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Detection and Measurement of Nuclear Radiation (1962)

Chapter: Auxiliary Electronic Instrumentation

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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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Suggested Citation:"Auxiliary Electronic Instrumentation." National Research Council. 1962. Detection and Measurement of Nuclear Radiation. Washington, DC: The National Academies Press. doi: 10.17226/18670.
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recording equipment is insensitive. For a system which has the sensitivity to count all pulses, the resolving time will be equal to the dead time. Figure 42 shows that a system which triggers on high-amplitude pulses will exhibit a resolving time greater than the dead time. Typical dead times for Geiger tubes are from 100 to 300 psec. Corrections applied to counting data because of the resolving time are especially large and, therefore, important when using Geiger tubes. A precise value for the resolving time of a particular tube can be determined only by experiment. Such a determination can be made by using the multiple-source comparison method. Another method which offers some advantages is to count repeatedly a sample of some short-lived nuclide as it decays from a high rate to a very low rate. The known half life may be fitted accurately to the points at low rates, for which the corrections are small or negligible, and the decay curve is extrapolated to time zero. The differences between the decay curve and the experimental points may be used to construct a correction curve directly or to compute the resolving time. The uncertainties in applying a resolving-time correction may be avoided by fixing the resolving time of the detection system electronically at a value somewhat greater than the Geiger-tube dead time. Once the resolving time T is known, the corrected counting rate N0 can be approximated for any measured rate N, by N (15) 1 - NT The time unit for T, N, and N0 must be the same. VI. AUXILIARY ELECTRONIC INSTRUMENTATION 1. General Introduction So far, this monograph has been concerned with the de- tectors used in a nuclear measurement system. From time to time it has seemed advisable to remark upon some of the consider- ations which are important in selecting the electronic accesso- ries to be used with a particular detector. The ensuing 88

discussion will be devoted to a more general treatment of some of the available electronic equipment. These devices will not be treated in detail, but rather their nature and application will be described in the hope that an experimenter will be guided to select the measuring system best suited to his needs. A nuclear measuring system capable of performing a variety of tasks is diagrammed in Fig. 43. If integral counting is the only requirement, the pulse-height selector may be set to pro- duce an output pulse for every input pulse whose amplitude exceeds a desired value. The scaler may record the number of pulses in a standard time interval, or the counting-rate meter may be used to indicate continuously the average counting rate. Should the experiment require data on the pulse-height distri- bution, the amplifier signals are fed to a pulse-height analyzer for sorting and information storage. Before describing the various components themselves, it may be noted that transistorized electronic devices are now available which are essentially equivalent to equipment using vacuum tubes. Thus, linear amplifiers, scalers, and pulse- height analyzers generally may be obtained in either transistor- ized or vacuum-tube versions. On the basis of experience to date, it appears that transistorized units are to be preferred, even though they may be considerably more expensive in some cases. The chief advantage of transistor circuits is their greater reliability; less maintenance is required, a par- ticular benefit for laboratories not equipped with extensive repair facilities. Other advantages of transistors are small size and low-heat dissipation. SHORT SHIELDED LEAD xLONC ( LOW- \ CABl -z .E DETECTOR] — ^— PREAMP T- MAIN AMPLIFIER Fig. 43. Typical nuclear measuring system, with pro- visions for either integral counting or differential pulse- height analysis. 89

2. Amplifiers The signal from a radiation detection is produced by delivering an amount of charge q onto an input capacitance C. Typical values for the output voltages (given by q/C) from several detectors are listed in Table 4. It is readily seen TABLE 4. DETECTOR PULSE CHARACTERISTICS Typical Output Signal* Detector Energy Dependent Rise Time G-M 0-10 volts No Slow Proportional 0-100 mv Yes Slow Pulse Ion Chamber 0-3 mv Yes Slow Semiconductor 0-25 mv Yes Fast Scintillation 0-2 volts Yes Fast For a circuit capacitance of 20 pf. that the pulse heights obtained are very small, and so an amplifier is needed between the detector and measuring appa- ratus. For spectrometry, where a precise analysis of the pulse-height distribution is to be made, vacuum-tube ampli- fiers with positive output pulses of 0-100 volts are often used; by contrast, transistorized amplifiers generally produce negative output pulses in the range 0-10 volts. To accommodate a wide range of detector operating con- ditions, vacuum-tube amplifiers for scintillation and pro- portional counters commonly have a maximum gain of 5,000 to 50,000, with attenuators for setting the gain over a range of at least a factor of 100. Transistorized amplifiers require a voltage gain only about 0.1 as great. The word amplifier as used here will be taken to mean a linear amplifier, i.e., one whose output amplitude is quite accurately proportional to the input amplitude. However, there are counting applications where nonlinear operation may be desired if the particular amplitude dependence can be kept reproducible and stable. See references 37, 68, 71, and 72. 90

A. Pulse Shaping. The generalized detector waveform shown in Fig. 44(a) defines the terms often used to describe such pulses. The rise time t depends on the particular -V(t] (b) Fig. 44. Radiation detector pulses. (a) Single pulse plotted on an expanded scale to show definitions of rise time t , and fall time, tf. (b) Pulses appearing at the input of an amplifier. All pulses have the same fast rise time, followed by a slow fall time. The high pulse rate causes the pulses to sum. detector; for example, the rise time of a scintillation detector pulse depends on the decay time of the fluorescent light and the photomultiplier characteristics. The fall time t. of the pulse depends on the load resistance R and the capacitance C of the signal lead to ground: t. 2.2 RC. Usually the fall time must be quite long relative to the rise time; this leads to the situation sketched in Fig. 44(b), which shows the pulses appearing at the input of an amplifier, all with the same characteristic fall time. Because of the high _k. 91

rate, the "tail" of one pulse does not decay to the base line before another pulse appears. Such a state of affairs will not permit an accurate pulse-height analysis to be made. Further, since the useful information is contained in the leading edge of the pulse and its top, the tail only complicates the problem to no purpose. The desired early portion of the detector pulse is 3 7 74 extracted by using a clipping, or differentiating circuit. Several electrical networks will perform the mathematical oper- ation of differentiation; the most obvious approach is to use a single coupling stage in the amplifier whose RC product (or time constant) is much less than the others. This system suffers from two defects: there is a signal present in the amplifier long after the peak is reached [Fig. 45(a)], even though the fall time now is about 100 times faster than for the detector pulse; therefore, the clipping is not complete. In addition, practi- cal amplifiers have many stages, and so there are, in effect, many differentiating circuits. An analysis shows that when only one RC time constant is short, every output pulse will be followed by a low-amplitude signal of opposite polarity (undershoot), which lasts for a very long time and whose area equals the area of the signal pulse. If additional pulses are processed during the recovery from an undershoot, the amplitude of such signals may be seriously altered. Further, the average voltage or base line will no longer be zero but will vary with changes in counting rate. Clearly, it is desirable to reduce the duration of the undershoot so that the probability of pulse overlap is small. If two time constants in the amplifier are equal to each other and are smaller than the remaining networks, then the undershoot will have the largest amplitude and the shortest duration. This pulse shaping is known as double differentiation or double clipping; a typical waveform is shown in Fig. 45(b). Although the areas under the main pulse and its undershoot are equal under the conditions of Fig. 45(b), the amplitudes are not. As a result, there may be serious difficulties if the amplifier is driven out of its linear range by very large detector pulses. For example, when the amplifier is set for high gain in order to study low-energy radiation, then high-energy pulses which are also detected will drive the amplifier to its saturation output value. Under this overload condition, it is unlikely

/ -*' t -*• 0 (c) Fig. 45. Output pulses from amplifiers using (a) RC clipping, (b) Double RC clipping, (c) Single delay-line clipping, and (d) Double delay-line clipping. that the undershoot will be distorted in the same way as the main pulse, and so at high counting rates, base line shifts can still occur. Clipping with a delay line is to be preferred over the RC clipping techniques just described. An example of an amplifier which uses a shorted delay line clipper (with provisions for RC clipping if desired) is the Oak Ridge National Laboratory Model AID, designed by Bell, Kelley, and Goss, and described in reference 39; the AID output waveform is sketched in Fig. 45(c). The advantages of delay-line clipping over RC clipping are: the pulse is almost rectangular, and so the long tail charac- teristic of RC clipping is eliminated; also, the top of the pulse is more nearly flat, a desirable circumstance when certain types of pulse-height analyzers are to be employed. A disad- vantage is that the delay-line circuits often used give rise to a small undershoot, which causes a base line shift at high counting rates. The best pulse shape for most work is obtained by double clipping with delay lines. The symmetry of such a pulse, shown 93

in Fig. 45(d), leads to excellent overload and counting rate properties, since the area balance between positive and nega- tive halves is essentially unchanged by overload. Double differentiation as a means of pulse shaping in a linear ampli- fier was proposed by E. Fairstein and R. A. Dandl. Practical applications of this technique are the Oak Ridge amplifiers model DD-2 and model A-8. A transistorized design by Goulding, et al., has recently appeared. The overload performance of an amplifier is extremely important in modern experiments, where it may be necessary to study low-energy radiations in the presence of a high-energy background. For example, the gain of an amplifier may be set so that maximum output is obtained for 50 kev of energy detected; if 5-Mev detector pulses are also present, they are said to drive the amplifier to 100 times overload. Such harsh treatment can lead to blocking, or a temporary amplifier paralysis following an overload pulse. Naturally, if high counting rates are to be tolerated, the amplifier should recover quickly after an overload. Double delay line differ- entiation and careful attention to blocking make it possible for the A-8 to recover after a 4000 times overload in less than 10 usec, with no positive base-line excursion after the main pulse. B. Noise. The extent to which amplifier noise is important will depend on the kind of measurement being made. If the amplifier is part of a simple counter, noise introduces spurious counts; thus, the lowest amplitude of usable signal is approximately equal to the noise level. If the amplifier is part of a spectrometer, the noise signals are not counted directly but appear as a broadening influence on spectral lines. As mentioned in Section IV.3.A., the noise is often stated in energy units such as kev. This is an experimenter's way of expressing the more fundamental noise unit, the equiya- 78 lent charge, which is a convenient concept because nuclear detector signals consist of bursts of charge collected on the input capacitance. By the use of units of charge instead of voltage, the capacitance need not be known. The main sources of noise in a well-designed amplifier are those arising from the thermal motion of electrons in the input grid resistor and the noise from the input tube due to flicker effect, grid current, and shot effect. The last two of these 94

are usually the dominant contributions. The general trend is that noise increases with input capacitance. For more details, :en1 68 37 78 the reader may consult the recent reviews by Fairstein ' and the earlier book by Gillespie. In a measuring system, sources of noise other than those associated with the amplifier must be evaluated. The photo- cathode of a photomultiplier tube releases electrons by thermal agitation which appear as random noise; if a scintillation counter is to be useful at low energies (and therefore, low- light intensities), this source of noise is usually far more important that the amplifier noise. At present, noise from the leakage current of a semiconductor radiation detector, rather than amplifier noise, limits the energy resolution of this device. The noise problem becomes acute when an amplifier must be used for spectrometry with detectors of low output amplitude but with high-energy resolution. Examples of this case would be a semiconductor radiation detector or pulse ionization chamber. These detectors usually are not required to accom- modate a large range of signal amplitudes, so overload per- formance is not very critical. An analysis shows that these conditions can best be satisfied with single RC clipping if the counting rates are not very high. Double differentiation gives a relatively higher noise contribution but may be justi- fied if the counting rates are to be high. Scintillation detectors produce large signals (see Table 4) but exhibit rather poor resolution. Therefore, the slight worsening of the noise level by double differentiation is negligible. On the other hand, the wide range of detector signal amplitudes requires double differentiation to achieve good overload characteristics. Presently available transistors cannot equal the low noise performance of vacuum tubes at low input capacitances. With input capacitances of 15 to 20 pf, transistor amplifiers exhibit 3 to 10 times more noise than the best vacuum-tube amplifiers. At input capacitances of about 1000 pf the two systems are 79 equal. The poorer noise level for transistor amplifiers, while serious in the most critical high-resolution applications, is well within the acceptable limits for Nal(Tl) scintillation spectrometry. C. Window Amplifiers. In many experiments it may not be 95

desirable to cover the energy range starting at zero. For example, alpha particles from heavy nuclides all have energies greater than about 4 Mev, and thus some way of shifting the amplifier threshold is indicated. This is accomplished by first amplifying the pulses in the usual way and then subtracting a constant amount of height from each pulse. The resulting pulses then are amplified to the required size by an amplifier with good overload properties. Such output amplifiers are variously known as expander amplifiers, window amplifiers, or more recently, as post amplifiers. This technique, especially as regards its application in improving the precision of pulse- on. height analyzers, is reviewed by Van Rennes; some consider- ations based on recent developments in alpha spectroscopy were 7 8 discussed by Fairstein. The Oak Ridge Model Q-2069 amplifier 81 system is a good example of a low-noise amplifier for alpha spectrometry and includes a convenient post-amplifier arrangement. D. Preamplifiers. An amplifier system usually is divided into a preamplifier and the main amplifier (Fig. 43). It is undesirable to couple the detector to a voltage-sensitive amplifier through a long cable because of the attendant signal losses and the increase in noise level associated with high cable capacitance. The use of a preamplifier mounted on or near the detector provides the shortest possible detector leads. A preamplifier may have a gain ranging from 1 to 30 and should have as its output stage a cathode follower capable of driving long sections of low-impedance cable, such as 93-ohm RG-62/U, with good linearity. This permits the detector and preamplifier to be located 500 feet or more from the complex of measuring equipment with good results. As was stressed earlier, nuclear particle detectors pro- duce a packet of charge. Until recently, all preamplifiers were of the voltage-sensitive type, i.e., the output pulse height is proportional to q/C. However, it is now realized that a charge-sensitive amplifier is to be preferred in most applications. Since the output is essentially proportional to q alone, the pulse height does not vary with input capacitance, as has already been mentioned in connection with semiconductor radiation detectors (Section IV.3.A.). Therefore, the experi- menter is able to alter the input circuit and still retain 96

approximately the same gain calibration. It is not necessary to compromise on noise specifications, since for the same input capacitance as for a voltage-sensitive amplifier, the charge- sensitive device exhibits nearly the same noise contribution. In view of its convenience, it is likely that most new „ preamplifiers will be of the charge-sensitive type. • 3. Trigger Circuits • Nuclear detection systems make frequent use of devices known as trigger circuits, which produce a pulse of constant height and width for each incoming pulse whose height exceeds a set value. A trigger which is adjusted by a front panel control is called an integral pulse-height selector (PHS) or integral discriminator. As shown in Fig. 43, it may be used to produce pulses of standard height for operating a scaler or counting-rate meter. Also, a PHS is needed in most integral counting work for discrimination against amplifier noise, or low-amplitude pulses from unwanted radiations. 4. Scalers It is essential that a counting system be capable of accurate counting at high rates. Electromechanical registers can only accommodate counting rates up to 60 per sec, while many experiments demand recording data at rates of 30,000 counts/sec or more. This is accomplished by dividing the number of incoming pulses by a known factor (the scaling factor), so that a register will follow the reduced rate. The electronic device for performing this division is called a scaler. A. Binary Scalers. The simplest high-speed scaling device is the scale-of-2, often called a binary, because it is a circuit having two stable states representing the binary numbers 0 and 1. The first input pulse transfers the state from 0 to 1; the second event will reset the binary to the 0 state and also generate an output, or carry pulse. Thus, only one output pulse is produced for two input pulses, so for a series of n such stages, a scaling factor of 2 is obtained. An array of 4 binaries in cascade to give a scale-of-16 is shown in Fig. 46(a). Each stage is connected to an indi- 97

cator such as a lamp, which functions when the stage is switched to the 1 state. In Fig. 46(a), the first pulse causes the lamp labeled "1" to light. The second pulse resets the first binary to 0 and sets the second binary to 1; this has the effect of extinguishing the "1" lamp and lighting the "2" lamp. A third pulse causes the "1" lamp to light also; a fourth will extinguish these but will light the "4" lamp, and so on until 15 events have been recorded and all lamps are lighted (1+ 2+«4+ 8= 15). The next pulse resets all binary stages, extinguishing the indicator lamps, and produces a carry pulse at the output. This latter pulse can be used to drive a register, or further binaries. B. Decimal Scalers. When many binary stages are con- nected in cascade to form a large electronic register, it becomes tedious for the experimenter to translate the binary information into decimal form. Obviously, it is desirable to employ decimal scalers wherever possible. Improvements in electronic components and circuitry during the past few years have made it possible to construct decimal scalers which are as reliable as the binary ones. A functional diagram for a transistorized decimal scaling stage usable to a pulse rate of 1 Me is shown in Fig. 46(b). It is composed of four binaries and a "feedback" circuit to modify the scale-of-16 to a scale-of-10 as follows: The first 7 counts are recorded as described above for a binary scaler; on the 8th count, the last binary switches to indicate an "8," but also a short pulse is fed to the second and third binaries, setting up a "2" and a "4," respectively. Thus, on the 8th count the binaries are switched as though 14 (2 + 4 + 8) counts had been received. The 9th count records normally, and on the 10th, all binaries are reset, and a carry pulse emerges from the output. The leads A0, A, , B0, Bt, etc., sense the state of each binary, and may be used to indicate the number of stored counts. However, indicators cannot be connected directly to these leads; unlike the binary scaler, a translating circuit is required. For visual presentation and automatic recording on punched cards, it is useful to translate the information into decimal form, i.e., the digits 0-9; however, for many automatic recording systems, it is more economical to employ binary-coded decimal (BCD) format, in which the numbers 0-9 are expressed as combi- 98

OUTPUT J MANUAL RESET (a) BINARY SCALER BQ RESET FEEDBACK u , S> rv— -— 'iS TV- i i 2 4 ( 3i ;, i DECIMAL SCALER Fig. 46. Functional diagram of scalers. (a) A cascade of 4 binaries, yielding a scaling factor of 16. (b) A scaler made up of 4 binaries wired for decimal counting. nations of the digits 1, 2, 4, and 8, or 1, 2, 2, and 4. Some- times the decimal code is called a "10-line" format, and the BCD is called a "4-line" format. Other reliable decade scalers have been devised and are in everyday use. The cold-cathode, glow-discharge scaler tubes made by several manufacturers (Ericsson Telephone Company, Sylvania Electric Products Company, and Raytheon Manufacturing Company) are capable of operation between 20-100 kc. The electron beam-switching tubes made by the Burroughs Corporation will function above 1 Mc. Often a beam-switching tube is used as a high-speed scaling stage, followed by a series of glow 99

tubes. The operation and use of some of these devices have been 82 described by Millman and Taub. ' 5. Counting-Rate Meters It is extremely convenient to be able to measure the counting rate continuously, without the necessity of counting with a scaler for a measured amount of time. A device which indicates continuously the average counting rate is called a counting-rate meter. This is the indicator most often used on portable survey instruments. Host counting-rate meters exhibit a linear relationship between output and counting rate. This is obtained by coupling a pulse of constant amplitude from a pulse-height selector onto a "tank," or storage, capacitor which is shunted by a resistor. Each pulse transfers a known charge to the tank capacitor; the steady-state voltage developed across the tank capacitor is reached when the rate of charge loss through the shunt resistor equals the rate of charge input from the pulses. A good quality vacuum-tube voltmeter is used to indicate the voltage across the RC tank circuit. Linear counting-rate meters have 72 39 been discussed by Elmore and Sands, " and by Price. When wide ranges of counting rate must be measured, a loga- rithmic response is desirable. Usually this is done by using a logarithmic vacuum-tube voltmeter to read the voltage. It is very difficult to achieve very high accuracy or stability with such a technique, although adequate logarithmic counting-rate 39 meters have been designed for survey purposes. Price has reviewed the various approaches to this problem. 6. Pulse-Height Analyzers Several of the detectors used in nuclear studies yield pulses whose heights depend on the energy deposited in the detector. This suggests that if these energy-dependent pulses can be sorted according to their height, energy spectra can be obtained. The device for performing this sorting is usually called a pulse-height analyzer. A simple illustration of the problem is shown in Fig. 47. In (a), a series of pulses from a detector are viewed very much 100

as they would appear as voltage-time waveforms on an oscillo- scope. The example shows the pulse-height scale divided into five channels of equal width. Over the counting interval shown, a five-channel pulse-height analyzer would record no events in channels 1 and 5; two events in channels 2 and 4; and five events in channel 3. Thus, the data from such an analysis may be plotted as the histogram shown in Fig. 47(b); usually, it is more convenient to plot the number of events per channel as a point at each channel number. A smooth curve drawn through these experimental points is easier to interpret. A. Single-Channel Analyzers. The number of events shown in Fig. 47 is, of course, a ridiculously small sample of a random source of pulses. Although it is more efficient to record the events in all channels at once, it requires only very simple equipment to look through an electronic "window" at a single portion of the spectrum at a time. The window might be adjusted to the width of a channel in Fig. 47(a) and set to the position of each channel shown. At each setting, a count would be taken for sufficient time to obtain a valid statistical sample of the spectrum. The data may be plotted as in Fig. 47(b). The operation of such a single-channel pulse-height analyzer is simple in principle although fairly complex in practice. Figure 48 shows the general arrangement and mode of operation for three pulses. Two pulse-height selectors (PHS) units are used: a lower PHS is biased to trigger on a pulse of height E, and an upper PHS biased to E + AE. The anticoinci- dence circuit will permit an output pulse only if the lower PHS is triggered without a pulse from the upper PHS. The E dial in the case shown is set at 200 dial divisions; pulse "1" does not have sufficient amplitude to affect either PHS. Pulse "2" falls within the AE window, which causes the lower PHS to trigger; as there is no accompanying pulse from the upper PHS, an output pulse is recorded. The third pulse is high enough to trigger both PHS units, so the anticoincidence circuit prevents an output. Several versions of vacuum-tube single-channel analyzers have been described (see, for example, the reviews by Chase 80 and Van Rennes. Transistorized versions are also in use which are compatible with the transistorized linear amplifiers. ' B. Multichannel Analyzers. Many applications require 101

faster data acquisition rates than are possible with single- channel analyzers. A notable example is found in the field of radioactivation analysis, where it has become increasingly important to measure short-lived nuclides for highest sensi- tivity. Not only is there a great increase in speed and con- venience if the pulses are sorted in a single counting interval, but there is also an improvement in the precision of the data obtained, because many instrumental drifts will affect all channels of a multichannel pulse-height analyzer in the same way. For circuits used in these instruments, the reader is directed to the excellent discussion by Chase. CHANNEL NUMBER 5 4 PULSE HEIGHT 3 2 n _n 1 II TIME-*- « rmiMTiKir: IMTFPWAI _ (0) AMPLIFIER PULSES NUMBER/CHANNEL O — r\> iji & i / \ / \ /_ \ I/ \ — A \ 1 01 2345 CHANNEL NUMBER (6) PULSE-HEIGHT DISTRIBUTION Fig. 47. Illustration of the pulse-height analysis problem. (a) Idealized pulses from a linear amplifier are shown, plotted on a pulse-height scale which is divided into five equal channels. (b) The pulse-height distribution from (a) is shown plotted as a smooth curve through the points. The most obvious approach to the design of a multichannel analyzer is to construct a number of pulse-height selectors, whose trigger (or bias) levels are progressively increased. Anticoincidence circuitry is provided, so that, in effect, the array consists of a series of single-channel analyzers, 102

"stacked" up in terms of pulse height. A successful version of this scheme is the 20-channel analyzer designed by Bell, Kelley, and GOSH. This analyzer, together with a review of the general problem of pulse-height analysis, is discussed by 80 Van Rennes. Improvements in detector resolution and the growing need for more automated data recording have created a need for multichannel analyzers with a very large number of channels. The 20-channel analyzer just mentioned costs about $350/channel; hence, a stacked-discriminator type of analyzer is too expen- sive to build in large configurations. By making use of techniques developed for digital computers, it is possible to construct multichannel analyzers having hundreds of channels SIGNAL INPUT OUTPUT . r A f onn iiKjiT^ - 1 . n E © (2) (3) 1 UJ <J I s n TIME-*- Fig. 48. Functional diagram of a single-channel pulse- height analyzer. Pulse shapes for the different parts of the circuit are shown below the block diagram. 103

and very large storage capacities per channel. A simplified diagram illustrating the general method of operation of such an analyzer, as well as some of the methods of handling the data, is sketched in Fig. 49. The heart of the analyzer is the analog-to-digital converter (ADC), which converts the pulse height to a train of pulses. The number of pulses produced determines the channel number in which the pulse is to be stored. These address pulses are counted by the address scaler, which may be either a binary or a binary-coded decimal (BCD) type. The information is stored in a ferrite-core memory unit, which resembles the memory of a modern digital computer. The memory usually stores data in BCD format, as this is most use- ful for operating readout equipment. Some of the early instru- ments used all binary logic, which is more economical but a little more troublesome for the experimenter. Once the address scaler has selected a memory address (channel number), the number of counts already stored in the memory at that address is read out into a scaler called the data register, or add-one scaler. Then, the"store" command is given, the data register increases the old number by one, and the new number is written back into the memory. This memory cycle requires 10 to 20 usec for most analyzers. Analysis of a pulse-height distribution in this way requires a rather long time. A typical analyzer might have an 18 \isec memory cycle and a 0.5 |~isec spacing between address pulses (2 Mc address pulse rate); this leads to an analysis time for each pulse (during which the analyzer is incapable of recording any further pulses) of (18 + 0.5 v) psec, where v is the channel number. The dependence of the rather long "dead time" on channel number shows that the average dead time is a function of the spectrum under measurement. However, it can be shown that the spectrum shape is undistorted under this condition, and so it is only necessary to correct for the dead time to obtain accu- rate counting rates. Instead of working with dead time, it is more convenient to count for a given amount of "live time," that is, time during which the analyzer was free to analyze incoming pulses. The device for measuring live time, a live timer, is an electronic clock which counts standard-frequency pulses. When the analyzer is processing a count, the ADC pro- 104

Fig. U9. Multichannel pulse-height analyser, showing relation- ships between principal subassemblies and accessory equipment. duces a busy signal, which stops the clock. Therefore, only live time is recorded. Because the analyzer operates on computer principles, it has the ability to subtract as well as add. It is quite help- ful to subtract background spectra using the analyzer. Some commercial analyzers have provisions for storing a spectrum in one part of the memory; the intensity of this spectrum may be multiplied by normalizing factors and then added to or sub- tracted from the contents of another portion of the memory. A variety of readout equipment is possible. The decimal numbers may be recorded by using a typewriter or printer; BCD information may be recorded in computer format on punched paper tape or on magnetic tape. Digital information also may be converted to analog voltages, which are used to display spectra on a cathode-ray tube and may also be used to drive an X-Y curve plotter. 7. Coincidence Measurements In many nuclear counting problems, it is necessary to decide whether two events are time-correlated. Such infor- 105

mation may be required for investigations of nuclear decay schemes, for which it may be necessary to know whether two radiations are emitted at the same time. Also in many types of counting, imposing the condition that two events must be coinci- dent in time will serve to discriminate effectively against noise pulses, which are randomly distributed in time. Electronic circuits which make such decisions are called coincidence circuits and produce an output pulse only if all inputs to the device receive a pulse simultaneously. A. Resolving Time. Coincidence equipments may be classi- fied according to their resolving time. If a two-channel system is used, each channel applies a gate pulse of width T to the mixer circuit; therefore, to be in coincidence, the two gate pulses must fall within the time interval 2r, the resolving time. A resolving time of less than a few tenths of a jisec is termed "fast," and longer resolving times are called "slow." With special-purpose photomultiplier tubes and high-speed circuitry, resolving times of less than 10~9 sec (1 nanosec) have been obtained. The esoteric subject of fast coincidence measurements in the nanosecond region will not be treated here o c but has been reviewed extensively by De Benedetti and Findley 86 and by Lewis and Wells. ' Resolving times of > 50 nanosec are possible, however, with rather conventional equipment. Short resolving times are required wherever high counting rates are involved, because the random nature of radioactive decay leads to a chance that two uncorrelated pulses will happen to occur within the coincidence resolving time. The random coincidence rate N is given by Nr = Zr N,N2 , (16) where NI and N2 are the counting rates in the two channels. Note that, because N! and N2 are related to the disintegration rate N- by counting efficiencies €1 and e2, the random coinci- dence rate is proportional to the square of the disintegration rate: Nr = 2r ND2 €,€2 . (17) The relationships of Eqs. 16 and 17 are correct to the first order in most coincidence systems. If the rates N, and N2 are 106

very high, it may be necessary to make higher order random coincidence corrections. The equations to be used for computing 87 such corrections are discussed by Paul. A criterion for the feasibility of a coincidence experi- ment is the ratio of real coincidences to random coincidences. Since the real coincidence rate is given by Nc = then Thus, the real-to-random ratio increases only as the reciprocal of the first power of the resolving time and disintegration rate. B. Electronics. A block diagram of a typical coincidence system is given in Fig. 50. The coincidence circuit requires that, to be quantitative, the timing pulses should not "walk," i.e., change their position in time as the pulse height varies. The output from the usual trigger circuits will exhibit such a walk, because low-amplitude pulses will trigger near their peaks, while high-amplitude pulses will trigger proportionately nearer the base line. The output pulses will be distributed through a time range about equal to the amplifier rise time (~ 0.2 \isec for Nal(Tl) scintillation counter systems). A convenient solution to this problem was proposed by Love, who showed that the cross- over point (A in Fig. 50) of the pulse from an amplifier with double delay-line differentiation (Section VI. 2. A.) exhibits negligible walk with pulse height, since the point is only determined by the delay-line parameters. Several timing circuits 88 based on this idea have been constructed by Peele and Love, On and by Fairstein. Transistorized versions of such a system 83 84 have also been designed. ' All pulses are subjected to a fast coincidence (2r =0.1 (jsec) in Fig. 50. Then, if coincidence measurements are desired between two energy bands, these are selected by the two single- channel pulse-height analyzers. Thus, of all the integral coincidences recorded by the fast unit, only a few will be selected by the analyzers. The slow coincidence unit, which may 107

have a resolving time of 2 to 5 jasec, imposes these additional pulse-height conditions. As a result of this arrangement, the resolving time of the system is determined by the fast coinci- dence; the relatively low rates and less sharply timed signals from the single-channel analyzers can be mixed quite accurately with the fast coincidence output in a slow coincidence unit. Fig. 50. Coincidence apparatus. For use with a multichannel analyzer, the connection to single-channel analyzer "1" is broken at "X," and the connection shown as a dotted line is used. Often, it is desirable to include a multichannel analyzer in a coincidence arrangement in order to measure the spectrum at one detector in coincidence with a selected energy from another detector. As shown in Fig. 50, the connection to single- channel analyzer "1" is broken, and a slow coincidence is demanded only between the "Fast" and "Slow 2" channels. With the multi- channel analyzer connected to amplifier "1," a coincidence between detector "1" and a count in the window of single-channel analyzer "2" will supply a gate signal which commands the multi- channel analyzer to record the pulse appearing at its input. The ideal arrangement for acquiring coincidence information would record the pulse-height from both Detectors 1 and 2 of Fig. 50 each time a fast coincidence occurred, so that all possible coincidence combinations can be recorded in a single experiment. Further, it is desirable that the number of events corresponding to each possible set of coordinates be sorted and stored in a fast-access memory device (such as a ferrite-core memory). The instrument just described is really a pulse-height 108

analyzer with two ADC units (Section VI.6.B.), capable of gener- ating an "X" and "Y" address for storing each coincidence event in a matrix whose "Z" axis is the number of events. The concept of a storage matrix leads to the term "three-dimensional pulse- height analyzer" for this device. A much less versatile but less expensive instrument may be constructed from two ADC units which record the two addresses for each event on magnetic or punched tape as they occur. In this case the data must be sorted by reading the tape with a modified pulse-height analyzer storage unit or with a computer. This procedure is very time consuming and has the disadvantage that because of the additional sorting step, the condition of the data cannot be determined during the experiment, or even very soon thereafter. The development of the three-dimensional analyzer approach to coincidence spectrometry is still in the early stages but promises to be extremely useful. The general problem was reviewed by Chase and a 20,000-channel, three-dimensional analyzer with a ferrite-core memory was described by Goodman, et al.90 A related technique makes use of a signal which inhibits the multichannel analyzer or other apparatus from recording particular events. One application of this anticoincidence arrangement is discussed below in Section VII.2. C. Delayed Coincidence Measurements. Coincidence tech- niques are well suited to the measurement of very short half- lives. If delay lines are inserted between the timing circuit and fast-coincidence input, first in one channel and then the other, a delay curve can be obtained, which is just the coinci- dence counting rate as a function of added delay. This curve will have a width at half-maximum counting rate of 2r, if the two radiations are prompt; however, should one of the radiations be delayed, the delay curve will be steep on one side but will exhibit a smaller slope on the other side. The analysis of such data to obtain lifetimes of nuclear states is discussed in references 85, 91, and 92. D. Calculation of Intensities. Quantitative coincidence measurements, especially gamma-gamma coincidence spectrometry, have become essential in the study of nuclear decay schemes. Relative intensities are easily determined, and if the decay scheme includes two or more gamma rays with the same energy, it 109

may be possible to determine the relative intensity of each by a series of coincidence experiments involving the gamma-ray cascades in question. It is important to emphasize that all peaks in a coinci- dence gamma-ray spectrum are not necessarily due to coincidences with the gamma peak on which the single-channel window is set; indeed, an intense coincidence peak may be due to random coincidences (Part A., above), or to true coincidences with events in the single-channel window arising from Compton-electron, gamma-ray scattering, or bremsstrahlung spectra. Thus, it is usually not enough merely to observe that a series of peaks appears in the coincidence spectrum; rather, a quantitative examination of the gamma-ray intensities is required to obtain a meaningful interpretation of the experiment. Consider first an experiment in which a peak of area P(y, ) due to y, is observed in coincidence with counts of y2 in the single-channel window: The quantity qt 2, the "coincidence quotient," is the number of events of y, , the gamma ray of interest, in coincidence with y2 , divided by the number of counts due to y2 in the single-channel window; e^ corrects for absorption of yl in the beta absorber; C is the number of counts in the window of the single-channel analyzer; ep(y,) and n are the peak efficiency and solid angle for detection of yl ; and W1>2(0) is the angular distribution function for the indicated pairs of coincident gamma rays 34 integrated over the face of the crystal. Although Eq. (19) is useful in many situations, two additional corrections are needed: one to correct for the fact that only a fraction of the counts in the window may be due to y2 ; it is also very important to remove the coincidence contri- bution from higher-energy gamma rays which give Compton-electron events falling in the single-channel window. When these effects 93 are taken into account, the following expression for qt f 2 results: I I D2 ¥1,2(0> , (20) 110

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