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The development of a fast time-sorter and its use in the measurement of the lifetime of positrons in… Jones, Garth 1955

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THE DEVELOPMENT OF A FAST TIME-SORTER AND ITS USE IN THE MEASUREMENT OF THE LIFETIME OF POSITRONS IN ALUMINIUM AND MICA by GARTH JONES  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE  Members of the Department of Physics  THE UNIVERSITY OF BRITISH COLUMBIA September, 1955  ABSTRACT  A new type of fast "time-sorter" has been developed, employing a germanium diode as the detecting element.  This  instrument converts time delays between coincident events into a pulse amplitude d i s t r i b u t i o n , which i s then analyzed by a "kick-sorter", enabling a complete coincidence resolution curve to be recorded simultaneously.  The resolution curves  obtained with this apparatus were found to have half-widths of about 1 milli-microsecond, comparable with those obtained by delayed coincidence c i r c u i t s . Using this time-sorter, the lifetimes of positrons i n Aluminium and Mica wer* then studied.  The positron l i f e - t i m e  i n Aluminium was obtained by measuring the centroid s h i f t s between the coincidence resolution curves r e s u l t i n g from the 22 observation of a Na  source embedded i n A l , and an assumed  "prompt" source of cascade gamma rays, A s ^ .  This l a t t e r  source was employed for the comparison because the energies of i t s coincident gamma rays are s i m i l a r to the 1.28 Mev and 22 511 Kev. gamma rays of Na  . This eliminates the problem of  centroid s h i f t s due to inequalities i n pulse-height and r i s e time between the two sources.  The  positron l i f e - t i m e i n mica was  comparing the centrold  obtained  s h i f t s of the resolution  by  curves  r e s u l t i n g from the annihilation of positrons i n mica and Aluminium. The measured positron l i f e t i m e i n Aluminium i s (1.6 r 0.4) and  x 10"  10  sec,  the l i f e t i m e i n Mica i s longer than this value by (0.7  t  0.4)  x 10"  1G  sec.  in  ACKNOWLEDGMENTS  I would l i k e to thank my supervisor, Dr. J.B. Warren, f o r many suggestions  during the course of t h i s research,  and Dr. C.A. Barnes f o r . h e l p f u l discussions during the thesis preparation. I also wish to thank Mr. G.C. Neilson f o r many h e l p f u l discussions and assistance. Thanks are also due the other members of the Van de Graaff group, e s p e c i a l l y Dr. K.L. Erdman, Mr. L.P. Robertson and Mr. J.B. E l l i o t t who offered much i n the way of knowledge and assistance. F i n a l l y , I wish to thank the National Research . Council f o r scholarships which have enabled me to carry out these studies.  TABLE OF CONTENTS Chapter I. II.  Page INTRODUCTION  1  THE CONSTRUCTION OF A FAST TIME-SORTER CIRCUIT  3  1.  2.  A Discussion of Previous Fast Coincidence C i r c u i t s  3  A. B. C. D.  4 4 5 6  The P a r a l l e l Coincidence C i r c u i t . . . The Bridge Coincidence C i r c u i t . . . . The Series Coincidence C i r c u i t . . . . Fast Time-Sorters  Description of the C i r c u i t  8  A. B.  8 8  PreliminaryElementary Description of Operation i. il. iii. iv. v.  .  Counters . . ,. ' Limiters and Shorting Stub . . Time-Sorter Main Amplifier Side-Channel Pulse-Height Analyzers v i . Slow Coincidence Unit and Gate Pulse Generator v i i . The Gated Biased-Amplifier . . . . C.  The The The The The  A Detailed Description of the Components and Associated Problems . . i . The Counters . . . . . . . . . . . a. The Counter Assembly . . . . . b. Voltage Supply and Socket Considerations , . c. Degeneracy of Output Pulses . .  8 9 9 10 11 11 12 12 12 15 16 16  i i . The Limit ers a. Choice of the Limiter Tube . . b. Discussion of C i r c u i t Operation and Component Values .  18 18 19  i i i . The H e l i c a l Delay Line i v . The Pulse Length Equalizer . . . . v. The Time-Sorter a. The Diode and Integrator . . . b. The Output Pulse Formation . .  21 21 23 24 24  TABLE OF CONTENTS - CONTINUED Chapter  Page  II  v i . The Temperature S t a b i l i z e r . . . . v i i . Associated Equipment . . . . . . . 3.  4. III  Performance of the Time-Sorter  29  A. B. C.  29 30 31  Resolution Stability Linearity  32  Discussion of C i r c u i t  USE OF THE FAST TIME-SORTER TO MEASURE LIFETIMES OF POSITRONS IN ALUMINIUM AND MICA 1.  33 .  33  Summary of Previous Results . . . . .  33  Discussion of Positron Decay i n Metals A.  i . Theory of A n n i h i l a t i o n by Collision . . . . . i i . Theory of Formation of Positronium B. The D i f f i c u l t i e s Inherent i n Absolute Lifetime Measurements, and Their Solutions i . B e l l and Graham's Solution . . . . i i . Minton's Method i i i . The A r t i f i c i a l Na22 Method . . . . 2.  3.  26 29  35 38  40 41 42 43  The Measurement of the Absolute Lifetime of Positrons i n Aluminium  43  A. B. C.  Use of A s ^ as the "Prompt" Source . Preparation of the Sources . . . . . The Experiment  43 45 48  i . The Experimental Procedure . . . . i i . The Time Calibrations i i i . Pulse Height Dependence on Counting Rate i v . Results  48 49 49 50  The Measurement of Positron Lifetime ; i n Mica  50  A. B. C.  51 51 51  Method Procedure Results  TABLE OF CONTENTS - CONCLUDED Pa^e  Chapter 4.  Discussions and Conclusions  Appendices A.  The Derivation of Theoretical Coincidence Resolution Curves f o r Fast Coincidence Circuits.  B.  Calculation of the R e f l e c t i v i t y of Amphenol Connectors f o r Fast Pulses  C.  Derivation of the Equation Relating Mean Lifetimes with Centroid S h i f t s . BIBLIOGRAPHY  51  LIST OF ILLUSTRATIONS Table  Facing Pag.e 76  1.  As'  Gamma-Ray Energies and Intensities . •  1^  Fast Rossi ( P a r a l l e l ) Coincidence C i r c u i t .  Ij.  b  Bridge Coincidence C i r c u i t . . . . . . . . .  ij.  c  Series Coincidence C i r c u i t  Figure la  ., d  l±  Block Diagram of a Series Time-Sorter . . .  l|.  2  Block Diagram of the Fast Time-Sorter . . .  3  Method of Time-Sorter Operation  10  4  Limiter C i r c u i t  16  5  Distorted Resolution Curve due to Capacitive De-coupling of Photo-multiplier  ....  8  17  6  Time-Sorter C i r c u i t . .  23  7  Temperature S t a b i l i z e r C i r c u i t  26  8  Gated Biased-Amplifier C i r c u i t  29  9  T r i p l e Coincidence C i r c u i t  29  10  Gate Pulse Generator  29  11  Side-Channel Pulse-Amplitude Analyzers  12  A s ^ C o i n c i d e n c e Resolution Curves  13  Effect of Side Channel Discriminator Settings on Resolution Curves . . . . Coincidence Resolution Curves I l l u s t r a t i n g S t a b i l i t y of Apparatus Decay Scheme of A s ^  14 15  7  . .  ....  29 30 30 31 kk  LIST OF ILLUSTRATIONS - CONTINUED Figure 16  17  Facing Page 76 22 Gamma-Ray Spectra of As and Na Using a Nal Crystal and a RCA 634-2 Photomultiplier 22 Na Gamma-Ray Spectrum, Using Diphenylacetylene Crystals and RCA 1P21 Photomultipliers  k5  k&  . .  I4.8  19  Experimental Arrangement  20  Example of^Coincidence Resolution Curves for As7o (Prompt), and Positron A n n i h i l ation i n A l  49  18  Side-Channel Energy C a l i b r a t i o n Curves  21  Time C a l i b r a t i o n Curve  22  Pulse Height Dependence on Counting-Rate  23  Coincidence Resolution Curves for Positron Annihilation i n A l and Mica  5"1  Coincidence Resolution Curve ( P a r a l l e l Coincidence C i r c u i t ) with Theoretical Fit  57  24  ^ .  50  1  CHAPTER I INTRODUCTION  Accurate measurements of time i n t e r v a l s of the m i l l i microsecond range were f i r s t made possible by the development of the s c i n t i l l a t i o n counter as a nuclear p a r t i c l e detector (Kallmann 1947) Deutsch 1948) and the a p p l i c a t i o n of associated " f a s t " electronic techniques.  The development of this  technique was responsible f o r rapid advances i n many f i e l d s of nuclear physics, one example being the i n v e s t i g a t i o n of the various modes of positron a n n i h i l a t i o n .  This problem i s  important, since i t i s a d i r e c t experimental method of testing fundamental electrodynamical considerations, such as those which led to the derivation of the Dirac cross-section f o r a n n i h i l a t i o n of a moving positron.  (Heitler 1 9 5 4 ) .  The consideration of possible hydrogen-like, bound states of positrons and electrons by Ruark (1945) and Wheeler ( 1 9 4 6 ) , l e d to detailed t h e o r e t i c a l investigations of this new "atora , Positronium, ,,  M  H  by Pirenne  Benedetti and Corben 1 9 5 4 ) .  (1947) and others (De  The development of devices f o r  measuring very short time Intervals enabled workers l i k e Deutsch ( 1 9 5 D » and De Benedetti ( 1 9 5 4 ) , to detect the existence of this "atom" and measure many of i t s physical properties.  2 The measurement of absolute positron l i f e t i m e s i n various materials vas also attempted ( B e l l and Graham 1953) i n order to determine the cross-section f o r a n n i h i l a t i o n . C o n f l i c t s between the results of the measurements and the o r i g i n a l Dirac theory, such as:  the existence of two ex-  ponential l i f e t i m e s i n gases and many amorphous substances, and the constancy of the l i f e t i m e of positrons i n metals, were attributed to the formation of positronium. inconsistencies between the experimental  However, since  and t h e o r e t i c a l data  are s t i l l evident (Garwln 1953> Dixon and Trainor, 1955)» the project of constructing a suitable fast-coincidence apparatus and the measurement of some of these l i f e t i m e s was deemed worthwhile. The object of this work has thus been the construction of a fast-coincidence c i r c u i t and an attempt to measure the absolute l i f e t i m e of positrons i n Aluminium and Mica.  3 CHAPTER II THE CONSTRUCTION OP A FAST TIME-SORTER CIRCUIT  1,  A Discussion of Previous Fast Coincidence Circuits A coincidence c i r c u i t , as defined by Bell (1954)»  is:  "A nonlinear circuit having two inputs and one output,  such that a pulse i s delivered from the output only when the two inputs have received pulses within a short time of each other."  This short time is termed the resolving time of the  coincidence c i r c u i t .  The definition of resolving time usually  is taken as 2r ^the f u l l width at half height of the prompt c  coincidence resolution curve, (the measured curve of coincidence counting rate as a function of delay time a r t i f i c i a l l y inserted between the pulses from the two counters). The reduction of this resolving time has thus been the primary objective i n the design of these circuits.  B e l l , Graham and  Petch (1952) were the f i r s t to construct a coincidence circuit with a resolving time i n the mlllimiero-second range. For 1P21 phot©multipliers with stilbene phosphors excited by 100 Kev. electrons, they predicted and observed a minimum,, resolving time for ninety per cent coincidence efficiency of  Since 1949, a wide variety of coincidence circuits designed with resolving times i n this range have been published.  OUTPUT  I N P U T ,|  INPUT  6 OUTPUT  (O OUTPUT o  SERIES COINCIDENCE  INTEGRATOR  CIRCUIT INPUT  INPUT  I  2 INPUTS (SHAPED  NEG.  BIAS  FIGURE 1:  PULSES)  KICK  SORTER  NEG. BIAS  (a) PARALLEL COINCIDENCE CIRCUIT (b) BRIDGE COINCIDMCE CIRCUIT  (c) SERIES COINCIDENCE CIRCUIT (d) A SERIES TIME-SORTER  2  4  These c i r c u i t s have been c l a s s i f i e d by B e l l (1954) into three types, v i z . , the p a r a l l e l , bridge, and series c i r c u i t s . A.  The P a r a l l e l Coincidence C i r c u i t .  The f i r s t , and  one of the most popular of the fast coincidence c i r c u i t s , i s the one mentioned above, designed by B e l l , Graham, and ( 1 9 5 2 ) , which f a l l s  into the "parallel'  1  Petch  class, since i t i s a  development of a Rossi, or p a r a l l e l , coincidence c i r c u i t . This type of c i r c u i t consists of a pair of pulse s i z e l i m i t e r s (Vi and V  2  of F i g . l ) , an element for adding the equalized a  pulses (plate load), and an element for detecting pulses of larger than " s i n g l e " size (diode). Many such c i r c u i t s , some with s l i g h t modifications of 'these basic essentials, have been constructed i n reeent years. However, the o r i g i n a l c i r c u i t of B e l l , et a l . , ( 1 9 5 2 ) , remains one of the best of this type. B.  The Bridge Coincidence C i r c u i t .  Another type of  coincidence c i r c u i t (which f i r s t appeared i n 1948,  Meyer et  a l . ) , and which has the obvious advantages of being simple and compact, and requiring r e l a t i v e l y small input pulses, Is the "bridge" coincidence c i r c u i t .  This c i r c u i t embodies a balanced  bridge, usually of germanium diodes, across the diagonal corners of which are applied the two input pulses, with the output pulses being obtained aeross the other diagonal.  The p r i n c i p l e  of the c i r c u i t i s that such a bridge may be designed with two "balance" conditions, the f i r s t being the normal, s t a t i c  5  balance, and the second being an unstable one, reverting back to the f i r s t balance state, after a short time (about one microsecond)•  When a pulse from one counter i s applied to  the circuit, the circuit is switched into the second balance state described above, with no output pulse produced. The balance of the bridge is upset, however, when both pulses are incident upon the circuit simultaneously, and an output pulse is obtained.  As i n the other circuits, shaped input pulses  are usually employed.  A detailed description of the operation  of the Bridge circuits i s given i n the literature. (Bell 1 9 5 * ) . The main disadvantage of this type of coincidence circuit i s the d i f f i c u l t y in maintaining the balance of a bridge containing non-linear elements over a wide range of input pulse amplitudes.  Thus, large single pulses, w i l l , on  occasion, produce a sufficient output pulse to be recorded as a coincidence.  This fear of the single pulse effect has  apparently hampered the application of this type of circuit to actual coincidence experiments (Bell 1954). C.  The Series Coincidence Circuit.  c i r c u i t , the s e r i e s H  M  Bothe (1930) i n 193©»  The third type of  coincidence c i r c u i t , was originated by The basic circuit of this type i s  illustrated i n Fig. (Ic), i n which a multigrld tube incorporating two control grids i s used (such as the 6AS6, or more recently the 6BN6).  In this system, both grids are operated  at cut-off, so that, effectively, no plate current flows  6 either i n the quiescent s t a t e , or when only one of the c o n t r o l grids receives a p o s i t i v e pulse.  Only the simultaneous  application of p o s i t i v e pulses to both grids w i l l cause anode current to flow.  This type of coincidence c i r c u i t has the  advantages of not requiring equalized pulses, and of possessing a very p o s i t i v e action, since no anode current can flow i n the absence of overlapping input pulses.  A disadvantage  of the c i r c u i t l i e s i n the fact that troublesome effects occur when the series coincidence c i r c u i t i s used at resolving times of the same order as the electron t r a n s i t time through the tube.  Fischer and Marshall ( 1 9 5 2 ) , however, have shown that  these effects do not destroy the usefulness of the series c i r c u i t at these resolving times. D*  Fast Time-Sorters.  A useful/ modification of the  series coincidence c i r c u i t was developed by Neilson and James (1955)» i n which a 6BR6 tube i s used as a series detector (Fig. Id).  With shaped, rectangular pulses applied to the two  grids, the duration of anode current flow i s proportional to the overlap i n time of the input pulses.  When t h i s anode  current i s integrated by means of a M i l l e r c i r c u i t , the amplitude of the output pulse i s proportional to the degree of overlap i n time of the input pulses.  A c i r c u i t which performs this  type of time-amplitude conversion i s termed a "time-sorter." The time-sorter method of obtaining coincidence resolution curves possesses several advantages over the delayed  7 coincidence technique.  The investigator i s able to obtain  a complete resolution curve simultaneously, rather than obtaining the measurements point-by-point, with a resultant saving i n time by a factor of about f i f t e e n .  Because of the  shortening of time necessary to obtain the desired curves the results are less sensitive to slow variations i n gain and measurements involving weaker sources are made possible. Another advantage i s the inherent a b i l i t y to obtain as many points on the resolution curve as desired, with the upper l i m i t now being set by the number of channels l n the kicksorter rather than by the accuracy say, i n resetting a h e l i c a l delay l i n e to some p a r t i c u l a r point, as i n the c i r c u i t of B e l l et a l . ( 1 9 5 2 ) .  Perhaps the most a t t r a c t i v e character-  i s t i c ©f t h i s technique i s the i n s e n s i t i v i t y of a timesorter resolution curve to decay of the source.  Since the  whole curve i s obtained simultaneously, no corrections f o r source decay are required. Resolving times of the order of 2 x 10"9 sec. have been obtained with the apparatus of Neilson and James (1955)* Some speed i s l o s t with their c i r c u i t , however, since the 6BN6 requires r e l a t i v e l y large input pulses f o r proper operation, thus necessitating larger plate loads f o r the l i m i t e r s and the addition of cathode followers to feed the connecting cable.  Both these factors tend to r e s t r i c t the resolution  time obtainable to a value larger than that provided by the p a r a l l e l coincidence c i r c u i t of B e l l et a l . ( 1 9 5 2 ) .  SOURCE LIMITER  LIMITER  PULSE EQUALIZER SINGLE-CHANNEL PULSE-AMPLITUDE ANALYZER  SCALER  TIME  SINGLE-CHANNEL  SORTER  PULSE-AMPLITUDE  I  OELAY LINE  ANALYZER  SCALER  SLOW COINC. AMPLIFIER  GATE  GATED  PULSE  BIASED  GENERATOR  AMPLIFIER  FIGURE 2 :  BLOCK DIAGRAM OF FAST TIME-SORTER  30  CHANNEL  KICK-SORTER  8 A Hew.  Fast Tlme- orter. s  The f i r s t part of this thesis  describes the development of a " f a s t " time-sorter c i r c u i t of comparable r e s o l u t i o n time to the c i r c u i t of B e l l et a l (1952), employing a c r y s t a l diode as the non-linear detector, and which has been found useful i n measuring time intervals i n the 10"-*- sec. range. 0  2.  Description of the C i r c u i t . A.  Preliminary.  O r i g i n a l l y , the intention was  to  construct a fast coincidence c i r c u i t of the B e l l , Graham, and Petch (1952) type.  To this end, a h e l i c a l delay unit and  associated apparatus were constructed. was  After the apparatus  completed, test runs were made, with the results analyzed  to determine the coincidence e f f i c i e n c y and resolving times obtained. (See Appendix A). Consideration of the method of operation of the unit then suggested that with some a l t e r a t i o n s of the c i r c u i t r y , a time-sorter type of operation might be f e a s i b l e . object i n mind, work was  With t h i s  begun on the c i r c u i t described i n  the following section. B.  Elementary Description of Operation (Block Diagram, F i g . 2) i.  The Counters.  The counter, i t s e l f , i s composed  of an organic s c i n t i l l a t i o n phosphor with a very short deeay constant, coupled o p t i c a l l y to a photomuitiplier tube of high gain and short r i s e time.  With a high voltage supply greater  9  than two thousand v o l t s , t h i s type of counter i s capable of producing an output voltage pulse with a rise-time of the order of a millimicrosecond. ii.  The Limiters and Shorting Stub.  Since t h i s  time-sorter Is to analyze degrees of time overlap only, a l l other variables which would a f f e c t the electronic detector, such as pulse amplitude and length, must be normalized  and  kept constant f o r a l l pulses produced by the counters.  This  action Is performed by the l i m i t e r s and shorting stub.  The  l i m i t e r l i m i t s a l l pulses to an amplitude of about one  volt,  producing a step function, with a f i n i t e rise-time, of a length dependent on the length of the incident pulse. Thus the f i r s t part of the normalizing action i s accounted f o r . The shorting stub i s a shorted coaxial cable which serves to c l i p the incident pulse to a uniform length of about f i v e millimicroseconds.  By t h i s means, the equalizing  process i s completed, and a l l pulses observed by the detecting diode are uniform i n amplitude and length.  A slight variation  ( ^ l O " ^ sec) s t i l l e x i s t s , however, i n the rise-time of the 1  rectangular pulses as a r e s u l t of the v a r i a t i o n i n amplitude and rise-time o f the pulses produced by the counter iii.  The Time-Sorter.  itself.  The time-sorter consists  e s s e n t i a l l y of a biased germanium diode and a capacitor to ground.  I f both l i m i t e r s produce pulses within f i v e m i l l i -  microseconds,  then by the theorem of the superposition of  Pulse  FIRST  (a )  2 p  Pulse transmitted on S ^  PULSE  SECOND  E F F E C T I V E  (b  Length  Pulse reflected by S  PULSE  P U L S E  D i o d e  B i a s  S H A P E  A T  I N P U T  L e v e l - *  FIGURE 3: METHOD OF TIME-SORTER OPERATION  T O  D I O D E  10 potentials, there w i l l be a portion of the resulting pulse at the diode input which has an amplitude twice that of the single pulse.  With the bias of the diode adjusted to be equal  to the amplitude of the s i n g l e pulses, the diode w i l l conduct only when there i s an overlap of the pulses, (see F i g . 3)« The current passed by the diode i s then integrated by the following capacity to ground, producing a voltage pulse whose amplitude i s a function of the overlap i n time of the incident pulses. The diode i n the time-sorter also serves as a pulse stretcher, i s o l a t i n g the charge on the condenser from the rest of the c i r c u i t when the overlap portion of the incident pulse disappears.  Thus, r e l a t i v e l y "slow" amplifiers (a bandwidth  of about one megacycle/sec.) may be used following the timesorter. Time-sorter operation may therefore be obtained by modifications not only of the series coincidence c i r c u i t , but also of the p a r a l l e l coincidence c i r c u i t . iv.  The Main Amplifier.  Since the diode a c t u a l l y  conducts only a minute quantity of charge, the pulses on the condenser must be amplified before introducing them to the rest of the c i r c u i t .  This action i s performed by the main  amplifier.  ft Linear Amplifier, Type AEP 1444, by N.F.Moody and W.D.Howell, Chalk River, Ontario.  11 4  v.  The Side-Channel Pulse-Height Analyzers.  Since the  amplitude and rise-time of the output pulses of the counters i s strongly dependent on the energy expended i n the s c i n t i l l ator ( B e l l et a l . 1 9 5 2 ) , the pulses introduced to the timesorter are not absolutely uniform i n s i z e and shape.  To over-  come this d i f f i c u l t y , i t i s necessary to count only those time-sorter output pulses which correspond to counter pulses selected i n amplitude, since the output pulse amplitude of the counter i s a function of the energy expended by the gamma ray i n the c r y s t a l .  The side-channel, pulse-amplitude analyzers,  which accept untreated pulses from the second-to-last dynode of the photomuitiplier, perform the task of selecting the counter pulses. The side channels also enable one to select gamma rays of a s p e c i f i c energy by adjusting the discriminators so that only the voltage pulses corresponding to that energy are selected.  A square negative pulse of one microsecond duration  i s produced by the analyzers when the input pulse amplitude l i e s within the preset bias l e v e l s . vi.  Slow Coincidence Unit and Gate Pulse Generator.  The  outputs of the side channels are connected to a slow (ro leasee) coincidence unit which then produces a square, negative pulse when both side channel analyzers have received acceptable  A Pulse Amplitude Analyzer, Designed by R.E.Bell and R.L. Graham. A.E.C.L., Chalk River, Ontario  12  pulses within a resolution time of about one  microsecond.  These pulses, when incident upon the Gate Pulse Generator, trigger a univibrator, which i n turn produces the large (30 v. ), p o s i t i v e pulses needed to operate the "gate" of the biased-amplifier. vii.  The Gated Biased-Amplifier.  The gated biased-  amplifier amplifies those input pulses from the f a s t , centre channel, which have an amplitude greater than an adjustable bias voltage.  These amplified pulses are then released to ft  the 30 channel, Marconi Kick-sorter whenever the "gate" i s activated by the gate-pulse generator, thus ensuring that the pulses counted by the Kick-sorter do correspond to the selected counter pulses. In order f o r the biased-amplifier to receive the p o s i t i v e gate pulses and the time-sorter pulses i n coincidence, i t i s necessary to insert a delay l i n e of about l£ microseconds between the time sorter and the Moody l i n e a r amplifier to correct for the natural delays inherent i n the side channel equipment and gate pulse generator. G.  A Detailed Description of the Components and Associated Problems. i.  The Counters.  The ultimate l i m i t a t i o n Imposed on  the resolving time of coincidence c i r c u i t s i s due to the un-  ft Pulse Amplitude Analyzer (Kicksorter); Marconi Type #115-935  certainty i n the time of ejection of the f i r s t  photeelectron  from the photocathode a f t e r the e x c i t a t i o n of the phosphor by the p a r t i c l e being counted.  ( B e l l et a l . 1 9 5 2 ) .  Post and  S c h i f f (195©)» by considering the phosphor, o p t i c a l coupling, and photo-cathode as a u n i t , derived the following expression for  the mean time delay for the appearance of the f i r s t  photoelectron: t =  ~?kQ + n) > ( /)K>>  where *t i s the mean l i f e of the l i g h t f l a s h from the phosphor, and R i s the t o t a l number of photo-electrons  produced during  the pulse. Thus, the desirable features of the s c i n t i l l a t o r are that the s c i n t i l l a t i o n s be intense (large R) and of short duration (small ^ ).  Diphenylacetylene  was chosen for the 4  s c i n t i l l a t o r i n preference to s t i l b e n e , since the manufacturer supplies the following data concerning  these c r y s t a l s .  Material  Relative Light Y i e l d to Betas  Decay Constant (x 10"9 sec.)  Stilbene  0.65  8  Diphenylacetylene  0.8  4  The choice of the photomuitiplier tube then depends on obtaining high gain and a short r i s e time ( i n response to a square pulse), ensuring that the spread i n electron t r a n s i t time i s small.  4  To date, the RCA 1P21 i s the only commercially  National Radiac Inc., 10 Crawford St., Newark 2 , N.J. B u l l e t i n #5.  14 available tube which combines a high gain with short rise time as indicated by the following table taken from Bell (1954). Photomultiplier  Dynode Structure  Gain (10^) Rise Time (xlO-9  RCA 1P21  931A  RCA  5819  Large Cathode * 931A  0.6  5  RCA 6342  Large Cathode «• 931A  0.6  5  RCA H4646  Curved dynodes in line  EMI  Venetian Blind  10  Quarter-circle boxes  1  5 3 1 1 .  Du Mont 6292  sec)  about 100 (2000 v) 1  1000  2  about 10  When the 1P21 is operated in excess ©f 2000 volts, Bell et a l .  ( 1 9 5 2 ) ,  have shown that the gain is about  2  x  1 0  8  since one photo-electron w i l l produce an output pulse of the order of 3 volts across 1 0 pf. They have also indicated that at these voltages, the transit-time spread is not a serious -9 effect for resolving times of the order of 1 ©  sec. Although  the 1P21 photomultiplier i s designed for a voltage of 1 2 0 0 volts, most w i l l operate at the higher voltages without breaking down i f the high voltage is applied gradually over a period of about a day.  At voltages In excess of  2 0 0 0  volts, however,  noise and spurious pulses are found to increase tremendously. A close-fitting conducting shield seems to be effective in decreasing the noise intensity somewhat. (Mackenzie  1 9 5 3 ) *  This shield is insulated from the rest of the circuit & . • > , .  and allowed to f l o a t to the H.T. p o t e n t i a l .  Of the tubes  used, one was s i l v e r e d over the surface of the tube, with the exception of the photo-cathode window, and the other was wrapped with .001 inch aluminium sheet.  Since even with this  added protection, the noise i n one of the tubes became excessive at voltages greater than about 2200 v o l t s , t h i s value was used as the photomuitiplier supply voltage i n the subsequent experiments. a.  The Counter Assembly.  Since the manufacture of  the 1P21 phototubes was found to be inconsistent as far as physical s i z e and alignment i s concerned, a s o l i d c r y s t a l mount (as described by Mackenzie 1953) was found unsuitable. The following method of mounting the crystals was used i n the equipment and found to be quite s a t i s f a c t o r y . The diphenylacetylene c r y s t a l was 1 i n . x 3/8 i n . x 3/8 i n . , with one longitudinal face being machined by the manufacturer to f i t the side of a 1P21 phototube ( i . e . an arc of 19/32 l n . radius).  This c r y s t a l was then placed i n a  small cardboard box with MgO  packing around the sides*  Optical coupling between the c r y s t a l and the phototube was provided by a f i l m of 10^ centistoke o i l .  To insure a firm  contact between the c r y s t a l and the glass, several rubber bands were wrapped around the c r y s t a l mount and tube.  The whole  mount was then well covered with black scotch tape to prevent l i g h t leaks.  +  275  v.  R e g u l o t e d  .5K; .25 —I  .01 100, .01 250*  -||  ®  O U T P U T  .01 -r C o l l e c t o r  BA  -100 v.  ^  1  (A/VV  82 K  .0/  •ol  8  i  -5  -<50v.  S i d e '  0  0  C h a n n e l  Input,  T e r m i n a t e d  -zoocw. VX5038  IP2I FIGURE 4:  LIMITER CIRCUIT  +150,  »> k.  ttt(.(lOma)  +275*  16 b.  Voltage Supply and Socket Considerations.  The  use of black, c l o t h ^ f i l l e d bakelite sockets f o r the photom u l t i p l i e r tubes was found to be highly unsatisfactory, since large spurious pulses were observed on the output pin at voltages i n excess of 1500 v o l t s , the amplitude and increasing with increasing voltage.  frequency  These pulses were present  without the tube inserted i n the socket and were believed to be associated with water adsorption on the surface of the bakelite, since washing with pure ethyl alcohol eliminated this condition for about ten to f i f t e e n minutes. however, the noise would gradually recur.  Then,  The use of brown,  m i c a - f i l l e d bakelite sockets e s s e n t i a l l y eliminated this problem, as they produced very few of these spurious pulses at the voltages employed. The socket wiring i s shown i n F i g . 4.  With the  bleeder-chain values indicated, the following potentials were obtained; 190 v o l t s between dynodes, 90 v o l t s between the dynode and c o l l e c t o r , (kept lower than the dynode-dynode potentials for reasons of s t a b i l i t y —  see RCA Tube Handbook),  and 270 volts between the dynode and cathode (larger than the dynode-dynode voltage to reduce electron transit-times). c.  Degeneracy of Output Pulses.  The fact that the  f i n a l dynode produces fast positive pulses during operation, ofthe same amplitude as the negative, c o l l e c t o r pulse, introduces the p o s s i b i l i t y of degeneration of the negative output pulse, by capacitive coupling between the f i n a l dynodes  «-b«> ' w  700  FIGURE 5:  DISTORTED RESOLUTION CURYE  (Capacitive De-coupling of Photo-  600  Q  multiplier)  500 — Z D O J  400  W  O  z  § 3 0 0  z o o  200  IOO  -5  -4  -3  1  -  2  -  INSERTED  1  O D E L A Y — (m^j.SEC)  I  17 and the anode.  For this reason, the p o s s i b i l i t y of high-  frequency by-passing by means of small ceramic capacitors to ground from the l a s t two dynodes was  Investigated.  The results were quite unsatisfactory, however, since extra peaks were introduced curves,  (see F i g . 5)«  in  the coincidence resolution  It i s believed that the e f f e c t i v e  short c i r c u i t to ground through the ceramic capacitors completed a series resonant c i r c u i t between the inductance of the dynode lead wire and the inter-dynode c a p a c i t i e s .  Damped  o s c i l l a t i o n s of this c i r c u i t would superimpose a " r i n g  11  on the  main pulse, permitting the p o s s i b i l i t y of i t s being detected as two or more pulses rather than just one.  A rough c a l c u l -  ation seems to support this view. Inductance of straight wire (#22); about 1/40^uh/in. In the ease of a 1P21,  the dynode lead i s about 2 i n . long  leading to an inductance of l/20^«h. The capacity between the l a s t dynode and the other dynodes and anode i s about 10 pf. (RCA Tube Handbook).  and the time per cycle, i s then XK*  7x/d' s*c. a  ^  4.3. ryu..  s e c , which i s close to the separation time of the peaks. After these investigations, the photo-tube bleeder chain was  returned  to the form as shown i n F i g . 4:  Since  the  inter-dynode capacities are about 4 pf., i t i s believed that the l a s t dynode i s e f f e c t i v e l y shunted to earth v i a the 100  ohm  18 load of the eighth dynode, as far as the high frequencies involved are concerned. ii.  The Limiters.  As mentioned previously, the  purpose of the l i m i t e r s i s to produce voltage pulses of uniform amplitude,  independent of the amplitude of the input  pulses. a.  Choice of the Limiter Tube.  l i m i t e r tube was  governed by the following  The choice of the requirements.  As i s shown i n F i g . 4, the plate load of the l i m i t e r consists of a 100 ohm, 100 ohm  Telcon- AS48 cable i n p a r a l l e l with a  terminating r e s i s t o r .  As a r e s u l t , to be able to  produce one v o l t l i m i t pulses at the anode, about twenty ma. of current must be cut-off i n the l i m i t e r tube.  Thus, one  requirement of the l i m i t e r i s that i t be capable of withstanding the plate d i s s i p a t i o n demanded. Since under normal operation, the negative pulse applied to the grid of the tube i s at least an order of magnitude larger than the anode l i m i t pulse, a low grid-anode capacity i s necessary to preserve the fast wave front of the l i m i t pulse. Also, i n order to r e t a i n as many high-frequency  compon-  ents as possible i n the output pulse, a very low time constant per unit gain i s desired.  It i s w e l l known that secondary-  emission pentodes are much superior to conventional pentodes i n this respect. ( B e l l 1954).  19  For these reasons, the tube chosen f o r the l i m i t e r was the VX 5038* which possesses the following c h a r a c t e r i s t i c s . Since the manufacturer  of the VX 5038 states under  " t y p i c a l operating data" f o r t h i s tube, a plate current of 15 ma. at 350 v o l t s , the current-handling requirement i s s a t i s f i e d . Secondly, the grid-anode capacity i s : 0.008 pf., a factor of three or four better than conventional pentodes. Also, with a transconductance of 21 ma/volt  (at 20  ma. anode current), the time-constant per unit gain, dp/g (where C  T  m  i s the grid-anode capacity, and g^ Is the trans-  conductancej B e l l 195^)» i s 6.2 x 1 0 ~  10  lowest of commercially-available tubes.  s e c , one of the Thus, with gains of  less than one-tenth i n the l i m i t e r , there should be no loss of speed at t h i s point, the time-constant of the l i m i t e r being much l e s s than the time-constant of the input pulse. b.  Discussion of C i r c u i t Operation and Component Values  The occurrence of s a t e l l i t e pulses following the main pulse In the (see Mackenzie  1P21 has been f u l l y described i n the l i t e r a t u r e 1953).  To prevent the p o s s i b i l i t y of separate  l i m i t pulses being formed f o r each s a t e l l i t e pulse, the g r i d c i r c u i t time-constant must be s u f f i c i e n t l y long compared to the s a t e l l i t e spacing that the tube remains cut-off while the s a t e l l i t e s are occurring.  In the l i m i t e r c i r c u i t of F i g . ij., the  stray capacity to ground of about f i f t e e n p f . f o r the c o l l e c t o r grid c i r c u i t , y i e l d s a time-constant of 0.15  microseconds.  * E.M.I. Research Laboratories Ltd., Hayes, Middlesex, England.  Since the s a t e l i t e spacing i s of the order of 0 . 1 microseconds (Mackenzie 1953)5 this time-constant  i s sufficiently-  large. One d i f f i c u l t y associated with secondary emission pentodes, however, i s the large fluctuations i n gain to which they are subject.  These fluctuations were considerably  reduced by the use of a large, variable cathode r e s i s t o r ( 2 5 K ) ,  which causes cathode follower action as far as d.c.  i s concerned.  When the c i r c u i t was i n operation, this v a r i a b l e  r e s i s t o r was adjusted so that the l i m l t e r produced one v o l t l i m i t pulses.  S t a b i l i z a t i o n of the quiescent-state operation  of the secondary emission pentode was also improved by allowing the tube to warm up at the desired operating point f o r several days before using.  Voltage s t a b i l i z a t i o n was ensured  by using regulated d.c. power supplies , fed by regulated 110 ftft  v o l t a.c.  When this procedure was followed, s t a b i l i z a t i o n  over short and long periods was quite s a t i s f a c t o r y . For good high-frequency  decoupling i n the l i m i t e r ,  ceramic capacitors with short leads were used, and a copper chassis with point-to-point wiring was employed.  The supp-  ressor grid and i n t e r n a l shield were grounded d i r e c t l y to the copper chassis as suggested by Mackenzie (1953)• ft Regulated Power Supply, Model 28, Lambda Electronics Corp., Corona, N.Y. ftft Sorenson Regulator, Model 500, Sorenson and Co. Inc., Stamford, Conn.  21 iii.  The H e l i c a l Delay Line.  viously, a h e l i c a l delay l i n e was Chalk River s p e c i f i c a t i o n s .  As mentioned pre-  constructed according to  This part of the equipment was  a c t u a l l y unnecessary for the time-sorter c i r c u i t but  was  retained since i t f a c i l i t a t e d the production of time c a l i b r a tions, as i t was  a method of introducing variable delays with-  out introducing impedance d i s c o n t i n u i t i e s . ductor, #12 B&S  The centre con-  hard-drawn copper wire, was wound onto the  brass h e l i x using l u c i t e spacers for p o s i t i o n i n g . The diameter of this conductor was inch.  4 7/16  final  i n . , with two f u l l turns/  Thus, when the h e l i x i s rotated one turn, the r e l a t i v e  delay between the two channels i s changed by two turns (or 2.36 millimicroseconds). Connection was made to the h e l i x by means of short pieces of 100 ohm  cable mounted inside the h e l i x drum, which  i n turn were connected to the stationary end-plates by means of f r i c t i o n a l contacts situated within the h e l i x bearings. Connection to the l i m i t e r cables was made by employing f i f t y ohm Amphenol connectors.  Although this represents an impe-  dance discontinuity, the path length i s s u f f i c i e n t l y short, that a transmission of about ninety per cent i s obtained (Appendix 6 ) . iv.  The Pulse Length Equalizer.  equalization was  The pulse length  obtained by the use of a shorted coaxial  cable, i n which a voltage pulse undergoes r e f l e c t i o n at the  short c i r c u i t , the reflected pulse being out of phase, or of opposite p o l a r i t y , to the incident pulse. A pulse from the l i m i t e r , upon meeting the junction of the shorting stub and h e l i x sees an impedance d i s c o n t i n u i t y and suffers a r e f l e c t i o n , the resultant pulse height at the junction being  —  smeJA^Mackenzie 1 9 5 3 ) , where i? Is s  the c h a r a c t e r i s t i c impedance of the shorting stub, and j£ the c h a r a c t e r i s t i c impedance of the h e l i x . have a smaller amplitude  0  is  Since these pulses  than the c r y s t a l diode bias, the  loading effect of the detector w i l l be n e g l i g i b l e .  However,  during pulse overlap, the diode i s i n a conducting state, with a resultant impedance of about 600to 100 ohms.  Thus an  accurate d e s c r i p t i o n of the pulse formation during overlap i s made d i f f i c u l t by the variable nature of the diode resistance, a strong function of the pulse amplitude, i t s e l f . * Although a shorting stub of c h a r a c t e r i s t i c impedance equal to 1/2  should be used to prevent the occurrence of  multiple r e f l e c t i o n s l n the shorting stub, i t was experimentally, that the use of a 100 ohm pulse size (an increase of Z<  in  the form of the resolution curves. ohm  found,  stub increased the  • -) and did not a l t e r For this reason, a 100  shorting stub was used In the f i n a l c i r c u i t .  The duration  of the voltage pulse formed i s equal to(twiee the cable length)*(the v e l o c i t y of propagation of the pulse). As f a r as the operation of the c i r c u i t i s concerned, the actual length of the shorting stub i s immaterial, provided that i t i s s u f f i c -  o B*  B*o-  4.6 k  JVWW—O  *l70y/.  Regulated  To Limiter  PULSE  .01  Grounded Shield  + /J0-  1  250K  001  EQUALIZER .01  ^ ^  To Limiter  TO OUTPUT ond IOO  OHM  TERMINATION  O- •! v.  417 A  IN56  FIGURE 6:  TIME-SORTER CIRCUIT  Inside Power  Supply  i e n t l y long f o r 100$  coincidence e f f i c i e n c y to be r e a l i z e d .  It i s obvious, a l s o , that when measuring small l i f e t i m e s , the change i n the degree of overlap w i l l be equal to a few x 1©"**" sec.  In order for this change to be an appreciable f r a c t i o n  of the t o t a l conducted pulse, very large overlaps  (about  Q  1G"° sec.) for the prompt curve are undesirable.  Since the  coaxial cables have a f i n i t e attenuation factor at the f r e quencies involved, long shorting stubs w i l l have poorer pulse length equalization (more pulse shape d i s t o r t i o n ) , than shorter ones. As a r e s u l t , an equalizing stub length of about f i v e millimicroseconds was adopted for the apparatus and believed to be a reasonable compromise.  was  Variations of t h i s  length by a factor of two, however, did not seem to produce any s i g n i f i c a n t differences i n the coincidence r e s o l u t i o n curves  obtained. S u f f i c i e n t delay was  inserted i n one side of the  coincidence system to produce an overlap of about 1/2 f o r prompt pulses.  Since the pulse length was  5*1 m i l l i m i c r o -  seconds, this delay amounted to about one turn from the e l e c t r i c a l centre of the h e l i x (equivalent to about  2.3  millimicroseconds of inserted delajr). v.  The Time-Sorter.  The complete diagram of the  time-sorter c i r c u i t i s shown i n F i g . 6.  a.  The Diode and Integrator.  The equivalent  c i r c u i t of the diode and g r i d c i r c u i t of the cathode follower i s the following:  A grounded shield was placed around the diode to decrease the shunt capacity. i s the resistance of the diode, varying from about 500K at -11 v o l t s , through 3 0 K at - 0 . 3 v o l t s , 20K at *0.1 v o l t s to about 63 ohms at 0 . 8 v o l t s . C  g  i s the shunt capacitance; about one p f .  C i s the integrating capacitor: 25 pf. • stray and input capacity fc2 35  •  R i s the dc. bias supply r e s i s t o r of 15 K. b.  The Output Pulse Formation.  In considering the  various output pulses, we may d i s t i n g u i s h several possible cases: For no overlap, (hence, R v i s i b l e at B i s equal to C / G g  d  t o t a l  about 25 K), the pulse = 1/35 of the amplitude  of the pulse at A. For no overlap, but f o r the case where the pulses occur within the integration time of the following a m p l i f i e r ,  the pulse obtained i s twice as large as i n the preceding example. In both cases, however, the output pulse i s obtained by the voltage divider action of the two capacities i n s e r i e s . Thus the length of the pulse w i l l be the same as the input palse (no pulse-stretching w i l l occur).  These pulses, there-  f o r e , when incident upon the r e l a t i v e l y long integration time constant of the following amplifier (about 0.5yuse*.), w i l l appear many times smaller than the factor of 1/35 In cases of overlap, R  d  i s of the order of 500 ohms,  with the result that charge i s conducted  onto G. o  then decays with the time constant RC = 15 x 10• 375 x 10"*^& 1/3 microseconds.  given here.  3  This charge —12 x 25 x 10  The integrating capacitor C  charges up with the time-constant set by R<jC s 500 x 35 x 10"  1 2  • 17.5 millimicroseconds.  the type 1N56,  The c r y s t a l diode used  was  chosen for i t s high conduction c h a r a c t e r i s t i c s .  Although a larger value of the r e s i s t o r , R, would have the advantageous effect of increasing the pulse length, most stable results are obtained when R i s less than the nonconducting R  d  (Lewis and Wells 1954)#  Since the back r e s i s -  tance of the germanium diode i s extremely temperature dependent, a more constant bias voltage i s obtained with R much less than Rd, due to the voltage divider action of the two resistors.  ERROR  AMPLIFIER  6SJ7 FIGURE 7:  PHASE—SENSITIVE TEMPERATURE STABILIZER CIRCUIT  6AS6  DETECTOR  26 b.  The Cathode Follower.  As far as the cathode  follower Is concerned, the tube Western Electric type 417 A was chosen because of i t s high g^; i t s output cable termination was used as the dc. cathode load to keep the heatdissipating components l n the time-sorter chassis to a minimum. vi.  The Temperature Stabilizer.  In preliminary runs  with the apparatus as described above, shifts of the peak covering up to six channels were noticed on the kicksorter. These shifts were ascribed to .resistance changes of the germanium diode following small changes i n room temperature, since the diode was by far the most sensitive component of the ft  apparatus.  The published data  on the IN56 diode gives as the  variations of static characteristics with temperature: a variation of about 0 . 0 7 9 ma., or l/2# of the forward conduction current at an applied voltage of 0 . 8 volts for a change i n temperature of one degree Centigrade, and, a variation of about 2y amperes i n 10/*amperes of the reverse current for a change i n temperature of one degree Centigrade. For these reasons the temperature stabilizer of Fig. 7 was constructed.  A continuously-operating stabilizer was  desired in preference to a simpler discontinuous type because of the diode sensitivity to temperature variations.  A modi-  fication of Benedict's "A.C. Bridge for Temperature Control" ft Sylvania Crystal Diodes, Slyvania Electric Products Inc. 1740 Broadway, N.Y. 19, N.Y.  (1937) was employed since i t i s a relatively simple, yet sensitive instrument. A Western Electric D164699 Thermistor was used as the temperature-sensitive detector, employed as the sensitive element of a Wheatstone bridge. Variations i n i t s impedance cause a corresponding variation in the amplitude of the output signal with a 180° change i n phase when the thermistor impedance passes through the balance point. This signal is then amplified by means of a one-stage audio amplifier of gain 280, whose grid circuit is tuned to 60 cycles with a Q of about 2. The output of the amplifier i s then fed into a phase-sensitive detector which compares the phase and amplitude of the error signal with the standard mains a.c.  The operation of the  circuit is essentially the same as that described by Benedict except for the phase-sensitive detector. As suggested i n the original a r t i c l e , a thyratron (in this case, a type 2D21) was f i r s t tried as the phase-sensitive detector, with the phasesensing reference signal applied to the plate and the error signal to the grid.  The output current then passed through a  IK heater, also situated i n the time sorter chassis. The temperature stabilization of this circuit was very good with temperature stabilities within 0.©5°C. obtained over the course of a day and s t a b i l i t i e s within 0.1°C. over several days. However, the discontinuous mode of operation of the thyratron inserted radio-frequency hash into the coincidence c i r c u i t .  28 At the expense of some sensitivity, the use of a 6AS6 tube as the phase detector (as shown i n the diagram) eliminated this d i f f i c u l t y .  In this case, the heater current is well-  filtered by by-passing the a.c. component of the plate current to ground. The value of the wire-wound resistor used as a heater had to be increased to 20&, though, because of the lower anode current obtainable with this type of tube. A diode is employed in the grid circuit of the phase-sensitive detector to prevent the drawing of grid current on the positive half cycles of the error signal.  The anode current  meter reads about 25 ma. f u l l scale. The stability of the time-sorter was greatly improved by using this device, although greater sensitivity, obtained by adding another stage of audio amplification, might be advisable. To prevent any variation of the diode temperature due to gross room-temperature fluctuations and draughts, the whole time-sorter apparatus (Including the helical variable delay line) was enclosed in a polystyrene box, to which was added an air mixer and thermostat*, used in conjunction with a 60 watt light-bulb heater, for increased temperature stabilization.  The resulting stability of the circuit under these  conditions is described in the section on performance.  ft Thermoswitch, Catalog No. 17500-4/6, Penwal Inc., Ashland, Mass., U.S.A.  GATE  PULSe  CATHODE  AMP.  COIMCIJ6WCQ.  CIRCUIT  +295  DlSCRIM-  IOK tow IOK I0W S E T  IOK  V7 ]>1K UPPtK LIMIT  I5K  15 K  VI GAH6  > * >50K  V3 6AN5  .1  &ATE  •H09 v.  >27K  IN  s2w  (•)  .»  o-j|yw  V4  (00  i ob  i)  IOOK:  ft AH 6 ANTI.6, .100 K  COINC.  1  -±.02. I  IV v  h v W t  100  2.5 K  V2  Z O W  )|0oK >  6AL5 -55  v.  .  IM  A«n. CO  \  ?  /  8^F  -AA, 6.8 K  IOOK<«»-  HELI-^ POT '  x., ^  GAIN 5  I.5K W V -  30K  3  »  - 1 5 0 v.  IOOK  FIGURE 8: G A T E D  BIASED  AMPLIFIER  * NOBLELOY  FOUU.  v.  G80  PULSE FROM LOWER0  bi sc. (A)  5  '2.2K  Tryyyr>—AAAH ,« 8° .25 j*sec. 2« DELAY J25<?jv. go,  CHANNEL  oi ^  6  4V  /T PUT  IN34  PULSE  75  —w— IN34-  S  4v  IOK .01  1 S  w  w  .  2ISC. v W 5K  > I5K  i  -0 PROM UPPER  (B)  1  V9  6J6  01  COINC.  V 14  OUTPUT  6J6 IOO  J L L ^ ) COINC. "ZJ  1 0 0  >5k  <I00K  100 K  ^  >(OOK  TRIPLE COIMC.  SENS.  +75 v.  '20K  .01 -r  '50K  PULSE  FIGURE 9 : AMPLITUDE  ANTICOINCIDENCE COINCIDENCE  ANALYSER AND  CIRCUITS  TRIPLE  INPUT  COINC  INPUT  FIGURE 10:  GATE  PULSE  GENERATOR  PHASE  VI  SPUTTi*  6iL5_  AMPLIFIER  V2 G A H S ^  CATHODE  V3 6AH6  V4  6AN5  FIGURE 11:  V5  VIO  AMPL.  FOLLOWER  6AH6  6AH6  V6  VII  FUP  6AH6  VI2-6AK5  *  NOBLELOY  t  TRIM  ANALYSER  -  DISCRIMINATORS  R,  RESISTOR  Rj.  CAPACITY f  TRIM N  AMPLITUDE  F LOP  6AH6  A p  PULSE  -  TO  TO  MAKE r  A  VI3 OUT  BALANCE  PULSE.  2 v H C O  "  _^ 20v ON  (BETWEEN , = lOO n  o  M  NARROW  ft ^  6AK5 J>IOPE S  & I M).  NORMAL CHANNEL.  29 vii.  Associated Equipment.  The c i r c u i t s for the  side-channel pulse amplitude analyzers, gate-pulse generator, and Biased-amplifier are given i n F i g s . 8 , 9 , 1 0 , 1 1 .  Since these  are standard c i r c u i t s , a detailed description of t h e i r operation w i l l not be given here. 3.  Performance of the Time-Sorter. With diphenylacetylene crystals used i n the s c i n -  t i l l a t i o n counters, and the c i r c u i t operated under the conditions described i n the previous pages, the following performance data were obtained. A  »  2 T ; of 1.1  Resolution. A resolution curve of e f f e c t i v e width -9 76 x 10 ' sec. was obtained using an As source of  coincident gamma rays of energy 1.20  and 0.57 Mev.,  The reason that the resolution time ( 2 f )  (Fig.12).  calculated from  c  these curves i s less than that obtained by B e l l et a l . ( 1 9 5 2 ) , i s due to the fact that the delay corresponding to the width of one channel on the kicksorter ( 2 ^ • 1.8  x 10"  1 0  sec.) i s  shorter than the equivalent quantity* i n the c i r c u i t of B e l l et a l ; namely, the e,o«e./.W pulse, length. (2 7 s 1.5  x 10"^ sec).  It i s shown i n Appendix A, that the e f f e c t i v e width of the resolution curve i s given by:  2 r  °~73  _ r  ^i  r  > where ~t i s the  mean time delay for the appearance of the f i r s t photo-electron,  ft See Appendix A.  PULSE HEIGHT (VOLTS) : I VOLT = 1.8 x 10~'° sec. 27.67 33.88 40.13 46.28 52.48 • t, . i tt I • t, I i i i 1 1 1— 4 6 8 JO 12 14 16 18 20 22 24 2 6 CHANNEL  FIGURE 12:  As  7 6  NUMBER  COINCIDENCE RESOLUTION CURVE  100  UJ  _l  <t o w  I V 0 L T = 1.8 x I0~ sec.  >  ,0  cc <t cc CD  or  \  UJ  z z 10  T  i  <t I o  cc  Ul 0.  v  CO  Z D O  o  o t  (VOLTS) P U L S E HEIGHT 33-88 40-13  27-67 8  10  12  CHANNEL FIGURE 13:  14  16  18  46- £ 8 22  52-48  JL  24  26  NUMBER  EFFECT OF SIDE CHANNEL DISCRIMINATOR SETTINGS ON THE RESOLUTION TIME  (Solid l i n e corresponds to wider Side Channel window)  30 the electron transit-time spread of the photomultiplier being assumed n e g l i g i b l e ( B e l l et a l . 1 9 5 2 ) . B e l l et a l . ( 1 9 5 2 ) , where  In the c i r c u i t of  i s much greater than * , the  e f f e c t i v e width of the coincidence resolution curve approaches 2 ^.  However, as the time &  becomes small, the resolution  time approaches the value 2 t. Figure 13 shows the dependence of the resolution time of the coincidence resolution curves on the side-channel pulse-amplitude analyzer s e t t i n g s , i l l u s t r a t i n g the effect described i n section v, Chapter I I , 2 . The source used i n 76 76 22 this case was an As' gamma source. For the As and Na resolution curves, one of the side-channel  pulse-amplitude  analyzers was set so that only pulses corresponding to the Compton electrons a r i s i n g from the 500 Kev. gamma rays would be registered, while the other was set i n a s i m i l a r fashion for the Compton electron pulses of the 1.20 Mev. Gamma rays. 76 The slopes of the As curves ( F i g . 12) indicates that -10 the coincidence rate drops by a factor of two i n 1,9 x 10 ( l e f t ) and 2.3 x 1 0 "  10  sec.  sec. ( r i g h t ) , indicating that the  inherent resolution of the apparatus  (determined c h i e f l y by  the counters), i s comparable with that obtained by other workers ( B e l l et a l . 1 9 5 2 ) . B. obtained.  Stability.  Figure 14 i l l u s t r a t e s the s t a b i l i t y  The curve of F i g . 14a was obtained i n four hours  one afternoon, while that of 14b was the r e s u l t of a ten hour  2  4  6  8  FIGURE 14:  10 12 13 16 18 CHANNEL NUMBER  20  22 2 4  28  28  COINCIDENCE RESOLUTION CURVES ILLUSTRATING STABILITY OF TIME-SORTER (a) Open Points  (b) Solid Points  run over-night.  I t i s evident that the s t a b i l i t y of the de-  vice was quite s a t i s f a c t o r y .  Over a period of at least a day,  the mean of a coincidence resolution curve could usually  (80%  of the time) be reproduced within a tenth of a kick-  sorter channel width. The s t a b i l i t y of the apparatus would probably be improved by incorporating a d.c. current s t a b i l i z e r i n the l i m i t e r s , to ensure long-term s t a b i l i t y of the anode current. Also, the i n s e r t i o n of a boot-strap or clamping c i r c u i t i n the d.c. restoration portion of the l i m i t e r cathode c i r c u i t would enable the t o l e r a t i o n of higher counting rates (Lewis and Wells 1954). C.  Linearity.  One obvious disadvantage of this  c i r c u i t as compared to the o r i g i n a l B e l l et a l . (1952)  circuit  i s the lack of a completely l i n e a r time c a l i b r a t i o n f o r the experimental curves.  In order to keep the conducting r e s i s -  tance of the diode constant for the overlap pulses, the voltage drop across the diode must be kept constant.  This can  be accomplished i f the diode output pulse i s kept much smaller than the input overlap pulse (by employing a large integrating capacitor).  An actual M i l l e r integrator rather than the  capacitor i t s e l f (as i n the c i r c u i t of Neilson and James 1955) offers advantages i n this respect. However, the a b i l i t y to r e t a i n the very high frequency components necessary i n these measurements sets a very severe r e s t r i c t i o n on the electronics employed.  Also, the size of the integrating capacity i s  limited by the requirement that the output pulses be kept well oat of the noise region for good resolution.  For these  reasons the use of the ceramic capacitor was deemed advisable. Actually, with an Integrating capacity of about 40 pf., one is able to operate the time sorter i n a linear portion of the calibration curve by choosing a suitable degree of pulse overlap for the prompt point, as i s shown in Fig. 21.  This c a l i -  bration curve can be obtained quite readily by observing the peak shifts of a prompt source as a function of either i n serted delay or gamma-ray time of flight when using a source of coincident gamma rays. 4. Discussion of Circuit. The circuit described l n the previous pages, although essentially the same as the B e l l et a l . (1952) fast coincidence circuit as far as the actual components are concerned, has, with some circuit modifications of the coincidence detector, been operated i n a fashion similar to that of the time-sorter of Neilson and James (1955)•  This type of operation lends  i t s e l f to an improvement i n the resolution time obtainable without an undue loss i n counting rate, and enables the Investigator to secure his data with greater speed, since the whole coincidence resolution curve i s recorded simultaneously.  33  CHAPTER I I I BSE  OF THE FAST TIME-SORTER TO MEASURE LIFETIMES OF POSITRONS IN ALUMINIUM AND MICA  1.  D i s c u s s i o n o f P o s i t r o n Decay In Metals A.  Summary o f Previous R e s u l t s .  The mode o f  a n n i h i l a t i o n of positrons i n various materials follows a f a i r l y complex p a t t e r n .  I n gases, both two-photon and t h r e e -  photon a n n i h i l a t i o n s a r e observed  (Deutseh 195D and have been  a t t r i b u t e d t o t h e a n n i h i l a t i o n o f para- and o r t h o - p o s i t r o n l u m respectively. three-photon  I n many amorphous and l i q u i d substances, the decay i s r e l a t i v e l y weak.  The two-photon decay,  however, i s c h a r a c t e r i z e d by the presence  o f two l i f e t i m e s ,  one s h o r t , ( o f the order ©f 5 x 10*" ® sec.) and one l o n g 1  (about 3 x 10  7  s e c ) , w i t h r e l a t i v e i n t e n s i t i e s o f about  which remains f a i r l y constant ( B e l l and Graham 1953).  from substance  2:1,  t o substance  The same authors a t t r i b u t e the l o n g e r  l i f e t i m e t o c o n v e r s i o n o f the t r i p l e t  p o s i t r o n i u m t o the  s i n g l e t s t a t e by c o l l i s i o n s w i t h atoms o f the sample m a t e r i a l . The a n n i h i l a t i o n p r o b a b i l i t y o f the " l o n g " l i f e t i m e i s then determined  by the c o n v e r s i o n r a t e .  Dixon and T r a i n o r (1955)>  on the other hand, b e l i e v e the l o n g - l i v e d component t o be due to  d i r e c t a n n i h i l a t i o n from the second e x c i t e d s t a t e o f  singlet  positronium.  In metals, only the short-lived component of the positron l i f e t i m e i s observed.  M i l l e t t (195D  was  one of the  22  f i r s t to attempt to measure the l i f e t i m e of Na  positrons i n  -10 metals, v i z . gold and lead.  His r e s u l t s of 9 x 10  vere obtained by measuring the slope of his delayed dence resolution curve.  sec. coinci-  Since his results do not agree with  subsequent measurements, one can probably assume that the above figure was  the inherent uncertainty introduced by h i s  apparatus, and that a t r u l y "prompt" resolution curve would possess e s s e n t i a l l y the slope quoted.  De Benedetti and  Rlchings (1952) then published a l i s t of differences i n p o s i tron h a l f - l i v e s between aluminium and other m e t a l l i c and amorphous substances.  Their r e s u l t s indicated that the  life-  -10 time of positrons i n metals was sec.  constant within 0.5  x  10  Next, B e l l and Graham (1953) measured the absolute  l i f e t i m e of positrons i n various materials, and found that i n a l l metals the l i f e t i m e was(l.5 t P.5]x 10~  10  sec. with a  tendency f o r s l i g h t l y shorter mean l i v e s i n metals of larger atomic number.  Then Minton (1954) measured the absolute  l i f e t i m e of positrons i n aluminium and lead, obtaining the r e s u l t s , 2.9 x i o " 1 0 and 3.5 x 10"*1G seconds, respectively. Since B e l l and Graham s work was more thorough than Minton's, 1  their value of 1*5  x 10"  of positrons i n metals.  10  sec. i s the accepted mean l i f e t i m e The t h e o r e t i c a l i n t e r p r e t a t i o n of  this r e s u l t , however, has not been altogether s a t i s f a c t o r y .  i.  Theory of A n n i h i l a t i o n by C o l l i s i o n .  Since no  evidence of a long-lived component i n the l i f e t i m e measurements was observed, the f i r s t approach at predicting the mean l i f e t i m e of positrons i n metals was made by assuming that positronium i s not formed, but that slow positrons annih i l a t e during c o l l i s i o n with free electrons with Dirac's crosssection for annihilation; c/= r  0  ^  ( H e i t l e r , 1954), where  i s the c l a s s i c a l electron radius, and v i s the v e l o c i t y of  the positron r e l a t i v e to the electron.  The t o t a l l i f e t i m e f o r  a n n i h i l a t i o n of positrons would thus be the sum of the l i f e time of the thermal positrons and the mean time required f o r the positrons to slow down.  This l a t t e r time was f i r s t c a l -10  culated by De Benedetti et a l (1950) to be 3 x 10 m e t a l l i c gold.  see. f o r  A more detailed consideration of the c o l l i s i o n  phenomena involving slow positrons and conduction  electrons  by Garwin (1953) and Lee-Whiting (1955) led to a r e v i s i o n of -12 the slowing-down time of positrons i n metals to about 3 x 10 sec.  Therefore, as far as the t o t a l l i f e t i m e of positrons i n  metals i s concerned, the slowing-down time can be ignored. Ore and Powell (1949) showed that the p r o b a b i l i t y f o r a n n i h i l a t i o n of a positron with an electron when the spins are p a r a l l e l i s 1/1120 times the p r o b a b i l i t y f o r a n n i h i l a t i o n when the spins are a n t i p a r a l l e l , since such an a n n i h i l a t i o n must take place with the emission of three photons, a much less probable process than the emission of two photons.  36  Rich  ( 1 9 5 D  and De Benedetti  ( 1 9 5 4 )  have both observed a  three-photon disintegration rate In aluminium which agrees with this value —  further evidence i n support of the type of  annihilation process assumed. The p r o b a b i l i t y of a n n i h i l a t i o n w i l l be given by: ( B e l l and Graham  where C  1 9 5 3 ) s  i s the Dirac cross-section, and N i s the electron  density.  Thus \^l*r?~tLN or t , the mean l i f e of the positron i s :  A being the atomic weight of the material of d e n s i t y y o , N_ i s the e f f e c t i v e number of electrons per atom of the metal. The results of Green and Stewart et a l ,  ( 1 9 5 5 ) »  ( 1 9 5 5 ) »  and also Lang  indicate that positrons rarely annihilate with  the electrons of atomic cores, but that they annihilate c h i e f l y with the electrons of the Fermi Gas having the same density as that of the free, conduction electrons i n the metal. N  e  Thus,  i s given by the valence of the atom. Applying these results to the cross-section formula, A  we f i n d that the quantity - ~ — v a r i e s widely for d i f f e r e n t S> bimetals , being, for example, 2.44 f o r Beryllium and 2 3 . 7 for Sodium.  This simple model of the a n n i h i l a t i o n process i s  therefore unable to aecount for either the shortness of the mean l i f e i n metals, or i t s constancy from metal to metal.  37 It has been suggested that Coulomb a t t r a c t i o n may cause an increased electron density near the positron and hence a shorter l i f e t i m e (De Benedetti et a l . 1950, 18).  footnote  It i s doubtful, however, whether this factor could  de-  crease the sodium l i f e t i m e , say, by a factor of at least ten. This statement i s supported by the calculations of F e r r e l l (1955)» who  only predicts a decrease by a factor of two for the  a n n i h i l a t i o n l i f e t i m e of positrons i n sodium due to Coulomb enhancement. Another method for attempting to correct t h i s model would be to assume that the Dirac cross-section for a n n i h i l a t i o n i s not inversely proportional to the f i r s t power of the r e l a t i v e v e l o c i t y but to a higher power.  However, the angular c o r r e l -  ation results of Green and Stewart (1955) indicate that the 1/v  dependence f i t s the experimental results most s a t i s f a c t -  orily.  I f , though, a 1/v  dependence i s assumed, then the  a n n i h i l a t i o n p r o b a b i l i t y i s proportional to 1/v.  In a Fermi  electron gas, i n which n(p)dp i s proportional to p dp, where 2  n(p)dp i s the number of electrons per cc. with momenta between p and p • dp, we then find that the t o t a l a n n i h i l a t i o n probability, \ and, since  T  = )h(p)dp  cc } f p^*p  - £ /V ,  J)cc  then X. , rather than being l i n e a r l y proportional to D (the 2/3 T  electron density), as before, i s now  proportional to D  Since a range i n l i f e t i m e s from about 3 x 10""  10  sec. for  .  -10 beryllium to 22 x 10 sec. f o r sodium would s t i l l r e s u l t n with this hypothesis, a v e l o c i t y dependence of 1 A  , with n  greater than 2 would be required to decrease the l i f e t i m e v a r i a t i o n from metal to metal.  However, the angular c o r r e l -  ation results of Green and Stewart  (1955) requires 04n*2.  Thus another interpretation of the phenomenon of positron a n n i h i l a t i o n i s required. ii.  Theory of Formation of Positronium. The second  approach at predicting the mean l i f e t i m e of positrons i n metals was made by B e l l and Graham (1953)) who assumed that when positrons are slowed down to thermal energies, they have a high p r o b a b i l i t y of forming the bound state, positronium, which then decays with i t s c h a r a c t e r i s t i c l i f e t i m e ; the l i f e t i m e s of s i n g l e t and t r i p l e t positronium being 1.25 x 10 sec.  and 1*4 x 10  sec. respectively.  Dixon and Trainor  (1955) state t h a t i f positronium h a s a stable binding i n M  s o l i d media, then i t s formation i s a highly nonequilibrium process.  Once the positronium atom i s formed i t has a high  probability of persisting u n t i l a n n i h i l a t i o n takes place, since the i o n i z a t i o n energy required to free the pair i s not readily a v a i l a b l e . " Since the momentum of the centre-of-mass annihilating pair determines  of the  the deviation from c o - l i n e a r i t y  of the a n n i h i l a t i o n gamma rays, "the positronium model" i s consistent with the results of Green and Stewart  (1955) i f  39 the positron i s assumed to be e s s e n t i a l l y at rest at the time of positronium formation.  One might expect the p o s i -  tronium atom to r e t a i n i t s k i n e t i c energy during c o l l i s i o n s with other atoms of the metal because of i t s extremely  low  Since B e l l and Graham's measurements (1953) of the l i f e t i m e of positrons i n metals indicated a constant value of about 1,5 x 10~^° s e c , the above interpretation seemed i n agreement with their r e s u l t s , i f one assumed that the slowingdown time of the positrons and the positronium formation time were n e g l i g i b l e , and that only the singlet positronium formed.  was  However, i t i s d i f f i c u l t to conceive of such a  process by a random c o l l i s i o n of positrons with the electrons comprising a Fermi Gas. (Garwin 1953)  For this reason, i t was  suggested  that a rapid conversion process takes place  between para- and ortho-positronium by electron exchange.  In  such a case, the p r o b a b i l i t y that a positronium atom annih i l a t e while i n the t r i p l e t state i s very small, equal, as a matter of f a c t , to the p r o b a b i l i t y of a thermal positron annihilating with an electron when their spins are aligned i n the same d i r e c t i o n .  This i s stated as being 1/370  times as  frequent as the two-photon a n n i h i l a t i o n rate (Ore and Powell 194-9), a prediction i n agreement with the experimentally determined  three-photon a n n i h i l a t i o n rate i n aluminium.  Doubt was  cast on the v a l i d i t y of the above i n t e r -  pretation of the data, however, when Garwin (1953) also r e marked that a fast conversion process would lead to a lengthening of the short l i f e t i m e component by a factor of four, since the positronium atom would exist i n the orthostate 3/4 of the< time and i n the para-state only 1/4. assuming as correct the t h e o r e t i c a l estimate of 1.25  Thus, x  10~*  G  seconds for the l i f e t i m e of para-positronium, a positron  -10 l i f e t i m e of 5 x 10 the 1.5  x 10"  10  seconds would be expected, rather than  sec, observed.  Since this discrepancy has  not been s a t i s f a c t o r i l y explained to date, i t was deemed worthwhile to attempt to measure the absolute l i f e t i m e of positrons i n a metal to check the results of B e l l and Graham, B.  The D i f f i c u l t i e s Inherent i n Absolute Lifetime  Measurements, and Their Solutions.  In nearly a l l measure-  ments of l i f e t i m e s by the delayed coincidence method, i n which the l i f e t i m e measured i s short compared to the resolution time of the instrument, a "prompt" resolution curve i s needed to complete the analysis.  One of the major d i f f i c u l t i e s  associated with measuring short l i f e t i m e s i s that of obtaining a suitable prompt source; the reason being that the "time of occurrence" of the counter pulse i s a function of the energy dissipated i n the phosphor (Post and S c h i f f 1950).  It i s  therefore desirable to obtain as the prompt source, a source of gamma rays of the same energy as those being measured.  41 F a l l i n g t h i s , side-channel s e l e c t i o n could be employed to insure the equality of the amplitudes of both the prompt and delayed pulses. i.  B e l l and Graham s Solution. 1  Another method of  circumventing t h i s problem was that adopted by B e l l and Graham  (1953) i n which  the positron i t s e l f was used to produce  both the prompt and delay pulses without the necessity of employing the 1.28 Mev.  gamma ray as a zero time indicator.  In one end of a beta-ray spectrometer they inserted a fast 22 s c i n t i l l a t i o n counter with a Na  positron source imbedded i n  the crystal.. The pulse produced as the positron l e f t t h i s c r y s t a l provided the zero of time for the coincidence c i r c u i t . The positrons were selected i n energy and trajectory by the spectrometer before s t r i k i n g either the c r y s t a l of the second counter to produce the prompt curve, or an absorber situated immediately i n front of the second counter f o r the delayed curve.  In the l a t t e r case the second counter observed the  a n n i h i l a t i o n gamma rays rather than the positrons themselves. This procedure possesses a number of advantages simpler methods.  over  I t gives the value of the mean l i f e absol-  utely, and not merely by comparison with that of another sample.  The method does not depend on the nuclear properties  of the source; and i t i s nearly free of chance coincidences, since nearly every true count i n the sample counter corresponds to a coincidence event.  42 Some disadvantages are also associated with this method, however.  The prompt carve consists of coincidences between  pulses of constant amplitude i n both counters due to the energy s e l e c t i o n of the spectrometer.  The delayed curve,  however, consists of coincidences between pulses of constant amplitude f o r the "zero time" counter, and a spectrum of pulses from the second counter, ( v i z . , the Gompton spectrum of the 500 Kev. a n n i h i l a t i o n gammas).  The symmetry of the arrangement  i s altered somewhat, since, i n one case, the second counter views the primary positrons, and i n the second, the annlh i l i a t i o n gamma rays of these positrons. Also, the positrons s t r i k i n g the second c r y s t a l f o r the prompt curve dissipate a l l their energy i n a very short distance, causing the formation of the s c i n t i l l a t i o n s e s s e n t i a l l y at the front face of the one cm.3 c r y s t a l .  In the case of the delayed curve, the  510 Kev. gamma rays penetrate, on the average, some distance into the c r y s t a l before producing the s c i n t i l l a t i o n s .  The  exact effect of these phenomena on the measured l i f e t i m e i s d i f f i c u l t to ascertain, and are not present i n the other two methods of measuring the l i f e t i m e s . ii.  Minton's Method.  Minton (1954) measured the  l i f e t i m e of positrons i n aluminium and lead, by using the 1.28 Mev. gamma ray of N a " to determine the zero of time, and obtained the prompt curve by using the cascade gamma rays of Co^®.  Coincidences between pulses originating from appropriate  43  parts of the gamma-ray Compton spectra were obtained by employing side-channel pulse amplitude s e l e c t i o n . of 2.9 x 1 0 "  sec. f o r A l , and 3.5 x 10""  10  i n disagreement  10  His results  sec. f o r Pb are  with the absolute measurements of B e l l and  Graham, although their difference of about 0.5 x 10"" sec., 1G  i s within the error of previous measurements.  Due to the  d i f f i c u l t y , however, i n r e s t r i c t i n g the side-channel widths s u f f i c i e n t l y to insure good equality of pulse amplitudes between the Na  and Co  sources, and s t i l l maintain an adequate  counting rate, the d e s i r a b i l i t y of using an " a r t i f i c i a l " Na  22  source for the prompt curve i s obvious. iii.  The A r t i f i c i a l N a  2 2  Method.  By an " a r t i f i c i a l "  22 Ha  source i s meant a source which emits two prompt gamma  rays, one of energy near 1.28 Mev., and the other near 510 Kev.  With such a source, s i m i l a r spectra are produced by the  counters f o r both prompt and delayed curves.  Thus the  d i f f e r e n t i a l pulse height selectors i n the side channels need only define the pulse size s u f f i c i e n t l y to prevent the resolution curve from being too broad. 2.  The Measurement of the Absolute Lifetime of Positrons i n Aluminium. 76 A.  Use of As  as the "Prompt" Source.  A search of  the l i t e r a t u r e on Nuclear Data and decay schemes indicated that A s ^ might be a suitable prompt source. relevant data were obtained: (Hubert 1953).  The following  FIGURE 15: DECAY SCHEME OF A s  / b  (a) Favoured. Schane (b) A l t e r n a t i v e Scheme  GAMMA NO. 1  ENERGY IN COMPTON  MEV.  PHOTOELECTRONS  RELATIVE COMPTON  0.553+ 0.002  0.550  2  INTENSITY PHOTOELECTRONS 1  1  0.648+0.002  0 . 0 7 ' + 0 . 0 4 0 . 0 9 5 ± O.OI  3  1.17  1.210 ± 0 . 0 0 5  0.21  4  1.4  1.410 ± 0 . 0 0 6  O . O l 4 ± 0.005 0.016 ± 0 . 0 0 4  5  2  2 . 0 © ± O.OI  0 . 0 4 + O.OI  TABLE 1:  ± .04  0.25  0 . 0 5 5 ± O.OI  A s ' GAMMA RAYS (Energy and Relative Intensity) D  ± 0.02  i.  The h a l f - l i f e of As  i s 26.7 hours, of suitable  duration for many runs with the apparatus. ii.  I t possesses cascade gamma ray energies of 1.21  Mev., and 555 Kev.  (see decay schemes, F i g . 15; scheme 1 being  the favoured one),  76 iii.  A necessary requirement  for the use of As as a 76 prompt source, i s that the f i r s t excited state of Se' have a very short l i f e t i m e . I t appears that a reasonable estimate  76  of the l i f e t i m e of the 560 Kev. state of Se  10"  11  i s a few times  sec. (Stewart 1955). iv.  The energies and r e l a t i v e i n t e n s i t i e s of the gamma  rays are given i n Table 1, indicating that the 550 Kev. gamma ray and the 1.21 Mev. gamma ray are c e r t a i n l y the most intense, the other gamma rays being r e l a t i v e l y weak except for the 650 Kev. gamma ray, which i s 0.4 times the strength of the 1.2 Mev. gamma.  However, since only the 550 Kev. gamma ray i s i n  coincidence with the 1.21 Mev. gamma ray, the presence of the 650 Kev. gamma should have no effect on the resultant c o i n cidence resolution curve except to increase the chance background. Possible competing sources of coincidences are possible from the 1.41 Mev, 0.65 Mev. and 2.06, 0.55 Mev. pairs of cascading gammas.  One would expect from Intensity consider-  ations, however, less than %  of the t o t a l number of c o i n c i -  dences to be due to the former, and a correspondingly small  511 KEV.  9  12  560KEV.  15 18 21 C H A N N E L NUMBER  24  27  FIGURE 16: GAMMA-RAY SPECTRA OF A s 7 6 (DOTTED CURVE) AND Na  22  (SOLID CURVE) USING Nal CRYSTALS  contribution from the l a t t e r , since the side-channel window, set at the Compton edge of the 1.2 Mev.  gammas, would be  viewing a r e l a t i v e l y low i n t e n s i t y portion of the Compton spectrum a r i s i n g from the 2.06 Mev.  gamma ray.  I f decay  scheme two ( F i g . 15) were found to be the correct one, then only the first-mentioned competing source of coincidences would be present. v.  The Nal spectra of A s ^ and N a  2 2  are given i n  F i g . 16 to indicate the basic s i m i l a r i t y of the two sourees. The r e l a t i v e i n t e n s i t i e s of the two gamma rays being the c h i e f difference between the two curves. vi.  Since the NRX reactor at Chalk River was inoper76 ative at the time the experiment was performed, the As source  75  was  obtained by means of neutron bombardment of As  . The  neutrons were produced by means of a p r o l i f i c (d,n) reaction using the deuterons accelerated by the U.B.C. Van De Graaff generator.  For this purpose, i t i s indeed fortuitous that  75 natural arsenic i s composed t o t a l l y of the As isotope. B. Preparation of the Sources. 22 22 1. Na i n Aluminium. The Na i n aluminium source consisted of an aluminium rod of dimensions 6 i n . x 1/4 i n . One end of which was d r i l l e d out to a diameter of 2/8 i n . and 22 contained a deposit of Na  CI. Thus, no intermediate ab-  sorber, such as mica backing, etc. was employed.  I t was  assumed that the f r a c t i o n of positrons stopping i n the NaCl  46 was n e g l i g i b l e , due to the high s p e c i f i c a c t i v i t y of the s a l t . The source strength was ii.  about 0.01  As 6 i n Aluminium.  mc. To obtain a source as nearly  7  equivalent to that described i n ( i ) above, As ^0^, prior to bombardment, was placed i n an aluminium capsule, also. capsule (size 2% i n . x 3/8 22 larger than the Na  in.) was  The  of necessity s l i g h t l y  source, however, i n order to obtain a  s u f f i c i e n t l y strong source.  P r i o r to bombardment, the source  was composed of chemically pure, 99,9$% 2 ° 3 thermal 75 A neutron cross-section for As i s quoted as four barns , A s  #  T t i e  whereas the cross-section f o r oxygen i s only 0.2 mb.,  and i s  less than s i x barns for a l l the impurities quoted i n the analysis of the As 0^ sample. 2  Thus i t was  f e l t that no  appreciable impurity a c t i v i t i e s would be produced. Another reason for using an aluminium container lay i n the fact that aluminium possesses one of the smallest thermal neutron cross-sections of a l l metals, (0.2 barns). 28 h a l f - l i f e of A l  i s only 2.3 minutes, the r e s i d u a l a c t i v i t y  at the time the experiment was was  Since the  begun (a few hours l a t e r ) ,  thus of n e g l i g i b l e i n t e n s i t y . a.  The Reaction Employed.  For the production of  neutrons, the reactions H (d,n)He3, Be^(d,n)B^°, and 2  ,n)Be  ft Handbook of Chemistry and Physics, 35th e d i t i o n . Published by: Chemical Rubber Publishing Co. 2310 Superior Ave. N.E. Cleveland, Ohio  were considered.  These reactions are l i s t e d i n terms of i n -  creasing neutron y i e l d for deuteron bombarding energies greater 7 8 than one Mev. The Li'(d,n)Be reaction, however, i s extremely exoergic, with about 15 Mev. neutrons being emitted,  10  9  (Ajzenberg 1955)•  The Be (d,n)B 7  has a high y i e l d of slower neutrons  reaction, on the other hand, (about 10*^  neutrons per  sec. per microamp. of d) with the peak occurring at about 3 Mev.  (Segre, 1953). For this reason, and the ready a v a i l a b i l i t y of thick  Be^ targets, the beryllium reaction was chosen f o r the production of neutrons. b.  The Target Assembly.  The target assembly  consisted of a lump of beryllium of unknown p u r i t y fastened to a brass endplate which was provided with a brass tube f o r c i r c u l a t i n g cooling water.  P a r a f f i n wax sheets were then  stacked i n a criss-cross fashion around the target assembly to act as a moderator, the f i n a l dimensions  of the p a r a f f i n  box being about 55 cm. along each edge, with the length of the cube extended In the d i r e c t i o n of the beam to a distance of about one meter.  A v e r t i c a l hole reaching to the target  assembly was l e f t i n the p a r a f f i n stack to allow access to the  75 As  sample, which was suspended i n the center of the p i l e  near the target. c.  The Bombarding Conditions.  The target assembly  was bombarded f o r 4 ^ hours with a deuteron beam of about  19  O  2  4  6  8  10  12  C H A N N E L  14  16  N U M B E R  18  20  22  24 2 6  28f 30 o  Dotted Curve:  Upper Discriminator  S o l i d Curve:  Lower Discriminator  DIPHENYLACETYLENE  OUTPUT  FIGURE 19:  EXPERIMMTAL ARRMGEM1NT  46  mlcroamps. (average) at an energy of 1.6 Mev. of the beam h i t t i n g the Be  9  target was  The f r a c t i o n  found to be quite  large (<-> 90$), judging from the darkened area of the target 76 after bombardment. The f i n a l strength of the As source a f t e r the above exposure to slow neutrons was about 1/5 22 Na or about 0.002 mc. C.  that of the  The Experiment. 22  i.  The Experimental Procedure.  After the Na  spectra ( F i g . 17) were obtained using the two diphenylacetylene c r y s t a l s , the side-channel discriminator voltages were c a l i brated i n terms of energy dissipated i n the c r y s t a l s . c a l i b r a t i o n curves are given i n F i g . 18.  These  In the experimental  arrangement of F i g . 19, the distance between the counters and 76 the As' source was usually about 3 mm., while distances of 22 about two cm. were kept between the Na source and the counters, na-arly  i n order to keep the counting rates i n each counter more equal. A  The side channels were set at the bias points indicated by the arrows, (superscript one), on the spectra of F i g . 18 but were widened as I l l u s t r a t e d by the arrows, (superscript two), after running about ten hours, i n order to increase the c o i n c i 76 dence counting rate, since the As  source had decayed to  nearly 1/2 the o r i g i n a l i n t e n s i t y .  The procedure while making  these runs was  to alternate between the A s ^  and the  Na^  2  sources, so that an analysis of the results could be obtained, should slow gain s h i f t s of the apparatus occur.  An example  10  10  12  FIGURE 20:  14  16  18  20  CHANNEL NUMBER  22  EXAMPLE OF COINCIDENCE RESOLUTION CURVES OBTAINED FOR POSITRONS ANNIHILATING LN A l (Dotted Curve) (Solid l i n e i s A s 7 6 "Prompt" Curve)  24  of the resulting curves are i l l u s t r a t e d i n F i g . 20. Analysis of the coincidence resolution eurves was carried out by measuring the centroid s h i f t s (see Appendix C). This method applies to the time-sorter resolution curves, as long as the curves are obtained while operating i n a l i n e a r region of the instrument. ii.  The Time Calibrations.  The time c a l i b r a t i o n s  i l l u s t r a t e d i n F i g . 21 were also taken at this time and are based on voltage s h i f t s of the peak due t o both inserted time delay and gamma-ray t i m e - o f - f l i g h t . iii.  Pulse Height Dependence on Counting Bate. Since 76 the counting rate with the As source i n place was about 22 twenty times slower than when using the Na  source, i t was  necessary to determine whether the pulse height output from the apparatus was a function of counting r a t e .  This was 22  accomplished  by obtaining coincidence curves using the Na  source (1.28 Mev. and . 5 1 1 Mev. coincidences).  Different  coincidence counting rates were obtained by varying the distance between the source and the two counters, (the gamma-ray path length being kept equal f o r both counters).  The centroids of  the coincidence resolution curves were then plotted against coincidence counting rate.  The curve of F i g . 22 was the  result of this t e s t , indicating a p o s i t i v e dependence of pulse height on counting rate for the rates used. The l i f e t i m e measurements were then obtained by  correcting the eentroids of the Na  resolution curves f o r  this dependence, normalizing a l l runs to the coincidence 76 counting rate obtained when using the As  source.  Since the  l i f e t i m e measurement obtained i s such a c r i t i c a l function of this pulse height dependence on counting rate, the reproducib i l i t y of the pulse height c a l i b r a t i o n curve was tested by repeating the counting-rate dependent resolution curves a month l a t e r , under s l i g h t l y d i f f e r e n t experimental conditions. The r e p r o d u c i b i l i t y was found to be very good, the l a t t e r curve being almost an exact r e p l i c a of the previous one (with the slopes the same within 5 $ ) . l v  for  »  Results.  The average centroid s h i f t (corrected  counting rate variations) of the positron-in-aluminium  resolution curves as compared to their respective "prompt" curves, indicates a mean l i f e of  1.6 x 1 0 " "  1G  sec.  t  t  for positrons i n aluminium  To allow for the errors i n the various  c a l i b r a t i o n curves, a t o t a l experimental error of 0.4 x 1 0 " sec. i s given for these r e s u l t s .  1 0  Although the r e s o l u t i o n i s  not s u f f i c i e n t to determine whether the decay i s exponential, the results are consistent with this assumption (Newton 1 9 5 0 ) . 3.  The Measurement of Positron Lifetime i n Mica.  In order  to check that the apparatus was not introducing systematic errors i n the above measurements, i t was considered advisable to measure, under the same experimental conditions, the l i f e time In another absorber, to determine whether the difference  8  10  12  14  16  18  20  22  24  26  CHANNEL NUMBER FIGURE 23:  COINCIDMCE RESOLUTION CURVES  Comparison Curves f o r Positron A n n i h i l a t i o n i n A l and M i c a  51 i n l i f e t i m e between this new absorber and aluminium were consistent with the accepted r e s u l t s . A.  Method.  Since the arsenic source had decayed to a  p r o h i b i t i v e l y low strength by this time, i t was decided to measure the positron l i f e t i m e i n mica by the comparative method  of De Benedettl and Richings (1952). B  »  Procedure.  Resolution curves f o r the positron  l i f e t i m e i n aluminium and mica were obtained, alternating from  22 one absorber to the other.  The Na  -in-aluminium source was  that used i n the previous experiment.  The mica-absorber  source consisted of a small deposit of activated NaCl (about .05 mc) on the center of a .003 i n . mica s t r i p (about 0,7 cm x 1.5 cm.). This s t r i p was then covered on both sides with s u f f i c i e n t mica to completely stop the most energetic p o s i trons.  Thus, neither source required corrections for positron  absorption by the source material.  The experimental arrange-  ment was the same as before, with the "mica" source substituted for the A s ^ . C.  Results.  i n F i g . 23.  The two resolution curves are i l l u s t r a t e d  When the centroids of these curves were calculated,  a s h i f t of (0.7 -« jx 1 0 " 4  1 0  sec. was obtained, i n agreement with  the measurements of B e l l and Graham (1953). 4.  Discussion and Conclusions.  I t i s interesting to note  that the r e s u l t s of this experiment are i n agreement with the  measurements of B e l l and Graham (1953) of the h a l f - l i f e of positrons i n Aluminium ( 1 . 5 x 1 O ~ of Minton (1954) ( 2 . 9 x 1 O "  1 0  10  s e c ) , rather than those  see.).  As described before, a l l  three experiments involved d i f f e r e n t methods of obtaining the prompt resolution curve. i.  B e l l and Graham's method:  that of using the  positrons themselves, after appropriate energy s e l e c t i o n , to obtain the prompt curve; the zero of time being determined by passing the positrons i n i t i a l l y through a thin stilbene c r y s t a l , and the associated "prompt" pulse produced when the same positrons dissipate t h e i r energy i n the second c r y s t a l . ii.  Minton's method; that of using the 1.28 Mev. cas-  22  cade gamma of Ne the  9?  (the daughter product of Na  ) to determine  zero of time of the coincidence system, with the prompt  curve being obtained by using a Co^ source together with 0  side-channel energy s e l e c t i o n . ill.  The present method; s i m i l a r to Minton's, except 22 76 that an " a r t i f i c i a l " Na source i s used, namely As' , to obtain the prompt resolution curve. The s i m i l a r i t y of the results for the f i r s t and l a s t methods outlined above suggests that the effect of gamma-ray energy on centroid s h i f t s was not s u f f i c i e n t l y corrected f o r i n Minton's measurements. It i s also important to note that, since the 1.21 Mev.  76 gamma ray of As  precedes the 560 Kev. gamma, the l i f e t i m e  53 quoted i n t h i s experiment  for the a n n i h i l a t i o n of positrons  i n aluminium, i s actually 1.6  x 1O"  10  sec. + ^ 5 6 0 , where  ^560  76 i s the l i f e t i m e of the f i r s t excited state of Se  .  However,  judging from the narrowness of the prompt resolution curve as compared to the aluminium absorber curve, the assumption that the l i f e t i m e of this excited state i s much shorter than the l i f e t i m e of positrons i n aluminium seems j u s t i f i e d . It thus appears that the l i f e t i m e of positrons i n metals i s indeed about 1.5  x 10"^  sec. rather than a factor of four  larger as expected from the rapid conversion hypothesis (Garwin 1 9 5 3 ) .  Therefore i t seems that one i s foreed either  to admit of a process for the formation of positronium only i n the singlet state without the accompaniment of rapid conversion or to assume that the conversion process i s i r r e v e r s i b l e , that i s , the ortho-para conversion i s highly probable, while the para-ortho i s not.  At present, however, the t h e o r e t i c a l  explanation of such a process i s d i f f i c u l t (Garwin 1953)» since there i s very l i t t l e energy difference between the t r i p l e t and singlet states of positronium. Before a complete explanation of the positron annih i l a t i o n process i n metals can be given, there w i l l probably be a need f o r more knowledge concerning the dependence of the small l i f e t i m e variations ( B e l l and Graham 1 9 5 3 ) , of positrons i n metals as a function of the physical c h a r a c t e r i s t i c s of the metals, l i k e Atomic Number and Fermi energies, and also the  54 various environmental conditions (temperature, magnetization, etc.).  For the above projects, equipment with greater stab-  i l i t y , less experimental error, and better resolution w i l l be required than that which has been used i n the past.  An  improved f a s t time-sorter, based on the type described i n this thesis, might well be a suitable tool f o r these studies.  55 APPENDIX A THE DERIVATION OF A THEORETICAL COINCIDENCE RESOLUTION CURVE I.  For a P a r a l l e l Coincidence C i r c u i t . 1.  Assumptions: (1)  The p r o b a b i l i t y of emission o f the f i r s t photo-  electron from the cathode of the photo-multiplier  tube at a  time between t and t*-dt a f t e r the interaction of a gamma ray with the s c i n t i l l a t o r i s given by: --Sr o. ^ t  « where t i s the mean time delay of the f i r s t photo-electron (Post and S c h i f f 1950)  (ii)  The spread i n electron t r a n s i t time i n the  photo-multiplier  tube i s s u f f i c i e n t l y small, that i t s effect  on the p r o b a b i l i t y d i s t r i b u t i o n of ( i ) i s n e g l i g i b l e ( B e l l et a l . 1 9 5 2 ) . 2,  Derivation: Let the probability of an output pulse from the  counter occurring  between time t and t+dt after the i n t e r -  action of a gamma ray with the s c i n t i l l a t o r be: (1)  The  f.(±)o(t^  S9. dt St  r  where s s 1/t.  constant t r a n s i t time of the current pulse i n the photo-  m u l t i p l i e r tube i s neglected i n this diseussion,  since i t s  effect i s merely a t r a n s l a t i o n of the o r i g i n . The  following figure w i l l f a c i l i t a t e the discussion  of the resolution time.  Zero time i s the time of a r r i v a l of  the coincident gamma rays at the counters.  Counter #lt  Counter #2:  1%) f  i s the length of the equalized pulse determined by  the shorting-stub length. into counter 1, then:  I f t i s a time delay Inserted  an output pulse w i l l be produced by  the coincidence detector, i f the pulse from counter #2 follows that from counter #1 by a time between t - ^ and t+K Therefore the t o t a l probability of the recording of a coincidence when a delay of length t i s Inserted i n counter #1, i s the i n t e g r a l over a l l t ^ of the product of: (A) , the probability of a pulse from counter #2 i n the time i n t e r v a l t ^ t - ^ t o t ^ r t * - ^ , and, (B) , the p r o b a b i l i t y of a pulse from counter #1 at a time t . (Given by equation (1)) (A) the probability of a pulse from counter #2 i n the time i n t e r v a l t j * t - ? (2)  p(tftx)  (3)  and p ( t r t ) 1  m  )s£  s  to t ^ r t * ^ i s : MX^<L  1  - J ^ * y f t = 1-e 5  f  f  o  r  for  Before forming the product probability and integrating, i t  zr-t,foo)  Xl  f  t^r-t.  -  FIGURE 24:  1  0  1  2  3  INSERTED DELAY —tn/x SEC COINCIDENCE RESOLUTION CURVE FOR PARALLEL COINCIDENCE CIRCUIT Theoretical Curve Fitted to Experimental Points  57 is convenient to d i s t i n g u i s h between two cases: 1. and  The inserted delay  2.  Case Is  t> V t^J*.  I f t ^ J " , then t± i s necessarily £  - t , since t-j^O.  P ( t ) , the integral of the product p r o b a b i l i t y ,  (4)  ~  Case 2:  I f t ^ T ' , then the integration over t ^ must be  sinh  sire"' *; 8  carried out i n two parts, depending on whether t ^ i s greater than or less than V - t . i . e . P(t)  (5)  (See equation (2) and (3) above.)  a)s\l-4.  a l-e"  Jos r  di,+  cosh s t .  \s\o-  r_  - <L  J  *  The same expressions are obtained i f we consider the i n s e r t i o n of delay i n counter #2 instead of counter #1, Thus, the theoretical d i s t r i b u t i o n i s given by: P(t) « l - e - * c o s h st s  = sinh s r e "  s , t  ?  ' ,  ItU^, |t|£*\  This i s f i t t e d to an experimental curve i n F i g . 24, with the following values being assigned to the  parameters:  a  <* t v  3.  Conclusions:  (i)  As t-^G, ?(t)-*l-e~ *,  not ( l - e " ^ ) 3  s  by B e l l et a l . ( 1 9 5 2 ) .  2  as assumed  A coincidence e f f i c i e n c e of 90%  (90% p r o b a b i l i t y of detection of coincident pulses when t»0) 2. & - 4 . 6 t , rather than 6 t as given by  i s obtained with  A 95% coincidence e f f i c i e n c y i s given by  B e l l et a l ( 1 9 5 2 ) . 2^=  6t. (ii)  The resolving time or " e f f e c t i v e width," 2?  a  ,  of a coincidence resolution curve, i s defined as the area under the curve divided by the maximum height ( B e l l et a l . 1952). Area under curve • 2 ^ P ( t ) d t • 2 J . Maximum height '"-  2t =  I  = l-e~ \ S J  2^ .which i s close to 2J f o r #Vt, - e-sV * 1  and  i s within 90% of 2 ^ f o r c 7 > 2 . 5 t . (iii)  The r e l a t i o n between 2?  and the f u l l width  of the resolution curve at h a l f maximum, 2t^: can r e a d i l y be calculated:  e> r'  TOi)-  <L  =  sU so-*Z***-  a, — /  t ^ i s therefore somewhat greater than less than l . K T f o r ^ > 2 t .  , but i s  II.  For a Time-Sorter. 1.  Assumptions:  In addition to the assumptions of  part I, we assume: (i)  The time-sorter output pulse amplitude i s pro-  portional to the degree of overlap of the input pulse. (ii)  A fixed delay of time T i s inserted into  counter #2 so as to obtain a pulse overlap of about 1/2 for prompt pulses.  This has the effect i n the following d i s -  cussion, of always causing the counter #1 pulse to a r r i v e f i r s t at the detector. The equalized pulse length (about 2T) i s assumed to be much longer than the time resolution of the instrument. Let t be the time i n t e r v a l between the production of pulses by counter 1 and counter 2 from a coincidence event.  We  are interested i n the amplitude spectrum of the pulses from the time-sorter resulting from the natural variations i n this time t . 2.  Derivation:  The p r o b a b i l i t y of a pulse from counter #2 occurring between time (6)  t ] * t and t^t^-dt - s e - s ^ i ^ d t . Therefore the t o t a l p r o b a b i l i t y of a pulse amplitude  output corresponding to an overlap of T-t, to T-t-dt, i s the i n t e g r a l over a l l values of t ^ , of the product of the prob a b i l i t y functions ( 1 ) and ( 6 ) .  (7)  i . e . P(t)dt  .{Ve ^« i M  ^se- dt. s t  o Again, the same equation i s the r e s u l t of assuming that the counter #1 pulse i s delayed by t .  Thus, absolute  values of t are used. A c t u a l l y , the amplitude measuring device (a pulse height analyzer) has a f i n i t e resolution determined channel width.  by the  Let the corresponding time-width of a channel  be 2 J \ Then the probability of coincident pulses being observed i n channel " t , " i s given by the integral of (7) from t - ^ t o H-D* . i-e. Pt = J i  S  f  J  and  ^ ' " V ^  c  f t x* *«. * s  4  ctt4r j l s a ^ t  , f o r |t I  , for|t\^o'  o integrating over the peak of the curve; -so' = 1-e Since 2&  cosh s t .  i s the width of a channel, this l a t t e r function w i l l  apply only t o : a.  the centre channel, i f the peak i s centred.  b.  the centre two channels i f the peak i s s p l i t .  3.  Conclusions  (1)  The resulting formulae are i d e n t i c a l with those  a r i s i n g from the p a r a l l e l coincidence c i r c u i t , with the kicksorter channel width now playing the role of the equalized pulse length of the p a r a l l e l coincidence c i r c u i t .  61 (11)  These formulae were derived from the case  where t can approach i n f i n i t y :  therefore the standardized  pulse length must be much greater than t , to ensure essent i a l l y 100% coincidence e f f i c i e n c y . (iv)  Since the resulting formulae f o r the time-  sorter are the same as those f o r the coincidence c i r c u i t , the considerations f o r effective width, half width, etc., which were obtained for the coincidence c i r c u i t , also apply i n t h i s case.  62  APPENDIX B IMPEDANCE MISMATCHES  Fuchs (1952) gives the following formula f o r the r e f l e c t i v i t y ip) of a short impedance discontinuity? . Z ^° t Z  p  e  c  " Z„ . where T i s the t r a n s i t  time of the  ^°pulse along the discontinuous impedance Zl,  i s the r i s e time of the pulse, i s the c h a r a c t e r i s t i c impedance of the cable.  For a 50 ohm, Amphenol connector, of length 2.75 cm,, T Assuming:  s 2.75  3 x 10-  « 0.92 x 1<T  10  sec.  t &s? 0.5 x 10"^ sec. (since the slope of the p  resolution curve Indicates a r i s e time of about 3 x 1O""^ sec.) 0  =  0.12  Thus a transmission of better than 88$ Is obtained f o r the fast pulse.  APPENDIX C CENTROID SHIFT METHOD OF CALCULATING SHORT HALF-LIVES  B e l l et a l . (1952) state that "the centroid of F ( t ) , the delayed resolution curve, i s displaced p o s i t i v e l y along the time axis from the centroid of P ( t ) , the prompt resolution curve, by an amount  = 1/^,  the mean l i f e of the delayed  radiation, as f i r s t shown by Bay This result may  (195D » W  be simply deduced from Newton's  formula? ( 1 9 5 0 ) : 4?  -  X(P-F).  By multiplying both sides by tdt and integrating, we  X  obtain  6it  BIBLIOGRAPHY Ajzenberg, F. and Lauritsen, T. (1955)» Rev. Mod. Phys.22,77. Bay, Z., ( 1 9 5 1 |  Rev. S c l . Instr. 2 2 , 397.  B e l l , R.E., Graham, R.L., and Petch, H.E., Journ. Phys. ^ 0 , 3 5 .  (1952),  Can.  B e l l , R.E. and Graham, R.L. ( 1 9 5 3 ) , Phys. Rev. £ 0 , 644. B e l l , R.E. (1954), Ann. Rev. of Nuclear S c i . 4, 9 3 . Benedict, M., Bothe, W.,  ( 1 9 3 7 ) , Rev. S c i . Instr. 8 , 252.  ( 1 9 3 0 ) , Z. Physik,  1.  De Benedetti, S., and Corben, H.C. (1954), Ann. Rev. of Nuclear S c i . 4, 191, contains an extensive b i b l i o graphy. "" De Benedetti, S., Cowan, C.E., Konneker, W.R., H., ( 1 9 5 0 ) , Phys. Rev. 2Z» 0 5 .  and Primakoff,  2  De Benedetti, S. and Richings, H.J. ( 1 9 5 2 ) , Phys. Rev. 8£, 377. De Benedetti, S., and S i e g e l , R.T.,  ( 1 9 5 4 ) , Phys. Rev. ^4, 955.  Deutsch, M. (1948), Nucleonics, 2 ( 3 ) , 58. Deutsch, M., Q 9 5 D , Phys. Rev. 82, 4 5 5 . Deutsch, M., Dixon, W.R.  ( 1 9 5 1 ) , Phys. Rev. 8^, 866. and Trainor, L.E.H. ( 1 9 5 5 ) , Phys. Rev. j£, 733.  F e r r e l l , R.A. ( 1 9 5 5 ) , A.P.S. B u l l . ^ 0 , 5 , 2 7 A . Fischer, J . , and Marshall, J . ( 1 9 5 2 ) ,  Rev. S c i . Instr. 2^,417.  Fuchs, G. ( 1 9 5 2 ) , Proc. Instn. E l e c t . Engrs. ( A p r i l ) , Part i v . Garwin, R.L., ( 1 9 5 3 ) , Phys. Rev. ^ 1 ,  1952,  1571.  Green, R.E., and Stewart, A.T. ( 1 9 5 5 ) , Phys. Rev. $8, 4 8 6 . H e i t l e r , W. ( 1 9 5 4 ) , "The Quantum Theory of Radiation," (Clarendon Press, Oxford, 1 9 5 4 ) .  65  BIBLIOGRAPHY Hubert, P. (1953), Ann. de Phys. 8, 695. Kallmann, H., (194-7), Natur. u. Tech., July,  1947,  Lang, G., De Benedetti, S. and Smoluchowski, R. Phys. Rev. .22, 596. Lee-Whiting, G.E. ( 1 9 5 5 ) , Phys. Rev. 21,  (1955),  1557.  Lewis, I.A.D. and Wells, F.H. (1954), "Millimicrosecond Pulse Techniques," (London, Pergammon Press, 1954). Mackenzie, I.K. (1953), Unpublished PhD. Thesis, The University of B r i t i s h Columbia. Meyer, K.P., Baldinger, E., and Huber, P. (1948), Rev. S c i . Instr. 19_, 473. M i l l e t t , W.E.  ( 1 9 5 D , Pays. Rev. 82, 336.  Minton, T.D. ( 1 9 5 0 ) , Phys. Rev. £8, 490. Neilson, G.C., and James, D.B. S c i . Instr., 1955.  (1955),  to be published, Rev.  Newton, T.D. ( 1 9 5 0 ) , Phys. Rev. £8, 4 9 0 . Ore, A. and Powell, J.L. (1949), Phys. Rev. 21*  1696.  PIrenne, J . (1947), Arch. Sc. et Nat. 22, 257. Post, R.F., and S c h i f f , L. ( 1 9 5 0 ) , Phys. Rev. 80,  1113.  Rich, J.A. ( 1 9 5 D , Phys. Rev. 81, 140. Ruark, A.E. (1945), Phys. Rev. 68, 278. Segre, E. (1953), "Experimental Nuclear Physics," (John Wiley and Sons, Inc., N. York), V o l . I I , 1953. Stewart, A.T. ( 1 9 5 5 ) , Private Communication. Wheeler, J.A. (1946), Ann. N.Y. Acad. Sc. 48, 219.  

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