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A single crystal sodium iodide scintillation spectrometer for the investigation of gamma-ray spectra Azuma, Richard Ernest 1953

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A SINGLE CRYSTAL SODIUM IODIDE SCINTILLATION SPECTROMETER FOR THE INVESTIGATION OF GAMMA-RAY SPECTRA by Richard Ernest Azuma A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS  in 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 ARTS  Members of the Department of PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1953 ABSTRACT A single c r y s t a l sodium iodide spectrometer has been devel-oped f o r the investigation of gamma-ray spectra. The spectro-meter was tested with the gamma-rays from the sources Eul55 } RaD, Na 2 2, Z n 6 5 , Co 6 0, and RdTh. The spectra from these sources have been obtained by analyzing the pulse height d i s t r i b u t i o n from the s c i n t i l l a t i o n counter with a single channel d i f f e r e n -t i a l discriminator. A c r y s t a l mounting technique i s described i n which the cry-s t a l s are mounted dry with a layer of magnesium oxide powder surrounding them to provide diffuse r e f l e c t i n g surfaces. With mountings of t h i s type, 7% energy resolution has been achieved f o r gamma-ray energies of approximately 1 MeV. The expected pulse height d i s t r i b u t i o n s have been calculated and compared with the experimental d i s t r i b u t i o n s . The effect of multiple scattering events on the shape of the d i s t r i b u t i o n s i s discussed,2and the effect of c r y s t a l dimensions on the resolu-t i o n has been studied. I t has been found that f o r the energy region 0.5 to 2.5 MeV the best resolution i s obtained with small c r y s t a l s . A search has been made f o r the presence of low energy gamma-rays i n the decay of t r i t i u m , and i t was found that within the accuracy of the experiment no gamma-rays were present. A preliminary report i s presented on the investigation of possible s c i n t i l l a t i o n produced i n a i r by alpha p a r t i c l e s . The eff e c t has been shown to exis t but no systematic study has been made. ACKNOWLEDGMENTS The author wishes to express h i s thanks to Dr. J . B. Warren for suggesting t h i s research and f o r h i s advice and supervision i n performing the experiments. Thanks are also due to Mr. G. M. G r i f f i t h s f o r h i s many help-f u l discussions and suggestions. The author also wishes to thank the National Research Council f o r the Summer Research Grant and Bursary under which t h i s re-search was carried out. INDEX Page I. INTRODUCTION \ . . . II. THE INTERACTION OF GAMMA-RAYS WITH THE CRYSTAL AND THE SPECTRUM SHAPE A. Compton Effect 5 B. Photoelectric Effect 11 C. Pair Production Process 14 D. The Calculated Spectrum Shape .... 16 E. Mult i p l e Scattering 17 F. Resolution of the S c i n t i l l a t i o n Counter .... 20 I I I . CRYSTAL MOUNTING TECHNIQUES A. The Dry Box 24 B. C r y s t a l Mounts 25 C. Details of Technique 26 IV. THE GAMMA-RAY SPECTROMETER A. H.T. Power Supply 29 B. Count-Rate Meter and Head Amplifier Power Supplies............. • 30 C. Oscilloscope 30 D. The Photomultiplier Tube 30 E. The Pre-Amplifier 30 F. The Single Channel Analyzer 31 G. The Count-Rate Mete* 31 H. The Brown Recorder 32 V. EXPERIMENTAL RESULTS A. RaD and Eu x55 D i s t r i b u t i o n s 33 B. Na 2 2 D i s t r i b u t i o n s 35 C. Co60 Distributions 37 D. Zn 6? Distributions 3 8 E. RdTh Distrib u t i o n s 39 F. Energy Resolutions..... 41 G. The Search for Gamma-Rays From Tritium ..... 43 APPENDIX I - Calculation of the Compton Recoil Electron D i s t r i b u t i o n 45 APPENDIX I I - The S c i n t i l l a t i o n of Alpha P a r t i c l e s In A i r . 1 46 ILLUSTRATIONS Figure Number Facing Page I. The Compton Effect Showing Angular and Energy-Notations 6 I I . Compton Effect Cross-Sections 6 I I I . Calculated Compton Electron Distributions f o r 0.511 MeV and 1.28 MeV Gamma-Rays 10 IV. Cross-Section vs. Energy for the Compton Ef-f e c t , Photoelectric E f f e c t , and Pair Produc-t i o n 12 V. Electron Range vs. Energy Curve 13 VI. Calculated Pulse Height D i s t r i b u t i o n 2.62 MeV Gamma-Rays • • 16 VII. Calculated Pulse Height D i s t r i b u t i o n f o r 0 . 5 H MeV and 1.28 MeV Gamma-Rays 17 VI I I . Calculated Pulse Height D i s t r i b u t i o n f o r the Gob0 Gamma-Rays 17 IS. The Mount f o r the C y l i n d r i c a l Crystals 26 X. The Mount for the Rectangular Crystals 26 XI. The Mount f o r the Thin "Disc" Crystals 26 X I I . Block Diagram of the Spectrometer 29 X I I I . The 2500 V Power Supply 29 XIV. The Pre-Amplifier and the Schmitt C i r c u i t Input to the Count-Rate Meter 31 XV. The Count-Rate Meter 32 XVI. Experimental Pulse Height Distributions f o r RaD and Eu!55 . . . . 33 XVII. Experimental Pulse Height D i s t r i b u t i o n f o r Na 2 2 from the Large Crystal 36 XVIII. Experimental Pulse Height D i s t r i b u t i o n f o r Na 2 2 from the Small C r y s t a l 36 XIX. Experimental Pulse Height Distributions f o r Co^. 3S Figure Number Facing XX. Experimental Pulse Height D i s t r i b u t i o n f o r Zn°5 from the Large Crystal XXI. Experimental Pulse Height D i s t r i b u t i o n f o r Zn 5? from the Small Crystal XXII. Experimental Pulse Height D i s t r i b u t i o n f o r RdTh Number TABLES I . The Percent Probable Error f o r the Count-Rate Meter at Various Counting Rates and Time Con-stants Facing Page 32 I I . Experimentally Achieved Resolution Page 41 Number I. PLATES Photograph of the dry box Facing Page 24 I. INTRODUCTION The development of the s c i n t i l l a t i o n counter as an energy sensitive detector has produced a powerful t o o l f o r the study of X-ray and gamma-ray spectra. Recent refinements i n technique have resulted i n the design of spectrometers which are capable of measuring gamma-ray spectra from sources of the order of 10"^ curie and with resolution, (measured as the r a t i o of the f u l l width at ha l f maximum to energy at peak), of approximately £ per-cent, f o r the energy region 1 to 3 MeV. This d e f i n i t i o n of en-ergy resolution w i l l be used throughout the te x t . The resolu-t i o n attainable, to date, f o r the energy region below 1 MeV has been r e s t r i c t e d by the s t a t i s t i c a l variations associated with the photomultiplier tubes, and below 100 KeV, these variations become dominant and a resolution of about 40$ can be expected, getting worse as the energy drops. The poor resolution i n t h i s very low energy region may quite often be tolerated since the high e f f i c i e n c y of the s c i n t i l l a t i o n counter makes possible the detection and measurement of spectra from extremely weak sources. The use of thallium-activated sodium iodide c r y s t a l s as a means of distinguishing gamma-ray energies was f i r s t reported by R. Hofstadter i n 1943 (1). This i n i t i a l report showed that the fluorescent l i g h t output of sodium iodide was considerably larger than that from most of the known organic phosphors, but not an-thracene, and that the i n t e n s i t y of fluorescence was an increasing function of the incident gamma-ray energy. A subsequent publica-t i o n by the same author (2) showed that sodium iodide counters gave a c h a r a c t e r i s t i c pulse height d i s t r i b u t i o n f or an incident 2 beam of monoenergetic gamma-rays. This "spectrum" was charac-te r i z e d by the presence of a continuous d i s t r i b u t i o n with a sharp cut-off at the high energy side, and by. the presence of a number of sharp peaks. The peaks were attributed to the i n t e r a c t i o n of the gamma-rays with the heavy component (iodine, z=53) of the cry-s t a l by means of the photoelectric and pair production processes, and the continuous d i s t r i b u t i o n was interpreted as the r e s u l t of interactions by the Compton e f f e c t . The position of thejhoto-e l e c t r i c and pair peaks i n the d i s t r i b u t i o n was reported to be a l i n e a r function of the incident gamma-ray energy. This l i n e a r i t y with respect to incident gamma-ray energy of the fluorescent out-put of the c r y s t a l , along with the presence of sharp peaks i n the spectrum, and the high absorption e f f i c i e n c y has made sodium iodide the i d e a l type of c r y s t a l to use f o r the measurement of gamma-ray energies. Recent advances i n the design of photomultiplier tubes have resulted i n marked improvement i n the performance of the s c i n t i l -l a t i o n counter. Those factors of photomultiplier design which are of most importance i n t h i s application are the following: ( i ) High e f f i c i e n c y i n photocathode emission, and u n i f o r -mity of emission over the whole photocathode surface, ( i i ) High gain and low dark current, ( i i i ) Large photocathode area to increase l i g h t c o l l e c t i o n ef-f i c i e n c y . (iv) I n s e n s i v i t i t y of the gain to stray magnetic f i e l d s (v) Large output current pulse without a f f e c t i n g l i n e a r i t y of the response or causing ion feedback. 3 (vi) Maximum e f f i c i e n c y i n c o l l e c t i o n of the electrons from the photocathode. ( v i i ) Matching of the spectral response of the photocathode with that of the fluorescent ra d i a t i o n of the c r y s t a l . Although much research has been done to improve these operating c h a r a c t e r i s t i c s , the s t a t i s t i c a l f l uctuations introduced by them, esp e c i a l l y variations i n photocathode emission and g a i n , s t i l l account f o r approximately half of the observed spread of the peaks. The spurious pulses produced by thermionic emission from the dynodes of the photomultiplier are of the same magnitude as those pulses produced by very low energy gamma-rays and X-rays. These spurious pulses may be reduced both i n magnitude and i n number by cooling the tube to l i q u i d a i r temperatures. Hence the spectra of very weak i n t e n s i t y , low energy gamma-rays, ( <£ 1 KeV) may be investigated but t h i s method has not as yet been exploited to i t s f u l l e s t extent. The effect of the uniformity of the c r y s t a l ( i . e . uniform fluorescent y i e l d from a l l parts of the c r y s t a l f or a given of gamma-ray energy), the size of the c r y s t a l , the methodAmounting the c r y s t a l , and the degree of collimation of the incident gamma-ray beam on the energy resol u t i o n of the counter has been des-cribed i n the l i t e r a t u r e (2,3,4). Invesitgation has shown that aside from improved photomultiplier tubes and uniformity i n cry-s t a l s , the largest single gain i n resolution i s obtained by im-proved c r y s t a l mounting techniques. R.K. Swank has outlined ( 5 ) a method of mounting sodium iodide crystals i n order to ob-4 t a i n optimum l i g h t input into the m u l t i p l i e r and hence optimum reso l u t i o n . With t h i s method as a guide, a c r y s t a l mounting technique has been developed which i s capable of producing a counter with a res o l u t i o n , f o r example, of seven percent for the 60 two photoelectric l i n e s i n the spectrum of Co The technique^ of s c i n t i l l a t i o n spectrometry as introduced above has been used i n the performance of many kinds of experi-ments. A few of the more we l l known types of experiments are l i s t e d below: (i) The detection and measurement of gamma-ray spectra (especially i n the case of weak i n t e n s i t y spectra) produced by bombardment of target materials with accelerated p a r t i c l e s . ( i i ) The search f o r weak i n t e n s i t y gamma-rays from isotopes, ( i i i ) The, determination of cross-sections i n "bombardment" experiments, and absolute f l u x measurement of l i n e gamma-rays. (iv) The determination of decay schemes by means of ov-Tf, (3-ir and coincidences. (v) The measurements of i n t e r n a l conversion r a t i o s by measur-ing the r a t i o s of X-ray. f l u x . There are very many more specialized applications of t h i s tech-nique to p a r t i c u l a r experiments. So f a r t h i s technique has been applied by the author only to ( i i ) mentioned above. 5 I I . THE INTERACTION OF GAMMA-RAYS WITH THE CRYSTAL 'AND THE SPECTRUM SHAPE-. I t has been shown (3,4) that the pulse height d i s t r i b u t i o n obtained with a s c i n t i l l a t i o n counter f o r an incident beam of mono-energetic gamma-rays has a c h a r a c t e r i s t i c shape. In order that the energy of the incident gamma-rays may be determined from t h i s d i s t r i b u t i o n an analysis must be made of the effect on the shape of the spectrum of each of the three absorption processes: ( i ) Compton e f f e c t , ( i i ) Photoelectric e f f e c t , ( i i i ) Pair production. The c r y s t a l obtains i t s fluorescent energy from the energetic electrons which r e s u l t from the absorption processes. The pulse d i s t r i b u t i o n , i n i t s general aspects, i s then determined by the energy vs. number d i s t r i b u t i o n of these electrons. These d i s t r i -butions are calculated below f o r each of the absorption processes, from which the " i d e a l " d i s t r i b u t i o n can be calculated. The " i d e a l " d i s t r i b u t i o n i s , of course, distorted due to m u l t i -ple scattering events taking place i n the c r y s t a l , w a l l e f f e c t s , and by s t a t i s t i c a l fluctuations introduced by the photomultiplier tube. These effects are discussed below and a q u a l i t a t i v e argu-ment i s presented of these effects on the shape of the d i s t r i b u t -i o n . A. COMPTON EFFECT In considering the Compton effect i t i s assumed that the elec-trons i n the atom may be thought of as free and that the photon c o l l i d e s with an electron and i s deflected, the electron r e c o i l i n g INCIDENT PHOTON SCATTERED PHOTON W RECOIL ELECTRON FIGURE I The Compton Eff e c t , Showing Angular and Energy-Notations c o .Ol -O O.I LO IO PHOTON ENERGY IN MEV FIGURE I I Cross-Sections vs. Energy for the Compton Effect e<f the cross-section f o r the number of photons scattered; e Os the cross-section f o r the energy of the scattered photons; e OS. the cross-section f o r the energy absorbed by the electrons 4 6 i n a d i f f e r e n t d i r e c t i o n . I t i s the number vs. energy d i s t r i b u -t i o n of the r e c o i l electrons that must be calculated. In the calculations that follow, i t i s assumed that only primary proces-ses occur, i . e . , a l l degraded quanta escape from the c r y s t a l with no further interactions, and that the electrons lose a l l t h e i r energy to the c r y s t a l ( i . e . , no wal l effect) and radiate none i n the form of brehmstrahlung r a d i a t i o n . From the conservation of energy andnomentum i n the process, the r e l a t i v i s t i c equations f o r energy and mass, and the notation shown i n F i g . ( I ), the following expressions can be obtained: =U I (3) -nyl <f> J *<rv & = J — * (4) where o( = Kl e i n and Nishina ( 6 ) have carried out a quantum mechani-c a l c a l c u l a t i o n of the process and have obtained the following equation f o r the f r a c t i o n of the gamma-ray energy scattered i n a given d i r e c t i o n : ( 5 ) where l b = i n t e n s i t y of incident beam of gamma-rays, I = i n t e n s i t y of scattered beam at the angle Q and d i s -tance from the scattering electron of charge e and mass nr. 7 I f k(0) = cross-section f o r the number of photons scattered per electron and per unit s o l i d angle i n the d i r e c t i o n 9, t'hen equa-t i o n (5) may be written I * - j ? ? - - ' W « 0 Sir hv _± |[|+<A(I-. w h e r e k ( 9 ) . M ^ L ^ ^ t . ^ ; * 1 ' | t (6) In the above equation ^ - ( ^ ; = ^ eCt 'O) = cross-section f o r the number of photons' scattered i n to the s o l i d angle <Ln. i n the d i r e c t i o n e • The cross-section f o r the amount of energy scattered per electron and per unit s o l i d angle i n the d i r e c t i o n e i s Combining equations (1) and (6) K{9) becomes (7) where ^Os(©) i s the cross section f o r the energy of the photons scattered into s o l i d angle ASL i n the d i r e c t i o n & • I f the following definitions are made: (i ) e& = Compton t o t a l cross-section i . e . , cross-section f o r the number of photons scattered or for the t o t a l amount of energy removed from the beam. ( i i ) = Compton scattering c o e f f i c i e n t i . e . , cross-section for the amount of energy retained by the scattered photons then gCT' and e O^ are obtained by integrating equations (6) and (7) respectively over a l l possible d i r e c t i o n s . The re s u l t i n g equa-tions are: etf = „ ^ ^ l ^ - ± U i + " ] * k * > + > 4 - $ f e \ (8) , < & - ^ ^(H-*O+- ^ , + ^ x + 3 <:,+*o *J (9) Since e c ^ i s the cross-section f o r the t o t a l amount of energy re-moved from the incident beam, andgfl^ i s the cross-section f or the amount of energy retained by the scattered photons, then e<^ the cross-section f o r the amount of energy absorbed by the r e c o i l i n g electrons i s CM. Davisson ( 7 ) has calculated values f o r these cross-sections at various energies. They are shown i n F i g . ( H ) . Since the p r o b a b i l i t y that an electron w i l l be scattered into JLJXJ situated i n the d i r e c t i o n <b , i s the same as the pr o b a b i l i t y that a primary quantum w i l l be scattered into the s o l i d angle Juj-i n the d i r e c t i o n ^ , ^ and Abeing related by equation (4), then J r\ 1 «*-*•«• «*-*' (10) where k(0) and k((fr) have analogous meaning, but are f o r photons and electrons respectively and where k(^) i s given by equation (6). Now, i f equation (10) i s integrated only over (the polar angle $ ) the r e s u l t obtained i s isM, „ ^ . 4 H«i&„ ( u ) where the prime on the <S indicates that the $ dependence has been integrated out, and where ^effV^O ^ s cross-section d 4> . 9 fo r the number of electrons scattered between two cones whose hal f angles d i f f e r by unity. The quantity of interest i s the d i f f e r e n t i a l cross-section as a function of electron energy, which might be thought of as the number vs. energy d i s t r i b u t i o n s of the electrons. Mathematically t h i s i s dE*l ~ d<t> dEel (12) can immediately be found by d i f f e r e n t i a t i n g equation (3) and i t i s x  d* _ 1 [i+a<* -l- ( 1 + * ? W > J In order to f i n d (see equation (11)), - — ^ r m u s t f i r s t d<P d~&-be calculated. I f the polar coordinates are R, 0 and S, and i f the scatter-ing angle & or <f> i s associated with the polar angle 0, then the element of s o l i d angle i s for the photondjO- = sin 9 de d $ f o r the electron JLa! « sin 4 <*4> ^ Thus t^-a =: srn>e<*& d4> d-Cil $ d$ can be calculated from equation (4) The r e s u l t i s dxn ~ [0+*?- *(i+o<) W - * J * (14) On using equations (11), (12), (13), (14) the d i f f e r e n t i a l cross-section per unit energy becomes Mf^L J™LUfo){ o+«f-*x*~f4> lz (15) FIGURE III Compton e l e c t r o n d i s t r i b u t i o n f o r i n c i d e n t gamma-ray energies of 0.511 MeV and 1.28 MeV The dashed curves show these d i s t r i b u t i o n s spread out to 10$ r e s o l u t i o n . 10 in Now, i f the energy of the r e c o i l electron i s expressed Aunits of mc2 i . e . cXe|= Then equation (15) can be s i m p l i f i e d , (See Appendix I) giving where the maximum energy of the r e c o i l electron i s * e l < — - ) = - 7 ^ ( 1 7 ) Equation (16) has been calculated f o r the primary quanta energies of 0.511 MeV abd 1.28 MeV (<* = 1 and 2.5 re s p e c t i v e l y ) . The re-s u l t s are graphed i n F i g . ( I I I ) . In any experimental case the measured d i s t r i b u t i o n w i l l be spread out due to the f i n i t e energy resolution of the system. This spreading of the d i s t r i b u t i o n can be calculated i n the f o l -lowing way: (i ) The calculated d i s t r i b u t i o n i s divided up into t h i n v e r t i c a l s t r i p s . ( i i ) Each s t r i p i s put into the form of a Gaussian of the same area and with a width determined by the resolution of the system i . e . o" = ^ where E m = mean energy of the part i c u -l a r s t r i p R = resolution of system as de-fined i n the introduction cr = mean square deviation of the Gaussian. ( i i i ) The contributions from a l l the Gaussians are added up 11 and the resultant d i s t r i b u t i o n plotted. This has been done f o r the two d i s t r i b u t i o n s mentioned above as-suming a resolution of 10% which has been experimentally attained f o r energies of 1 MeV, and the r e s u l t s are shown i n F i g . (HI). In the Compton process, the electron with which the quanta i n -teracts has up t i l l now been assumed to be free. Since the bind-er ing energy of the K eleetron Aiodine i s approximately 29 KeV, t h i s assumption i s no longer v a l i d f o r incident quanta of energy less than, say, 100 KeV. I t would be expected then that there should be considerable modifications to the Compton d i s t r i b u t i o n at these low energies. Since the Compton d i s t r i b u t i o n i s r a r e l y observed at these energies due to the overwhelming presence of the photo-e l e c t r i c peak, these effects need not be considered. In general, i t has been found experimentally that the Compton d i s t r i b u t i o n i s not noticeable u n t i l incident quanta energies of several hundred KeV have been reached. In. t h i s energy region, and higher, then, the above mentioned effect i s negligble. B. THE PHOTOELECTRIC EFFECT The medium Z component (iodine Z - 53) of the c r y s t a l shows a reasonable photoelectric cross-section f o r gamma-ray energies up to several MeV. CM. Davisson has calculated ( % ) the photo-e l e c t r i c cross-section as a function of energy f o r various Z ab-sorbers. These calculations are discussed i n d e t a i l and the ac-curacy of the r e s u l t s i s stated f o r certain energy ranges. I t appears that over the energy range considered the r e s u l t s should be accurate to within 10%. FIGURE IV O S I . O 1 5 2 . 0 2 . 5 3 . 0 3 . 5 E N E R G Y O F T H E P H O T O N ( M E V ) 12 From the tables given i n t h i s report the cross-section f o r sodium iodide at various energies can be calculated. These values are plotted i n F i g . (IV). I t can be seen from t h i s curve tha t above 3 MeV the contribution due to the photoelectric effecjf i s n e g l i g i -b l e . When spectra of low energy gamma-rays are being investigated i t i s possible that the gamma-ray energy may go through the K ab-sorption edge of iodine (29 KeV). I f t h i s happens, the same con-siderations apply to the cross-section ( i . e . absorption c o e f f i c i e n t ) as those which apply i n the case of X-ray absorption theory,which can be found i n any text on X-rays. In e f f e c t , then, the c r y s t a l just becomes suddenly less e f f i c i e n t when the gamma-ray energy passes through an absorption edge. In the photoelectric process an electron i s ejected from one of the iodine (or sodium) s h e l l s , followed by the subsequent emis-sion of an X-ray. The photoelectron presumably loses a l l i t s en-ergy to the c r y s t a l (neglecting brehmstrahling and edge e f f e c t s ) , and the X-ray, due to i t s low energy, i . e . , K X-ray of iodine i s 29 KeV, i s assumed to be completely absorbed. Consequently, two or more electrons, one of which i s the o r i g i n a l photoelectron, simultaneously lose energy, where the t o t a l energy l o s t to the c r y s t a l must equal the f u l l energy of the gamma-ray. Hence, i n e f f e c t , the number vs. energy d i s t r i b u t i o n of the photoelectrons can be assumed to be a " l i n e " d i s t r i b u t i o n of e f f e c t i v e l y zero width, and corresponding to the f u l l energy of the gamma-ray. A "photopeak" should thus occur i n the d i s t r i b u t i o n and the posi-t i o n of t h i s peak can be taken as a measure of the energy of the incident gamma-ray. FIGURE V 13 For a counter with perfect resolution the pulse height d i s -t r i b u t i o n from the photomultiplier should be a " l i n e " d i s t r i b u -t i o n of zero width. This, of course, i s an i d e a l i z a t i o n and hence correction must be made f o r the f i n i t e resolution of the system. This i s done by replacing the * l i n e " by a Gaussian of the appropriate width, where the area under the Gaussian ( i . e . , the t o t a l number of photoelectrons produced) i s compatible with the photoelectric cross-section at the given energy. That the actual photopeak i s Gaussian has been v e r i f i e d by experiment. I f the c r y s t a l dimensions are very small, then the prob a b i l i t y of escape of the iodine X-rays i s no longer n e g l i g i b l e . An "es-cape peak" should then appear i n the d i s t r i b u t i o n with energy equal to the difference between the energy of the incident quanta and of the X-rays of iodine. With a very t h i n c r y s t a l i t might also be possible to have a peak at 2 9 KeV which would r e s u l t i f many of the photoelectrons escaped completely from the c r y s t a l while the X-rays of iodine were absorbed. Hower, due to "straggling" i n the w a l l effect and the f a c t that the above sequence of events i s not too probable, t h i s effect may be neglected. No peak at 2 9 KeV has yet been observed by the author, although escape peaks have. The magnitude of the wa l l effect depends on two factors: 1) The range i n Nal of the photoelectrons. 2) The dimensions of the c r y s t a l . The range vs. energy curve f o r the electrons has been calculated from Feather*s rule and i s shown i n F i g . (V ). Mateosian and Smith ( 8" ) have outlined a method for c a l c u l a t i n g the w a l l effect but due to the nature of the experiments so f a r performed by the author i t has not been found necessary to make t h i s c a l c u l a t i o n . C. PAIR PRODUCTION PROCESS 2 At energies greater than 2 mc , i . e . , greater than 1.02 MeV, absorption of gamma-rays by the process of pair production occurs. The cross-section at di f f e r e n t energies for t h i s process i n sod-ium iodide can be calculated from the tables published by Davis-son (7 ). A graph of these values i s shown i n F i g . (IV). The absorption of energy by the c r y s t a l due to pair produc-t i o n occurs i n the following manner: Consider an incident quantum of energy E y MeV (i ) The quantamannihilates, producing an electron-positron pair whose t o t a l k i n e t i c energy i s Ey -1.02 MeV. Both positron and electron are assumed to lose a l l t h e i r energy to the c r y s t a l . ( i i ) The positron then annihilates with an electron, produc-ing two quanta each with energy 0.511 MeV. ( i i i ) Both the a n n i h i l a t i o n quanta may be absorbed by the cry-s t a l , only one may be absorbed with the other escaping, or both may escape from the c r y s t a l . Hence, three peaks, designated Pair I , Pair I I , and Pair I I I should appear i n the spectrum with energies corresponding to Ey (both a n n i h i l a t i o n quanta captured), Ey - 0.511 MeV (only one an n i h i l a t i o n quanttf/n captured) and - 1 . 0 2 MeV (both a n n i h i l a -t i o n quanta escape) respectively. These peaks are i d e a l l y zero width peaks, but due to the f i n i t e resolution of the counter they are subjected to the same conditions of broadening as was i n d i -15 cated for the photoelectric peaks. The r e l a t i v e heights of the three pair peaks depend c r i t i c a l -l y on the dimensions of the c r y s t a l . These r e l a t i v e heights can-not be calculated exactly as a function of c r y s t a l dimensions but q u a l i t a t i v e l y , at l e a s t , some estimation can be made. For example, consider a c y l i n d r i c a l c r y s t a l whose dimensions are 3 cm. i n d i a -meter and 3 cm. i n length. Now i f i t i s assumed that a l l pairs are produced and annihilate some^where along the axis of the cry-s t a l or very close to i t , ( this i s a f a i r assumption for incident quanta energies up to 2 or 3 MeV and for good collimation) then f o r an order of magnitude c a l c u l a t i o n i t may be assumed that a l l a n n i h i l a t i o n quanta have a 1 . 5 cm. path length on the average be-fore escaping from the c r y s t a l . Suppose i t i s further assumed that i f an a n n i h i l a t i o n quantam suffers one scattering event i n the c r y s t a l that i t i s then completely absorbed, otherwise i t es-capes completely. For a . 5 1 1 MeV quantum the absorption c o e f f i -cient i n Nal i s 0 . 3 4 cm~^. From t h i s value and the above assump-tions the following p r o b a b i l i t i e s f o r a pair of a n n i h i l a t i o n quan-ta can be found: (i ) P r o b a b i l i t y that both quanta escape = 0 . 3 6 ( i i ) P r o b a b i l i t y that only one quantum escapes = 0.4&* ( i i i ) P r o b a b i l i t y that both quanta are absorbed = 0 . 1 6 Hence fo r these conditions the three pair peaks should be i n the r a t i o Pair I I I : Pair I I : Pair I = 0 . 3 6 : 0.1+B : 0 . 1 6 These three peaks, where the t o t a l area under them must be compa-t i b l e with the cross-section at the given energy, are superimpos-FIGURE VI Calculated pulse height d i s t r i b u t i o n f or the 2.62 MeV gamma-ray of RdTh assuming a l l a n n i h i l a t i o n quanta es-cape. A resolution of was assumed i n the calculations. 500 4 0 0 3 0 0 UJ 2 0 0 < tr o z H Z o 1 0 0 u Pair III Peak I..60 MEV 1 i Compton Distrlbutin 2.62 MEV Photopeak 1.0 2.0 ENERGY IN UNITS OF 3.0 4.0 S O 6.0 mc" (i.e. pulse height) 16 ed upon the Compton and photoelectric d i s t r i b u t i o n s to give the resultant d i s t r i b u t i o n s . At 0.511 MeV the absorption i s mainly by the Compton process,so that due to multiple scattering of the absorbed a n n i h i l a t i o n quanta,it would be expected that there would be considerable broadening of the Pair I and Pair I I peaks. At high energies (e.g., > 10 MeV) further broadening effects would res u l t from losses by brehmstrahling and by w a l l e f f e c t s . The rough calculations presented above show that the dimen-sions of the c r y s t a l are the most s i g n i f i c a n t factor i n deter-mining precisely the d i s t r i b u t i o n due to pair production. An i n -crease i n o v e r a l l dimensions w i l l make Pair I and Pair I I the dom-inant peaks, and for very large dimensions only Pair I should be s i g n i f i c a n t . For very small c r y s t a l s ( i . e . "disc" crystal) only Pa i r I I I would be s i g n i f i c a n t , but i n t h i s case w a l l effects are very important and considerable spreading of the d i s t r i b u t i o n due to t h i s effect would be probable. Since no rigorous calculation has been made for the r e l a t i v e heights of the three peaks the only diagram on the pair process F i g . ( VI ) i s constructed assuming that only the Pair I I I peak occurs" ( i . e . l i m i t i n g case for small c r y s t a l s ) . D. THE CALCULATED SPECTRUM SHAPE I t has been shown that, assuming primary events only, and neglecting other broadening effects each of the absorption proces-ses give r i s e to a c h a r a c t e r i s t i c pulse height d i s t r i b u t i o n . The r e l a t i v e number of pulses f o r a given gamma-ray energy due to each process can e a s i l y be found from t h e i r r e l a t i v e cross-sect-ions, i . e . , the r a t i o of the areas under the d i s t r i b u t i o n s must FIGURE VII Calculated pulse height d i s t r i b u t i o n s f o r gamma-ray energies 0.511 MeV and 1.28 MeV. The curves calculated assuming p r i -mary processes only and a resolution of 10$. FIGURE VIII x7 be equal to the r a t i o of the cross-sections. On t h i s basis, the expected pulse height d i s t r i b u t i o n has been calculated f o r i n c i -dent gamma-ray energies of 0.511 MeV, 1.28 MeV, and 2 .62 MeV. The f i r s t two d i s t r i b u t i o n s were calculated assuming 10 percent re s o l u t i o n , and the t h i r d assuming 8" percent resolution. These d i s t r i b u t i o n s are shown i n F i g . (VI) and (VEI). The pulse height f\C\ d i s t r i b u t i o n .for the Co gamma-rays (1.7 and 1.33 MeV i n cascade) has also been calculated, assuming 10 percent resolution, and i s shown i n F i g . (VII). The calculated d i s t r i b u t i o n s mentioned above hold only i n the l i m i t i n g case of very small c r y s t a l s . As the c r y s t a l dimensions are increased these d i s t r i b u t i o n s w i l l only be an approximate i n -d i c a t i o n of the shape. The effects of c r y s t a l dimensions and mul-t i p l e scattering w i l l be considered i n the next section. E. MULTIPLE SCATTERING Figures (VI), and (VII), and (VLLT) show the spectrum shape calculated on the assumption that multiple scattering events do not occur. This assumption i s i d e n t i c a l to the assumption that the c r y s t a l i s very small. Since experimentally, the cry s t a l s are of f i n i t e dimensions, i t can be expected that with increasing dimensions multiple scattering events w i l l become more prominent. Multiple scattering events play a n e g l i g i b l e r o l e i n the d i s -t r i b u t i o n from the photoelectric effect (aside from the pos s i b i -l i t y of an escape peak and a 29 KeV peak mentioned e a r l i e r ) . I f brehmstrahlung i s construed as a multiple scattering event, then at high energies t h i s e f f e c t w i l l become apprecistie, and pulses 18 w i l l be l o s t from the photopeak due to escape of brehmstrahlung r a d i a t i o n . This effect can be neglected except at f a i r l y high energies. (>10 MeV) The presence of three peaks i n the pair production d i s t r i b u -t i o n has been demonstrated previously. The dependence of the r e -l a t i v e heights of these peaks on the dimensions of the c r y s t a l has been indicated but no quantitative estimations have been made. The largest contribution to multiple scattering comes from the Compton process where a secondary quantum i s produced i n every c o l l i s i o n . Q u a l i t a t i v e l y , i t would be expected that many pulses from t j i e region of the Compton peak w i l l be transferred to the photopeak due to the capture of the soft back-scattered quanta. For example, again consider a c y l i n d r i c a l c r y s t a l 3 cm. i n d i a -meter and 3 cm. i n length and a collimated beam of, say, 1.28 MeV gamma-rays incident upon i t . The back-scattered quanta w i l l be of the order of 300 KeV. Assume that a l l these quanta o r i g i n -ate uniformly along the axis of the c r y s t a l , (this assumption i s v a l i d within the accuracy desired since the h a l f thickness i n Nal for 1.28 MeV gamma-rays i n 4.3 cm.) and that the average escape path length of the quanta i s 1.5 cm. Then from the absorption c o e f f i c i e n t 0.6 cm""-*- for 300 KeV quanta see F i g . (IV ) approxima-t e l y 60% of the back-scattered quanta are absorbed, mostly through the photoelectric process. On t h i s simple c a l c u l a t i o n i t would be expected that approximately 60% of the pulses i n the Compton peak would be shifted upwards to some extent. A l l other quanta which are scattered in a d i r e c t i o n other than back w i l l be subject to the same considerations but with a correspondingly smaller ef-19 f e e t . Consequently, the photopeak w i l l have added to i t very many pulses from the Compton d i s t r i b u t i o n . Experimentally i t has been found that the photopeak i s much larger than the cross-sec-t i o n would indicate, where the increase i s roughly i n agreement with the above c a l c u l a t i o n s . These r e s u l t s w i l l be described l a t e r i n the section on experimental r e s u l t s . I t i s quite obvious from these arguments that there are two l i m i t i n g cases: ( i ) Very small c r y s t a l s where a l l degraded quanta escape. These calculations have been carried out e x p l i c i t l y i n the preced-ing sections. ( i i ) Very large c r y s t a l s where a l l the degraded quanta are completely absorbed and the resultant d i s t r i b u t i o n consists of only one peak corresponding to the f u l l energy of the incident gamma-ray. As the c r y s t a l dimensions are varied from very small to very large between these two l i m i t s , t h e r a t i o of Compton peak height to photopeak height should decrease steadily to zero. The cry-s t a l dimensions which give the best resolution cannot be predic-ted unless the above calculations are carried out exactly. These dimensions are determined experimentally as w i l l be described i n the section on experimental r e s u l t s . Whenever possible, experiments have been done using a precise-l y collimated beam to reduce the broadening effects of multiple scattering. I t i s quite easy to see how an uncollimated beam would r e s u l t i n very poor resolution by assuming i n the argument above that scattered quanta could originate at any point within the cry-20 s t a l . R. Hofstadter (2 ) has demonstrated very f o r c i b l y the ef-fe c t of collimation on the resolution. » F. RESOLUTION OF THE SCINTILLATION COUNTER The s t a t i s t i c a l spread i n the pulse height d i s t r i b u t i o n of a s c i n t i l l a t i o n counter i s influenced by the following factors: ( i ) The number of photons emitted by the phosphor, ( i i ) The number of photons transmitted to the photocathode. ( i i i ) The quantum e f f i c i e n c y of the photocathode. Xiv) The number of photoelectrons reaching the f i r s t dynode. (v) The secondary emission r a t i o of the dynodes. Each of these factors has associated with i t a s t a t i s t i c a l un-ce r t a i n t y . P.W. Roberts has deduced an expression ( 9 ).which gives the spread of the d i s t r i b u t i o n due to these uncertainties. This expression i s t where C = f r a c t i o n a l variance i n pulse height d i s t r i b u t i o n NI = number of photons emitted by the phosphor & = variance of N m i = gain of the f i r s t stage m - gain of each succeeding stage Bi = variance of the secondary emission r a t i o of the f i r s t stage S = variance of the secondary emission r a t i o of each suc-ceeding stage 2 variance = (standard deviation) f- = f r a c t i o n of photons transmitted to the photocathode 21 -/» = quantum e f f i c i e n c y of the photocathode ^ = f r a c t i o n of photoelectrons which reach the f i r s t dynode A binomial d i s t r i b u t i o n was assumed i n calculating the effects of the factors f, p, and q, and the expression has been approxi-mated to the case of a large number of dynode stages. Equation (1) can be rewritten R J = 5 * | ^ J ? ) ( 2 ) where R 2 = [width of peak at h a l f max. (MeV)] 2 = (2 x 1.18 <S~)2 \ energy of peak (MeV) / The numerical factor i s that one which converts the standard de-v i a t i o n of .a Gaussian into the f u l l width at half maximum. » • *(•#- ') E = energy of peak i n MeV _ N ^ P f r — _ n u m D e r 0 f photoelectrons per MeV reaching the f i r s t dynode I f the number of photons per MeV produced by the incident gamma-ray i s assumed to follow a Poisson d i s t r i b u t i o n then the term A becomes zero. However, A has been found to be non-zero, i n most cases, but very small, so i t i s l e f t as a parameter to be determined by experimental r e s u l t s . This term, then, represents the spread of the d i s t r i b u t i o n due to non-uniform response of the c r y s t a l . Since the term A has been found to be very small, the second term only of equation (2) need be considered. 22 Then R a ~ s. £ I f the photomultiplier gain per stage i s assumed to be 3 , then B. i s approximately 4 / 3 . For an incident energy, say, of 1 MeV I t i s quite obvious that n, the e f f e c t i v e number of photoelectrons produced at the photocathode per MeV, determines the ultimate re-solution attainable with the counter, e.g. i f n = 500 then R ^ 12.2% I f n = 1000 then R » 3 .7$ For a given c r y s t a l and photomultiplier tube the only factor of which can be increased i s f, the f r a c t i o n of the photons which reach the photocathode. I t i s es s e n t i a l , then, that e f f i c i e n t c r y s t a l mounting^ techniques are developed. 23 I I I . CRYSTAL MOUNTING TECHNIQUES I t has been shown that the largest single gain i n resolution, aside from improved cr y s t a l s and photomultiplier photocathode e f f i c i e n c i e s , can be obtained by improved c r y s t a l mounting tech-niques. Considerable work has been done on improving the e f f i -ciency of l i g h t c o l l e c t i o n of the mounts. Sodium iodide c r y s t a l s are very deliquescent, the surfaces immediately becoming discoloured on contact with the water vapour i n the atmosphere, so that any mount designed f o r the c r y s t a l must provide perfect protection against water vapour. The o r i -g i n a l method of mounting used by the author consisted of immers-ing the c r y s t a l i n a clear, water free, mineral o i l i n a l i g h t t i g h t aluminum container. This container was highly polished on the i n s i d e , and the o i l contact between the c r y s t a l and the con-ta i n e r provided the necessary o p t i c a l coupling f o r optimum r e f l e c -t i o n e f f i c i e n c y . The o i l f i l m also acted as a preservative for the o p t i c a l properties of the c r y s t a l surfaces. The resolution obtained with mountings of t h i s type was never very good. For mountings of t h i s type G i l l e t t e has shown (10) that the entrapment of l i g h t due to Fresnel r e f l e c t i o n s constitutes a very serious loss i n the transmission of l i g h t to the photocathode. I t i s also shown that the transmission i s increased many times by using some form of diffuse r e f l e c t i o n at the surfaces of the cry-s t a l . Consequently, a method of c r y s t a l mounting was sought which provided t h i s necessary property. R.K. Swank has reported (5 ) a method of mounting c r y s t a l s PLATE I THE DRY BOX 24 using the highly e f f i c i e n t , d i f f u s e r e f l e c t i n g properties of powdered magnesium oxide. This method requires that the cr y s t a l s be mounted dry ( i . e . , completely free from a l l traces of o i l i n which they are stored) since the r e f l e c t i n g properties of the mag-nesium oxide are destroyed i f the powder becomes "matted" with o i l . This has made the design and construction of a "dry box" nec-essary so that a l l mounting operations can be carried out in. a dry atmosphere, thus preventing the surfaces of the c r y s t a l from being discoloured due to contact with moisture. The magnesium oxide, i t s e l f , i s s l i g h t l y deliquescent so that i t must be baked for several hours at about 500°C before i t i s used. A. THE DRY BOX The "dry box" i s a large metal box, of dimensions 30" wide x 18" deep x 20" high. I t has a sloping front window 27" x 11" made of p l e x i g l a s s . Construction i s of aluminum sheet throughout, a l l j o i n t s are butt welded, and the whole enclosure i s made a i r - t i g h t . An a i r - t i g h t door i s provided on one side of the box to permit materials to be conveniently placed i n s i d e . Illumination i s pro-vided by a small, 15 watt fluorescent tube inside the box. The box contains a f l a t , removable tray 8" long x 11" wide x 1/2" deep i n which i s placed a mixture of sand and phosphorous pen-toxide as the drying agent. A small a i r blower i s so located that the atmosphere within the box i s continually circulated over the drying agent. A Moisture indicator i s placed inside the box. Two valves are supplied, one on each end of the box, so that a contin-uous flow of dried nitrogen may be passed through the box. This 25 ThiO' serves the purpose of sweeping out any organic vapours which may have accumulated due to the f i n a l c r y s t a l polishing process carried out inside the box. This i s necessary since the surfaces of the c r y s t a l quickly become clouded on contact with most organ-i c vapours. Work i s done i n the box through long sleeve rubber gloves which enter through glove ports i n the front panel. The ends of the gloves are attached to these ports by an a i r t i g h t s e a l , but may r e a d i l y be removed and replaced. The d e t a i l s of construction of the box are shown i n Plate . I . B. CRYSTAL MOUNTS The mounting f o r a sodium iodide c r y s t a l must s a t i s f y the f o l -lowing three requirements: (1) The gamma-rays must enter the c r y s t a l with l i t t l e absorp-t i o n or scattering. (2) The fluorescent l i g h t must be extracted with a uniformly high e f f i c i e n c y from a l l parts of the c r y s t a l . (3) The mount must be l i g h t t i g h t and impervious to water vapour. (4) O p t i c a l coupling to photocathode of photomultiplier must be good. In addition, such obvious requirements as ruggedness and i n -s e n s i t i v i t y to o r i e n t a t i o n and temperature variations must be met. The f i n a l design, with which most of the re s u l t s have been ob-tained, consisted of an aluminum container with a lucite window. S u f f i c i e n t space i s l e f t between the c r y s t a l and the container so FIGURE IX Rubb Mount f o r the c y l i n d r i c a l c r y s t a l drawn to scale. The mount i s o p t i c a l l y coupled to the photomulti-p l i e r tube with D.G. 200 s i l i c o n e ' o i l , and held i n place by a r i n g which f i t s i n the retaining r i n g groove. FIGURE X Nal Crysta Al. foil top held in place with black Duco paint Rectangular Al. foil container I with flanged bottom Al. retaining ring to hold container in place Lucite cylinder Black Duco paint D .C.200 Silicone oil Mount for the rectangular c r y s t a l drawn to scale. The mount i s attached to the photomultiplier tube with black e l e c t r i c a l scotch tape using D.C. 200 s i l i c o n e o i l f o r o p t i c a l coupling. FIGURE XI Lucite cylinder Mount f o r the t h i n c y l i n d r i c a l c r y s t a l drawn to scale. The mount i s attached to the photo m u l t i p l i e r tube with black e l e c t r i c a l scotch tape. Any places which may leak l i g h t are painted with black Ducco paint. 26 that powdered magnesium oxide may be packed i n to form a r e f l e c t -ing surface. The c r y s t a l i s o p t i c a l l y coupled to the l u c i t e win-dow by the use of D.C. 200 (Dow Corning) s i l i c o n e o i l (10^ c e n t i -stokes v i s c o s i t y ) • Movement of the c r y s t a l i s prevented by a l u -c i t e positioning r i n g ( i n mounts f o r c y l i n d r i c a l c r y s t a l s only) and by t i g h t packing of the assembly. This basic design has been adapted f o r mounting three types of c r y s t a l s : (1) C y l i n d r i c a l c r y s t a l s . (2) Rectangular c r y s t a l s . (3) Thin "wafer" c r y s t a l s . The d e t a i l s of the design of the mounts f o r each type of c r y s t a l are shown i n F i g . (IX ), ( X ), and ( X I ) respectively. Data par-t i c u l a r to each design are shown on the Figures. C. DETAILS OF TECHNIQUE A l l rough polishing of the c r y s t a l i s done outside the dry box. This i s carried out by using white b l o t t i n g paper soaked i n acetone as the abrassive surface. After being rubbed on t h i s surface several times the c r y s t a l i s transferred to a piece of b l o t t i n g paper soaked i n mineral o i l on which i t i s rubbed to r e -move a l l traces of acetone. This process i s repeated several times u n t i l the surfaces of the c r y s t a l are quite cle a r . The c r y s t a l i s then placed i n a bath of mineral o i l to preserve i t s surfaces. I t i s then transferred to the dry box, along with the other thor-oughly dried out components. A two hour "drying-out" time i s a l -lowed so that the atmosphere within the box can become thoroughly 27 dry. The c r y s t a l i s then removed from i t s o i l bath, i t s surfaces wiped completely free of a l l traces of o i l , and i f necessary i s given a f i n a l p o l i s h i n g . This i s done by "dry" polishing the c r y s t a l on b l o t t i n g paper. I t has seldom been found necessary that further polishing with organic solvents i s required once the c r y s t a l i s placed i n the dry box. However, provision i s made i n case t h i s i s necessary. After the f i n a l polishing, the mounts are assembled, and any joins i n the mount which may leak moisture into the c r y s t a l are covered with a t h i n layer of para f f i n wax. These joins are then painted over with black "Due$o" paint to form a permanent j o i n . The mountings are then removed from the box and attached to the photomultiplier tube, using D.C. 200 •technique s i l i c o n e o i l as the optical couple* With t h i s arrangement and the dry MgO, cr y s t a l s remain clear and the ,ps^ £orffiaa&e has not varied over a three month period. 2% IV. THE GAMMA-RAY SPECTROMETER It has been shown ( 11) that a pulse amplitude d i s t r i b u t i o n curve obtained with a d i f f e r e n t i a l analyzer i s subject to a smal-l e r s t a t i s t i c a l uncertainty than the curve obtained by d i f f e r e n -t i a t i n g an i n t e g r a l bias curve. Hence, the simplest d i f f e r e n t i a l analyzer was used f o r t h i s work, a "Single Channel Kicksorter", i n which only those pulses which l i e above a "baseline" voltage and within a "window" immediately above i t are counted. Either the base l i n e and window voltages can be adjusted separately, or as i s us-u a l f o r most of the work of t h i s t y p e , i t i s more convenient to set the window width and s h i f t the baseline. There are two main types of experiments which can be done with t h i s equipment: (a) Experiments involving bombardment of target materials with accelerated p a r t i c l e s i n which case one has to use either the integrated target current as a monitor, or a separate gamma-ray monitor as a reference, or perhaps both. (b) Experiments involving the measurement of gamma-ray spec-t r a from radioactive sources of reasonably constant or slowly de-caying a c t i v i t y . Most of the author's work consisted of experiments of the type (b). For t h i s purpose the baseline of the kicksorter was driven at a constant rate (with a f i x e d window width) by a synchronous motor through acsystem of gears. The gear system i s so designed that three d r i v i n g speeds are possible (1 volt/36 s e c , 1 v o l t / l min. 12 s e c , 1 volt/6 min.). The kicksorter output pulses are fed FIGURE XII P.M. H.T. Power Supply Pre -omp. Scope Pre—amp Power Supply Pulse Height Analyzer Scaler Count Rate Meter Power Supply Brown Pen Recorder BLOCK DIAGRAM OF THE SPECTROMETER FIGURE X I I I H,T. POWER. SUPPLY 2SOOV. MAX. 2 9 into a l i n e a r count rate meter, and the counting rate i s recorded on a "Brown" recording potentiometer. A block diagram of the sys-tem i s shown i n F i g . (XEE). I t has been found that f o r t h i s method to give r e l i a b l e r e -s u l t s the lowest counting rate (for a given channel width) that could be tolerated was of the order of 1 0 counts per second. In any experiment the window width was set so that t h i s minimum count-ing rate was always exceeded, with the added condition that the narrowest peak i n the d i s t r i b u t i o n should be at least three chan-nels wide. Measurements involving very weak i n t e n s i t i e s cannot be done by t h i s "continuous drive" method, and f o r these cases manual operation of the k i c k s o r t e r would be necessary. A description of each element of the spectrometer, along with the operating c h a r a c t e r i s t i c s are given below. A. H.T. POWER SUPPLY The gain of the photomultiplier tube i s very sensitive to the voltage applied across i t . In the type of tube used (E.M.I, type 6 2 6 2 ) the gain was found to increase by 5 0 percent f o r a v o l -tage change of 5 0 V. Consequently, a voltage supply of exception-a l l y long term s t a b i l i t y i s required. A supply has been construc-ted whose measured long term s t a b i l i t y was better than 0 . 1 percent. The supply i s e l e c t r o n i c a l l y s t a b i l i z e d using a 1 5 0 V. battery as reference and i s capable of d e l i v e r i n g 1 0 milli-amps. at 2 0 0 0 v o l t s . The c i r c u i t diagram i s shown i n F i g . (xm). 30 B. COUNT-RATE METER AMD HEAD AMPLIFIER POWER SUPPLIES Both these supplies are commercially b u i l t units obtained from the "Lambda Elec t r o n i c s " Corporation, and are designated "Model 2 8 " . A negative " r a i l " capable of de l i v e r i n g 10 mill.-amps, at minus 150 v o l t s has been b u i l t into each u n i t . Both these sup-p l i e s , and the H.T. supply are driven from a constant-voltage mains transformer. C. OSCILLOSCOPE A model 5HD "Tetronix" oscilloscope was used f o r in v e s t i g a t -ing pulse shapes and sizes at various points i n the c i r c u i t . No quantitative measurements were made with i t , and i t was used s o l e l y f o r convenience i n "s e t t i n g up" the apparatus. D. THE PHOTOMULTIPLIER TUBE An E.M.I, type 6262 fourteen stage m u l t i p l i e r was used f o r a l l the experiments. The tube was operated between 1000V and 1400V depending on the spectra being investigated. The noise background was found to be ne g l i g i b l e at a l l voltages, but when measurements on gamma-rays of energy less than 10 KeV were attemp-ted the noise becomes overwhelming. The maximum gain of these m u l t i p l i e r s i s of the order of 10? and the output was found to be l i n e a r f o r pulses up to 30 v o l t s at l e a s t . The si g n a l was taken from the l a s t dynode and not the f i n a l c o l l e c t o r since a posi t i v e pulse was required to d r i v e the analyzer. E. THE PRE-AMPLIFIER The pre-amplifier consists of a cathode follower stage only F I G U R E X I V .OOI 4: OOI =± . 390K V / / / / / D I 2 ; 5 0 0 K A \ \ \ \ \ D I 3 ,OOl=j= 5 5 0 0 K 68O K Collector H.T. + 2 Q O V 6 J 6 .1 -f pulses PRE-AMPLIFIER H.T. +- 2 0 0 V • 5 0 0 K <5K IOK .Ol From analyzer 1/2 6J6 25 - W \ A 4 - -3 0 K V I C j 82K p3 I Meg 1/2 6J6 >47K To .count rate meter •IOK SCHMITT CIRCUIT INPUT TO COUNT-RATE METER 31 (see F i g . (XIV)) f o r feeding into a 100 ohm l i n e . No ampl i f i e r stage was included since i t was f e l t that the pulses available from the photomultiplier tube were s u f f i c i e n t l y large f o r analyz-ing purposes. F. THE SINGLE CHANNEL ANALYZER The analyzer i s a commercially b u i l t unit supplied by the Atomic Instrument Company, and designated "Model 510". The operat-ing c h a r a c t e r i s t i c are given i n the pamphlet e n t i t l e d "Interim In-str u c t i o n Manual, Model 510 Single Channel Pulse Height Analyzer" obtainable from the Atomic Instrument Company. The operating char-a c t e r i s t i c s of the analyzer were found to be quite adequate f o r handling the pulses obtained from a Nal(Tl) s c i n t i l l a t i o n counter ( r i s e time & 0 .25 sec). The analyzer i s capable of handling pul-ses up to 100 V maximum, and has a maximum window width of 7.5 V. The maximum pulse input rate i s 2500 c p s . (for 5f? l o s s ) . G. THE COUNT RATE METER Elmore and Sands ( 12 ) give the theory of the operation of a count rate meter. A discussion of the l i n e a r i t y i s given and an expression i s deduced f o r the f r a c t i o n a l probable error i n the counting rate. This expression i s I 6 = o.&7 j where n = average counting rate RC = integrating time constant Cooke-Yarborough has designed ( 13 ) a count rate meter which uses a 100% feedback D.C amplifier to ensure l i n e a r i t y . A model was b u i l t to t h i s c i r c u i t and found to be li n e a r to better than . F I G U R E X V C O U N T RATE M E T E R TABLE I. Counting Rate f.s.d. Time (S Constant ec) % P.E. at Half 11 Scale de f l e c t i o n 1 0 5 c.p.s. 4.8 2 4 ' 1 2 0 4 8 0 X X X X 10-3 1 0 - 3 1 0 - 3 1 0 - 3 3.0 1 . 5 0 . 6 0 . 3 c.p.s. 4S 2 4 0 1 . 2 4 . 8 X X 1 0 - 3 1 0 - 3 3.0 1 . 5 0 . 6 0 . 3 1C-3 c.p.s. 4 8 2 4 0 1 . 2 4 . 8 X X 1 0 - 3 1 0 - 3 1 0 . 0 5.0 2 . 0 1 . 0 i o 2 c.p.s. 0 . 2 1 . 0 5 . 0 2 0 . 0 1 5 . 0 6.7 3.0 1 . 5 1 0 c.p.s. 0 . 2 1 . 0 5 . 0 2 0 . 0 47.0 2 1 . 0 1 0 . 0 5.0 This table shows the percent probable error f o r the count-rate meter at various counting rates and time constants. 32 one percent and to possess excellent long time s t a b i l i t y . The c i r -c u i t diagram i s shown i n F i g . ( X V ) . The count rate meter has s i x ranges, from 1 c.p.s. to 1 0 ^ c.p.s., with variable time con-stants f o r each range. Table I shows the percent probable error f o r the various time constants f o r each range. In h i s report, Cooke-Yarborough gives a detailed analysis of the c i r c u i t , and outlines the procedure f o r "setting-up" the meter. H. THE BROWN RECORDER A Brown dir e c t reading potentiometer Model N o . 1 5 3 X 1 2 i s used to record the output of the count rate meter. Pulse height d i s t r i b u t i o n f o r RaD and E u 1 ^ obtained with the t h i n c y l i n d r i c a l c r y s t a l . 33 V. EXPERIMENTAL RESULTS The pulse height d i s t r i b u t i o n s for the gamma-rays of Eu-^5^ RaD, Na 2 2, Z n ^ and RdTh have been obtained with d i f f e r e n t size c r y s t a l s with a view to comparing the experimentally obtained , shapes with the calculated shapes. These d i s t r i b u t i o n s have also been used to determine the conditions under which optimum resolut i o n i s obtainable with t h i s technique and to calculate from the s t a t i s t i c a l formula f o r resolution (equation (2)), page 6) the e f f e c t i v e number of photoelectrons produced at the photo-cathode per MeV of incident energy. The d i s t r i b u t i o n s f o r each source are considered i n d e t a i l below. The c r y s t a l s with which the d i s t r i b u t i o n s were obtained are designated #1, #2, and #3 f o r the t h i n c r y s t a l (1/6*" t h i c k -ness, 1-3/4" diameter), the 3/4" x 3/4" x 1-1/2" block, and the 1/2" cube respectively. A. RaD AND E u 1 5 5 The d i s t r i b u t i o n s f o r these two sources are shown i n F i g . (XVI) and were obtained with c r y s t a l #1. In the region below 20 KeV the resolution i s very poor, approximately 100%, so that the precise determination of energy i s impossible. From 20 KeV upward, the resolution r a p i d l y improves and i s about 50% f o r the 85 KeV l i n e i n Europium. The c r y s t a l container was made as t h i n as possible (see F i g . (X! )) to increase the detection e f f i c i e n c y f o r low energy (<20 KeV) quanta. The mounting technique f o r t h i s case was very d i f f i c u l t and usually resulted i n a loss of e f f i c i e n c y of l i g h t c o l l e c t i o n and hence poorer r e s o l u t i o n . More 34 work is being done to improve this technique, and by sacrificing some detection efficiency i t should be possible to improve the resolution. The relatively large 13 KeV peak in the RaD distribution shows the detection efficiency possible in this region. With better resolution i t may be possible to resolve the escape peak which should appear at approximately 17 KeV. This would probably show as a change of slope or a "bump" on the high energy side of the 13 KeV peak. ~" The distribution for Eu-^5 shows the presence of the well known gamma-ray at #5 KeV and of a 40 KeV X-ray resulting from K- conversion de-excitation of the #5 KeV level in Gadolinium. The 100 KeV gamma-ray has not yet been resolved, but with the possible increase in resolution mentioned above and by manual op-eration of the Kicksorter baseline so that improved statistics are possible, the peak should appear. The distribution also shows the presence of a peak at 10 KeV which is presumably the escape peak due to photoelectric absorption of the 40 KeV X-ray. Mateosian and Smith (8) indicate a method of calculating the in-tensity of this peak. However, since no attempt has yet been made to measure absolute intensities, relative intensities, or conversion coefficients this calculation has not been carried through. If experiments of this type are to be done a correction for the wall effect in this thin crystal must be made. An examination of Fig. (XVI) shows that there exists a small amount of non-linearity of response. If the RaD distribution is 155 used as the calibration curve,it can be seen that the Eu dis-35 t r i b u t i o n i s s h i f t e d a small amount ( & 5%) i n the low energy-d i r e c t i o n . The rapid deterioration of the MgO r e f l e c t i n g sur-face and hence the decrease i n l i g h t c o l l e c t i o n e f f i c i e n c y i s assumed to be responsible f o r t h i s non-linearity,since consider-able time elapsed between the runs on the two sources. As has been indicated above, further work i s i n progress to improve the technique i n t h i s energy region and i t i s f u l l y expected that the non-linearity w i l l be removed. Mateosian and Smith (8) describe a method Aobtaining spectra, both gamma and beta, by using a sodium iodide c r y s t a l which con-tains a small quantity of the source under investigation as an impurity. This method removes the d i f f i c u l t i e s introduced by the absorption of gamma-rays ( or beta p a r t i c l e ) i n the c r y s t a l container, and i n cases where source thickness i s important, a source of e f f e c t i v e l y zero thickness i s obtained. In experiments where t h i s i s not feasible i t i s possible to place the source i n d i r e c t contact with the c r y s t a l , both source and c r y s t a l being;, enclosed by the container. 22 B. Na * 22 The spectrum of Na consists of a 1.28 MeV gamma-ray and a 0.511 MeV a n n i h i l a t i o n r a d i a t i o n . F i g . (VII) shows the expected pulse height d i s t r i b u t i o n f o r these two energies on the assump-t i o n that only primary processes occur. The r a t i o s of the Compton peak height to the photopeak height are 0.92 and 3 . 6 f o r the 0.511 MeV and 1.28 MeV radiations respectively. Figs. (XVII) and (XVIII) show the experimentally observed F I G U R E X V I I 5 0 0 O 5 IO 15 20 25 3 0 35 PULSE HEIGHT - V O L T S FIGURE XVIII COUNTING RATE Arbitrary Units O 5 IO 15 20 25 30 35 PULSE HEIGHT VOLTS 36 d i s t r i b u t i o n obtained with c r y s t a l s #2 and #3 respectively. Both of these curves have an intense low energy (^r250 KeV) peak with the high energy side consisting of two components of d i f f e r e n t slope. I t has been assumed that the point at which t h i s change of slope occurs on each curve corresponds to the peak of the Compton d i s t r i b u t i o n . The majority of the counts i n these peaks, however, are assumed to be caused by back-scattered quanta (# 250 KeV f o r 1 MeV radiation) o r i g i n a t i n g i n the walls of the c r y s t a l mounting, the photomultiplier tube, and surround-ing objects. This second assumption can be supported by the f o l -lowing experimental evidence: (i ) A peak of approximately 250 KeV appeared i n a l l the d i s -t r i b u t i o n s whenever high energy (y 500 KeV) gamma-rays were pre-sent • ( i i ) Collimation of the incident beam reduced the irtensity of the peak and changed i t s shape, but never eliminated i t . ( i i i ) Without collimation the peak shape could be changed con-siderably (but not the r e l a t i v e i n t e n s i t y very much) by changing the position of the source. Under s i m i l a r conditions the Compton, and photoelectric d i s t r i b u t i o n s always remained constant i n shape and r e l a t i v e i n t e n s i t y . (iv) With s i m i l a r source geometry, the peak took on diffe r e n t shapes f o r cr y s t a l s of di f f e r e n t dimensions but, again, the Comp-ton and photoelectric d i s t r i b u t i o n s remained e s s e n t i a l l y the same Aside from t h i s rather intense low energy peak the shape of the d i s t r i b u t i o n i s roughly that expected from previous considera-t i o n s . The r e l a t i v e i n t e n s i t i e s of the Compton and phtopeaks 3 7 has been shown to be c r i t i c a l l y dependent on c r y s t a l dimensions as the r e s u l t of multiple scattering events. This effect as a function of c r y s t a l dimensions i s quite evident from the curves as can be seen i f the r a t i o r = Compton peak height f o r the 1.28 photopeak height MeV radiation i s considered. (The 0.511 MeV radiation i s not con-sidered since the Compton d i s t r i b u t i o n i s not w e l l defined). The following values of r have been obtained: ( i ) Calculated d i s t r i b u t i o n (primary processes only) r = 3 * 6 ( i i ) C r y s t a l #2 r = 1.1 U i i ) C r y s t a l #3 r = 1.25 The r a t i o increases as the dimensions become smaller thus v e r i f y -ing the q u a l i t a t i v e arguments presented previously. The resolu-t i o n also improves but t h i s w i l l be discussed separately i n a following section. The tr a n s f e r r i n g of pulses from the Compton peak to the photo-e l e c t r i c peak by multiple scattering processes l i m i t s the accur-acy of determining r e l a t i v e i n t e n s i t i e s by comparing areas under photopeaks. Although the 0.511 MeV Compton d i s t r i b u t i o n i s not wel l defined there i s an ind i c a t i o n that t h i s effect i s a funct-ion of energy as w e l l as c r y s t a l dimensions. Consequently, a rigorous ca l c u l a t i o n must eventually be rmade on the magnitude of t h i s process as a function of energy and c r y s t a l dimensions C. C o ^ , The Co spectrum i s known to consist of two gamma-rays, 1 . 1 7 MeV and 1 . 3 3 MeV i n cascade. The calculated d i s t r i b u t i o n (primary processes only) i s shown i n F i g . (VIII) and the experi-FIGURE XIX COUNTING RATE Arbitrary Units 10,000 IOOO IOO IO 1 I t PULSE HEIC HT DISTRIBUT ION FOR C( ^ 60 \ \ \ \ / / * \ Compton di( \ \ .tribution \ \ / \ \ \ 7 MEV Photop cak \ 1.33 MEV f \ D ft i\\ ^hotopeak Curve A Curve B obtained usir Obtained usir \q a 1/2 cub \q a 3/4 X 3/< e of Nal 4 X 1 1/2" block of Nal m u 1 10 15 2 0 25 30 PULSE HEIGHT VOLTS 35 F I G U R E X X 5 0 0 O 5 IO 15 2 0 25 3 0 P U L S E HEIGHT - VOLTS FIGURE XXI 38 mental d i s t r i b u t i o n s i n F i g . (XIX). An intense low energy peak ( # 2 5 0 KeV) also appears i n these d i s t r i b u t i o n s and i s interpre-22 ted i n a s i m i l a r manner to that of Na i n the previous.section. The effects of multiple scattering, again, are quite evident, and the values f o r the r a t i o r as defined i n the preceeding sec-t i o n are: (i) Calculated d i s t r i b u t i o n Ml.17 MeV) = 3 .0 ^-(1.33 MeV) = 8.3 ( i i ) C r y s t a l #2 A ( 1 . 1 7 MeV) = 1.05 A ( 1 . 3 3 MeV) = 1.45 ( i i i ) C r y s t a l #3 A U . 1 7 MeV) = 1.4 A ( 1 . 3 3 MeV) = 2 .1 These r a t i o s are larger for the smaller c r y s t a l , as expected, and the resolut i o n i s also markedly improved as w i l l be described l a t e r . The importance of c r y s t a l dimensions i s again emphasized by these curves, p a r t i c u l a r l y by the increased height of the photopeaks due to the transfer of Compton pulses. The above r a t i o s do not give a true picture since two Compton d i s t r i b u t i o n s are superimposed and the resolution was not s u f f i c i e n t l y good to resolve them. D. Z n ^ There are two main radiations i n the gamma-ray spectrum of Zn 6 5: a 1.114 MeV l i n e and 0.511 MeV a n n i h i l a t i o n r a d i a t i o n . The experimental d i s t r i b u t i o n s are shown i n F i g . (XX) and (XXI) for c r y s t a l s #2 and #3 respectively. Q u a l i t a t i v e l y , these d i s -t r i b u t i o n s are very s i m i l a r to those of Na 2 2 except that the F I G U R E X X I I 39 r e l a t i v e i n t e n s i t y of the a n n i h i l a t i o n r a d i a t i o n i s much smaller Hence an interpretation f o r these curves, s i m i l a r to that 22 f o r Na i s v a l i d . I t w i l l be noticed that the r a t i o r i s not as d i f f e r e n t , ( i . e . r = 0.94 and 1.02^as would be expected. E. RdTh DISTRIBUTIONS The radio-thorium spectrum has a number of gamma-ray l i n e s less than 1 MeV i n energy, and a reasonably strong one at 2.62 MeV. Since i t was f e l t that the above re s u l t s adequately covered ..the ensrgy region below 1.5 MeV, the high energy end only of the radio-thorium spectrum was investigated. At 2.62 MeV the pair production cross-section i n Nal i s s i g -n i f i c a n t so that the pair peaks should appear i n t h i s d i s t r i b u t i o n . F i g . (XXII) shows the experimental d i s t r i b u t i o n obtained with c r y s t a l #2. As was indicated on page 15 the r e l a t i v e i n t e n s i t i e s of the three pair peaks cannot be predicted on any reasonably simple theory so that no quantitative comparison with theory can be made. Q u a l i t a t i v e l y , however, these three peaks a r i s e i n the following manner: (i) The low energy peak. This peak i s due e n t i r e l y to the Pair I I I contribution and i s superimposed on the low energy.tail of the Compton d i s t r i -bution. I t s position corresponds to 1.60 MeV. ( i i ) The medium energy peak. This peak i s the sum of two contributions: the Com-pton d i s t r i b u t i o n from the 1.2S MeV gamma-ray, and the Pair I I d i s t r i b u t i o n . The position of the peak cannot be predicted accura-40 t e l y since the energy of the Compton peak i s not known precisely, the Pair I I d i s t r i b u t i o n i s broadened an indeterminate amount by multiple scattering of the absorbed a n n i h i l a t i o n quanta, and the r e l a t i v e contribution of each d i s t r i b u t i o n i s unknown ( i i i ) The high energy peak. This peak consists of three components: the photoelec-t r i c contribution, the Pair I contribution, and the multiple scattering contribution from the Compton peak. I t s position cor-responds to 2.62 MeV and due to.multiple scattering events the low energy side would be expected to be broadened. The presence of these three w e l l defined peaks i n the d i s -t r i b u t i o n shows that when pair, production occurs an accurate energy measurement i s possible. The use of a larger c r y s t a l w i l l increase the r e l a t i v e i n t e n s i t y of the high energy peak as w e l l as increasing t h e . e f f i c i e n c y of detection f o r high energy gamma-rays. I f both the low and high energy peaks can be i d e n t i f i e d in an unknown d i s t r i b u t i o n , an energy c a l i b r a t i o n i s immediately possible since t h e i r difference i n position corresponds to 1.02 MeV. The appearance of three peaks i n the pair production d i s t r i -bution has the disadvantage that i f a spectrum consists of two or more gamma-rays d i f f e r i n g i n energy by 1.2 MeV or l e s s , the resultant d i s t r i b u t i o n w i l l be very d i f f i c u l t to analyze, i . e . , fo r two gamma-rays s i x peaks w i l l be i n a very small region. In many experiments where t h i s occurs, the use of a single c r y s t a l s c i n t i l l a t i o n counter i s unsatisfactory and alternative schemes must be sought, e.g., the 3 c r y s t a l pair spectrometer ( 1 5 ) . 41 F. ENERGY RESOLUTION One of the main reasons f o r undertaking t h i s work was to f i n d the conditions under whin optimum resolution i s achieved f o r a given energy range. For the region below 100 KeV i t was found that a t h i n c r y s t a l gives the best r e s u l t s , both i n detection e f f i c i e n c y and i n re s o l u t i o n . With a d d i t i o n a l work, further im-provements are expected i n t h i s energy region. In the energy range 0 .5 MeV to 1.5 MeV i t has been found that the small c r y s t a l gave the better r e s o l u t i o n . Table I I shows the resolution i n % achieved with both c r y s t a l s #2 and #3 f o r the peaks i n the Na 2 2, Zn^5f and Co^O d i s t r i b u t i o n s . No values were assigned the 1.17 MeV photopeaks i n the Go^° d i s t r i b u t i o n s since i t was very d i f f i c u l t to determine t h e i r h a l f heights. For the same reason, the resolution assigned to the 0.511 MeV A c peaks i n .Zn ' i s subject to considerable error. TABLE I I Crystal No. Na22 .511 MeV Peak N a ^ 1.28. MeV Peak ZnO .511 MeV Peak Znt>5 1.114 Mev Peak Co°U i 1.33 MeV Peak #2 14.7 9.1 18.8 11.3 9.3 #3 12.7 8.0 12.2 8 . 0 7 .0 The e f f e c t i v e number of electrons produced at the photocath-ode per MeV of energy incident on the c r y s t a l has been calculated from the Na d i s t r i b u t i o n s using equation (2) page 21 . The values obtained are 680 and 930 f o r cr y s t a l s #2 and #3 respectively. 42 The values of A (see page 21) were found to be zero within^ the accuracy of the calculations. The smaller c r y s t a l gives better resolution as a r e s u l t of the following two e f f e c t s . ( i ) Less broadening due to multiple scattering as has been previously emphasized. ( i i ) Better l i g h t c o l l e c t i o n due to the smaller dimensions of the c r y s t a l . I t should be noted the "n", the e f f e c t i v e number of photo-cathode electrons per MeV i s not a true values since the equat-ion f o r c a l c u l a t i n g i t does not include a factor accounting f o r broadening by multiple scattering. I t i s concluded from these r e s u l t s that to about 2 MeV, the best resolution i s achieved with a c r y s t a l of rather small dimen-sions ( 4. 1/2" cube). A lower l i m i t , of course, i s set on the dimensions by; 1. The magnitude of the w a l l effect which increases with decreasing dimensions and higher energies, and 2. by the i n t e n s i t y of the r a d i a t i o n being measured i n which case the dimensions must be chosen so that a reasonable counting rate i s obtained. I t i s doubtful whether further s i g n i f i c a n t improvements i n reso l u t i o n w i l l be obtained by a d d i t i o n a l work on mounting tech-niques. Improvements w i l l have to wait on the development of more e f f i c i e n t phosphors and photocathode surfaces. 43 G. THE SEARCH, FOR GAMMA-RAYS FROM TRITIUM The t r i t o n i s known to decay (14) to He3 by beta-emission with an end point of approximately l£ KeV and with a h a l f - l i f e of approximately 12 years. A source of t r i t i u m adsorbed i n z i r -conium on a thick tungsten backing was investigated with the t h i n c r y s t a l to determine the presence, i f any, of a low energy gamma-ray. Since t r i t i u m decays by beta-emission, the pulse height d i s -t r i b u t i o n would consist mainly of accontinuous d i s t r i b u t i o n , c u t t i n g o f f at IB KeV, as the r e s u l t of brehmstrahlung radiation from the beta-p a r t i c l e s . Any low energy peak would be superim-posed on t h i s continuous d i s t r i b u t i o n . With the resolu t i o n ach-ieved with the t h i n c r y s t a l , i t would be necessary f o r a gamma-ray to be greater than 7 KeV i n energy and at least comparable (to an order of magnitude) i n i n t e n s i t y to the brehmstrahlung radiation,to be detectable. To t h i s degree of experimental ac-curacy, there i s no in d i c a t i o n of the presence of a gamma-ray. The d i s t r i b u t i o n had a plateau at a very low energy, partly obscured.by the large noise background. I t was thought at f i r s t that t h i s plateau resulted from the presence of a gamma-ray. However, by in s e r t i n g t h i n aluminum absorbers (from .001" to .015") between the source and the counter i t was found that the plateau developed into a peak, and as the absorber thickness was i n -creased the peak shifted upward i n energy to a maximum of IS KeV. The i n t e n s i t y , of course, dropped rather d r a s t i c a l l y . Since A Obtained from the Atomic Energy Commission of Canada. 4 4 the absorption of gamma-rays increases very rapidly with a de-crease i n energy the above phenomena was attributed to the i n -creasing absorption of the lower energy quanta i n the continuous brehmstrahlung d i s t r i b u t i o n . The fact that the upward s h i f t i n peak energy ceased at IB KeV v e r i f i e s t h i s . A sim i l a r experiment was done with the 13 KeV peak i n the RaD d i s t r i b u t i o n . No s h i f t i n the energy of the peak was noticed with increasing absorber thickness. From t h i s , and the above argument i t was concluded that the plateau i n the t r i t i u m d i s t r i b u t i o n was not due to a low energy gamma-ray. 45 APPENDIX I Calculation of the Compton Electron D i s t r i b u t i o n , The formula obtained on page 9 f o r the Compton electron d i s t r i -bution i s zans a> i (1) where k(&) i s given by eqn. (6).page 7 This equation can be s i m p l i f i e d giving equation (16) page 10 by converting the units of the electron energy to c / ^ = (a) The s i m p l i f i c a t i o n of cos2<f> £•/ ~ ki/j v £ e i — - —./ see eqn. (3) page .6 Solving t h i s equation f o r cos2<^ , the result i s c o ^ = ^ L i ^ i l ( 2 ) (b) A s i m i l a r s i m p l i f i c a t i o n f o r cos 0 gives (c) *he expression f or k(6) given on page 6 can be s i m p l i f i e d with the .iU.se of equation (3) above and the new energy u n i t s , giving k $ = ^ | ± i ^ o c ^ ^ ( 4 ) Then using equations (2 ) and (4), equation (1) becomes de cf _ TTA> APPENDIX I I 46 THE SCINTILLATION OF ALPHA PARTICLES IN AIR As a preliminary to the investigation of the s c i n t i l l a t i o n s produced by i o n i z i n g p a r t i c l e s i n gasses and vapours, the s c i n -t i l l a t i o n s produced i n a i r by alpha p a r t i c l e s have been examined. •* This i n v e s t i g a t i o n was carried out i n the following manner: ( i ) A polonium alpha source was mounted i n a l i g h t t i g h t box. ( i i ) The i n t e r i o r of the box was viewed with an R.C.A. 5^19 photomultiplier so situated that any s c i n t i l l a t i o n s produced by the alpha p a r t i c l e s would be detected. ( i i i ) The source was so placed that i t s self-luminescence could not reach the photomultiplier. A suitable shutter was con-structed such that the alpha p a r t i c l e s could, when desired, be prevented from traversing the box. (iv) The counting rate from the photomultiplier was measured with the shutter "covering" the source and with the shutter re-moved from the alpha p a r t i c l e beam. A s i g n i f i c a n t increase, approximately eight times the back-ground, was observed when the alpha p a r t i c l e s were allowed to t r a -verse the box. This increase was attr i b u t e d to the s c i n t i l l a t i o n s produced i n the a i r within the box. The pulse amplitudes were small, of the same order as large noise pulses, but the l i g h t c o l l e c t i o n was not very e f f i c i e n t . This preliminary investigation established the existence of the e f f e c t . In view of the meagre information on the number of photons and t h e i r energy produced by i o n i z i n g events i n gasses, 47 further work i s indicated; namely the v a r i a t i o n of the effect with pressure and with the nature of the gas. The t h e o r e t i c a l side of t h i s problem, unlike the associated one where ion pairs are produced, has been l i t t l e discussed. However, the publica-t i o n by Grun and Schopper (16) showed that t h i s l i n e of work was more advanced elsewhere, and since the author's main interest was i n the investigation of gamma-ray spectra with s c i n t i l l a t i o n coun-t e r s , the above work was discontinued. This effect could c l e a r l y be responsible f o r some of the strange r e s u l t s reported by Richards and Cole (1#) and Richards and Dee ( l g ) . BIBLIOGRAPHY (1) Hofstadter Physical Review 7 4 , 1 0 0 , 1948 (2) Hofstadter and Mclntyre Physical Review 7 8 , 6 1 7 , 1950 (3) Hofstadter and Mclntyre. Physical Review 7 9 , 3 8 9 , 1950 (4) Hofstadter Physical Review 8 0 , 6 3 1 , 1950 (5 ) Swank and Moenich Rev.Sci. Instruments 23, 5 0 2 , 1952 (6 ) Klein and Nishina Z.Physik 5 2 , 8 5 3 , 1929 (7) Davisson and Evans Review of Modern Physics 2 4 , 7 9 , 1952 (8) der Mateosian and Smith Physical Review 8 8 , 1 1 8 6 , 1 9 5 2 (9) Roberts Proc.Physical Society A, 192 , 1 9 5 3 (10) (11) G i l l e t t e Westcott and Hanna Report f o r the Linde A i r Products Co. Tonawanda, New York. Rev.Sci.Instruments 2 0 , 1 8 1 , 1949 (12) Elmore and Sands Electronics McGraw H i l l , 1949 (13) Cooke-Yarborough Proc.Inst.Elect.Engs. Part I I 9 8 , 1 9 1 , 1 9 5 1 (14) Langer and Moffat Physical Review 8 8 , 6 8 9 , 1952 ( 1 5 ) Johansson P h i l . Magazine 4 3 , 2 4 9 , 1952 (16) Grun and Schopper Z.Naturforsch. 6 A , 6 9 8 , 1 9 5 1 (17) Richards and Cole Nature 1 6 7 , 2 8 6 , 1 9 5 1 (IS) Richards and Cole Nature 1 6 9 , 7 3 6 , 1 9 5 1 

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