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An intermediate image nuclear spectrometer Walton, Thomas George 1967

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AN INTERMEDIATE IMAGE NUCLEAR SPECTROMETER by Thomas George Walton 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 standard required from candidates f o r the degree of MASTER OF SCIENCE Members of the Department of PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA September, 1967 In presenting this thesis in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and Study. I further agree that permission for extensive copying of this thesis for s c h o l a r l y purposes may be granted by the Head of my Department or by h.i;s representatives. It is understood that copying or p u b l i c a t i o n of this thesis for f i n a n c i a l gain shall not be allowed without my written permission. Department of PA*^***^  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date l^pJji^J^ / 96"? Abstract An intermediate image beta ray spectrometer has been con-structed using the two magnets from two thin lens spectrometers, previously i n use i n t h i s laboratory. A surface b a r r i e r type detector replaces the s c i n t i l l a t o r -photomultiplier arrangement used before, r e s u l t i n g i n greatly reduced background noise. The performance of t h i s spectrometer i s considerably better than the two i t replaces, having resolutions of 0 . 5 1 % , 0 . 7 % , 0 .94 % and 2.2 7o at transmissions of 0 .49 % , 0 .96 % , 1.26 % and 5 .96 %. The normal energy range i s from 25 Kev, to 1 .5 Mev but i t can be ex-tended to 2 .0 Mev with some loss of transmission. 154 An examination of the beta spectrum of Eu was c a r r i e d out with t h i s instrument. A Kurie pl o t of the continuum has been made and s i x primary beta groups found with end point energies of 1.866 Mev, 1 .198 Mev , 0 .976 Mev , 0 .843 Mev , 0 .579 Mev , and 0.274 Mev with r e l a t i v e abundances of 10 .8 %. 0 . 6 7 % , 4 .6 % , 17 .0 7o, 3 7 . 8 %, and 2 9 . 1 %. Both end-points and r e l a t i v e i n t e n s i t i e s are i n excellent agreement with data from other workers. I Introduction Table of Contents Page 1 A Nuclear Spectroscopy 1 B A Typ i c a l Decay Scheme 2 C Beta Spectrometers 8 i D e f i n i t i o n s 9 i i F l a t spectrometers 12 i i i H e l i c a l spectrometers 16 i v Comparison of performance of spectrometers 18 II The Development of an Intermediate Image Spectrometer 22 A Design and Conctruction 22 B Alignment 26 C Optimization 29 D Results 34 154 II I The Beta Spectrum of Eu 37 A Previous Investigation 37 B Current Investigation 39 IV Conclusions 51 V References 53 Table of i l l u s t r a t i o n s Figure Page 1. Simple decay scheme 4 2. Simple beta spectrum 4 3. Composite beta spectrum 4 4. Fermi pl o t 7 5. Experimental plot 7 6. Resolution 7 7. E f f e c t of r e s o l u t i o n 10 8. Di r e c t d e f l e c t i o n spectroscope 13 9. Semicircular spectrometer 13 10. Double focusing p r i n c i p l e 13 11. Third order focusing 15 12. Sector f i e l d focusing 15 13. "Orange" spectrometer 15 14a. Solenoidal spectrometer 17 14b. Axial view of electron t r a j e c t o r y 17 15. Thin lens spectrometer 17 16. F i e l d shape f o r intermediate focusing 19 17. Intermediate focusing t r a j e c t o r i e s 19 18. The spectrometer i n t h i s laboratory 20 19. Spectrometer dimensions 23 20a. Detector assembly i n p o s i t i o n 25 20b. Detector assembly 25 21. Source assembly 27 22. Exposed "Q" plates i n holder 30 23. Family of peaks for varying detector distances 32 24. Family of peaks f or varying source distance 32 25. E f f e c t of source b a f f l e s l i t width 33 26. E f f e c t of central b a f f l e s l i t width 33 154 27. Decay scheme of Eu 38 28.. E f f e c t of discriminator l e v e l at low energies 42 29a. Low energy beta spectrum of Eu^"^ 44 29b. Medium energy beta spectrum of E u ^ ^ . 45 30a. Successive Fermi-Kurie pl o t s (high energy) 47 30b. Successive Fermi-Kurie plots (low energy) 48 31. Primary beta groups 49 Acknowledgements Thw work described i n th i s t hesis was supported by a Grant-in-aid-of-Research a l l o t t e d to Dr. K. C. Mann by the National Research Council of Canada. I am indebted to Dr. Mann f o r much advice and able a s s i s t -ance given throughout the course of t h i s work. I am g r a t e f u l to Mr. L. K. Ng f o r h i s help and the prep-154 aration of the Eu sources. Acknowledgement i s made also to Mr. A. Frazer, Mr. W. Mor-r i s o n , Mr, R.P. Haines, and Mr. E. Price f o r t h e i r technical assistance. - 1 -I Introduction A Nuclear Spectroscopy A l l the forces and i n t e r a c t i o n between the p a r t i c l e s that constitute a nucleus are not completely understood. There i s no "theory" to explain the dynamics within a nucleus, but rather a number of "models" which with c e r t a i n l i m i t a t i o n s are used to explain various nuclear properties. A l l models have i n common the following assertions 1. that the nucleus i s composed of nucleons. The nuc-leons consist of two types, p o s i t i v e l y charged pro-tons and neutral p a r t i c l e s c a l l e d neutrons. The number of protons Z, i s c a l l e d the atomic number and the t o t a l number of nucleons A, i s c a l l e d the mass  number, and 2. that these nucleons i n t e r a c t with each other under the influences of d i f f e r e n t forces to form a conf i g -uration or state of the system. To each configuration an energy l e v e l i s assigned. The models d i f f e r from each other i n the types, and r e l -a tive magnitudes of the forces. Important properties of a state are i t s energy W, spin J , and p a r i t y TT . The spin i s the t o t a l angular momentum of the nucleus expressed i n units of "fc and i s the vector sum of the spins of the i n d i v i d u a l nucleons. P a r i t y i s a symmetry property of the wave function, which represents mathematically the state of the nucleus. For example, cos (x) i s an even function pos-- 2 -sessing even p a r i t y and s i n (x) i s an odd function possessing odd p a r i t y . The lowest energy state i s c a l l e d the ground state, while states of higher energy are c a l l e d excited states, which may de-cay to the ground state with the emission of the appropriate en-ergy. For some nu c l e i the ground state i s stable; f o r others i t i s not, i n which case, i t w i l l decay to lower energy states by a com-plete change of configuration. The energy emitted i n t h i s kind of decay must always equal the d i f f e r e n c e i n energy between the i n i t i a l and f i n a l state. Nuclear spectroscopy i s the measurement of the emitted energy, i t s form, i t s amount, and i t s sequence of emission. The r e s u l t s of these measurements make i t possible to determine the energy d i f f e r e n c e between configurations and the sequence of emission. It i s then possible to construct the pattern of the energy states through which an unstable nucleus moves i n a t t a i n i n g a stable state. The pattern i s c a l l e d a decay scheme. The decay scheme aids the t h e o r i s t s i n checking ( t h e i r ) models or i n modifying them so they conform to the sequence of events described i n the scheme. B A Typical Decay Scheme De-excitation may be e i t h e r by electromagnetic r a d i a t i o n ( Y -rays) or by p a r t i c l e s ( - p a r t i c l e s , i . e . p o s i t i v e electrons or positrons, and negative electrons or negatrons) i n which the en-ergy i s c a r r i e d k i n e t i c a l l y . Of prime i n t e r e s t i n t h i s work are - 3 -the electrons, which are measured d i r e c t l y with a p -spectrometer, and ^--rays, which can be measured i n d i r e c t l y with a ^ - s p e c t r o -meter, and by other means. Figure 1 i s an example of a simple decay scheme invo l v i n g p - p a r t i c l e s and Y -ray emission, A parent nucleus of Z protons and mass number A decays into a daughter nucleus of Z + 1 protons and mass number A. The p - p a r t i c l e groups l a b e l l e d />( and , rep-resent decays from the unstable ground state of the parent to d i f -ferent energy states of the daughter nucleus. These are c a l l e d primary beta decays. In t h i s example, one neutron i n the parent system has converted to a proton i n the daughter system. The primary b.eta spectra are not monoenergetic but have bell-shaped continua, ( F i g . 2). This i s because the decay process involves not only the emission of the elect r o n , but a neutral p a r t i c l e c a l -led a neutrino, as we l l , and the decay energy i s shared s t a t i s -t i c a l l y between them. The neutrino, f i r s t suggested by P a u l i \ has no rest mass, no charge 9and therefore i n t e r a c t s so weakly with matter i t i s v i r t u a l l y undetectable. The t o t a l neutrino energy Wjplus the t o t a l ^ - p a r t i c l e energy always equals W q , the t o t a l energy d i f f e r e n c e between i n i t i a l and f i n a l states of the decay. If n(W) i s the probable number of ^ - p a r t i c l e s emitted with energy W i n a decay, then i t can be shown that 2 n(W) = C F(Z,W)(Wn - W) pW n ° where p i s the momentum of the electron , W i s the t o t a l energy of the electron , - 4 -Parent nucleus Daughter nucleus Z, protons, A, nucleons Z + 1 protons, A, nucleons F i g . 1 Simple decay scheme F i g . 2 Simple beta spectrum F i g . 3 Composite beta spectrum - 5 -F(Z,W) i s the "Fermi-function" - a co r r e c t i o n f a c t o r f o r the e f f e c t of the nuclear coulomb f i e l d on the ^ • - p a r t i c l e . This has been tabulated by the U.S. 2 3 National Bureau of Standards and by Bhalla and Rose . C i s a shape fa c t o r that depends on the spin and p a r i t y 4,5 of the parent and daughter states. I f i n the t r a n s i t i o n from the i n i t i a l to the f i n a l state, the spin change i s 0 or 1, and there i s no p a r i t y change, the t r a n s i t i o n i s c l a s s i f i e d as allowed and the shape fa c t o r C Q i s a constant. Tra n s i t i o n s i n which there i s a spin change of 0 or 1 and a p a r i t y change are c a l l e d non-unique f i r s t forbidden, and ones i n which A J = * 2 and a p a r i t y change are c a l l e d unique f i r s t forbidden. 4 Generally, the shape f a c t o r f o r f i r s t forbidden t r a n s i t i o n s i s 2 2 2 = q + ?\P + k ( l + aW + b + cW ) (2) W where k,a,b and c are parameters which are functions of the nucleus, q and p are the neutrino and electron moments resp e c t i v e l y and usually written i n units of m c, 2 W i s the t o t a l electron energy i n units mQC , and A i s a constant which depends on Z and Wo. For f i r s t forbidden, unique t r a n s i t i o n s (dj = 2, p a r i t y change) the 2 2 shape fa c t o r reduces to C-j_ - q + p „ For non-unique t r a n s i t i o n s (^J = 2, p a r i t y change) the general form holds. However, for most non-unique decays the shape fa c t o r i s i n d i s t i n g u i s h a b l e from the allowed case because k i s so large and a,b, and c are small, the - 6 -4,5 energy dependence i s masked. Kotani et a l have shown that i n some cases k i s not so large and a,b and c are. very small, so that i n t h i s approximation ( c a l l e d the B i j approximation) 2 2 = q + ^p + D where D i s a constant which can be determined experimentally. I f the end point WQ i s approximately known, then C n can be determined experimentally from the equation C = const. n(W) ( l a ) n FpW(Wo - W) [jderived from the basic Fermi equation (1)J which can sometimes help to i d e n t i f y the type of decay by matching i t s slope to theo-r e t i c a l shape f a c t o r s . With the form of C n known, the t o t a l trans-i t i o n energy WQ can be determined more accurately as i t i s the i n t e r -cept of the equation n(W) = constant (W - W) (3) o CnF(Z,W)pW Such a plot i s c a l l e d a Kurie p l o t and makes the determination of the end point (as an extrapolation of a st r a i g h t l i n e ) comparatively easy. The Kurie analysis i s i n fa c t a very powerful method of sep-arating independent beta groups. Using the example decay used before, (Figure 1) the plot of measured counts per unit momentum N(p) = n(p) P w i l l be composites of the two groups, ( F i g . 3). The Kurie method i l l u s t r a t e d i n Figure 4 e a s i l y separates these two groups. I f a nucleus i s i n an excited state, i t may de-excite to a lower state of the same system by ei t h e r the emission of e l e c t r o -magnetic . r a d i a t i o n i n the form of gamma ray of energy h ^ , equal to the energy d i f f e r e n c e between i n i t i a l and f i n a l states, or by the *—' c F i g . 6 Resolution - 8 -emission of an o r b i t a l electron. In t h i s l a t t e r case, the e x c i t -ation energy may be transferred d i r e c t l y to the o r b i t a l electron which i s then ejected with energy E g = hO - where i s the Coulomb binding energy of the emitted electon. The process i s c a l l e d i n t e r n a l conversion and provided the energy i s s u f f i c i e n t , the most l i k e l y e j e c t i o n i s from the K s h e l l , then the L s h e l l , etc. The Y -emission and the electron conversion process occur independently. The decay rate of the excited state i s equal to the sum of the rates of the two processes (Ty ) and ( T e ) . Both rates can be measured and the r a t i o = T e c a l c u l a t e d . This r a t i o i s c a l l e d the conversion c o e f f i c i e n t and i s dependent upon the change i n energy, spin, and pa r i t y involved i n the . t r a n s i t i o n . I t also increases with higher Z. Figure 5 i s the /"-spectrum which would be observed f o r the de-cay scheme of Figure 1. The dotted l i n e s i n d i c a t e the primary groups jg and j?^> whose t o t a l energies are Wol and W02 . The sharp peaks are the conversion electrons from the K and L o r b i t s . The s o l i d l i n e i s the t o t a l observed spectrum. C Beta-Spectrometers Since a knowledge of the ^-spectrum of a nucleus provides much information on the nature of the decay, a beta-ray spectro-meter becomes a very important a n a l y t i c a l t o o l . There are many types of ^-spectrometers, each with c e r t a i n i n d i v i d u a l character-i s t i c s . The choice of spectrometer i s governed by the s p e c i f i c requirements of the problem at hand. There are, however, some s p e c i f i c c h a r a c t e r i s t i c s by which the performance of a spectro-- 9 -meter can be judged. i D e f i n i t i o n s a Resolution (R): F i n i t e source s i z e , width of b a f f l e s l i t s , s c a t t ering and alignment i r r e g u l a r i t i e s w i l l contribute to the broadening of a moncenergetic electron l i n e . Figure 6 i s a con-version electron spectrum plotted as counts per minute versus mo-mentum set t i n g p where p = mv, the momentum of the electron. A good measure of the re s o l u t i o n of a spectrometer i s the r a t i o R = ap_ , where Ap i s taken as the width of the peak at hal f the Po maximum, and p Q i s the momentum of the conversion l i n e , ( F i g . 6 ) . R, expressed as a percentage, i s c a l l e d the r e s o l u t i o n of the spectrometer. C l e a r l y , i t i s desirable to make R as small as pos-s i b l e i n order to resolve l i n e s that l i e close together i n momen-tum. Figure 7 shows the e f f e c t of re s o l u t i o n on re s o l v i n g adjacent conversion l i n e s . The curves are drawn for constant transmission, i . e . the area under each peak remains constant. b Transmission (T): A spectrometer has source or entrance baf-f l e s that define an envelope of t r a j e c t o r i e s f o r the p - p a r t i c l e s , a l -lowing only a f r a c t i o n of the t o t a l r a d i a t i o n from the source sam-ple to reach the detector. The r a t i o of the t o t a l beta r a d i a t i o n at a given energy a c t u a l l y counted divided by the t o t a l emitted at that energy by the source and expressed as a percent i s c a l l e d the trans-mission. T, of the spectrometer. The higher the transmission, the shorter the counting times required, which i s important f o r weak sour-ces, where counting times can become p r o h i b i t i v e l y long. c Over-all luminosity ( L ) : For a given transmission, the count - 10 -F i g . 7 E f f e c t of r e s o l u t i o n rate i s proportional to the strength of the source. Hence, a stronger source w i l l give more counts. I f the area of the source used i s <r, and the transmission i s T, then L (the o v e r - a l l luminosity) i s defined as T<r and i s a measure of the a b i l i t y of the instrument to handle sources of larger area. A spectrometer with low trans-mission can compensate f o r i t , i f the spectrometer i s able to u t i l i z e a larger source area without loss of r e s o l u t i o n . d Dispersion (Y): Spectrometers focus the electrons, or to use the o p t i c a l analogy, produce an image of the source at a c e r t a i n spot i n the spectrometer. The change of p o s i t i o n of t h i s focus, <sx, with a s l i g h t change of momentum *ap, i s c a l l e d the dispersion of the spectrometer y , i . e . JT = i x . If two spectrometers have the same dimensions and r e s o l u t i o n , that with the larger d i s p e r s i o n can accept a larger source area. Beta-spectrometers can f o r convenience be c l a s s i f i e d as e l e c t r o s t a t i c focusing, which are energy s e l e c t i v e , and magnetic focusing, which are momentum s e l e c t i v e . The magnetic focusing instrument i s by f a r the most commonly used type, and as such w i l l be the only type discussed here. The equation of motion of an electron i n a magnetic f i e l d i s written as o Bev - mv / where B i s the component of the magnetic f i e l d perpendicular to the electron v e l o v i t y v, - 12 -e i s the charge on the e l e c t r o n } and J>is the radius of curvature of the electron path. Equation 4 may be rewritten as p = mv = eB/> . Therefore, i t i s convenient to express the momentum p, of a - p a r t i c l e i n terms of i t s B/> value since t h i s value w i l l i n d i c a t e the magnitude of the magnetic f i e l d , and si z e of apparatus required to focus p -rays of a p a r t i c u l a r momentum. Magnetic spectrometers can be c l a s s i f i e d as " f l a t " i n which case, the electrons t r a v e l nearly perpendicular to the magnetic f i e l d , and " h e l i c a l " i n which the electrons t r a v e l at comparatively small angles to the d i r e c -t i o n of the magnetic l i n e s of force, i i F l a t Spectrometers a Direct d e f l e c t i o n spectroscope: The d i r e c t d e f l e c t i o n spectro-6 scope was used by von Baeyer and Hahn to make the f i r s t deter-mination of the energies of -rays. Beta rays from a radioactive source were passed through a t h i n s l i t and deflected by the per-pendicular magnetic f i e l d . At an a r b i t r a r y distance, a photographic plate was placed as shown i n Figure 8. The amount of d e f l e c t i o n of the beam was dependent upon i t s energy and i t s p o s i t i o n was re-corded on the photographic p l a t e . As the rays were not focused the spectrometer had poor r e s o l u t i o n , but i t did have the advantage of being able to record the whole spectrum at once. 7 b Semicircular spectrometer: Danysz found that the envelope of monoenergetic electrons defined by the source b a f f l e f i r s t diverged and then almost refocused again a f t e r 180 , (Figure 9). g Geoffrion and Giroux b u i l t such an instrument with a radius of curvature of 30.5 cm., a r e s o l u t i o n of 0.25 7o at a transmission of - 13 -F i g . 8 D i r e c t d e f l e c t i o n spectroscope F i g . 9 Semicircular spectrometer Plane view Elevation view T F i g . 10 Double focusing p r i n c i p l e - 14 -2 0.07 % } and a maximum aource area of 3 . 5 mm . 9,10 c Double focusing spectrometer: In 1946, Svartholm and Siegbahn found that by taking a semicircular spectrometer and decreasing i t s f i e l d as _1 i n the v i c i n i t y of the central path, the electrons focused a f t e r an angle of "IT Vz i n two planes, (Figure 1 0 ) . This greatly reduced the spherical aberation of the semicircular type, ax i n Figure 8 . Arbman and Svartholm ^ have b u i l t t h i s type of instrument with af>o£ 18.5 cm., a r e s o l u t i o n of 0 . 3 7o at a trans-2 mission of 0 .35 % and a source area of 20 x 1 mm. . At f i r s t , i r o n core magnets were used to achieve the required f i e l d form, but t h i s had the disadvantage of making i t necessary to measure B a f t e r each change of current s e t t i n g , because of the hysteresis of the i r o n . More recently, i r o n free spectrometers have been 12 b u i l t (eg. Chalk River ) which has a f of 100 cm., resolutions of 0.01 % , 0 . 1 7o, and 1.0 % at transmissions of 0 .08 7«, 0 .20 %, and - 5 2 - 3 2 0.80 7° with luminosities of 7.6 x 10 cm. , 7 .9 x 10 cm. , and 2 1.01 cm. . 13 d Third order Focusing spectrometers: Beiduk and Konopinski 14 i n c o l l o b o r a t i o n with Langer , found that the spherical aberation could also be reduced by having the f i e l d vary as a polynomial of ( f— fa ) where P i s the radius of the central path. In t h i s type of f f i e l d , the electrons focus a f t e r an angle of TT instead of a f t e r an angle of TT V"?1, (Figure 1 1 ) . Their spectrometer with a f of 40 cm. had a r e s o l u t i o n of 0 . 5 % at a transmission of 0 . 1 7o and a source 2 area of 0 . 4 x 2 .5 cm. . e Sector f i e l d spectrometer: Sector f i e l d spectrometers consist - 15 -F i g . 13 "Orange" spectrometer - 16 -of a segment of a double focusing type with source and detector outside the magnetic f i e l d so that, the electrons are bent through an angle of less than IT )/ 2'T (Figure 12). This spectrometer was 15 1 6 f i r s t developed by Lauritsen et a l . Sakai b u i l t such an instrument with a r e s o l u t i o n of 0.6 7. at a transmission of 0.3 % and a source area of 50 mm, , In order to obtain more transmission 17 Kofoed-Hansen, Lindhord, and Neilsen produced the "orange" spectrometer which i s e s s e n t i a l l y six sector f i e l d spectrometers i n p a r a l l e l , (Figure 13). This spectrometer has a r e s o l u t i o n of 2 2.5 % at a transmission of 12 % and a source area of 5 x 10 mm. . i i i H e l i c a l Spectrometers a Solenoidal spectrometer: The uniform f i e l d of a solenoid i s used to focus electrons i n a solenoid spectrometer, (Figure 14a). Figure 14b shows the c i r c u l a r projection of an electron path i n the solenoidal f i e l d as viewed along the axis of the spectrometer. One advantage of t h i s type of spectrometer i s the uniform f i e l d shape which allows the electron t r a j e c t o r i e s to be calculated very accurately. Hence, i t i s useful f o r absolute momentum measure-ments. One disadvantage i s the spherical aberation, (Figure 14a) which prevents an exact focus at the axis but which does produce an approximate r i n g focus at F. Another disadvantage i s the fa c t that the source and detector are i n s i d e the magnetic f i e l d , which 18 d i s t o r t s the response of some type of detectors. Schmidt made a solenoidal spectrometer with a r e s o l u t i o n of 0,4 % at a trans-mission of 2 7. and a source diameter of 1.6 mm. 19 b Thin lens spectrometer: Deutsch, E l l i o t amd Evans f i r s t studied the t h i n lens arrangement, (Figure 15) and found that - 17 -— F s v. -J ^* L F i g . 14a Solenoidal spectrometer F i g . 14b Axial view of electron t r a j e c t o r y X \ r ^ - F s L J L X F i g . 15 Thin lens spectrometer - 18 -greater transmission could be achieved than with the solenoid arrangement, although there was greater spherical aberation which reduced the r e s o l u t i o n . Later, the r e s o l u t i o n was improved by the 20 use of detectors at the r i n g focus F, (Figure 15). Mann using ring focus detection, developed a t h i n lens type with a r e s o l u t i o n of 1.37 7o at a transmission of 1.38 % and a source diameter of 1.6 mm. 21 c Intermediate image spectrometer: S l a t i s and Siegbahn found that by changing the uniform f i e l d of the solenoid to one that concaves upward, (Figure 16) which can e a s i l y be done with two separated t h i n lens magnets, that the spherical aberation was greatly reduced. Using photographic ray tra c i n g they found that the envelope of electrons comes to an intermediate focus at the minimum of the magnetic f i e l d and then diverges to refocus on the a x i s , (Figure 17). This increases the transmission as well as improving the r e s o l u t i o n . Another advantage of intermediate f o -cusing i s the small image s i z e which allows a smaller detector to be used. In a d d i t i o n , the instrument i s characterized by ease of construction and modest cost. Figure 18 shows the spectrometer under i n v e s t i g a t i o n i n t h i s laboratory. i v Comparison of performance of spectrometers Some of the c h a r a c t e r i s t i c s of the spectrometers mentioned above are tabulated i n Table I. The r a t i o M = L x 100 R i s a crude f i g u r e of merit by which a spectrometer's performance may be judged, although i t does not take into account a l l the factors to be considered when choosing a spectrometer f o r a - 19 -D (distance along axis) Fig." 16 Field shape for intermediate focusing Fig. 17 Intermediate focusing trajectories - 20 -F i g . 18 The spectrometer i n t h i s laboratory - 21 -p a r t i c u l a r problem. Table I Comparison of spectrometers Type Reference Resolution Transmission Source area M - _T x 100 7o 7o cm. R S.C. 8 0.25 0.075 3.5 x 10"2 1.04 x 10" D.F. 12 0.01 0.06 -2 1.26 x 10 7.6 x IO-1 12 0.1 0.20 -4 3.94 x 10 7.9 12 1.0 0.80 126 101 T.O.F. 14 0.5 0.1 1.0 20 Sect. 16 0.6 0.3 5 x l O - 1 25 Orange 17 2.5 12 5 x 10"1 240 Sol. 18 0.4 2.0 2 x 10"2 10 T.L. 20 1.37 1.38 -2 2 x 10 2 I . I . 22 0.5 1.0 1.96 x 10"3 3.9 x l O " 1 22 4.0 8.0 1.96 x 10"3 3.9 x i o ' 1 Present 0.51 0.49 2.83 x 10"3 2.7 x io - 1 Invest-i g a t i o n 0.70 0.96 -3 6.36 x 10 8.7 x i o '1 0.94 1.26 1.13 x 10"2 1.5 •1 Legend: S.C.— Semi-circular spectrometer j Orange—Orange spectrometer D.F.—Double focusing spectrometer^Sol. Solenoidal spectrometer T.O.Fr-Third order focusing spectrometer S e c t . — Sector f i e l d spectrometer T . L . — T h i n lens spectrometer I.I. Intermediate image spectrometer - 22. -II The Development of an Intermediate Image Spectrometer P r i o r to t h i s i n v e s t i g a t i o n , t h i s laboratory was equipped with two i d e n t i c a l t h i n lens spectrometers modified f o r r i n g focus detection. Experience has shown that because of the extended detection area ( i . e . a r i n g diamter of 10 cm.) i t was necessary to use p l a s t i c or anthracene s c i n t i l l a t o r s , coupled by means of a l u c i t e l i g h t pipe to a photomultiplier. The l a t t e r i s very sen-s i t i v e to magnetic f i e l d s , and i n s p i t e of elaborate s h i e l d i n g , the e f f e c t of the f i e l d on the detection system was always troublesome. P a r t i a l l y f o r t h i s reason, the two i d e n t i c a l mag-nets from the two spectrometers were incorporated i n t o a si n g l e spectrometer of the intermediate image type, as the small focus achieved by t h i s type of spectrometer makes possible the use of surface b a r r i e r detectors, which have low background noise, and are extremely i n s e n s i t i v e to magnetic f i e l d s . What follows i s a des-c r i p t i o n of the design methods used and the tests applied to the magnet system to optimize i t s performance. A Design and Construction i Dimensions Figure 19 gives some of the main dimensions of the spectro-meter. The vacuum chamber of the spectrometer i s 150 cm. of 8" (20.3 cm.) brass tubing with 1/8 inch wall thickness. The magnet assemblies are spools with an outside diameter of 69 cm. and i n -side diameter of 20.8 cm. and 21 cm. thick. On t h i s spool are wound four layers of No. 8 gauge Formex magnet wire, each of about Dimensions i n cm. F i g . 19 Spectrometer dimensions 7 4 . 8 5 3 . 9 2 1 . 0 >-6 2 . 7 4 . 9 31.9 -Source 37 .5 Fs S 150 .0 - 24 -510 turns and separated from each other by a layer of cooling c o i l s . 10 amperes i n d e f i n i t e l y and 15 amperes f o r 30 minutes can be c a r r i e d by the c o i l s before they become too warm. The magnet centers were chosen to be 53.9 cm. apart, to produce approximately the desired shape of B f o r t h i s type of instrument. The axes of the magnets are coincident and one magnet i s free to move along the axis. The vacuum chamber tube has a diameter of 0.5 cm. less than the diameter of the magnet. The tube f i t s i n -side the magnets and rests on stands. As t h i s maintains the tube concentric with the magnets, i t s axis coincides with those of the magnets. The stands on which the tube s i t s , have both a v e r t i c a l and ho r i z o n t a l adjustment to allow the tube to be s h i f t e d or ro-tated by small amounts within the magnets. The magnet axes are p a r a l l e l to the horizontal component of the earths magnetic f i e l d . Two 195 xl95 cm. Helmholtz c o i l s reduce the v e r t i c a l com-ponent of the earth's magnetic f i e l d to less then 1.0 7o of i t s value. As the whole assembly i s situated between the Helmholtz c o i l s , change of electron t r a j e c t o r i e s due to the earth's mag-neti c f i e l d i s l a r g e l y eliminated, i i Detector and assembly 23 • The detector i s an "0RTEC" surface b a r r i e r type with 1 cm. active diameter, 20 v o l t s operating bi a s , minimum detection energy of 25 Kev and a 50 Kev noise l e v e l . I t i s mounted on a carriage which i s able to move l o n g i t u d i n a l l y i n s i d e the vacuum chamber keeping the detector always on the chamber a x i s , (Figure 20a) Figure 20b i s a photograph of the movable carriage. A rod, passing through the chamber's end plate and attached to the car-- 25 -F i g . 20b Detector assembly __ - 26 -riage, enables the carriage to be moved a x i a l l y . The vacuum seal between the movable rod and the end plate i s provided by "0" rings. Measuring the length D, of rod protruding past the end plate wall determines the p o s i t i o n of the detector to within 0.5 mm. The source assembly, (Figure 21) enables the source and the source b a f f l e s , which are fixed with respect to each other on a platform, to be moved i n a plane perpendicular to the axis of the vacuum chamber. The platform moves on s l i d e s perpendicular to each other, each of which i s c o n t r o l l e d by a rack and pinion. The s l i d e bases are fixed to the vacuum chamber face plate by brass stand-offs. The s l i d e pinions are connected to f l e x i b l e rods, which pass through "0" rings i n the face p l a t e , enabling the source p o s i t i o n to be adjusted from outside the vacuum chamber. The long i t u d i n a l p o s i t i o n of the source i s varied by s l i d i n g the whole tube along the magnet a x i s . B Alignment For a good performance of h e l i c a l type spectrometers a high degree of c y l i n d r i c a l symmetry within the spectrometer i s neces-sary. Deviations from t h i s symmetry w i l l g r e atly reduce both the transmission and the r e s o l u t i o n . The magnetic f i e l d of the two magnets must be c y l i n d r i c a l l y symmetric and t h e i r magnetic axes must coincide. Also, i n order that the envelope of electron t r a j e c t o r i e s be symmetric about t h i s same a x i s , the axis of the source and source b a f f l e s must coincide with the magnetic a x i s . The magnet windings are probably reasonably symmetric on the central spool surface so that i t s magnetic axis i s l i k e l y - 27 -Fig. 21 Source assembly - 28 -very close to the geometric axis of the magnetic spool. The movable magnet was bolted to a carriage, which could be ra i s e d , lowered and moved from side to side, u n t i l the movable magnet was aligned with respect to the fi x e d one. The movable magnet rides on a track, to and from the f i x e d magnet. This track was adjusted u n t i l i t was p a r a l l e l with the geometric axis of the two magnets. The vacuum chamber was placed between the magnets concen-t r i c a l l y with t h e i r geometric axes. Spectra of the K-conversion 137 l i n e of the 662 Kev t r a n s i t i o n i n Cs were taken f o r a s e r i e s of rotations of the tube within the magnets i n the hori z o n t a l and i n the v e r t i c a l plane. A comparison of the peak i n t e n s i t i e s for d i f f e r e n t tube rotations showed that the best transmission was obtained when the tube was approximately co-axial with the magnets, although the d i f f e r e n c e was s l i g h t between t h i s case and the maximum r o t a t i o n allowed by the center hole of the magnet. The next step was the po s i t i o n i n g of the source by means of the rack and pinion controls mentioned above. The two mutually perpendicular motions of the source are horizontal and v e r t i c a l . 137 Spectra of the Cs conversion l i n e at several positions of the horizontal and v e r t i c a l d i a l s , c o n t r o l l i n g the racks and pinions were taken. Such sweeps showed sharp and well defined maxima of the peak i n t e n s i t i e s . In t h i s way, the source was "centered" with respect to the spectrometer axis. This proved to be a very s e n s i t i v e method of alignment of the source with respect to the spectrometer. Each time the b a f f l e s were changed or the tube moved a large distance, t h i s alignment procedure was re-- 29 -peated. To check the o v e r a l l c y l i n d r i c a l symmetry of the electron envelope, photographs of the rin g focus were taken. I t was 137 necessary to use a very intense Cs source to give a reason-able photographic exposure, and t h i s unfortunately resulted i n a larger source area than was normally used. Photographic "Q" plates , made up i n sections as shown i n Figure 22 were placed at the p o s i t i o n of the ring b a f f l e . The conversion l i n e showed up as a r i n g on the exposed p l a t e s , (Figure 22). The rin g was found to be both symmetric and concentric to a high degree, although i t s measured radius was not useful because the extended source area al t e r e d the mean tangent of the emergent electron en-velope. However, the symmetry of the image and the knowledge that the intermediate image i s indeed a good c i r c l e was reassuring. C Optimization To obtain the best performance from the spectrometer, several parameters must be optimized. The parameters to consider are rin g focus diameter and width, source distance from magnet centers, detector distance from magnet centers, and source diameter. To test the e f f e c t of each, f a m i l i e s of spectra of the 662 Kev conversion 137 l i n e of Cs were taken f o r a number of parameters. The outside diameter of the rin g focus b a f f l e was fixed at 18 cm. i n order to u t i l i z e the high f i e l d gradients and high d i s -persion f i e l d regions near the wall of the tube. An a r b i t r a r y s l o t width of 5 mm. was chosen to begin with. Without entrance b a f f l e s , the source was set at the center of the f i r s t magnet and a spectrum of the conversion l i n e was taken f o r a series of - 30 -- 31 -detector p o s i t i o n s . Figure 23 shows a family of these spectra with the optimum detector distance f o r a given source distance and central b a f f l e s l i t . Another family of spectra was taken f o r varying source distances and t h e i r corresponding optimum detec-tor distances, (Figure 24). The focusing current f o r the conversion l i n e as well as the peak i n t e n s i t y was noted, because a lower focusing current means a wider energy range f o r the spectrometer. Over a distance of 5 cm. from the center of the magnet, the trans-mission remained nearly independent of source p o s i t i o n . Hence, the optimum p o s i t i o n was taken to be the one requiring the least focusing current. To optimize the r e s o l u t i o n , the proper choice of the width of the central b a f f l e s l i t and a "matched" source b a f f l e was re-quired. This was performed by f i x i n g a s l i t width and taking a spectrum of the conversion peak, without source b a f f l e s , then i n s e r t i n g outer source b a f f l e s with smaller and smaller diameters u n t i l the i n t e n s i t y of the peak commences to decrease. The pro-cess was repeated using succesively larger inner b a f f l e s . By using the outer and inner source b a f f l e s chosen i n t h i s manner, the best "match" of the source b a f f l e s to the center b a f f l e s i s insured and optimum r e s o l u t i o n and transmission r e s u l t s . In-creasing the s l i t width of the source b a f f l e s from t h i s point w i l l not increase the peak i n t e n s i t i e s , but r e s u l t s i n lower trans-mission and poorer r e s o l u t i o n , (Figure 25). A family of optimized conversion l i n e spectra was found f o r d i f f e r e n t central b a f f l e s l i t widths, (Figure 26). The choice of the ce n t r a l b a f f l e s l i t width, depends on - 32 -24.2 24.4 P F i g . 23 Family of peaks f o r varying detector distances S i n cm. 37.5 36.5 35.5 34.5 33.5 P F i g . 24 Family of peaks f o r varying source distance F i g . 26 E f f e c t of central b a f f l e s l i t width - 34 -the p a r t i c u l a r requirements of the i n v e s t i g a t i o n at hand. A compromise usually must be made between transmission and res-o l u t i o n . The separation of conversion peaks may require high r e s o l u t i o n , whereas high transmission i s more important f o r the measurement of the continuum, p a r t i c u l a r l y i n the high energy region where count rates are low. Another configuration was optimized f o r a small diameter ce n t r a l b a f f l e s l i t , which allowed the source to be extended further away from the center of the magnet. This arrangement had both poorer r e s o l u t i o n and trans-mission, but i t d i d focus the electrons with less current, there-by extending the energy range of the spectrometer from 1.5 Mev to 2.0 Mev. D Results The spectrometer was optimized for the two configurations. The set up data f o r both are given below i n Table I I . The transmission of the spectrometer was measured i n the following way. F i r s t , the gamma a c t i v i t y of the source was deter-mined by a d i r e c t comparison (using i d e n t i c a l geometries and a 137 Nal (Tl) c r y s t a l ) with a c a l i b r a t e d source of Cs . The a c t i v i t y was found to be 4.97 x 10^ gamma-rays per second. Since the K-conversion c o e f f i c i e n t f o r t h i s gamma-ray i s accurately known to be cC^  = 0.093, then the number of K-conversion electrons emitted 3 by the source i s 4.62 x 10 per second. The number of counts, f o r example, i n the K-conversion peak of the conversion spectrum with the spectrometer set at 0.7 % r e s o l u t i o n i s measured to be 44.2 + 0.4 electrons per second. Therefore, at t h i s s e t t i n g the - 35 -Table II Spectrometer Set Up Data Low Energy High Energy Data Energy range (Mev ) Source diameter (mm.) Resolution (70) Transmission (%) Outer diameter of central b a f f l e s l i t (cm.) S l i t width (mm.) Source distance from the magnet center (cm.) Source to detector distance (cm.) "S" (cm.) "D" (cm.) "Fs" (cm.) See F i g . 19 High Resolution High Transmission 0.025 - 1.5 0.025 - 1.5 0.9 0.7 0.96 18.0 1.0 4.9 62.7 31.9 24.4 37.5 0.9 2.2 5.96 18.0 2.5 4.9 62.7 31.9 24.4 37.5 0.025 0.9 1.8 I. 3 I I . 5 3.0 16.7 75.4 38.3 31.5 31.9 - 2.0 - 36 -transmission i s cal c u l a t e d to be 44.2 x 100 % = 0.96 + 0.05 % 4.61 x 10 3 Sources of diameters 0.6 mm., 0.9 mm., and 1.2 mm. were used to test the e f f e c t of source s i z e on the maximum obtainable r e s o l u t i o n . The r e s u l t s are given below i n Table I I I . Table I I I Source diameter Resolution Transmission Merit f i g u r e 0.6 mm. 0.51 % 0.49 % 2 0.27 cm. 0.9 mm. 0.70 7o 0.96 % 2 0.87 cm. 1.2 mm. 0.94 7o 1.26 % 2 1.51 cm. The r e l a t i o n between source diameter and maximum obtainable res o l u t i o n appeared to be l i n e a r and could be approximated by the r e l a t i o n R = 0.73 D + 0.06 where R i s the re s o l u t i o n i n %,and D i s the source diameter i n mm. - 37 -154 I I I The Beta-Spectrum of Eu A Previous Investigation While other workers have attempted to measure d i r e c t l y the primary beta-spectrum of Eu^^^,( with some success i n the higher energy groups )by and large both the end-point energies and r e l a t i v e i n t e n s i t i e s have been deduced from gamma-ray measurements. An example i s provided by the work of Juliano and 24 Stephens . In t h i s i n v e s t i g a t i o n using a double focusing semi-c i r c u l a r spectrometer, they ran the primary spectrum and came to the following conclusions. " In addition to the electron l i n e s , i t was possible to determine beta end points at 1850, 870, 590, and 250 Kev , although at the low energies the r e s o l u t i o n of the Fermi-Kurie p l o t was not very good. The reason f o r t h i s i s not c l e a r ; however i t might be at l e a s t p a r t i a l l y explained i f the the above beta groups had forbidden rather than allowed shapes. It w i l l be shown that the log Ft values f o r these t r a n s i t i o n s are a l l around 10 or larger. Because of these u n c e r t a i n i t i e s , and others which w i l l be discussed l a t e r , i t was not possible to obtain r e l i a b l e r e l a t i v e i n t e n s i t i e s f o r any of the beta groups." In Table IV, the estimates of Juliano and Stephens on the beta spectrum are given. A l l these data are deduced from t h e i r gamma-ray measurements. Figure 27 shows the decay scheme of 154 154 Eu - Gd as presented i n the Nuclear Data Sheets, using mostly the r e s u l t s of J u l i a n o and Stephens. - 38 -- 39 -Table IV 154 Beta groups of Eu ( i n d i r e c t ) according to Juliano and Stephens Energy (Mev ) Abundance (%) 0.25 281 5 0.59 42 t 5 0.86 1 3 l 5 0.99 6 + 5 1.62 6 t 5 1.87 6±5 Another i n v e s t i g a t i o n c a r r i e d out i n t h i s laboratory i s that of L.K. Ng. His conclusions on the beta i n v e s t i g a t i o n are again de-duced from gamma-ray measurement, (Table V). B Current Investigation i Source preparation 154 An Eu source from the Oak Ridge National Laboratory was 153 used i n the present i n v e s t i g a t i o n . The source was 98.76 % Eu , 154 which was neutron i r r a d i a t e d f o r seven days, thus forming Eu almost 152 free from Eu . The source was deposited on a t h i n v i n y l backing to reduce back-scattering. The backing was prepared by d i s s o l v i n g powdered v i n y l (Union Carbide Vyns-3 Blend 1813) i n cyclohexanol. A drop of the v i n y l s o l u t i o n was placed i n a tray of water on which i t spread into a thin f i l m before hardening. The hardened v i n y l f i l m was removed from the water with a wire loop and placed on the source holder. By evaporating a t h i n coating of aluminum onto the v i n y l , the backing was made e l e c t r i c a l l y conducting to eliminate - 40 -Table V End points from End point* Fermi-Kurie p l o t (Kev. (Kev.) (Ng) ) Relative inten- Relative inten-s i t i e s (area plot) s i t i e s from y -7o i n t e n s i t i e s % 2741 10 270.1 579 i 5 591.6 29.1i 2.5 26.3 37.8 ±3.5 38.1 843 115 861.6 17.0 i 3.9 17.8 976 *30 993.2 4.6 ±3.8 2.8 1198 ±60 1174.2 0.67±0.49 1.3 1866 ±12 1866.0 10.8 t0.12 11.1 Total 100 98.4** * In column 2, the end point 1866 .0 i s assumed. The others are deduced from l e v e l d i f f e r e n c e s . ** There i s evidence of po s s i b l e weak beta groups other than the six found i n the Fermi-Kurie a n a l y s i s . - 41 -e l e c t r o s t a t i c charging of the source. The E u ^ ^ C ^ was dissolved i n a weak hydrochloric acid s o l -u tion and concentrated by evaporating the water with a heat lamp. By using a dropper with a very f i n e nozzle, a drop of the concen-trated s o l u t i o n was applied to the coated v i n y l and the remaining water i n the sample was evaporated with the heat lamp. A th i n coating of the c o l l o d i o n was applied over the dried sample to insure that the sample would not leave the backing. Mr. Ng suc-ceeded i n producing a very intense source by t h i s method, with a diameter of 0.9 mm. With t h i s source the spectrometer had a re s o l u t i o n of 0.7 % at a transmission of 0.96 %. i i Experimental procedure The noise l e v e l of the surface b a r r i e r detector had approx-imately the same amplitude as pulses from 50 Kev electrons. In the higher energy region, above 75 Kev , the pulses from the electrons were large enough that i t was possible to set a discriminator l e v e l above the noise l e v e l . A l l the electrons could s t i l l be counted, but very few noise pulses. However, f o r low energy electrons, i t was necessary to reduce the discriminator l e v e l to count both noise and counts, the di s c r i m i n a t o r l e v e l being reduced i n stages u n t i l no further gain i n s i g n i f i c a n t counts resulted. Figure 28 shows the e f f e c t of d i s c r i m i n a t o r s e t t i n g on s i g n i f i c a n t counts i n the the low energy region. 154 The complete beta-conversion l i n e spectrum of Eu was taken using the spectrometer described above. This was done using a combination of d i f f e r e n t sources and spectrometer s e t t i n g . For higher r e s o l u t i o n i n v e s t i g a t i o n of the conversion l i n e s , an .Fig. 28 E f f e c t of d i s c r i m i n a t o r l e v e l at low energies - 43 -intense source with a diameter of 0.9 mm. was used at o.7 % r e s o l u t i o n , 0.96 % transmission. The energy range was 25 - 980 Kev. This spectrum i s shown i n Figure 29a and 29b. The analysis of the primary beta continuum does not require high r e s o l u t i o n but does require high transmission and a lower Mev per ampere ra t i n g i n order to reach higher electron energies with-out excessive c o i l heating. Therefore, using the same source but with the spectrometer set at 2.2 % r e s o l u t i o n , and 6 7. transmission, the continuum between the conversion peaks was taken from 0.14 to 1.5 Mev. Higher energies were reached using a larger diameter source and the "high energy" spectrometer s e t t i n g . In t h i s case, because of the extended source area, the r e s o l u t i o n was 3 %. The transmission with t h i s source was not measured but was probably about 1 %. Care was taken that no measured continuum point over-lapped a conversion peak. The spectrometer was c a l i b r a t e d at each s e t t i n g and source combination used with the 246.8 Kev K-conversion l i n e , taking the electron energy as 196.6 Kev. The counting times f o r each point were long enough to c o l l e c t at least 10,000 counts, thus reducing the s t a t i s t i c a l f l u c t u a t i o n to 17.. i i i Fermi-Kurie analysis and r e s u l t s 154 The data on the Eu continuum was analyzed much as indicated i n Figure 4. We were guided i n t h i s a nalysis by a knowledge of the approximate end points of the groups from the work of e a r l i e r wor-kers and of Ng i s t h i s laboratory. F i r s t , the shape correction f a c t o r f o r the 1.87 Mev beta groups was determined experimentally ( see equation l a ) then, 154 Figo 29a Low energy beta spectrum of Eu o 0.5 0.6 0.7 0.8 Relative momentum 154 F i g . 29b Medium energy beta spectrum of Eu - 46* -4 following the suggestion of Kotani , the equation which best 2 2 f i t t e d t h i s function was determined using C-^  = q + 0.807p + D where D i s an a d j u s t i b l e constant. The best value of D was 20 - 2, i n agreement with that determined by Langer and Smith. A l e a s t -square f i t to the Fermi-Kurie p l o t using t h i s form of was then extrapolated back to lower energies. The extrapolation de-parted from the experimental points near 1170 Kev«, From the residue, r e s u l t i n g from a subtraction of 1.87 Mev group, a new group emerged which proved to be of a very low i n t e n s i t y . This group was s i m i l a r l y analyzed between 1170 and 980 Kev , although the experimental values of C-^  for t h i s group, showed a wide scatter, 2 2 A least square f i t gave an experimental of q + 0.794p + (0-2). The F^rmi-Kurie function, using t h i s form of was plotted and extrapolated back again. Again, the extrapolation departed from the experimental points i n the neighborhood of 1 Mev. The procedure outlined above was repeated down to and i n -cluding a group of end point 270 Kev. The experimental shape fa c t o r s f o r a l l but the most energetic groups could be f i t t e d best by constants, independent of energy. The r e s u l t i n g p l o t s are shown i n Figure 30. The r e l a t i v e i n t e n s i t i e s of each group could now be deduced by extracting from the corresponding Fermi-Kurie s t r a i g h t l i n e s , the function n(p) versus p. These are shown plotted i n Figure 31 and the r e l a t i v e i n t e n s i t i e s are simply the area r a t i o s under each curve. The data i s summarized i n Table V. It can be seen that the i n t e n s i t i e s 25 are i n good agreement with the data of Ng. The end points agree - 47 -I I I 1 Energy (Mev ) Fig. 30a Successive Fermi-Kurie plots (high energy) - 48 -Energy (Mev ) F i g . 30b Successive Fermi-Kurie p l o t s (low energy) - 50 -within the estimated error l i m i t s and i n a l l cases the d i f -ferences are less than 2 7». - 51 -IV Conclusions In the two e a r l i e r chapters, a d e s c r i p t i o n has been given of the design and construction of an intermediate-image spectrometer, the adjustments and tes t s to optimize i t s performance under d i f -ferent conditions of use and one example of i t s a p p l i c a t i o n to a p a r t i c u l a r problem. The r e s u l t s are quite rewarding. While the spectrometer cannot compare i n re s o l u t i o n with the high p r e c i s i o n instruments a v a i l a b l e i n a few other l a b o r a t o r i e s , i t does represen a good compromise between high r e s o l u t i o n and high transmission; i t s c a p a b i l i t i e s make i t a very useful instrument f o r most types of beta-decay problems. Its performance i s at least as good as that of others of the same type reported i n the l i t e r a t u r e . The instrument has proved to be remarkably f l e x i b l e to desired changes i n r e s o l u t i o n and/or transmission. These changes we have found may be made quickly and conveniently. It i s quite obvious that the instrument's ultimate r e s o l u t i o n i s strongly dependent upon a v a i l a b l e source diameters. For t h i s reason, since the method of source preparation used here (drop deposition) often leads to non c i r c u l a r and non uniform sources, i t would be better to use a more c o n t r o l l a b l e method of preparing them. Preparations are being made to use a sublimation method whereby source material can be deposited on the source backing, using an evaporation technique. It i s well known that such sources are uniform, and since the s i z e can be determined by masks, the d i f f i c u l t y of preparing sources that are very small i n diameter i s much reduced. - 52 -It must be admitted however, that long before the source size l i m i t i s reached, the small and seemingly unavoidable i r -r e g u l a r i t i e s i n f i e l d homogeneity, b a f f l e s , etc, w i l l begin to i n t e r f e r e . Where t h i s comes i t i s hard to say. Nor can one rea-sonably predict the optimum performance. To hazard a guess, perhaps a r e s o l u t i o n of 0.2 - 0.3 % might be reached. - 53 -References 1. W. P a u l i : Handbuch der Physik 24 (1933) 226-227. 2. Natl. But. Std. (U.S.): Appl. Mat. Ser, 13, "Tables f or Analysis of Beta Spectra (1952) Chap. 2. 3. C P . Bha l l a and M.E. Rose: Phys. Rev. 128 (1962) 1774, and Ornl 3207 (1962) Chap. 2. 4. T. Kotani and M. Ross: Phys. Rev. 113 (1959) 622. 5. L.A. Langer and D.R. Smith: Phys. Rev. 119 (1960) 1308. 6. O.V. Baeyer and O.Hann: Phys. Z e i t s c h r 11. (1910) 488.( 7. J.Danysz: Le Radium 9 (1912)1; 10 (1913) 4. 8. C. Geoffrionrand G. Giroux: Can. J . Phys. 34 (1956) 920. 9. N. Svartholm: Ark. F. Fysik 1 (1949) 115. 10. A. Hedgran, K. Siegbahn and N. Svartholm: Proc. Phys. Soc. London 63 (1950) 960. 11. E. Arbman and N. Svartholm: Ark. F. Fysik 10(1955)1. 12. R.L. Graham, G.T.Ewan and J.S.Geiger: Nuc. I n s t , and Methods 9 (1960) 245. 13. F. M. Beiduk and E.J.Konopinski: Rev. S c i . Inst. 19 (1948) 594. 14. L.M. Langer and C. S. Cook: Rev. S c i . Inst. 19 (1948) 257. 15. C S . Snyder, S. Rubin, W.A. Fowler and C C Lauritsen: Rev. S c i . Inst. 21 (1950) 852. 16. M. Sakai, H. Ikegami and T. Yamazaki: Nucl. Inst, and Methods 9 (1960) 154, 25 (1964) 328. 17. 0. B. Nielsen and Kofoed-Hansen: Dan. Mat-Fys. Medd. 29 (1955) No.6. 18. F. H. Schmidt: Rev. S c i . Inst. 23 (1952) 361. 19. M.Deutsch, L. E l l i o t t and R. Evans: Rev, S c i . Inst. 15 (1944) 178. - 54 -20. K. C. Mann and F.A. Payne: Rev. S c i . Inst. 30.(1959) 408. 21. H. S l a t i s and K. Siegbahn: Ark. F. Fysik 1 (1949) 339. 22. D. E. Alburger: Rev. S c i . Inst. 108 (1957) 341. 23. S c i e n t i f i c American,. 207 (1962) No. 4, 78. 24. J . 0. Jul i a n o and F. S. Stephens: Phys. Rev. 108 (1957) 341. 25. L. K. Ng: Ph. D. Thesis, U. B. C,.1967. 

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