r t i c a l s etting. To take t h i s p o s s i b i l i t y into account, repeat runs should form part of the set t i n g up procedure. After considerable experimentation v/ith several combi- nations of entrance and e x i t b a f f l e s , a procedure was decided upon which appeared to give the optimum position. This pro- cedure may be described by l i s t i n g a sequence of steps to follow: 1) Select and i n s t a l l the desired entrance b a f f l e . 2) I n s t a l l some e x i t b a f f l e . Preferably, the e x i t s l o t width should be larger than the s l o t width expected from previous experience. 3) Align the chamber v i s u a l l y i n the center of the magnet opening and perpendicular to the plane of the magnet. 4) Obtain an optimum source-magnet distance by moving the chamber l o n g i t u d i n a l l y u n t i l i t i s set at the pos i t i o n 1*37 giving the best Cs conversion electron p r o f i l e . 5) Rotate the chamber successively i n a horizontal and v e r t i c a l plane about the source p o s i t i o n u n t i l an optimum p r o f i l e i s found. Repeat t h i s procedure as many times as i s necessary to obtain the same d i a l readings on two successive runs. - 3 7 - 6) Rotate the chamber successively i n a horizontal and v e r t i c a l plane about the magnet center u n t i l the best p r o f i l e i s obtained. 7) Cut down the siz e of the ex i t s l o t u n t i l a match has been obtained. The ex i t b a f f l e giving the best resolution without loss i n transmission i s considered to be the matching b a f f l e for any p a r t i c u l a r entrance b a f f l e . While t h i s procedure was f a i r l y r e l i a b l e , we found i t necessary to check back and i*epeat aft e r certain other steps had been completed. The optimum S position after v i s u a l alignment was sometimes found to be s l i g h t l y d i f f e r e n t than the optimum after r o t a t i o n a l alignment or after a better e x i t s l o t match had been made. Also the chamber pos i t i o n thought to be the optimum with one ex i t b a f f l e was not always the i optimum found after another b a f f l e with smaller exit s l o t width had been i n s t a l l e d . The necessity to check the S position i s to be expected since i t i s obtained i n the beginning when the chamber i s poorly aligned and the ex i t s l o t width i s too large. Ideally, a repeat on the r o t a t i o n a l alignment should not be necessary. It would be necessary i f the position of the e x i t b a f f l e v/ith respect to the chamber i s changed i n the process of changing the b a f f l e . It would also be necessary i f the optimum position found with the large e x i t s l o t width i s only approximate. After some experience i t v/as concluded that the r o t a t i o n a l procedure should be repeated because the optimum pos i t i o n 1 Q obtained with a large e x i t s l o t width i s generally not the true optimum as determined with matching b a f f l e s . We also found that, for the majority of runs, ro t a t i o n about the magnet center after r o t a t i o n about the source did not give a noticeably better p r o f i l e . Thus we concluded that, because of the f i n i t e s i z e of the source and because of the small source-magnet distance, (approximately 18 cms.) the magnetic axis probably passed through the source area even after v i s u a l alignment only. Therefore, ro t a t i o n of the chamber about the source was s u f f i c i e n t to alig n the axes s a t i s f a c t o r i l y . Conceivably with a smaller source or greater source-magnet distance (necessary i f entrance b a f f l e s giving a smaller emergence angle were used) rotation about the magnet center would be necessary. I n i t i a l l y , we thought 'that a t r a n s l a t i o n a l motion, after v i s u a l alignment would give the same r e s u l t s as r o t a t i o n about the source. However, when t h i s method was t r i e d , the r e s u l t s v/ere far less s a t i s f a c t o r y and so the method v/as abandoned. Changes i a chamber pos i t i o n required to produce s i g n i f i - cantly poorer performance were much smaller than o r i g i n a l l y expected. Figure 12 shows the change i n peak p r o f i l e produced by a horizontal tr a n s l a t i o n . It shows that a misalignment of 0.25 mm. has a noticeable e f f e c t on the peak p r o f i l e and that a misalignment of 0.5 mm. i s intolerable. This set of curves was taken with a poor b a f f l e match, before the chamber had  been properly centered and while using the less s e n s i t i v e 2.4 mm. diameter source. After good alignment with the smaller source, a r o t a t i o n a l motion away from the optimum caused by moving the inner support by 1.0 mm. and the outer support by 2.5 mm. was found to have a noticeable e f f e c t . This source rotation i s equivalent to changing the angle between the source-detector axis and the magnetic axis by 0°09'. Unfortunately, this extreme s e n s i t i v i t y caused us considerable trouble f o r , not a n t i c i p a t i n g such s e n s i t i v i t y , the chamber supports lacked the r i g i d i t y required for good s t a b i l i t y . Backlash i n the screw threads also contributed to our experimental d i f f i c u l t i e s . One other point should be mentioned. We had hoped, i n the design of the source and detector assemblies, that the e x i t b a f f l e , crystals,, etc. and the entrance b a f f l e and source could be changed without requiring further centering. The detector system may be removed and replaced without disturbing the centering. However, i t seems that any change in entrance b a f f l e s and c e r t a i n l y any change i n source re- quires recentering. This i s probably because the source assembly i s much closer to the center of the magnetic f i e l d than the detector assembly and therefore i t s p o s i t i o n i s much more c r i t i c a l . Using an entrance b a f f l e giving a gathering power of .70% at a mean emission angle of arc-tangent 1.50 i t was found 137 that the optimum S position was IS cms. With the large Cs -40- source, a. resolving power or half peak-height width of 1.0S _+ .01% was obtained. Mann and Payne, with t h e i r spectrome- ter, obtained 1.15% with si m i l a r entrance s l o t c h a r a c t e r i s t i c s , i The large source was then removed and the smaller one i n s t a l l e d . Before further centering the resolution was observed to be 1.00%. After further centering the optimum pos i t i o n gave a resolving power of .94 +_ .01%. Figure 13 shows a sample of the curves giving these r e s u l t s . — 8 0 A - 4 0 A A - 7 0 / \ — 6 0 — 3 0 1 — 5 0 / 1 <* CD •I- / \ 1 | 1 0 8 % \ c / I 0 0 % \ 1 9 4 % \ - 4 0 c o u n te d  /m  - 2 0 - 3 0 j \ tides  | \ j \ — 2 0 o p t i m u m w i t h l a r g e s o u r c e P A R T I C L E M O M E N T A t. o a —*- - 1 0 p e a k o b t a i n e d a f t e r c h a n g i n g t o s m a l l s o u r c e o p t i m u m w i t h s m a l l s o u r c e F i g . 13. Some Sample Conversion Peaks C. CONCLUSION I t has been mentioned chat r o t a t i o n about the magnet c e n t e r g e n e r a l l y was not n e c e s s a r y . One might s u s p e c t t h a t the p r e s e n t c e n t e r i n g mechanism g i v e s the same a l i g n m e n t as can be o b t a i n e d by Mann and Payne. The d i f f e r e n c e i s t h a t they move the s o u r c e t o o b t a i n an optimum p o s i t i o n w h i l e our r o t a t i o n about the so u r c e i s e q u i v a l e n t t o moving t h e d e t e c t o r . S i n c e the s o u r c e i s much c l o s e r t o the magnet than the de- t e c t o r , the p r o b a b i l i t y of the s o u r c e l y i n g on the magnetic a x i s a f t e r v i s u a l a l i g n m e n t i s c o n s i d e r a b l y g r e a t e r than the p r o b a b i l i t y t h a t the d e t e c t o r does. F o r t h i s r e a s o n i t i s l i k e l y t h a t r o t a t i o n the s o u r c e - d e t e c t o r a x i s about the s o u r c e g i v e s a x i a l a l i g n m e n t whereas p o s i t i o n i n g of t h e s o u r c e does not. A comparison of the rough f i g u r e s of m e r i t , ^ ~ x 100, ob~ \ R t a i n c d by Mann and Payne at d i f f e r e n t g a t h e r i n g powers, i s made i n T a b l e I I . A l s o the v a l u e s we o b t a i n e d w i t h a g a t h e r i n g power of .70% are shown i n p a r e n t h e s i s . TABLE II (%) ( i ^ ) x 100 Large source Small source 1 . 6 1 0 8 1 1 7 1.1 34 89 . 7 6 4 ( 6 4 ) 6 4 ( 7 4 ) Mann and Payne f o u n d t h a t the rough f i g u r e o f m e r i t became -42- p o o r e r as the e n t r a n c e s l o t w i d t h was decreased- We b e l i e v e t h i s change i n performance t o be caused by two f a c t o r s . 1) M i s a l i g n m e n t of axes. T h i s r e s u l t e d i n a n o n - c i r c u l a r r i n g f o c u s at the d e t e c t o r which d i d not c o i n c i d e e x a c t l y w i t h t h e e x i t s l o t . T h i s l a c k of c o i n c i d e n c e would cause p o o r e r performance a t a l l g a t h e r i n g powers. I t would become more s e r i o u s as the g a t h e r i n g power was d e c r e a s e d because the s m a l l e r the e n t r a n c e s l o t , the s m a l l e r the w i d t h o f the e l e c t r o n e n v e l o p e and hence the g r e a t e r the adverse e f f e c t ox a non- c i r c u l a r image on the r e s o l u t i o n . 2) F i n i t e s o u r c e s i z e . The s o u r c e d i a m e t e r was comparable t o the e n t r a n c e s l o t w i d t h . As a r e s u l t a performance t h a t would be p o o r e r than f o r a p o i n t s o u r c e i s e x p e c t e d and i n f a c t the d e v i a t i o n from the i d e a l p o i n t s o u r c e performance w i l l i n c r e a s e as the e n t r a n c e b a f f l e s l o t i s d e c r e a s e d . The r e s u l t s of Mann and Payne show chat a t l a r g e g a t h e r i n g powers the s m a l l s o u r c e g i v e s b e t t e r performance than the l a r g e s o u r c e . T h i s i s to be e x p e c t e d from the above argument. How- e v e r , a t a g a t h e r i n g power of ,70% the performance was not improved by r e p l a c i n g the l a r g e s o u r c e by the s m a l l one. T h i s would i n d i c a t e t h a t a t t h i s g a t h e r i n g power the a d v e r s e e f f e c t s due to m i s a l i g n m e n t were much more s e r i o u s than t h o s e due t o s o u r c e s i z e and so any advantage e x p e c t e d by s m a l l e r s o u r c e s i z e was l o s t . Our r e s u l t s seem t o c o n f i r m t h i s b e l i e f f o r , w i t h b e t t e r a x i a l a l i g n m e n t , we d i d o b t a i n b e t t e r performance w i t h the s m a l l e r s o u r c e . ) A more detailed study of the e f f e c t s of the diameter of the soiirce on the spectrometer performance i s necessary before any quantitative answers can'be given on the r e l a t i v e im- portance of these two e f f e c t s . The a c t i v i t y of the small source was measured by 137 H.R. Schneider of this laboratory by comparison with a Cs source which he c a r e f u l l y calibrated. It was found that the transmission obtained by Mann and Payne with a gathering power of 1.1% was . f>G'7o. Si m i l a r l y , we found that with a gathering power of .70% our transmission was .24%. This reiDresents a loss in t h e o r e t i c a l transmission of 50% and 55% respectively. This r e s u l t i s d i f f i c u l t to understand and. i t r e s u l t s i n a spectrometer performance considerably poorer than should be expected. As yet we have not found an explanation for t h i s and i t remains to check th i s e f f e c t , to explain i t and, i f possible, to correct i t . Two other recommendations for improvement might be made. F i r s t l y , the supports v/ere o r i g i n a l l y constructed without the r i g i d i t y necessary and with a large amount of backlash in the positioning screws. The most serious f a u l t of the supports i s their lack of r i g i d i t y which meant that during the ex- perimentation i t v/as very d i f f i c u l t to return to the position selected as the optimum, after i t had been passed. An im- proved support design might involve a jack supporting the chamber from below rather than from the sides and having s u f f i c i e n t r i g i d i t y to prohibit even minute motions under the - 4 4 - f r i c t i o n a l forces involved in moving the chamber. F i n a l l y , i f screw threads are used for moving the chamber they should be designed for a minimum amount of backlash. The other recommendation i s related to the compensating c o i l s . Deutsch et a l . * 1 ' found that "At low energies stray magnetic f i e l d s may be a serious source of trouble. A component of magnetic f i e l d per- pendicular to the axis of only 0.01 gauss w i l l displace the image by about 0.1 cm. with electrons of about 0.1 Mev. energy". We found that with the desired current of 1.1 amperes i n the compensating c o i l s the v e r t i c a l component of extraneous mag- netic f i e l d s varied from 0 gauss along 75% of the electron's trajectory to approximately .05 gauss at the extreme ends of the trajectory. Calculations show that t h i s extraneous magnetic f i e l d has n e g l i g i b l e e f f e c t on the electron t r a - j e c t o r i e s i n the energy i n t e r v a l used i n t h i s experiment (̂ > .6 Mev.). However, for work in the low "energy regions t h i s magnetic f i e l d would z-esult i n poorer performance. New compensating c o i l s to correct for the earth's f i e l d over the entire electron envelope are now being constructed and so the adverse e f f e c t s due to the earth's f i e l d experienced at low energies w i l l be eliminated. BIBLIOGRAPHY 1. M. Goldhaber and G. S c h a r f f - G o l d h a b e r , Phys. Rev. 73, 1472 (1948JT 2. M. Goldhaber and A.W. Sunyar, Phys. Rev. 83, 903 (1951). 3. E. Segre and A.C. Helmholz, Rev. Mod. Phys. 21, 271 (1949). 4. M. Goldhaber and R.I). H i l l , Rev. Mod. Phys. 179 (1952). 5. v. Baeyer and Hahn, Phys. Z. 11, 488 (1910). S. J. Danysz, Le Radium 9, 1 ( 1 9 T 5 ) and 10, 4 (1913). 7. IC. Siegbahn and N. Svartholm, Nature To7, 872 (1946). 8. F.M. Bei d u k and E . J . K o n o p i n s h i , R.S.TT"19, 594 (194S). 9. L.M. Langer and C.S. Cook, R.S.I. 19, 257~(1948). 10. H.O.W. R i c h a r d s o n , P r o c . Phys. Soc. 59, 791 (1947). 11. v. H. Busch, Ann. Physik 81, 974 (19"2~3). 12. R.A.R. T r i c k e r , P r o c . CambT Phvs. Soc. 22, 454 (1924). 13. O. Klemperer, P h i l . Mag. 20, 545 (1935). 14. C M . W i t c h e r , Phj's. Rev. T7(J, 32 (1941). 15. M. Deutsch, Phys. Rev. 59, 684A (1941). 16. M. Deutsch, L.G. E l l i o t T a n d R.D. Evans, R.S.I. 15, 178 (1944). 17. S. F r a n k e l , Phys. Rev. 73, 804A (1948). 18. J.W.M. DuMond, R.S.I. 2(57 160 (1949). 19. J.M. K e l l e r , E. Koenigsb"erg, A. P a s k i n , R.S.I. 21, 713 (1950). 20. W.W. P r a t t , F . I . B o l e y , R.T. N i c h o l s , R.S.I. _22, 92 (1951). 21. K.C. Mann, F.A. Payne, R.S.I. 30, 408 (1959). 22. I. K a p l a n , N u c l e a r P h y s i c s , AdcTTson Wesley. 23. K. Siegbahn, Beta- and Gamma-Ray Spectroscopy, North-Holland P u b l i s h i n g Company. 24. T.R. Gerholm, Handbuch der Physik, Vol. XXXIII.

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