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Lifetimes of gamma-ray transitions by delayed-coincidence measurements MacKenzie, Innes Keith 1953

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LIFETIMES OF GAMMA-RAY TRANSITIONS BY DELAYED-COINCIDENCE MEASUREMENTS by INNES KEITH MacKENZIE A Thesis submitted in Partial Fulfilment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY IN PHYSICS We accept this thesis as conforming to the standard required from candidates for the degree of Doctor of Philosophy Members of the Department of Physics The University of Brit i s h Columbia July 1953 - 1 -TABLE OF CONTENTS Page I INTRODUCTION 1 II EXPERIMENTAL PROCEDURE 10 A. General 10 B. The Counters 13 (1) Comparison of Counters 13 (2) The Sc i n t i l l a t i o n Phosphor .......... 14 (3) The Optical Coupling 18 (4) The Photomultiplier 18 a. Choice of tube 18 b. Noise and spurious pulses .... 19 c. Transit time spread 21 (5) Counter Assembly 25 C. The Pulse Limiters 26 D. The Delay Lines 29 E. The Pulse-Length Equalizer (Stub) 30 F. The Coincidence Detector 32 G. Main-Channel Amplifiers and Discriminator 35 H. Side-Channel Energy Selection and the Triple Coincidence Mixer 36 I. Performance of Complete Instrument 40 (1) Preliminary Tests 40 (2) Performance Without Side Channels ... 41 (3) Single Counter Operation 41 (4) Operation on a Prompt Source 44 - i i -TABLE OF CONTENTS Continued Page J . Suggested Improvements 46 I I I THE ANALYSIS OF MEASURED DELAY DISTRIBUTION.. 48 A. Methods o f A n a l y s i s 48 B. E x c i t e d S t a t e s of N i 6 ° ( C o 6 ° - ^ N i 6 ° ) ... 50 C. E x c i t e d States o f Co^ 9 (Fe5-2^Co59) ... 51 D. The Decay of E u 1 ^ 2 * 154 ^ 2 E. E x c i t e d S t a t e s o f W l 8 2 ( T a 1 8 - 2 - ^ W 1 8 2)... 52 F. E x c i t e d S t a t e s of T e 1 2 4 ( S b 1 - ^ T e 1 2 4 } . . 55 G. E x c i t e d S t a t e o f Ra E (Ra D—^-Ra E) ... 55 APPENDIX 58 LIST OF REFERENCES 6l - i i i -TABLE OF ILLUSTRATIONS Figure 1 A Simple Decay Scheme 2 Basic Delayed Coincidence System 3 Delay D i s t r i b u t i o n Curves 4 BlockliDiagram of Complete Equipment 5 Pulse Shaping by a Shorted Stub 6 Pulses Fed to Coincidence Detector 7 Pulse Height vs. Detector Posi t i o n 8 Large Pulse Plus S a t e l l i t e s 9 Longitudinal Section of S c i n t i l l a t i o n Detector Assembly 10 Pulse Limiter C i r c u i t 11 Pulse Equalizer and Coincidence Detector 12 Main Channel Pre-Amplifier 13 Pulse Shaper and Side Channel Amplifier 14 Suppression of S a t e l l i t e s by Pulse Shaping 15 T r i p l e Coincidence Mixer 16 Co^° Delay Distributions without Energy Selection 17 Pulse Height D i s t r i b u t i o n i n Main Channel 18 V a r i a t i o n i n Maximum Pulse Height along the Line - i v -TABLE OF ILLUSTRATIONS Continued Figure 19 Delay Distribution with Single Counter ; 20 Delay Distribution for Prompt Source (Ra E) 21 Decay Schemes of Some Sources Used 22 Co 6 0 Delay Distribution (^-j.) 23 F e 5 9 Delay Distribution ^5-^) 24- Eu 1^ 2- 4- Delay Distribution ^-^) 25 T a 1 8 2 Delay Distribution ty3-p 26 S b 1 2 4 Delay Distributions L4-y) ACKNOWLEDGEMENTS The work described in this thesis was supported by a Grant-in-Aid-of-Research allotted to Dr. K. C. Mann by the National Research Council of Canada. I am indebted to Dr. Mann, who suggested the problem, for aid in a l l phases of the work. Scholarships from the Ontario Research Council and the Bri t i s h Columbia Telephone Company in addition to financial assistance from the Defence Research Board of Canada, have enabled the author to carry out this work. - v i -ABSTRACT An apparatus for the measurement of the lifetimes of gamma-ray transitions between nuclear excited states has been designed and constructed. With this apparatus, lifetimes as short as 1.5 x 10~^° seconds may be determined. This lower limit is shown to be inherent i n the s c i n t i l l a t i o n detectors available and not in the electronic circuits which are them-selves capable of much better performance. Measurements have been carried out on several radioactive nuclei and have yielded the following results: 60 (1) The two excited states of Ni have half-lives less than 1.6 x IO" 1 0 seconds. (2) The three excited states of Co-^9 have half-lives less -10 than 2 x 10 seconds. (3) No detectable h a l f - l i f e is found in the decay of E U 1 5 2 , 154. (4) An excited state with a h a l f - l i f e of 1.1 x 10~ 9 sec-onds is present in W-1-82. We identify this transition as magnetic quadrupole. (5) A h a l f - l i f e . o f 2.3 x 1 0 " 1 0 seconds is found for the .607 Mev transition in Te 1 2 4" which has previously been cla s s i -fied as electric quadrupole. LIFETIMES OF GAMMA-RAY TRANSITIONS BY DELAYED-COINCIDENCE MEASUREMENTS I INTRODUCTION A valid nuclear theory is expected to predict exactly a l l the allowed energy values of any nucleus as well as the quantum numbers (angular momentum, parity) associated with each level. Parity i s a mathematical property of the nuclear wave function specifying i t s symmetry characteristics. One might expect that thorough investigation of the simplest systems of nuclear interactions such as neutron-proton scattering would yield a l l the essential information. However, experience with complex nuclei revealed several effects which were not apparent from studies of the simple systems. Among these effects are the saturation of nuclear forces and the single particle characteristics of some nuclear wave functions as evidenced by the successes of the shell model. It is not impossible that careful experimental study of energy levels i n complex nuclei w i l l lead to further understanding of nuclear forces. In this research we have been concerned with nuclear transitions which involve no change i n the number of nueleons - 2 -or nuclear charge. Such transitions can take place i n three distinct ways: (1) Gamma-ray transitions: The gamma-ray carries off the f u l l energy difference between the two states. (2) Internal Conversion: An atomic electron is emitted carrying away an energy equal to the energy difference between the states minus the atomic binding energy. Subsequently characteristic X-rays and Auger electrons are emitted of energy depending on the atomic level from which the electron was removed. Measurements of the intensity and energy of the X-rays or, more commonly, of the conversion electrons, reveals the extent to which conversion takes place i n the different atomic levels. (3) Internal Pair Production: If the energy available for the transition exceeds 2 ifl-C2 the nucleus may expel, an electron from the "Dirac sea" of negative energy states, resulting i n the emission of a positron-negatron pair of total kinetic energy equal to the transition energy minus 2 m 0c 2. This effect i s generally negligible except in the case of high energy transition between states of zero angular momentum (spin). It is conventional to classify the transitions by analogy with classical electromagnetic phenomena. The multir polarity i s defined as 2 1 where 1 i s the absolute value of the vector change i n spin between the states. The transitions are further classified as either electric (E) or magnetic (M) on the basis of parity change as follows: Radiation Type Ei Mi E 2 M2 E 3 M3 Spin change, i I I 2 2 3 3 Parity change Yes no no yes yes no - 3 -Thus a magnetic quadrupole (M2) transition i s one involving a spin change of two units of i\ and a change of parity. Several types of experiments can be performed to yield information on the spins and parities of the states i n -volved in.these transitions: (1) Angular Correlation (Blatt, '52). In this case i f the excited state i s reached as the result of another nuclear transition in which a detectable particle was emitted by the nucleus, the angle at which the gamma-ray from the excited state i s emitted sometimes shows a positive correlation with the emission angle of the preceding particle. Measurement of this correlation can yield information regarding the spins of the states involved. (2) Polarization Correlation (Blatt, '52). If i n measuring an angular distribution as above only gamma-rays of a particular polarization are counted, the data may yield.a value for parity change as well as spin change. (3) K-Cqnversion Measurements: The K-conversion coefficient is defined as the ratio of transitions resulting i n conversion in the K-shell to the number resulting i n gamma-rays. Accurate calculations of these coefficients for various transition types are available for a wide range of transition energies (Rose f 5 D . Provided the measurements can be carried out with 4 high accuracy, the spin and parity change can usually be assigned with certainty. (4) Ratio of Conversion Coefficients: Although accurate values of conversion i n other than the K-shell are not yet available, empirical curves of the conversion ratio have been published showing good correlation with transition type, particularly for high nuclear charge and low energy (Goldhaber '5D. Accurate values of K/L ratios are relatively easy to obtain experimentally. When exact values of L-conversion coefficients become available, these measurements should lead to accurate classification of a large number of transitions. (5) Measurement of Lifetimes. As yet, i t is"not possible to assign spin and parity changes on the basis of lifetime measure-ments with any assurance, except perhaps for M4 transitions. In this case good correlation exists between lifetime and energy only i f account i s taken of the spin of the i n i t i a l state (Goldhaber '5D. We may then hope that, when accurate correlation between energy and lifetime is found for a l l transi-tions i n a l l nuclei, the measurements w i l l yield values of the spins and parities of the individual states. The object of our research i s to add to the rapidly accumulating data on gamma ray lifetimes so that the necessary correlations can be estab-lished. It i s , of course, not possible to calculate accurate - 5 -transition probabilities between states without exact knowledge of the nuclear wave functions involved. In the absence of this knowledge, many attempts have been made to obtain estimates based on admittedly crude nuclear models. There is considerable disagreement regarding the dependence of lifetime on the parity change involved but a l l estimates show a very strong dependence on spin change. This i s borne out i n a rough fashion experi-mentally and i s the chief reason why so much effort has recently gone into lifetime measurements. The implication of theory i s that a very crude measurement of lifetime would yield an accurate value of spin change i f the proper correlation were known. Of the various estimates of lifetimes the most success-f u l to date i s based on the single particle model of the nucleus (Weisskopf ' 5 0 ) . He arrives at the following expression for the h a l f - l i f e of electric multipole radiation: T (E) = Ht+j£ [ 1 . 3 . 5 . — - ( a f r i f • JL. ( 1 2 Z ) 2 / + 1 J L \T) 2 tf+l) r 2 T w 5cS where r is the nuclear radius i n units of e2/mC2, w i s the transition energy i n units of mC2 and the other quantities have their usual significance. For magnetic radiation he obtains: ,2 T (M) = T (E) x J^-^Y x where M is the mass of a nucleon and R i s the nuclear radius i n centimetres. These formulae are calculated on the basis that the excited state can decay only by gamma emission. In general, however, some of the transitions proceed by internal conversion. - 6 -The lifetime is inversely proportional to the total transition probability which is equal to the sum of the individual proba-b i l i t i e s . The above formulae should therefore be divided by (1 + 6 0 where OL i s the total conversion coefficient, i.e. the ratio of the probability for conversion to that for gamma emission. The resulting correction becomes particularly important for transitions of low energy and high multipole order i n nuclei- of high atomic number. These formulae predict that an Increase of one unit in spin change w i l l increase the lifetime by a factor of about one million for energies below 1 Mev. On the other hand a parity change gives a factor of only thirty going from electric to magnetic radiation of the same order. The\single particle model of the nucleus on which Weisskopf's formulae are based i s not an accurate representation of the nucleus even when modified by strong spin-prbit coupling. Hence we could not expect Weisskopf's predictions to be highly accurate. However, much evidence has been .accumulated which suggests that, at least for odd-A nuclei, a large part of the nuclear wave function can be ascribed to a single particle (Goldhaber, ' 5 2 ) . If this interpretation is correct, Weisskopf's formulae should represent a valid though very inaccurate approxi-mation. It may be possible to correlate departures from the predictions with other measurable properties of the nuclei involved. As an example many nuclei possess very much larger - 7 -electric quadrupole moments than can be explained on the basis of a single particle model (the shell model). Predictions of the lifetimes of excited states of these nuclei based on the shell model would be expected to show gross errors which might be closely correlated with the measured quadrupole moment. At present not enough lifetimes have been measured to establish the form of these corrections should they exist. If i n time It is possible to obtain the necessary corrections, one would expect to be able to assign unambiguous values to the spin change in a transition on the basis of an extremely crude l i f e -time measurement. Parity change could be assigned on the basis of measurements which would demand l i t t l e accuracy, but the assignment of individual spins purely on the basis of lifetimes might require very good technique. At present more than a hundred gamma-ray lifetimes are known with f a i r accuracy. Most of these have values of greater than 10~ 1 0 seconds, although a few very short lifetimes are known. It i s believed that most states de-exite by low multipole transitions with lifetimes of the order of lO""1^ seconds. Most of these transitions cannot be measured by present techniques. We may anticipate that the development of very high resolution spectrometers w i l l yield reasonable values for many of these transitions based on level width measurements. Level widths under bombardment in accelerators should also yield some z. \ BETA -GAMMA Z + l A SIMPLE: DECAY S C H E M E SOURCE B E T A COUNTER G-AMMfl COUNTER SETfl > rCHflNNtL GRMMN CHANNEL V VARIABLE D E L A Y COINCIDENCE MfXER BASIC DELAYED COINCIDENCE SYSTEM .A A-PROMPT SOURCE B-50URCE WITH DELAY B DELAY INSERTED FIG. 3 DELAY DISTRIBUTION CURVES - 8 -useful information. At present the most f r u i t f u l method is the delayed coincidence technique which i s limited to the range of 10"^ to lO""^1 seconds. The principle of the measurements i s depicted in Figures 1 to 3 . Suppose that the source has a simple decay consisting of the emission of a negatron group followed by a gamma-ray transition to the ground state of the daughter nucleus (Figure 1). For simplicity we w i l l assume that the h a l f - l i f e of the negatron group i s very long compared to the duration ©f the experiment. If one plots on semi-log paper the coincidence rate as a function of the delay inserted in one channel, a curve such as A i n Figure 3 i s obtained i f the beta-ray and gamma-ray are emitted simultaneously. The slope on the sides of the curve should be characteristic of the radiation detectors used. If an easily measurable lifetime i s present, a curve such as B i n Figure 3 i s obtained and the l i f e -time of the transition is easily obtained from the slope of the straight line portion of the curve to the right. This simple method of analyzing the data restricts one to the measurement of lifetimes giving slopes greater than the slope imposed by the detector. More complicated analysis to be discussed later can reduce this limit by approximately a factor of ten. The Geiger counter detector imposed a limit i n excess —8 of 10" seconds even with the best techniques. With the advent of the fast organic phosphor-photomultiplier combination as a - 9 -radiation detector, the situation was greatly improved so that i t i s now almost routine to measure lifetimes of the order of 10~9 seconds. By combining the usual delayed coincidence equipment with a coincidence spectrometer, lifetimes of approxi-mately 10~^® seconds have been measured accurately and upper limits of 2 x 10"^ seconds placed on some transitions (Bell •52) . We have constructed a delayed coincidence circuit which we show to be limited i n performance solely by the proper-ties of the scintillation,detector. " Lifetimes as.short as 1.7 x 10 seconds can be measured with 10 per cent accuracy when using trans-stilbene phosphors with 1P21 photomultipliers. The apparatus has been applied successfully to the study of excited states i n several nuclei as w i l l be reported in the following pages. SOURCE V A R I A B L E D E L A Y L I N E P U L S E S H R P E R > r AMPLI F I E R DISCRIMINATOR SCALAR P U L S E E Q U A L I Z E R C O I N C I D E N C E D E T E C T O R > f PREAMPLIF IER > < M A A M P L IN FIER. 1 OlSCRWiNRToR. D, T R I P L E C O I N C I D E N C E MIXER. DISCRIMINATOR DA N. PUL5E SHAPER AMPt JFIER DlSCRlM\NflT0R SCALER SCALER FIG-. 4 BLOCK DIAG-RHM of COMPLETE; EQUIPMENT II EXPERIMENTAL PROCEDURE A. General: A block diagram of the delayed coincidence apparatus i s shown i n Figure 4. It i s similar to that used by many workers and described in some detail by Bell (Bell '52). A somewhat idealized account of the functions of the various com-ponents w i l l f i r s t be presented, to be followed by a more detailed description of the circuits and the problems arising i n their operation. A eounter consists of an organic s c i n t i l l a t i o n phos-phor, optically coupled to a type 1P21 photomultiplier. The high voltage supply for the photomultiplier i s set sufficiently high that a single electron emitted by the photocathode w i l l generate an output pulse of approximately one volt. The pulses, which vary over a range of two decades i n amplitude, are equal-ized to about 0.6 volts by the limiters. The duration of the pulses delivered by the limiters to the delay lines is dependent on the unlimited pulse amplitude from the photomultiplier and varies from 1 0 " 8 seconds to several microseconds. Such pulses are not suitable for driving a coincidence mixer since resolving F.o. 5 PULSE SHAPING- BY A SHORTED STUB (a)PRIMARY PULSE (b)REFLECTED PULSE Cc) WET PULSE (b) (c) -9 10 SEC. F\Cr. 6 PULSES FED TO COINCIDENCE DETECTOR faiWx 10'9SEC. APART (b>IO"95EC (c)4xlO"'°SEC. (A)ZERO - 11 -time could not be defined. A shorted coaxial stub shapes a l l pulses to a width of 1G"9 seconds (Figure 5). Since the delay lines and the stub are linear elements we may use the principle of superposition and treat the pulses from the two counters independently. The single stub then shapes each pulse into a rectangular pulse of amplitude 0 . 3 volts and duration 10~ 9 seconds. The coincidence detector1 w i l l "see" a signal of this form for each pulse unless the front edge of two pulses arrive at the detector within 10~ 9 seconds. The signals seen by the detector for different degrees of overlap... are shown i n Figure 6 . If we assume that the counters and the limiters are perfect and we are always measuring truly coincident events, the signals seen by the detector w i l l always appear as i n Figure 6 (d) provided the detector i s at the position of zero delay. Now suppose the detector behaves as an instantaneous peak-reading voltmeter, and i s moved along the delay line providing a measure-ment of the peak voltage at each point. The curve 7 (a) would be found i n such a case. If, i n addition to the coincidence events, a background of single pulses is present a curve such as 7 (b) would result. However, i f the detector is biased to just reject single events we again obtain a curve such as 7 (a) but with the amplitude reduced by a factor of two. Since the experimental procedure i s to count the number of pulses above a 0-6 ! J O 0 > (a) X u) 0-6 Q_ 0 (b) Z X 10 6EX FIG>.7 PULSE HEIOHT VS. DETECTOR POSITION ( a ) COINCIDENT PULSES ONLY (b) COINCIDENT PLUS SIWOLE PULSES 0-25 0-5 , TIME (MICROSECONDS) FIO-.8 LARG-E PULSE PLUS SATELLITES - 12 -certain amplitude as a function of detector position on the delay l i n e , i t is necessary to amplify the pulses from the detector to operate a scaler. This function i s performed by a low gain pre-amplifier followed by an Atomic Instruments type 204-B linear amplifier. We w i l l show later that the detector cannot completely reject pulses due to non-coincident events and so i t is necessary to use a further amplitude discriminator for this purpose. Thus far we have assumed that the response of the counters i s instantaneous but, i n fact, they show a strong energy dependence i n this respect. In order to obtain the steepest slopes on the sides of the delay distribution curve i t i s neces-sary to discriminate against events in which l i t t l e energy i s expended i n the phosphor. This function i s carried out by the side channels in combination with the t r i p l e coincidence mixer (Figure 4). Positive pulses from a photomultiplier dynode are equalized to a duration of 0.20 microseconds by a shorted stub. They are then amplified and fed to a discriminator which rejects a l l pulses below a certain amplitude. The discriminators produce output pulses which are used to give the counting rates . i n each side channel and also to operate a gate for the pulses i n the main channel. If the pulse height in the side channels were directly proportional to the energy of the particle detected, then an output from the t r i p l e coincident mixer would only fesult for coincident events of more than a prescribed minimum energy as determined by the side channel discriminators. - 13 -B. The Counters: (1) Comparison of Counters: An ideal counter for the type of coincidence work reported here would have 100$ efficiency, very short recovery time, no fluctuations in reaction time, and produce large, uniform amplitude pulses with a very short rise time. The cylindrical Geiger counter is inefficient for gamma-rays of more than 100 Kev i n energy but i t s chief drawback is the large fluctuations in reaction time which are a direct result of the geometry of the counter. If a particle causes ionization only near the outer wall of the counter, a period of the order of a microsecond must elapse before an avalanche i s created i n the high-field region. If, however, primary ionization takes place in the region of high f i e l d s , the reaction time i s extremely short. The large spread in reaction times introduces a corres-ponding uncertainty i n the timing of events. The parallel plate spark counter presents another possi-b i l i t y and possesses several attractive features for fast coinci-dence work. In this counter two closely-spaced parallel plates maintain a strong uniform f i e l d in the intervening gap. The f i e l d i s sufficiently strong to start an avalanche at any point within the active volume. The spread i n reaction time i s relatively small and i s almost independent of the energy of the particle detected. The pulses produced are very large and nearly uniform in amplitude. The efficiency i s low except for electrons but, since most low energy gamma-ray transitions are - 14 -strongly converted, this i s not a serious drawback. We have attempted to use these counters i n our work but the attempt was abandoned because of the short l i f e of the counters (see appen-dix). The s c i n t i l l a t i o n counter using an organic phosphor has been the most successful although i t is not ideal. Its properties w i l l be discussed i n considerable detail below. (2) The Sc i n t i l l a t i o n Phosphor: One of the most important limitations on the performance of a coincidence circuit using s c i n t i l l a t i o n counters is the time taken for the decay of lumin-escence in the phosphor. Post and Schiff have treated this problem theoretically in order to establish a lower limit to the resolving time of s c i n t i l l a t i o n counters (Post, 5 0 a ) . Consider-ing the phosphor, the optical coupling, and the photocathode as a unit, they derive the following expression for the mean delay i n the appearance of the Qth photoelectron from the cathode: RX ( 2 R ) where R is the total number of photoelectrons resulting from a pulse and i s the decay constant of the phosphor. The expression holds for R Q and includes only the f i r s t two terms in a rapidly converging, i n f i n i t e series. The expression is easily seen to be a minimum for Q = 1, i.e. i f the f i r s t photo-electron i s detected. If R i s assumed to be directly proportion-al to the energy and a l l components of the coincidence mixer - 15 -other than the phosphors are considered ideal (i.e. infinitely-fast), the slope of a delay distribution curve would correspond to the mean l i f e : T- = i , , . i and would be almost R~X R ^ a linear function of the energy. For a given photomultiplier, different phosphors and identical optical coupling, we see that the speed of a circuit is almost directly proportional to R . R is proportional to the number of photons emitted by the phosphor and hence a measure of phosphor sensitivity. It is customary to assign a value of 100 for the sensitivity of pure, single-crystal anthra-cene at room temperature and relate other phosphors to i t . There is considerable disagreement in the literature regarding both the decay constant and sensitivity of the different phosphors. The different degree of purity of the samples tested may be the cause of the discrepancies or i t may be due to lack of standard-ization of measuring technique. The data we use for comparison of phosphors were a l l compiled by the M.I.T. group (Sangster '52), using the same technique on a l l samples. We define a figure of merit as the sensitivity divided by the mean l i f e in units of 10" 9 seconds for the decay of*-luminescence. Table I lists only the fast organic scintillators in the solid state. Some liquid scintillators are reported to be faster than stilbene, but have not been included in the l i s t since they have not been measured by the identical procedure. - 16 -TABLE I P h o s p h o r F i g u r e o f M e r i t A n t h r a c e n e ( R o o m T e m p e r a t u r e ) 3 .3 A n t h r a c e n e ( - 196° C ) 15.6 T e r p h e n y l ( R o o m T e m p e r a t u r e ) 2 . 7 S t i l b e n e ( R o o m T e m p e r a t u r e ) 5*7 D i p h e n y l a c e t y l e n e ( R o o m T e m p e r a t u r e ) 3.4-Q u a t r a p h e n y l ( R o o m T e m p e r a t u r e ) 9*9 It was originally our intention to use anthracene cooled to liquid nitrogen temperatures. However, this was found to be. impractical for several reasons. Since the limiter tubes produce a considerable amount of heat they could not be included i n the thermally stable enclosure. ' This necessitated long coupling leads with attendant loss of speed i n the limiter c i r c u i t . Also the necessity of achieving temperature equilibrium would require that a long period elapse between mounting a source and obtaining measurements. Our results were obtained using stilbene phosphors which were the fastest immediately available. The fundamental limit on slope imposed by the phosphor can be calculated i n the following way. The peak quantum efficiency of the photocathode i s approximately ten per cent (Morton, ' 5 2 ) , i.e. approximately one photon out of every ten incident on the cathode w i l l produce a photoeleetron. Stilbene produces about 400 photons per 100 Kev expended i n the phosphor (Morton, ' 5 2 ) . For this energy, assuming an optical coupling efficiency of 50 per cent, 20 photoelectrons w i l l be released from the cathode. This yields a slope on the side of a distribu-tion curve corresponding to a h a l f - l i f e of: TA = .69 x 8 x 10-9 ( l + l ) = 3 x 1 0 " 1 0 sees. 20 20 We have observed definitely steeper slopes under these conditions so we must conclude that one or more of the estimates involved i s considerably in error. - 18 -(3) The Optical Coupling: In addition to uncertainties introduced by the decay time of the phosphor, i t i s apparent that, due to the f i n i t e velocity of both the incident particle and the luminescence photons, variations i n the point of origin of the photons can lead to a form of straggling. It has also been shown that the use of a long light pipe w i l l increase this effect (Post, ' 5 2 ? ) . These effects have been minimized in our work by using small phosphors and l i t t l e or no light piping, and are negligible compared with the straggling effects which we w i l l show to be present i n the photomultipliers. (4) The Photomultiplier: a) Choice of Tube. A f i r s t consideration i n deciding upon tube type i s the degree of optical coupling obtainable between the phosphor and photocathode. In this respect the end-window construction is,very superior to the older 931 type. However, of the two end-window types available, one (the R.C.A. 5819) breaks down at voltages high enough to produce the necessary gain and the other (E.M.T. type 5311) introduces a large spread i n transit time. A new R.C.A. tube, type 4646, should provide an excellent solution to the problem. It i s a 16-stage tube of end-window construction providing adequate gain at normal operating voltages (Greenblatt, 5 2 ) . The use of electrostatic focussing should make the transit time spread much less than that i n the new E.M.I, tubes. Since this tube was not commercially available, we have - 19 -used R.C.A. type 1P21 tubes which are of side window construc-tion. Although they are designed for operation at 1200 volts or less, we have found i t possible to operate them at voltages in excess of 2000 in a l l cases tested (4 tubes). This was achieved by gradually Increasing the applied voltage over a period of several days. In two cases the tubes withstood 2700 volts without breakdown. Approximately 2100 volts i s necessary i n order that a single electron from the photocathode w i l l develop a signal of 1 volt across 15 mmfds., as required to drive our coincidence c i r c u i t . This figure i s , of course, not identical for a l l tubes but the degree of uniformity observed i s surprising. b) Noise and Spurious Pulses. The rather low work function of the material used i n the photocathode results in appreciable thermionic emission even at room temperature. Approximately 15,000 electrons are emitted per second from the cathode of a 1P21. Two such tubes operating a coincident: . mixer of 2 x 10~9 sees, resolving time without energy selection would yield a coincident counting rate - 9 ©f 2? 0NiN 2 = 0-5»OOO)2 x 2 x 10 x 60 = 27 counts per minute. However, most of this background is removed when energy selection is used. In addition to the thermionic noise, at least three other types of undesirable signals are produced at high operating voltages. One has the characteristics of a brush discharge, - 20 -presumably arising from sharp points l e f t i n the construction of the tube. It is greatly reduced by the aging process mentioned in the previous section and may be effectively elimi-nated . It has been known for some time that a close-fitting conducting shield about a photomultiplier materially reduces noise counts. When operating with a positive high voltage supply the shield should be connected to earth. We have found that, with a negative supply, noise increases i f the shield i s earthed but decreases i f the shield is connected to the supply line or is l e f t floating. The latter alternative is used for safety. The origin of the noise thus eliminated is unknown. It may be that surface charges on the glass envelope cause f i e l d distortions which stimulate brush discharges from the electrode structure. Another possibility i s that surface charges exert mechanical strains in the glass envelope which cause the glass to s c i n t i l l a t e . A third type of noise, generally referred to as "after-pulsing" or " s a t e l l i t e production", has been noted by many observers (Mueller ' 5 2 ) . Following a true pulse, or one result-ing from noise of other types, secondary pulses invariably occur when the 1 P 2 1 i s operated at high voltages (Figure 8 ) . These "s a t e l l i t e " pulses show a broad maximum in their frequency about .25 microseconds after the primary pulse and often pile up to produce a pulse height in excess of that of the primary pulse. There are, on the average, more satellites of a large pulse than - 21 -of a small pulse, but the correlation is by no means good. Occasionally the satellites may continue for eight microseconds after the main pulse, but these are probably satellites of sa t e l l i t e s . To simplify further discussion we w i l l refer to satellites occurring less than 0 . 1 microseconds after the main pulse as the fast component and the remainder as the slow com-ponent. The origin of neither of these groups has been established experimentally. It has been suggested (Davison '52) that the fast component i s due either to ionization of residual gas molecules or to fluorescence of the insulating supports for the electrode structure. The existence of a reasonably well-defined maximum in the slow component suggests that i t i s due to ion feedback from one dynode to the preceding one. If this assumption i s correct then the ions must be of approximately mass fifteen. Ions of this mass would traverse the mean inter-dynode distance i n 0.25 microseconds. Since no light metals are used on the dynode surfaces, the ions are probably from oxygen or nitrogen atoms occluded on the dynode surfaces. Our observations on satellites are quite different from those in the references quoted above but their investiga-tions were carried out at more normal operating voltages. Further reference to the sa t e l l i t e problem w i l l be made when we deal with energy selection. c) Transit-Time Spread. There are at least three effects which might be expected to lead to a variation i n transit time through a photo-- 22 -multiplier: (1) the time taken for emission of secondary electrons, (2) the variation i n i n i t i a l electron velocity, and (3) electron trajectory differences. It has been suggested recently that the process of secondary emission can be characterized by a decay time of the order of 3 x 1 0 - 1 Q seconds (Law, ' 5 2 ) . However, the theory of the effect predicts a value of less than 10""-1-1 seconds and numerous experiments establish an upper limit of the order of 10~ 1 0 seconds (McKay, ' 4 9 ) . We w i l l accept the verdict of the majority and consider the effect to be negligible. We have not found reference to any experimental work done on the distribution of i n i t i a l velocities of secondary electrons from the type of surfaces used on the 1P21 dynodes. Morton states that most ©f the electrons are grouped within a range of 3 volts (Morton, ' 5 2 ) . Accepting this value, we can calculate the resulting transit time spread i n a single stage due to this effect very simply. The transit time for an elec-tron, starting with zero velocity, from a point at zero potential to a point 6 mms. distant at 200 volts i s : t = . d e = 1.43 x 10~ 9 seconds. V m If the electron has an i n i t i a l velocity component corresponding to an energy of 3 electron volts i n the direction of the second point, the transit time becomes: t 1 = 2 d . = 1.26 x 1Q~9 sees. 72Vo £ + V2(V+V0)e " m m - 23 -and the transit time spread is 1 .7 x 10 sees. If one electron incident on a dynode produced a single electron at the dynode and we wished to measure the fluctuations i n the arrival time at the collector, the solution would be straight-forward. Since the fluctuations at the separate dynodes are s t a t i s t i c a l and not correlated, the total uncertainty would be equal to the square root of the number of stages times the spread per stage. For the 1P21 this would yield a total spread of 5 x 10"*^ ® seconds. The real problem to be solved, however, i s : what is the fluctuation i n arrival time of the n'th electron at the collector where n i s determined by the sensitivity of the apparatus following the photomultiplier? A proper solution would include fluctuations i n gain per stage as well as the fluctuations i n i n i t i a l velocity. The labour involved was not considered justifiable i n view of the other approximations made. We w i l l use the value taken from the simplified solution, i . e. 5 x 10~ 1 0 seconds. Since this uncertainty w i l l apply to each tube i n a coincidence c i r c u i t , one cannot expect a coincidence efficiency of 100 per cent for resolving times less than 10" 9 seconds (i.e.. some truly coincident events would not be recorded). Depending on i t s point of origin on the photocathode, an electron w i l l travel over a path of from 8 to 13 mms. before striking the f i r s t dynode. This yields a transit time spread of 1.2 x 10~9 seconds in the f i r s t stage of the photomultiplier. - 24 -However, the structure of the 1P21 is such that the electrons which follow a longer than average path in one stage produce secondaries which travel a shorter than average path in the next stage. The degree to which.transit time spreads w i l l be cancelled out is d i f f i c u l t to calculate. However, since the variation in path length in the f i r s t stage is approximately twice as great as i n any succeeding stage, we may assume that the over-all spread is at least half that calculated for the f i r s t stage alone. The total transit time spread for a 1P21 operating at 2000 volts must be at least 10""9 seconds and so any coincidence mixer using lP21's at this voltage with a resolving time less -9 than 2 x 10 ' seconds must be less than 100 per cent efficient. Furthermore, since transit time spread varies inversely as the square root of the applied voltage, the minimum permissible resolving time for 100 per cent efficiency at 4000 volts must be at least 10~ 9 seconds. Such voltages have been applied by pulsing the counters for brief periods (Post, ' 5 0 ) . Our calculations of transit time spread d i f f e r from those of Morton who neglects the compensating properties of the dynode structure. Measurements have been made of the rise time of single-electron pulses by observing them on a high speed oscilloscope with no vacuum tubes in the circuit (Post ' 5 2 ) . After corrections for the effects of the measuring equipment, Post obtains a value of 2.5 x 1 0 - 1 0 seconds for the rise time BRASS CRSE IP2I PHOTOMULTIPLIER STILBENE PHOSPHOR RLUMINUM FOIL FIG-. 9 LONGITUDINAL SECTION OF SCINTILLATION DETECTOR ASSEMBLY f - 25 -with an applied voltage of 5000. The rise time should be a rough measure of the uncertainty imposed by the variation in emission velocity. Converting his measurement to what would result at 2000 volts we obtain a value of "5.6 x 10""10 seconds which agrees satisfactorily with our calculated value. It should be noted that the imperfections of the photomultiplier result in uncertainties in timing which l i e within a f a i r l y definite range. Provided one does not attempt to use too short a resolving time, the t a i l of a delay distribu-tion curve should have a slope characteristic of the phosphor at the energy selected. 5) Counter Assembly: (Figure 9) A brass cylinder, closed at one end, of 1^" inner diameter and 1/16" wall thickness i s fitted over the glass envelope of the photomultiplier and taped to the tube base. A 1" by slot i s cut in the side of the brass shield facing the photocathode and a Jr" section of Br i t i s h 3 cm. waveguide is soldered i n the slot to serve as a support for the phosphor. The phosphor used i n a gamma counter has dimensions 1 cm x 1 cm x 2 cm., and is ground on one side to f i t the multiplier envelope. The remaining sides are covered with thin aluminum f o i l which is sealed to the phosphor with a thin layer of vihylite cement. This crystal is inserted through the wave-guide opening and pressed against the photomultiplier, optical f 26 -coupling being ensured by a layer of high viscosity silicone o i l . The phosphor i s then cemented to the waveguide with a hard wax and the waveguide opening is covered with a 1 G mg/em2 aluminum sheet. Light-tightness is ensured by sealing this sheet in place with hard black wax. In the assembly of a beta counter, a lucite light pipe of the same dimensions as a gamma phosphor i s used. A sheet of stilbene 1 mm. thick is held on the end of the light pipe by the high viscosity o i l and the assembly i s covered by thin aluminum f o i l . Otherwise the only difference from the gamma counter i s that a 2 mg/cm2 f o i l covers the waveguide open-ing. C. The Pulse Limiters: The spectrum of pulses generated by the photomultipli-ers must be converted into uniform amplitude pulses i n the delay lines. To some extent, the choice of delay lines dictates the properties of the pulse limiters. In order to retain the highest frequency components present i n the photomultiplier pulses we must not use delay lines of the lumped-parameter type or the distributed helical conductor type. The simplest solution i s to use low-loss coaxial cables which have the neces-sary frequency response. The characteristic impedance of these cables is approximately 1 0 0 ohms. The limiters should be capable of driving these with a total time constant much less than the rise time of the pulse from the photomultiplier. Of - 27 -the various circuits tried, the one shown i n Figure 10 has proved by far the most satisfactory. The tube employed, an E-2133? is an experimental secondary emission pentode of miniature construction. In the absence of a pulse the plate current is set to about 12 m.a., at which point the tube shows an incremental transconductance of 16 ma. per volt. A negative signal of 1 volt amplitude on the grid reduces the plate current to 1 ma. and 1.5 volts leaves only a few microamps of current. We w i l l treat the operation of the circuit on a large negative pulse from the photomultiplier collector. The total capacity to ground of the collector plus grid circuit i s approxi-mately 15 mmfd. which, combined with the grid resistor network, yields an input time constant for decay of 1.3 x 10~7 seconds} i f satellites did not occur the grid would return towards i t s normal voltage with this time constant. The satellites inject additional negative charge on the grid and keep the limiter from drawing f u l l current for a period of from one to eight micro-seconds. The time constant is sufficiently long relative to sa t e l l i t e spacing that very few satellites are capable of pro-ducing large pulses at the limiter output. If this were not so an increase i n coincidence background would result. Like most high transconductance tubes the E-2133 is subject to considerable fluctuations i n gain so that, even with fixed electrode voltages, variations i n plate current occur. FIG. 10 PULSE LIMITER CIRCUIT 0 + 3 0 0 REG-. VflRlABLfc DELRY LINE 6RK5 FIG*. II PULSE EQUALIZER AND COINCIDENCE DETECTOR - 28 -We have reduced these fluctuations by using a large cathode resistor, R6, which causes cathode follower action i n so far as D. C. is concerned. It is necessary to by-pass this resistor with a large condenser C 2 i n order to prevent variations i n pulse size for different spacing of' pulses i n time. The cathode resistor must also be by-passed for the very high frequency components of the pulse. Large condensers i n general behave as inductances at very high-frequencies and hence cannot provide suitable by-passing. If a good high-frequency capacitor is placed directly i n parallel with the large one, shocked o s c i l l a -tions may result due to the inductance of the lat t e r . R5 - a i non-inductive resistor - is used to damp out such oscillations i n our cir c u i t . Ci i s a barium titanate condenser connected to the copper chassis by very short leads. The time constant R5C1 must not be much larger than the grid time constant or some satellites would produce output pulses of a greater amplitude than the primary pulses. In order to prevent pulses being fed through the limiter tubes by other than the conduction process, some unusual precautions have been taken. A high conductivity material such as copper seems to be essential for the chassis. Although the suppressor grid is internally connected to an internal shield, i t is necessary to earth each of these electrodes separately by short leads. Small barium titanate condensers with minimum lead lengths are used for high frequency by-passing. The screen grid must not be by-passed or a considerable unwanted - 29 -coupling, presumably inductive, results. However, since the screen is adequately decoupled from the secondary cathode by a small resistance, l i t t l e loss of sensitivity results from the lack of by-passing. Parasitic oscillations i n the output c i r -cuit are suppressed by the non-inductive resistor R9. The effective plate load of the limiter consists of the delay line i n parallel with a matching non-inductive resistor R8. This is only true, of course, for that part of the pulse which precedes the return of a wave reflected from the detector junction. However, since we use only the f i r s t 10*9 seconds of the pulse, reflections can be neglected. Since a current of 12 m.a. is cut off by a pulse on the limiter grid, the resulting pulse i n the delay line w i l l be of amplitude 0.6 volts. To deliver this pulse, the output, capacity of the limiter tube plus the wiring capacity must be charged through R9 and the 5031 plate load. The total output time constant i s thus of the same magnitude as the rise time of a photomultiplier pulse. As a result some speed is probably lost at this point. D. The Delay Lines;: The variable delay is introduced by a slotted coaxial lin e , 140 cms. in length. The outer conductor i s a brass tube of inner diameter and 1/16" wall thickness. A slot, 3/16" in width, is milled along almost the f u l l length of the tube so that contact can be made to the centre conductor. The latter, a length of work-hardened no. 9 copper wire, is held by Series - 30 -140 Amphenol coaxial connectors ri g i d l y connected to the ends of the brass tube. The connectors are arranged so that any slack i n the centre wire may be taken up by a screw adjustment. The tube i s clamped at approximately 30 cm. intervals to the laboratory bench to eliminate a tendency to warp. The variable line is connected to the limiter circuits by flexible coaxial lines with a characteristic impedance of 100 ohms and a propa-gation velocity of 0.82C. The characteristic impedance of the variable line is approximately 95 ohms and, since air i s the only dielectric material present, the propagation velocity i s C. A slight mismatch occurs at the connections between the variable line and the flexible lines but, for reasons to be discussed below, this i s not harmful. It should be noted that when the detector is moved a distance along the variable l i n e , the resulting difference i n path length for the pulses from the limiters is 2 . The total range covered by the variable line i s , therefore, 2_E^G _ 10 - 9 seconds. Greater delays may be introduced by changing the length of flexible line from one of the limiters. E. The Pulse-Length Equalizer (Stub): In discussing the pulse equalizing process we w i l l neglect any loading effects due to the input impedance of the detector. A pulse moving along the variable line sees a discon-tinuity i n line impedance at the stub junction. Denoting the - 31 -characteristic impedance of the line by Zo and that of the stub by Zs, the pulse sees an impedance which changes diseon-tinuously from Zo to ZofZs* An inverted wave i s reflected back down the line with a resultant loss i n effective pulse height. If we take the i n i t i a l pulse height as unity then the voltage, V*1", developed at the stub junction i s V 1 = 2< % , } 2 Zs (Zo+Zs) =2Zs + Zo ( Zs +p * (Zo+Zs ) A pulse of this amplitude travels along the delay line and another, of the same amplitude, up the stub. The latter pulse is inverted at the end of the stub and travels back to the delay l i n e . At the junction this pulse sees an impedance of . If the stub impedance is equal to this value no further reflections occur and a pulse i s formed at the detector input of amplitude 2 2 s = 1 . 2 Zs + Zo 2 In general, however, a reflection w i l l occur when the pulse i n the stub reaches the delay l i n e , leaving an effective pulse height V 1 1 = ( 2 Zs ) x ( 2 ) (2 Zs + Zo) ( Zo + 1 ) 2 Zs = 8 Zs 2 . (Zo + 2 Z s r Differentiating this expression with respect to Zs we find extrema for Zs = G and Zs = ^  * Thus the condition for maxi-2 mum effective pulse amplitude i s the same as that for obtaining - 32 -only a single reflection in the stub. Experimentally we find that pulse size increases continuously with stub impedance up to a value of at least 200 ohms. We are able to account for this only by assuming that the connection from the stub to the line presents a high impedance regardless of the characteristic impedance of the stub. If this i s so, then the optimum value of stub impedance i s equal to that of the connection.1 We have used a 12-cm. length of 200 ohm cable for a l l our measurements. The pulse formed i s equal to twice the cable length divided by the propagation velocity, giving a value of approxi--9 mately.10 ' seconds. Due to the rise time of the pulse resulting from deficiencies in both the photomultipliers and the pulse limiters, the pulses fed to the detector w i l l not be of the ideal-ized shape presented in section A of this chapter. Rather, they w i l l be more closely represented by semi-sinusoids corresponding to a frequency of 500 mcs. (one half period = 10""9 seconds). F. The Coincidence Detector: The electrical connection between the detector and delay line i s made by means of an 8-24 brass screw which goes through the slot i n the line and is insulated from the outer conductor. Contact i s ensured by allowing the screw to force the centre conductor 1/32" from the centre position. The slight eccentricity resulting has a negligible effect on the electrical properties of the l i n e . - 33 -The circuit of the detector and pulse equalizer i s shown in Figure 11 . In section A we discussed the desirability of a very sharp break in the impedance of the detector element. In addition, the detector must react very rapidly so that i t can -9 read accurately the peak voltage in a pulse of 10 7 seconds duration. This requires that the reaction time constant be not much greater than 1 0 " 1 0 seconds, at least near the peak of a coincident pulse. Such speed i s far beyond that obtainable with voltage discriminators based on trigger ci r c u i t s . Reason-able success has been achieved with a circuit based on the non-linearity of a sharp cut-off pentode, but the simple diode dis-criminator has yielded the best results. The diode chosen, the 1N56, has a low shunt capacity, a sharp break in the current-voltage characteristic, and a high conductivity i n the forward direction. The input capacity of the cathode follower must be charged through the diode i n order that a signal be delivered by the circuit to the following amplifier. In order to know, with reasonable accuracy, the time constant through which this capacity is charged, i t i s necessary to know the effective pulse amplitude from the stub since the diode resistance is a very non-linear function of the applied voltage. An estimate based on the calculations presented in section E w i l l probably show a gross error in view of the discrepancies between theory and measurement reported there. We feel that the best estimate i s based on s t a b i l i t y tests (see below) which yield a value for single pulse amplitude of approximately 0.25 volts. If a bias - 34 -of G.l volts i s placed on the diode then the net peak voltage applied by coincident events i s 0.4 volts. At this voltage the 1K56 has an impedance of 200 ohms. The pentode-connected cathode follower has an input capacity of the order of 1 mmfd. and hence the minimum input time constant is approximately 2 x 10"^"° seconds. At the end of a pulse the diode cuts off and the charge on the grid of the cathode follower leaks off through the 10K resistor which acts as a pulse lengthener. Less ampli-fication would be required in succeeding stages i f this resistor could be increased in value preferably by at least an order of magnitude. However, st a b i l i t y requires that this resistance be very much smaller than the back resistance of the diode since the latter i s subject to very large fluctuations with changes i n temperature. The main limitation on germanium diodes as low-level detectors is their severe temperature dependence. When we attempted to reduce single counts to near the noise level of the following amplifier by biasing the diode, very serious fluctua-tions in coincidence counting rate resulted. The amplitude of coincidence pulses as observed at the output of the Atomic Instru-ments Amplifier (Figure 4) was reduced by a factor of two by directing a jet of air from the laboratory air line on the diode. To avoid this i n s t a b i l i t y we have found i t necessary to operate the diode with a bias of less than .05 volts. From manufactur-ers' data on temperature dependence we find a rapid improvement 6 A & 5 6 A H 6 6 J 6 6 A C 7 + 3 0 0 REG. Fi&. 12 MAIN CHANNEL PRE-AMPLIFIER - 35 -i n s t a b i l i t y when the forward voltage exceeds 0.4 volts. Hence our estimate of 0.25 volts for single pulse heights at the detector input since coincident pulses would allow operation in the stable region. As an additional precaution against temperature d r i f t s we have enclosed the diode i n a 1" cube of polystyrene foam. G. Main-Channel Amplifiers and Discriminator: Since i t is not feasible to use a large time constant in the detector cir c u i t , the output pulse is of too short a duration to be amplified with f u l l gain by conventional pulse amplifiers. To avoid the heed of constructing a very wide-band amplifier, we have simply used extra gain from a pre-amplifier to bring the pulses up to a desirable level. Since the pulses are many times greater than amplifier noise, this i s a perfectly satisfactory solution. The pre-amplifier i s a heavily fed back ring-of-three of conventional design (Figure 12). Triode connection i s used on the input stage to reduce the noise level. The measured rise time i s 0.1 microseconds and the gain approxi-mately 2 5 . The type 204-B amplifier i s operated with a rise time of 0.2 microseconds and the gain adjusted to give a maximum pulse height of 60 volts on coincident pulses. The discrimi-nator built into this amplifier i s used to select resolving time and the output pulses from i t are fed to the tr i p l e coincidence mixer. Generally the main channel i s monitored by connecting a Tektronix Oscilloscope to the low impedance output of the main amplifier. 6A&5 £ G J G 6 A & 5 ^ I 2 A U 7 & IEAU7 + 3 0 0 - H 5 » REG-. PULSE SHAPER AND Sioe CHAHNCL AMPLIFIER - 36 -H. Side-Channel Energy Selection and the Triple-Coincidence Mixer. The signal used to drive the pulse shaper i s taken from the eighth dynode and i s of positive polarity. It could not be taken from the collector without impairing the speed of the main channel. Operating at 2300 volts on the photomulti-pli e r as i s customary, pulses at the eighth dynode sometimes exceed 30 volts in amplitude. Space charge effects probably prevent pulse amplitude from being a linear function of the energy of the incident particle at this level. However, the production of satellites is a much more serious limitation to the desired linearity. We have tried to eliminate the slow component of the satellites by using a "quench c i r c u i t " to remove the voltage from the seventh dynode for a short period following the main pulse. To be reasonably effective the quench circuit must produce a pulse of more than 100 volts with a rise time of IO"? seconds. The inter-dynode capacities are so large that the quenching pulse i s fed to a l l dynodes at an appreciable amplitude. Operation of the main channel is impaired and oscillation could only be suppressed by slowing the rise time of the quench pulse to a point where i t would be almost useless. This i s true even when the quench pulse is applied to the f i f t h dynode. Thus we were forced to abandon this attack on the problem. An alternative attack i s to allow the satellites to be produced but minimize their effect by pulse shaping. The (o) — I 1 1 1 I I 1 0 CM 0-2 0-3 0-4- 0-5 TIME - (MICROSECONDS) FIO. 14 SUPPRESSION OF SATELLITES BY PULSE SHAPING, ( ^ C H A R G E D I S T R I B U T I O N (^ I N T E G R A T E D RND A M P L I F I E D (O P U L S E . FROi^ SvmPER. - 37 -/ circuit shown i n figure 13 i s an attempt to achieve this end. Although not completely satisfactory in i t s present form, we believe the principles on which i t was designed to be sound and more elaborate apparatus might yield the desired effect. In discussing the principles of operation of the c i r -cuit when using a fast s c i n t i l l a t i o n phosphor i t i s permissible to neglect the f i n i t e rise time of pulses from the photomultiplier. We w i l l also neglect the fast component of the sate l l i t e spectrum ' since the circuit is not designed specifically to eliminate i t s effect. Figure 14(a) shows a distribution of charges delivered to the dynode. With the usual technique this would yield a poor measurement of energy since much more charge i s delivered by satellites than by the primary pulse. Suppose, for simplicity, that an almost i n f i n i t e resistance is present i n the dynode ci r c u i t . The voltage on the dynode w i l l build up as i n 14(b) (dotted curve). The solid curve w i l l represent the same pulse after passing i t through an amplifier with a moderately fast rise time. If this pulse i s now fed to a pulse-shaping stub with a total transit time of G.l microseconds, a pulse as shown in 14 (c) i s obtained. Such a pulse would be read by a fast discriminator as having an amplitude equal to that of the primary pulse. If, however, a single s a t e l l i t e delivers more charge than the primary event, or i f several small satellites are very closely spaced, the energy determination w i l l again be incorrect. It can be easily shown - 38 -that a second pulse-shaping stub w i l l greatly reduce this effect. For the sake of s t a b i l i t y of the over-all system i t i s essential to maintain constant counting rates in the side channels and hence any amplifiers in these channels must not be subject to fluctuations i n gain. High s t a b i l i t y amplifiers of very wide band width, say 100 Mc/s, are unusually complex and were not considered justifiable from economy considerations. It may be that a relatively simple circuit based on the E-2133 tubes would prove satisfactory. We have used simple rings-of-three with a rise time of 0 . 1 microseconds. In order that the main component of the pulse l i e within the bandwidth of the amplifier, i t i s shaped to a width of 0.2 microseconds. Due to this choice of pulse width an appreciable fraction of the satel-l i t e s are included and hence the energy selection i s not satis-factory. No quantitative data have been recorded to check the improvement in performance resulting from pulse shaping. However, observation of the pulses on an oscilloscope shows that most of the pulses are similar to that shown in 14(c) and satellites occurring after 0.25 microseconds almost never exceed the main pulse height. A second advantage arises from the use of pulse-shaping. Due to the relatively short duration of the pulses, large single-channel counting rates can be tolerated without a shift occurring i n the discrimination level. The discriminators used i n the side channels are part 300 SIDE. CHANNEL I0K 47 K -150 -AAAA. o REG--FIG-. 15 TRIPLE COINCIDENCE MIXER - 39 -of the type 101-A Atomic Instruments scalers used to record single channel counting rates. The t r i p l e coincidence mixer (Figure 14) is a simple circuit based on the cathode follower. ;A side channel dis-criminator produces a positive output pulse of 0 .5 microseconds duration and 18 volts amplitude followed by a negative pulse of several microseconds duration. This pulse is fed to a pulse-shaping stage, tube T l or T2, which operates as follows: the tube is normally biased at 10 volts so that i t i s completely cut off. The positive discriminator pulse turns the tube hard on for approximately 0.45 microseconds. The 1N34 diode has a sufficiently low forward impedance to prevent the grid from going far positive and hence the output pulse has a f l a t top. Since the output pulse from the discriminator i n the main chan-nel amplifier i s only about five volts in amplitude, a sharper cut-off tube, T3> is used for pulse shaping i n this channel. The output pulse from this tube is more rounded on the sides than those i n the side channels and has a width of about 0.3 microseconds. Normally tubes T4, T 5 5 and T6 draw a total current of approximately 8 ma. A l l three tubes must be cut off simultaneously for the total current to change appreciably. The observed ratio of output pulses for tr i p l e coincidences versus doubles i s greater than 10 to 1. The following discrim-inator, i.e. D4 i n Figure 4, i s therefore not a c r i t i c a l element. We use another Atomic Instruments scaler model 101-A for this purpose and for recording t r i p l e coincidence counting rate. - 4-0 -I. Performance of Complete Instrument (1) Preliminary Tests: Most of the circuits used are based on standard electronic practice and can be tested by well-known techniques. The pulse limiters, however, are required to operate with unusual speed and have presented by far the most d i f f i c u l t problems of a l l the components. The following tech-nique has been devised for checking their performance. A single limiter circuit i s connected to the delay l i n e . The power supply which normally feeds the limiter is disconnected but high voltage i s l e f t on the associated photomultiplier. Bias is removed from the detector and maximum gain is used i n the main channel amplifier. Under these conditions amplifier noise i s clearly visible on the oscilloscope which i s set at about 5 microsecond sweep duration. When a source of f a i r l y high energy particles i s brought near the counter no signals should be detectable above noise level. This condition has been achieved in both our limiters for photomultiplier voltages of less than 2500. We were unable to approach this condition using conventional pentode tubes for limiters and many seemingly t r i v i a l adjustments were necessary with the type E-2133 tubes. The test establishes that pulses are not fed through the limiters at an appreciable amplitude by any process which does not involve electronic conduction. When the circuits had been adjusted to satisfy the test and the limiters again connected to the power supply, single pulses as observed on the oscilloscope at the Flfr. 16 Co 6 0 DELAY DISTRIBUTIONS WITHOUT ENERGY SELECTION (Y-Y) - 41 -output of the main channel amplifier showed a sharply defined maximum amplitude. 60 (2) Performance Without Side Channels: Using a Co source and two gamma-ray counters, delay distribution curves were obtained for three values of photomultiplier voltage as shown in Figure 16. The distributions are not corrected for background coincidence rate. It is apparent that a large background i s present at high voltages where thermionic noise pulses can be expected to f u l l y cut off the limiter current. At voltages below 2000 the background is low and the circuit would work well as a coincidence mixer for incident particle energies above a few tens of kilovolts (i.e. for energies such that most of the pulses produced are distinctly larger than noise pulses). H) Single Counter Operation: In order to prove that the main limitations on the circuit are due to. the counters, two limiters were built on a single chassis and driven by the same counter. Each pulse from a limiter was then truly i n coinci-dence with a pulse from the other limiter. In order to ensure that a l l coincidences recorded were due to f u l l amplitude pulses, a single side channel was used to drive both side-channel inputs of the t r i p l e coincidence mixer. A source of hard beta-rays (Ra E) was used to excite the counter. This arrangement provided several useful checks on the performance of the c i r c u i t . Unfor-tunately there was a very slight amount of coupling between the 460 300 200h j l O O -o a 100 Kev. 30 Flfr. 17 35 40 45 50 55 60 DISCRIMINATOR BIAS (VOLTS) PUL*E HEIGHT DISTRIBUTION IN MAIN CHANNEL or o a • ° « r* 1 1 1 -I I L_ -60 -40 -20 0 30 40 60 DETECTOR POSITION (CM) 18 VARIATION IN MAXIMUM PULSE HEIGHT ALON<y THE LINE - 42 -limiter circuits at high photomultiplier voltages.. This forced us to use voltages somewhat under 1800, and hence the rise time of pulses from the photomultiplier was slightly longer than normal. Placing the detector at the mid-point of a delay dis-tribution we obtained the amplitude distribution of pulses i n the fast channel which were i n coincidence with pulses above a certain amplitude i n the side channel (Figure 17). The side channel was not calibrated accurately since, as we have pointed out, energy selection is unreliable. The energy values assigned to the two curves are only crude estimates. It i s interesting to note that at the higher energy selection the out-put pulses l i e entirely within a range of 15 percent of the maximum pulse height. Since the detector is highly non-linear this implies that the pulses from the pulse equalizer show a much smaller spread. Furthermore we have reason to believe that the coupling mentioned above was not entirely absent at the voltage used and could be responsible for much of the spread. A check on the detector was carried out by plotting main channel pulse height as a function of the position of the detector on the delay line (Figure 18). This distribution, though satisfactory, i s very much different from the ideal one discussed in section A of this chapter. The asymmetry is due to the coupling between limiters. This has been established by repeating the curve at a higher photomultiplier voltage and noting a marked increase i n the asymmetry. The ratio of pulse 0 •2-0 -1-6 FIG. 19 -1-2 -03 -0-4 0 0 4 0-8 1-2 1-6 2-0' DELAY-UNITS IO-*SEC. DELAY DISTRIBUTION WITH SINGLE COUNTER - 43 -height for coincident events to that for single events (the singles-doubles ratio) appears to be only about 3*5 to 1. Actually the ratio is approximately twice this value. The pulse amplitude at the ends of the line results from two pulses which are nearly coincident in time. Since the diode has a f a i r l y high impedance for single pulses the input time constant of the detector w i l l be long relative to pulse width. It w i l l therefore integrate these pulses rather than respond to their peak voltage. Finally with this arrangement delay distribution curves were obtained for several values of resolving time as determined by the main channel discriminator level (Figure 1 9 ) . The energy selection is estimated to be near 200 Kev. It was established by lowering the main channel discriminator level, that Curve I corresponds very closely to 100 percent coincidence efficiency. A 15 per cent decrease in efficiency results from reducing the resolving time to approximately 1.3 x 10~9 seconds (Curve II, Figure 1 9 ) . This cannot be taken as proof of the val i d i t y of our calculations regarding transit time spread i n the photomultiplier. The decrease i n efficiency is due to the rise time of the output pulse from the limiters and imperfections -9 of the detector. At resolving times less than 10 ' seconds the efficiency begins to f a l l off very rapidly with an attendant decrease i n slope (Curve III). Operation i n this region might be the most suitable for time of flight measurements where i t is important to locate the centre of a distribution with accuracy. - 44 -At resolving times of greater than 2 x 10~9 seconds the slope on the side of a distribution curve corresponds to a h a l f - l i f e of approximately 3 x 1 0 " - 1 1 seconds. This slope i s approximately five times as steep as any we have obtained using separate counters with each limiter and so we are certain that the limitations on the speed of the equipment are imposed entirely by the counters. 4. Operation on a Prompt Sourcet In order to obtain a truly prompt source (i.e. no variation i n the difference i n exci-tation times of the two phosphors) hard beta particles were allowed to pass through the thin crystal ( 0 . 5 mmi1) of one counter and expend their remaining energy i n the crystal of the second counter which was a normal gamma counter. The source used was a spent radon needle which produces a beta group of 1.2 Mev end-point from the decay of radium E. It was mounted in a recess i n the light pipe immediately below the phosphor. Most of the beta particles causing coincidences would lose approximately 200 Kev i n the thin phosphor. The radon needle subtended a rather large angle at the phosphor so that much of the light must have been lost. Thus the number of photons reaching the photocathode i n this counter would correspond to a considerably lower energy than 200 Kev. We estimated that the minimum total energy lost by a beta ray before entering the second phosphor was about 400 Kev. This is the sum due to the glass walls of the radon capsule, iO4 -3 -2 - | O I 2, 3 4 5 DELAY - U M I T S IO" S E C . FIG-. 2 0 DELAY DISTRIBUTION FOR PROMPT SOURCE (RaE) - 45 -the aluminum reflectors, and the f i r s t phosphor. Thus the spectrum of pulses in the second counter would correspond to energies distributed continuously from zero to 800 Kev. The slope on the right i s seen to increase continu-ously with increased discriminator setting i n the side channel (Figure 20). The right side of the curve indicates delays i n the counter which has the continuous distribution of energies. Though there was some variation in slope on the l e f t with side-channel discriminator level i t was not so pronounced since the thin crystal automatically selected a rather narrow band of energies. Several features of the distributions are of interest. (1) The slopes on both sides are approximately equivalent to a h a l f - l i f e of 1 .3 x KP^ 0 seconds for energy selection near 200 Kev. (2) An increase in side channel discrimination i n one counter shifts the maximum of the distribution along the delay line i n the direction of the other counter. This i s the phen-omenon used i n the centroid shift analysis of delay distribu-tions. (3) At high photomultiplier voltage (2450 volts) as used i n this series of measurements, i t i s not feasible to use low energy selection because the sat e l l i t e effect makes elimina-tion of noise counts impossible. A decrease in slope for large delays is noticeable on the curve corresponding to approximately 50 Kev energy selection in Figure 2 0 . This i s due to the - 46 -increase in background due to noise pulses. Because of this effect we have used voltages near 2300 i n the balance of our measurements. J Suggested Improvements: The use of shorter stubs for pulse shaping and faster amplifiers i n the side channels should effect considerable improvement i n energy selection. If the necessary degree of linearity between pulse height and energy could be achieved, differential discriminators could be used i n the side channels to select narrow bands of energies. The more powerful methods of analysis based on the centroid shift (Newton ' 50) could then be used. The type 4646 tube should be almost free of sa t e l l i t e effects and could probably be used successfully with side chan-nel differential discriminators without requiring fast amplifiers. Since the 4646 is of end-window construction the limitations on energy selection imposed by the s t a t i s t i c a l fluc-tuations of the photocathode would be reduced (Morton, ' 5 2 ) . When using the centroid shift procedure the steepness of the slopes i s not so important as in the more straightforward analysis. It would probably be advantageous to use the slower sodium iodide phosphor which has a high photoelectric cross-section and could therefore yield improved energy selection. A much more attractive possibility i s the "loading" of a fast - 47 -liquid organic s c i n t i l l o r with an appreciable amount of high Z material. Although our equipment has been quite stable over the short periods required for our measurements, we have noted some d r i f t over long periods. Some of this d r i f t is probably s t i l l due to the diode detector which should be contained i n a thermally regulated enclosure for high s t a b i l i t y . However, we believe the main source of d r i f t i s the secondary cathode of the limiter tube. The cathode follower action i n the limiter stabilizes only the cathode current. Where long term s t a b i l i t y i s important i t would probably be essential to stabilize plate current by means of a D.G, feedback to the grid c i r c u i t . For very low energy transitions the limitations of organic phosphors become of the same order as those of the Geiger tube. A rather complex but effective method of retaining speed would be to use internal sources with continuously evacuated photo-multipliers. The particles to be detected would impinge directly on the photocathodes. Because of the low quantum efficiency of the surfaces i t would be necessary to measure coincidences between betas and conversion electrons. The method should allow lifetime measurements down to IO" 1 0 seconds for energies of a few hundred volts up to 50 Kev. I l l THE ANALYSIS OF MEASURED DELAY DISTRIBUTIONS A. Methods of Analysis: Suppose we are measuring a delay distribution for a simple decay scheme as in Figure 1, i n which the gamma-ray transition has a decay constant A a . We assume that the circuit reacts instantaneously to the beta r- ray so that the time at which this transition occurs i s known exactly. Since the slope on the side of a delay distribution i s constant for large delays even for a truly prompt source, i t is appropriate to characterize the instrument's performance by a decay con-stant A b . (This i s not the decay constant for the phosphor luminescence). The temporal distribution of pulses from the limiter in the gamma-ray channel i s then determined by a two stage process, each stage having a certain decay constant. Mathematically the process i s identical to that of a two stage chain decay. The coincidence rate as a function of delay i s equivalent to the amount of daughter product as a function of time, whence: N (coincidences) = . X a ( e ' ^ - e ~* b t) X b ^ i This equation is derived in most texts on introductory nuclear physics. (a.) 4 + (3-(0-31) X (1.17) tZ \ (i-w)Ea ' 0 + STABLE e 59 (b) A > -DAY f3,-(0.27) Y, (0.19) ,MI, 2-o% Yl(i.io),Ml,567% Pb2'°(R*D) — (c) ^ - ^ ^ /3- (o.oie) \ p-(i-i7) (0.803) E.2. ^IIII "ABLE FIG. 21 DECAY SCHEMES OF SOMC SOURCES USED - 49 -Some properties of the familiar curves of daughter product versus time are then of interest i n analysing delay distributions. (1) The slope of the curve on semi-log paper never exceeds that determined by the smaller of Aa, Ab. (2) After a few half-lives corresponding to the larger of Xa, \b the slope i s determined by the smaller decay constant. (3) Even in the extreme case Xa = Xb, the slope at one decade down from the maximum of the curve is constant and given by X- Xa = Ab. (4) The maximum of the curve is displaced from zero by an amount depending on a. A measured delay distribution w i l l d i f f e r from the daughter product curve for two reasons, (a) Since the apparatus has a fini t e resolving time the rate of change of slope w i l l be less than in the corresponding daughter product curve. This, however, w i l l not affect the value of the slope in a region where i t i s constant, (b) Our apparatus does not define the time of the beta transition exactly. We have demonstrated in the following way that this does not affect the value of the slope obtained on the gamma-ray side of a delay distribution. By increasing the bias on one side channel discriminator the slope on the corresponding side of the delay distribution is increased, which means that the timing of events in that side is made more accurate. We have shown that changing the slope on one side of a distribution by a factor of three has no detectable (i.e.less than 5 per cent) effect on the slope of the other side. -3 -2 FIG. Z 2 o t DELAY -UNITS I0~9SECS Co 6 0 DELAY DISTRIBUTION ((3-Y). - 50 -The above discussion makes plausible the practice of assigning lifetimes on the basis of slope measurements. For proper justification the reader is referred to the work of Newton who has treated, the problem i n a more detailed and rigorous manner (Newton, ' 5 0 ) . Newton also shows that the centroid shift of a delay-distribution is equal to the mean l i f e of the transition provided one measures coincidences due to a simple decay as i n Figure 1. Application of this property of a distribution to sources with a more complex decay necessitates accurate energy selection. This objective has been achieved by the Chalk River group by using, i n effect, two beta-ray spectrometers with a single source and measuring coincidences between conversion electrons and the continuous beta spectrum. In this way the delayed coincidence method has been extended to place upper -11 limits of 2 x 10 seconds on the lifetimes of some transitions (Bell, ' 5 2 , Graham ' 5 3 ) . Since our apparatus does not admit of reasonably accurate energy selection our results are based entirely on measurement of the slopes of distributions. B. Excited States of Ni 6° ( C o 6 0 — ^ Ni 6°): 60 The decay scheme of Co (Figure 21(a) ) is well established and the gamma ray transitions are certainly E2 (Hollander ' 5 3 ) . The experimental values of E2 lifetimes are DELAY-UNITS .io*ssec. DELAY DISTRIBUTION (/3 - y). - 51 -poorly correlated with the energy of the transition involved so that predictions of lifetimes are very uncertain. Our value for both the gamma transitions T^ . { 1.6 x 1 0 " 1 G seconds is not inconsistent with this transition type (Goldhaber 1513... The transitions have previously been given an upper h a l f - l i f e limit - 9 * of '2 x 10 seconds (Deutsch ' 5 0 ) . Our delay distribution is shown in Figure 22. C. Excited States of Co^9 (?e59_^ Co59): The decay scheme (Figure 21(b) ) for Fe^9 ±s certain, but the parity and spin values are not completely established (Schiff •53)- Since the source available for our measurement of the delay distribution was very weak (less than 0 . 1 micro-curies) the statistics on the points are not as good as with our other sources which were of the order of 10 microcuries. The discriminator i n the gamma-ray side channel was so adjusted that a few noise pulses were counted in the absence of a source. We could then be certain that pulses from the 191 kev gamma-ray were accepted. Although the slope obtained (Figure 23) gives a h a l f - l i f e of 1.5 x 10 1 0 seconds we w i l l place an upper limit of 2 x 1 0 " 1 0 seconds on each of the three transitions involved. For the 191 Kev transition one would expect a lifetime of the -10 order of 10 seconds provided i t is properly classified as Mi (Graham ' 5 3 ) . The other gamma-ray transitions are not expected to have lifetimes measurable by our apparatus. -3 -2 FIG. £4 I 2 DELAY - UNITS I0"9SEC. Eu 1 5 2 " 4 DELAY DISTRIBUTION (p-Y*) - 52 -* 152, 154 D. The Decay of Eu ' The study of this source is complicated by the fact that the two nuclear types appear to possess almost identical lifetimes. No successful attempt has yet been made to formu-late a decay scheme for either nucleus. Numerous gamma-rays are involved i n the decay, including two of approximately 120 Kev energy. The latter give strong conversion lines i n the beta spectrum (Ayers ' 53). We hoped to measure the lifetime of one or both of these decays but, since orbital electron cap-ture is known to take place, we cannot be certain that any of the B- coincidences recorded involve these transitions. The side channel discriminator was set to accept pulses from 120 Kev gamma^rays. The measured delay distribution (Figure 24) shows a slope of 1.5 x lO""1"0 seconds which corresponds to a "prompt" curve for our apparatus. Then the only conclusion we can draw is that no gamma-ray transition of energy greater than approxi-mately 100 Kev and in coincidence with either another gamma-ray or a beta group has a lifetime greater than 1.6 x lO" 1^, assuming an uncertainty of 10 seconds i n our measurements. E. Excited States of W 1 8 2 ( T a l 8 2 - v W l 8 2) The delay distribution for this source shows the presence of a transition with a lifetime of 1.1 x 10~ 9 seconds (Figure 2 5 ) . Since the slope is straight to within 50 per cent of the maximum coincidence counting rate, the lifetime must be r due to a transition which is. involved in a large percentage of DELAY - UNITS IO"9SCC. FIG. 25 Ta 1 8 2 DELAY DISTRIBUTION C/3-y) - 53 -the decays. In order to obtain a rough value for the energy of the transition involved we have used a delayed coincidence absorption technique. The detector was set at a positive delay position on the line corresponding to approximately 5 x 10 sec-onds and the coincidence rate obtained for different lead absorber thicknesses. The energy derived from these absorption measurements is approximately 1.1 Mev. This variation of the coincidence absorption technique gives a measurement which i s not affected by back-scattering. Nevertheless i t i s inaccurate since i t was necessary to use poor geometry i n order to obtain a reasonable counting rate. l ft? The decay of Ta i s very complex but i t is generally agreed that three high energy gamma-rays are involved of energies 1.12, 1.19, and 1.22 Mev. This group i s clearly distinguishable from the numerous lower energy transitions involved i n the decay (Cork ' 5 l » Muller ' 5 2 ) . Cork et a l have measured the ratios of the intensities of the conversion lines from these three transi-tions i n a spectrometer of sufficient resolution to separate the lines completely. For the sequence given above the intensity ratios are 10 : 5 s 7. Muller et a l have measured the relative intensities of the gamma rays in DuMond's crystal diffraction spectrometer, obtaining ratios 352 : 157 * 334. Combining these results we find for the relative values of the conversion coefficients: 3.5 - .5? 3 . 1 * .&V,4.8 - .9 • It is unfortunate that higher accuracy was not obtained on the measurement of conversion line intensities. However, these results, combined - 54 -with our lifetime measurement, we w i l l show, lead to a cla s s i -fication of a l l three transitions which is probably correct. The delay distribution shows a constant slope up to very near the maximum. This implies that we are measuring only a single lifetime and we estimate that the other high -1G energy gammas have lifetimes less than approximately 3 x 10 seconds. From Goldhaber"s empirical lifetime-energy curves we can predict what type of transition would yield a lifetime of 10~ 9 seconds for a 1 Mev transition in W 1 8 2 (Goldhaber '51). An E2 transition should have a lifetime in the range from 10~ 9 -12 -8 to 1G seconds while an M2 transition should be between 10 and 10 1 0 seconds. The latter assignment is definitely favoured. Since the other lifetimes are much shorter than 10""9 seconds i t i s highly improbable that they can also be classified as M2. The remaining possibilities are E2, E l , or Ml. An electric radiation of such an energy would have to be at least of multipole order three to have approximately the same conversion coefficient as the M2 transition (Rose ' 5 D -Since electric octupole radiation would lead to a much longer lifetime than has been observed we conclude that the transitions in question are M^ . Assuming our estimates on the relative conversion coefficients are correct we obtain the following classification of the high energy transitions i n The 1.22 Mev transition is. 112 with a h a l f - l i f e of 1.1 x 10 7 sees, while both the 1 .12 and the 1.19 Mev transitions are Mi with lifetimes less than approximately 3 x 1 0 - 1 0 seconds. h - o 10 h— u o z UJ o o z o o 10 "6- -\ - o— ____ o o m X I 3 0 V O L T S H ~ 35 VOLTS H I - 4 5 VOLTS 0 0-3 F i & . 2 6 Sb12* DELAY DISTRIBUTIONS (p-y) 1-0 1-5 2 0 2-5 3 0 3-5 D E L A Y - UNITS IO"9SEC. - 55 -F. Excited States of T e 1 2 4 ( S b 1 2 l ^ T e 1 2 4 ) With side-channel discrimination set to give a slope • -10 of 1.5 x 10 seconds on the gamma-ray side for a prompt source, we found a slope of 2.33 x 10"^"° seconds for the S b 1 2 4 source (Figure 2 6 - 1 ) . The measurements were repeated several times with the same results. The side channel energy selection was then increased to a point which would give a slope of 1.3 x 1 0 s e c o n d s with a prompt source but the slope remained the same (Figure 2 6 - 1 1 ) . A further increase (Figure 26 - III) showed the same result so we concluded that a 1 P 4 . measurable delay definitely existed in the decay of Sh . Delayed coincidence absorption predicted a value of 0 . 6 5 Mev for the transition but the statistics were rather poor. No generally accepted delay scheme exists for this nucleus, but the main gamma-ray transitions are known. Three of these f a l l within the limits of error of our absorption measurement, but only one (0 .607 Mev) is strongly converted. Since i t i s classified as E2 on the basis of several experiments (Wiedenbeck ' 5 2 ) , the other transitions must be E^ and hence have much shorter lifetimes. We therefore conclude that the slope on the delay distribution is due to the 0 .607 Mev transition which is E2 with a lifetime of 2.3 x 1 0 " 1 0 seconds. This i s not incon-sistent with the Goldhaber predictions. . G. Excited State of RaE (RaD—»RaE). Although several weak gamma-rays have been detected i n the decay of radium D i t is believed that most of the - 56 -transitions proceed as shown i n Figure 21(c). In order to detect the very soft beta rays we mounted a thin source of RaD directly on the thin stilbene crystal of the beta-ray counter. The assembly was then covered with aluminum f o i l i n the usual way. The gamma counter was expected to respond to both the gamma rays of RaE and the L.. x-rays of bismuth resulting from the internal conversion of the gamma ray. Since we could not hope to distinguish between noise pulses and those due to the soft beta particles we did not make use of the side channel on the beta counter. Instead, both side channel inputs of the triple mixer were fed from the gamma-ray side channel discriminator. We found a very high coincidence counting rate at the centre of the line. When the side channel discriminator setting was increased to a level that should have eliminated nearly a l l counts from the 47 Kev gamma-ray, the coincidence counting rate remained very high. Since the source used was chemically separated two years previously, both RaE and RaF were in secular equilibrium with RaD. In order to test the possibility that the measured coincidences were between the -particles and 0.8 Mev gamma-ray from the decay of RaF, a lead absorber 1/8" in thickness was placed between the two counters. The coincidence rate dropped by a factor greater than IO4" indicating that the counts i n the gamma-channel were definitely not due to high energy gamma-rays. The lead absorber was then replaced by a polystyrene absorber 4" i n thickness. This obsorber would reduce the intensity of the 47 Kev gamma-rays at - 57 -the gamma-ray counter by a relatively small factor while elimi-nating the hard beta rays of Ra E completely. With this arrangement the coincidence counting rate dropped by a factor 3 greater than 10 , thus establishing that most of the coincidences were due to hard betas in the gamma channel. Since Ra E is a pure beta emitter the counts in the beta channel must have been due to Bremsstrahlung in coincidence with the hard betas i n the gamma channel. The source backing, the phosphors and the aluminum f o i l are a l l materials of low atomic number and hence have low Bremsstrahlung cross-section, so i t is probably that inner Bremsstrahlung produced most of the quanta detected. Our investigation of the Ra D decay has yielded no positive results. We include the discussion of our measurements in the thesis merely to emphasize the d i f f i c u l t i e s involved i n obtaining data on this source. The short h a l f - l i f e of Ra E brings i t into secular equilibrium with Ra D in a very short period. One should treat with skepticism any measurements made on Ra D unless they are carried out immediately after a thorough chemical separation. This is particularly true of coincidence measurements, as is demonstrated above. - 58 -APPENDIX Parallel-Plate Spark Counters: We have pointed out that the scintillation detector is not well-suited to the measurement of the l i f e -time of very low energy gamma-ray transitions. Due to the strong dependence of transition probability on the energy involved, one would expect1 many low energy transitions to -10 have lifetimes greater than 10 seconds. It was consider ered desirable to develop a counter with a very short reaction time which was not dependent on energy for the investigation of these transitions. In the presence of a strong external source of ionization there is a maximum value for the electrical field which can be.maintained between two parallel plates immersed in a gas. The value of this maximum is primarily a property of the gas provided the plates are smooth. For a given gas and plate-spacing there is a maximum voltage termed the spark-ing threshold. In the absence of a source of ionization, i t is possible to raise the voltage well above the sparking threshold provided the plates are made of the proper material and are kept smooth and free of foreign matter. By shaping the plates - 59 -so as to minimize the edge effects, Fletcher has been able to surpass the sparking threshold by more than 150 per cent. (Fletcher !49). When ionization took place in the space between the plates, he found that a voltage pulse formed between the plates had a rise time of approximately 10~^ seconds and the spread i n reaction time was of the order of -9 10 seconds. These values compare very favourably with the same quantities i n s c i n t i l l a t i o n counters and are not markedly dependent on the energy of. the particle causing ionization. Several workers have produced models of parallel-plate counters but they have found i t necessary to use very long dead times to eliminate spurious pulses (Madansky '50). We attempted to overcome this defect by various treatments of the plate surfaces and eventually were able to use dead times as short as 100 microseconds which is of the same order of magnitude as used with Geiger counters. The method employed was to plate smooth brass plates with a thin copper coating to serve as a base for a nickel plating.. The surface was then highly polished and washed. A mixture of Xylene and argon was used as a counter f i l l i n g . It was necessary to admit enough Xylene vapour so that i t formed a film over the elec-trodes when the argon was admitted. A total pressure of one atmosphere was used. We found i t possible to apply 100 per cent over-voltage without breakdown. Bright blue sparks were formed - 60 -which were dis t i n c t l y audible when a source was brought near the counter. In order to obtain a short reaction time i t is necessary to use a high voltage and hence a good deal of energy is expended i n the spark. We found that the Xylene was rapidly decomposed, so that at reasonable counting rates a tarry deposit was formed on the electrodes in a few minutes counting. After a very few hours of counting, a filament made up of decomposition products of the Xylene would form across the gap and the counter would cease to function. The project was abandoned for this reason. - 61 -LIST OF REFERENCES Ayers, W. R., M.A. Sc. Thesis, University of Br i t i s h (Ayers '53) Columbia, 1953. B e l l , R. E., R. L. Graham, and H. E. Petch, Can. J. Phys. (Bell «52) 3P_, 35 (1952) . Blatt J. M., and V. F. Weisskopf, Theoretical Nuclear Physics, (Blatt «52) John Wiley and Sons, New York, 1952. Cork, J.I., W. J. Childs, C. E. Branyan, W. C. Rutledge and (Cork «5D A. E. Stoddard, Phys. Rev. 81 , 642 ( 1 9 5 D -Davison, P. W., Nucleonics, 10, 3> 33 (1952). (Davison. '52) DeutschM., and W. E. Wright, Phys. Rev., 2Z> 139 (1950). (Deutsch ' 50) Fletcher, R.C., Phys. Rev., £6, 1501 (1949). (Fletcher «49) Goldhaber M., and A. W. Sunyar, Phys. Rev. 83_, 906 ( 1 9 5 D . (Goldhaber »5D Goldhaber M., and R. D. H i l l , Rev.. Mod. Phys., 24, 179 (1952) . (Goldhaber »52) Graham R.L., and R. E. Be l l , Can. J. Phys., 3J,, 377 (1953) . (Graham '53) Law, R. R., Nucleonics, 10, 3> 33 (1952). (Law '52) McKay, K., Advances in Electronics I, Academic Press Inc., (McKay fW) New York, 1949. Madansky L., and R. W. Pidd, Rev. Sc. Inst., 21 , 407 ( 1950) . (Madansky "49) Morton, G. A.. Advances i n Electronics IV, Academic Press Inc., (Morton '52) New York, 1952. Mueller, D. W., G. Best, J. Jackson, and J. Singletary, (Mueller «52) Nucleonics, 10 , 6 , 53 (1952) . - 62 -LIST OF REFERENCES Continued Muller, D. E., H . C. Hoyt, D. J. Klein and J. W. M. DuMond, (Muller '52) Phys. Rev., 88 , 775 (1952) . Newton, T. D., Phys. Rev. £8, 490 (1950) . (Newton 1 5 0 ) Post R. F., and N. S. Shiren, Phys'. Rev. 28, 81 (1950) . (Post • 50) Post R. F., and L. Schiff, Phys. ReV. 8 0 , 1113 (1950) . (Post «50a) Post R. F., Nucleonics, 10, 6, 56 (1952) . (Post «52). Rose M. E., G. Goertzel, B. I. Spinrad, J. A. Harr, and (Rose ' 5 D P. Strong, Phys. Rev., 8^, 79 (1951). Sangster R. C , Technical Report No. 55, Mass. Inst. Tech., (Sangster »52) Ian. 1 ( 1952) . Weisskopf, V. F., Phys. Rev., 8 j l , 1073 (1951). (Weisskopf "50) Wiedenbeek, M. L., and D. R. Hutchinson, Phys. Rev. 88, (Wiedenbeck «52) 699 (1952) . 

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