APPLICATION OF ELECTRON MULTIPLIERS FOR COUNTING ELEMENTARY PARTICLES AND QUANTA

T. M. Lifshits

This review contains an account of the methods developed up to the present time for using electron multipliers as counters of elementary particles and quanta.

In §§ 2–5 some characteristics of multipliers are considered that are of interest from the standpoint of their application as counters; in the remaining sections the methodology is described for registering and studying various kinds of radiation with the aid of electron multipliers, as well as the results achieved in this direction.

The review has been compiled from materials published in the periodical Soviet and foreign literature.

1. INTRODUCTION

Electron multipliers, which soon after their invention by Kubetskii*) (in 1930) gained universal recognition as indispensable instruments for the photoelectric registration of weak light fluxes, have in recent years come into wide use for counting elementary particles and quanta.

The very high resolving power (in time) of multiplier-counters, exceeding by several orders of magnitude the resolving power of ionization counters, their high efficiency for various kinds of radiation, including gamma rays, fast electrons, and neutrons, and the possibility of estimating radiation energies—all these merits of counter-multipliers determine the ever-growing interest in them and the enormous number of works devoted to them in recent years. Some authors regard the appearance of multiplier-counters of particles and quanta, in particular scintillation counters, as one of the most important achievements of experimental nuclear physics in recent years.

*) L. A. Kubetskii, Author’s Certificate No. 24040 of 4/VIII 1930.

Scientists of our country have played a leading role in the creation and improvement of electron multipliers.

Stoletov’s classical investigations of the photoelectric effect, subsequently continued by Lukirskii, Prilezhaev, Lukyanov, Timofeev, Khlebnikov, and others, as well as the systematic and comprehensive investigations of secondary emission carried out by Lukirskii, Semenov, Timofeev, Lukyanov, Vyatkin, Zernov, Khlebnikov, Kadyshevich, Kosman, Budinskii, Aronovich, and many other researchers, created a broad scientific foundation on the basis of which photoelectric technology has successfully developed and continues to develop.

The leading position of Russian and Soviet science in the field of the photoelectric effect and secondary emission predetermined the fact that, in the technical applications of these phenomena—in particular in the broad use in technology of the antimony–cesium photocathode, which forms the basis of the overwhelming majority of modern vacuum photoelectric devices, including photomultipliers, and also in the technical applications of secondary emission—the Soviet Union for a number of years outstripped other countries.

As a result of the inventions of Kubetskii, Timofeev, Vekshinskii, Krasovskii, Kvartsava, Butslov and Pyatnitskii, Mekhov, Braude, and Shmakov, a number of original designs of electron multipliers were created, in which all the principal types of devices of this kind now in existence are represented*).

Soviet engineers and physicists are still successfully continuing work on the improvement of electron multipliers, as is shown by recent work in this field.

A counting device with a multiplier usually consists of the multiplier itself, a pulse amplifier, a simple or differential amplitude analyzer, and pulse recorders. There are two ways of using multipliers as counters.

The first, most widespread method consists in using ordinary photomultipliers with a photocathode sensitive to visible light in combination with a luminescent substance (phosphor), which converts the energy of the radiation under investigation into light flashes—scintillations. A block diagram of such a device, which has received the name of a scintillation counter, is shown in Fig. 1. A particle or quantum produces in the phosphor placed in front of the photomultiplier window a light flash, which is converted in the photomultiplier into a current pulse recorded by the counting circuit. At the present time a large number of solid and liquid, inorganic and organic phosphors are known which possess a large light yield in converting the energy of particles and quanta into light energy. For a whole series of phosphors the light yield is proportional to the ener—

) ZhTF, 22*, 178 (1952).

particles, which makes it possible to use them to study the distribution of particles by energy. Many phosphors have a very short afterglow duration, of the order of \((2 \div 6)\cdot 10^{-9}\) sec. These circumstances make it possible to build scintillation counters with high efficiency and a high counting rate, as well as counters with which the energy of particles can be estimated.

With scintillation counters, however, it is difficult to register particles having low energy. The source of such particles is usually located in a vacuum behind a partition impermeable to particles of low energy, so that the particles cannot reach the phosphor. In addition, in the photomultiplier the background, determined mainly by thermionic emission from the photocathode, is large, and the scintillation from a particle of low energy may prove undetectable against this background.

Fig. 1. Block diagram of a scintillation counter.

Owing to these circumstances, when registering particles of low energy, and also in a number of other cases, another method of counting particles proves more convenient: the particles under study are directed immediately onto the cathode of the multiplier, and the secondary electrons emitted under their action are then amplified by the multiplier.

The emitters in such multipliers are made of metallic alloys, and the cathodes either of the same alloys or of pure metals. Because the thermionic emission of such cathodes and emitters at room temperature is negligible, the multiplier makes it possible to register individual elementary particles, quanta, or ions directly, even if their energy is relatively small.

The characteristics of electron multipliers used for counting particles largely determine the results that can be obtained with their aid. Thus, the accuracy of counting depends on the background of the multiplier; the accuracy of estimating particle energies depends on the spread of pulse amplitudes at the output of the multiplier when monochromatic radiation acts on its input; and the counting rate depends on the duration or rise time of a single pulse.

In the following paragraphs, certain characteristics of multipliers that play an essential role in counting particles and quanta are considered in detail.

2. BACKGROUND OF MULTIPLIERS

Superposed on the pulses caused by scintillations or by directly registered particles are pulses due to the background of the multiplier. The background of the amplifying device practically does not interfere with the measurements, since it is many times smaller than the magnitude of the signals arriving from the multiplier at the input of the amplifier.

The presence of background pulses considerably reduces the accuracy that can be achieved with a given device when counting during a specified time interval. Indeed, suppose that during a time interval \(T\) a total of \(N\) pulses have been counted. This number, evidently, includes, in addition to the pulses caused by particles, also the background pulses \(N_{\phi}\), the mean number of which during the specified time interval can be found by counting in the absence of the source.

The number of pulses from the source \(N_c\) is found from the difference between the total number of pulses \(N\) and the number of background pulses \(N_{\phi}\):

\[ N_c = N - N_{\phi}. \]

The mean-square deviation of the quantity \(N_c\) from its mean value is:

\[ \overline{\Delta N_c^{2}} = \overline{\Delta N^{2}} + \overline{\Delta N_{\phi}^{2}}, \]

and the accuracy of counting is

\[ \eta = \frac{\sqrt{\overline{\Delta N_c^{2}}}}{N_c} = \frac{\sqrt{\overline{\Delta N^{2}}+\overline{\Delta N_{\phi}^{2}}}}{N-N_{\phi}} . \]

Further, denoting the counting rate of pulses (the mean number of pulses per second) of the signal and of the background, and the total number of pulses per second, respectively by \(n_c\), \(n_{\phi}\), and \(n\), we have:

\[ N_c = n_c T;\quad N_{\phi}=n_{\phi}T,\quad N=nT . \]

Since each individual pulse arises independently of the other pulses, the mean-square deviation of each of the quantities \(N_c\), \(N_{\phi}\), and \(N\) from their mean values is equal to the square root of the quantity itself. Thus,

\[ \eta=\frac{\sqrt{n+n_{\phi}}}{(n-n_{\phi})\sqrt{T}} . \tag{1} \]

If, for example, the mean number of pulses from the source is equal to the number of background pulses \((n=2n_{\phi})\), then, as is readily seen from (1), in order to attain a prescribed accuracy it is necessary to count pulses for a time three times longer than that required to attain the same accuracy in the absence of background. The number of pulses in the first case will then be six times greater than in the …

second. Expression (1) indicates the substantial significance of reducing the background when counting pulses.

In photomultipliers the principal source of background pulses is thermionic emission from the photocathode and the first emitters. Thermoelectrons from the remaining emitters, being multiplied to a lesser degree, give pulses of considerably smaller magnitude. Pulses caused by ohmic leakage between the multiplier anode and the other electrodes are small, and they may be neglected when the multiplier is used in a counter circuit.

As the supply voltage is increased, the number of background pulses of the photomultiplier at first grows slowly, and then, beginning with a certain voltage, very rapidly. Fig. 2 illustrates the increase in the number of background pulses with increasing voltage on the multiplier[^1].

A sharp increase of the background at high voltages may be explained by the occurrence of autoelectronic emission from the sharp edges of the electrodes, and also by the occurrence of ion feedback between the last stages of the multiplier and the cathode. In the anode part of the multiplier, where the electron current has the greatest magnitude, positive ions arise in collisions of electrons with atoms of the residual gas. These ions, under the action of the voltage applied to the multiplier, move toward the cathode and, bombarding it, as well as the first emitters, cause the emission of secondary electrons, which are the source of additional background pulses.

Fig. 2. Increase in the number of background pulses with increasing voltage in a multiplier with an oxygen–cesium photocathode and emitters cooled by liquid air.

With increasing voltage, both the ionizing factor (the anode current of the photomultiplier) and the energy of the ions increase, as a result of which the background also increases.

The pulses caused by ion feedback, when observed on an oscilloscope screen, have the appearance of groups consisting of several pulses separated by a time interval of the order of \(10^{-7}\) sec[^2].

It has been observed[^3] that the number of dark pulses in multipliers with a glass envelope decreases if the inner part of the envelope in the region of the cathode and the first three or four emitters is covered with a conducting layer (for example, aquadag) and this layer is connected to the cathode. This shows that part of the background pulses must be attributed to those ions of the residual gas which are accelerated in the electric field between the walls of the envelope and the first electro-

...and bombard these electrodes. This does not occur if the walls of the bulb are coated with a conducting layer at the same potential as the cathode.

In some cases, when the glass of the multiplier bulb has appreciable conductivity, it is possible to reduce the number of dark pulses by placing a metallic screen over the multiplier from the outside and bringing it to a potential close to the cathode potential3, 4, 5, 6. Conversely, applying to the screen a large positive or negative potential relative to the cathode increases the number of background pulses. Figure 3 shows the dependence of the number of background pulses on the potential of the external electrostatic screen for one of the samples of 931-A3 multipliers. The cathode potential is \(-1000\) volts.

Fig. 3. Dependence of the multiplier background on the potential of the external electrostatic screen.

As a rule, an external electrostatic screen has a considerable effect on the noise level of poor multipliers and has little effect in good multipliers, whose noise is small. The potential of the external screen also has almost no effect on the noise level in those multipliers whose bulb is made of high-resistance glass.

Figure 4 shows the distribution of background pulses of photomultipliers 931-A (curve 1) and 5819 (curve 2) by amplitude. The pulse amplitude is expressed in numbers of primary electrons that caused the given pulse, i.e. in units of \(eM\), where \(e\) is the electron charge and \(M\) is the gain coefficient of the multiplier. The ordinates of the curve indicate the number of pulses whose amplitude is equal to or greater than the given one.

Most of the pulses have a magnitude of \(1\,eM\) or less. Pulses with an amplitude exceeding \(1\,eM\) constitute less than one percent of the total dark current of the photomultiplier.

A powerful means of reducing the background of a photomultiplier is cooling the photocathode and the first emitters, which leads to a sharp decrease in thermionic emission. In the region of room temperatures, the number of dark pulses is reduced by half when the temperature is lowered, on average, for every \(10^\circ\mathrm{C}\). The change in the number of background pulses with temperature from \(27^\circ\mathrm{C}\) to \(50^\circ\mathrm{C}\) for two photomultipliers is shown in Fig. 5. Deep cooling makes it possible to reduce the background of a photomultiplier to only a few dark pulses per minute.

Fig. 4. Distribution of background pulses by amplitude. The ordinates of the curves indicate the number of background pulses with amplitudes equal to, or exceeding, the values corresponding to the abscissas of the points of the curves.

Fig. 5. Dependence of the photomultiplier background on temperature in the region of room temperatures for two photomultiplier samples.

In the Kubetsky photomultiplier used by Rodionov and Osherovich in a photon counter, the background at a temperature of \(-183^\circ\)C amounted to from 12 to 45 pulses per minute. At a temperature of \(-76^\circ\)C the background increased to 320 pulses per minute\(^7\) (the multiplier operated at a voltage of 1300 volts). Engstrom indicates that, by cooling to \(-175^\circ\)C, he was able to reduce the background of the 1P21 multiplier to one or two pulses per minute at a supply voltage of 70 volts per stage. In Fig. 6

Fig. 6. Dependence of the background on voltage for the cooled photomultiplier 1P21.

is shown the dependence of the number of background pulses on the supply voltage for this multiplier in the cooled state\(^8\).

The author explains the increase of the background with voltage by the occurrence of cold emission from the sharp edges of the electrodes.

The amplitude distribution of the background pulses when the photomultiplier is cooled generally does not change; however, the number of pulses of large amplitude, which apparently arise from positive ion feedback, decreases more slowly than the number of the other pulses.

The use of cooling is associated with a number of practical inconveniences, because of which, wherever possible, one tries to dispense with it. To reduce the background of a photomultiplier in scintillation-counter circuits, an amplitude discriminator is usually provided, which does not pass pulses whose amplitude is less than a specified value. By changing the blocking negative bias on the grid of the discriminator tube, one can change the limiting amplitude, beginning with which pulses pass through the discriminator.

and are registered by the counter\(^{9,10}\). In Fig. 7 a curve is given showing the change in the number of background pulses when the discriminator bias voltage is varied (curve 1)\(^{9}\).

At a voltage on the grid of the discriminator corresponding to the blocking of all pulses smaller than \(7\, eM\), the background count practically disappears. However, the use of a discriminator, especially at large negative biases, considerably reduces the efficiency of the counter, since together with the background pulses all pulses produced by particles whose amplitude is less than the critical one are cut off.

Fig. 7. On increasing the sensitivity of the counter when photomultipliers are operated in a coincidence circuit.

In those cases where the pulses from particles are comparable in amplitude with the background pulses, it is evidently impossible to use large biases on the discriminator. In these cases it proves expedient to connect two multipliers, operating from one phosphor, in a coincidence circuit.

The number of coincident background pulses is so small that with the aid of such a circuit it is possible to register scintillations causing the photocathode to emit single photoelectrons.

The increase in the sensitivity of the counter when a coincidence circuit is used is illustrated by curve 2 of Fig. 7. When operating with one photomultiplier, in order to cut off the background it is necessary to apply to the grid of the discriminator a voltage which blocks pulses with amplitude less than \(7\, eM\). In this case the radiation source gives 1500 pulses per second. Using the coincidence circuit, one can reduce the blocking voltage on the discriminator to such a value that only pulses smaller than \(1\, eM\) are not passed, and nevertheless the number of coincident background pulses registered by the counter does not exceed one per second. The same source now gives 9000 counts per second. Thus the sensitivity of the counter has increased sixfold.

It was observed that, following each pulse caused by a scintillation, a series of satellite pulses of smaller amplitude arises at the anode of the photomultiplier\(^{11,12}\). The presence of these pulses under weak discrimination casts doubt on the correspondence between the number of pulses registered by the counter and the number of particles that have passed through the phosphor. Satellite pulses also accompany the pulses of the photomultiplier background.

The number of satellite pulses, their amplitudes, and their distribution in time depend on the amplitude of the primary pulse, the voltage at which the photomultiplier operates, and its amplification coefficient.

In different photomultiplier specimens the number and character of the satellite pulses may vary. Fig. 8 shows oscillograms of the primary pulse and the satellite pulses accompanying it in photomultiplier 5819[^12]. Curves a and b refer to the background pulse, curves c and d to the pulse from γ-scintillations in a terphenyl crystal. The sweep duration in oscillograms a

Fig. 8. Satellite pulses in photomultiplier 5819.

and c is 8 μsec, in b and d 40 μsec; the scale along the ordinate axis is logarithmic. The causes of the appearance of satellite pulses are not reliably known. Possible causes are positive ion feedback due to the presence of residual gas in the photomultiplier, motion of negative ions from cascade to cascade, and the occurrence of soft X-rays during electron bombardment of the emitters.

It has already been noted above that in electron multipliers intended for direct counting of particles or quanta, emitters made of metallic alloys and cathodes made of pure metals are used. In both, thermionic emission at room temperature is negligible and, if the necessary measures are taken to prevent the occurrence of ion feedback and field emission, the background in these multipliers does not exceed several pulses per minute.

Thus, according to published data, in a multiplier with silver–magnesium emitters[^13] the background count does not exceed 3–4 pulses per minute, and in another case[^14] 1 pulse in 2 sec at a multiplier gain of the order of \(10^8\).

When working with such multipliers it is not necessary to resort to any special measures to eliminate the background.

3. DISTRIBUTION OF MULTIPLIER PULSES BY AMPLITUDE

Each individual electron emitted by the cathode is multiplied a certain number of times, only on the average for many electrons, owing to the statistical character of amplification in the multiplier, equal to the gain coefficient of the multiplier. Accordingly, the pulses at the output of the multiplier, caused by one and the same number of primary electrons, are not identical in amplitude, but have a certain random distribution. If each of the observed pulses is caused by one primary electron, then in this case one may speak of the distribution curve of the gain coefficient of the multiplier.

To establish the form of the distribution curve of the gain coefficient of the multiplier, special experiments were carried out.^15–18 The photomultiplier under investigation was cooled with liquid air, so that thermionic emission was practically absent. A light source was placed in front of the photocathode so weak that the probability of the simultaneous emission of two or more photoelectrons was very small, and it could be assumed that each pulse in the multiplier was caused by a single photoelectron. The pulses were recorded by a counting circuit with a discriminator, which passed those of them that produced on its grid a voltage equal to or greater than the bias voltage \(A\). Here \(A\) is proportional to the number of electrons in the corresponding limiting pulse:

\[ A = A_N = \chi N. \tag{2} \]

If by \(Z_N = Z(A_N)\) we denote the number of pulses producing, at the output of the multiplier, voltages from \(A\) and higher, and by \(a_N\) the number of pulses each of which consists of \(N\) electrons, then, obviously,

\[ Z_N = \sum_{\nu=N}^{\infty} a_\nu , \tag{3} \]

and

\[ a_N = Z_N - Z_{N+1}. \tag{4} \]

Usually the number of pulses \(Z\) is large, and \(Z_N\) may be regarded as a continuous function of \(N\) and \(A\). Then

\[ a_N = Z_N - Z_{N+1} \to -\frac{dZ_N}{dN} = -\chi \frac{dZ(A)}{dA}. \tag{5} \]

From the measurements mentioned it was found that \(Z(A)\), on a semilogarithmic scale, is represented sufficiently well by a straight line

Accordingly, the dependence of \(Z\) on \(A\) must have the form:

\[ Z(A)=Z_N=Z_0 e^{-\frac{\overline{A}}{A}}=Z_0 e^{-\frac{\chi}{\overline{A}}N}, \tag{6} \]

where \(Z_0\) and \(\overline{A}\) are constants.

Taking such an expression for \(Z(A)\), from (5) we find:

\[ a_N=-\frac{\chi Z_0}{\overline{A}} e^{-\frac{\chi}{\overline{A}}N}. \tag{7} \]

The probability that one photoelectron will produce at the output of the multiplier a pulse consisting of \(M\) electrons, in other words, the probability of obtaining a value of the amplification factor equal to \(M\), is

\[ v_M=\frac{a_M}{Z_1}=\alpha e^{-\frac{\chi}{\overline{A}}M}=\alpha\beta^M. \tag{8} \]

Here \(Z_1\) is the total number of pulses, \(\beta=e^{-\frac{\chi}{\overline{A}}}\), \(\alpha\) is a constant.

If we assume that each of the primary electrons produces a recorded pulse, i.e. \(v_0=0\), then the event consisting in each primary electron being multiplied some number of times not equal to zero is certain, and

\[ \sum_{M=1}^{\infty} v_M=\sum_{M=1}^{\infty}\alpha\beta^M=1. \tag{9} \]

From this condition the coefficient \(\alpha\) is found:

\[ \alpha=\frac{1-\beta}{\beta} \]

and

\[ v_M=(1-\beta)\beta^{M-1}. \tag{10} \]

This is the analytic expression for the distribution curve of the amplification factor of the multiplier.

From (6) and (7) it is easy to find the mean value of the amplitude of the output pulse, expressed by the number of electrons composing it:

\[ \overline{N} = \frac{\displaystyle \sum_{N=1}^{\infty} Na_N} {\displaystyle \sum_{N=1}^{\infty} a_N} = \frac{\displaystyle \sum_{N=1}^{\infty} Z_N} {Z_1} \to \frac{1}{Z_1}\int_{1}^{\infty} Z_N\,dN = \frac{1}{\chi Z_1}\int_{0}^{\infty} Z(A)\,dA. \tag{11} \]

Since each of the pulses is produced by one primary electron, it is evident that expression (11) gives the mean value of the multiplier gain coefficient:

\[ \overline{M}=\frac{1}{\chi Z_1}\int_0^\infty Z(A)\,dA. \tag{12} \]

Using this formula, one can show that the mean-square spread of the gain coefficient is equal to

\[ \overline{\Delta M^2}=\frac{2}{\chi Z_1}\int_0^\infty A Z(A)\,dA-\overline{M}^2. \tag{13} \]

Thus, from the curve of the dependence of the number of pulses on the voltage on the discriminator grid, the mean value of the multiplier gain coefficient can be found; as is seen from (12), it is proportional to the area under this curve.

The spread of the amplitudes of the pulses at the output of the multiplier depends not only on the magnitude of the statistical fluctuations of the multiplier gain coefficient, but also on the mean number of primary electrons giving rise to an individual pulse, and on the fluctuations of this number.

Indeed, let \(m_0\) be the number of primary electrons emitted by the cathode under the action of a particle, quantum, or scintillation, and let \(\overline{\Delta m_0^2}\) be the fluctuation of this quantity.

Further, let \(m_1, m_2,\ldots,m_n\) be the mean gain coefficients of the 1st, 2nd, ..., \(n\)-th cascades, and let the mean-square fluctuation of each of these quantities be, respectively, equal to

\[ \overline{\Delta m_1^2},\ \overline{\Delta m_2^2},\ \ldots,\ \overline{\Delta m_n^2}. \]

Taking into account that the electron flux arriving at any cascade is amplified by all the preceding cascades, while the flux emitted by it is amplified by the subsequent cascades, we write the expression for the mean-square fluctuation of the number of electrons constituting the output pulse:

\[ \overline{\Delta N^2} = \overline{\Delta m_0^2} M^2 + m_0 \overline{\Delta m_1^2}\frac{M^2}{m_1^2} +\cdots+ m_0 m_1 \cdots m_{n-1}\overline{\Delta m_n^2} = \]

\[ = \overline{\Delta m_0^2} M^2 + m_0\left[ M^2\frac{\overline{\Delta m_1^2}}{m_1^2} + M^2\sum_{i=2}^{n}\frac{\overline{\Delta m_i^2}}{m_i^2}\, \frac{1}{m_1m_2\cdots m_{i-1}} \right]. \]

The expression in brackets is the magnitude of the mean-square spread of the output pulses due to each

to one primary electron, i.e. \(\overline{\Delta M^2}\):

\[ \overline{\Delta M^2} = M^2 \left[ \frac{\overline{\Delta m_1^2}}{m_1^2} + \sum_{i=2}^{n} \frac{\overline{\Delta m_i^2}}{m_i^2} \frac{1}{m_1 m_2\cdots m_{i-1}} \right]. \tag{14} \]

Thus, since \(N^2=m_0^2M^2\),

\[ \frac{\overline{\Delta N^2}}{N^2} = \frac{\overline{\Delta m_0^2}}{m_0^2} + \frac{1}{m_0} \frac{\overline{\Delta M^2}}{M^2}. \tag{15} \]

It is evident from this relation that, as the magnitude of the input pulse \(m_0\) increases, the influence of the spread of the multiplier gain coefficient on the relative spread of the output pulses decreases (although the absolute magnitude of the spread increases). In addition, the first term, which characterizes the relative spread of the input pulses, also decreases with increasing \(m_0\).

This means that the multiplier reproduces the amplitude distribution of the input pulses the more accurately, the larger these pulses themselves are, i.e. the more photoelectrons are emitted by the photocathode for each particle\(^{17}\).

We shall assume that the gain coefficients of all cascades, beginning with the second, are the same. Then from (14) we have:

\[ \overline{\Delta M^2} = M^2 \left[ \frac{\overline{\Delta m_1^2}}{m_1^2} + \frac{1}{m_1} \frac{\overline{\Delta m^2}}{m^2} \sum_{k=1}^{n-1} \frac{1}{m^{k-1}} \right] = \]

\[ = M^2 \left[ \frac{\overline{\Delta m_1^2}}{m_1^2} + \frac{\overline{\Delta m^2}}{m_1m(m-1)} \right] \quad (m^{n-1}\gg 1), \]

whence

\[ \frac{\overline{\Delta M^2}}{M^2} = \frac{\overline{\Delta m_1^2}}{m_1^2} + \frac{\overline{\Delta m^2}}{m_1m(m-1)}. \tag{16} \]

Thus, the relative magnitude of the fluctuations of the multiplier gain coefficient decreases with increasing gain coefficient of the cascade, or, equivalently, with increasing secondary-emission coefficient of the emitter in the multiplier.

As is seen from (16), the greatest influence on the fluctuations of the multiplier gain coefficient is exerted by the magnitude of the gain coefficient of the first cascade. This is explained by the fact that, by virtue of (15), the spread in the amplitudes of the output pulses decreases with an increase in the number of primary electrons. Since the electrons emerging from each given cascade are “primary” for the entire remaining part

multiplier, and since the smallest number of electrons comes from the first cascade, this cascade has the most substantial influence on the magnitude of the fluctuations of the multiplier gain coefficient.

From what has been said it follows that, in order to estimate the energy of particles or quanta with a sufficient degree of accuracy, it is necessary, as far as possible, to have a more sensitive photocathode, effective focusing of the photoelectrons from the photocathode onto the first cascade of the multiplier, a high value of the coefficient of secondary emission, especially in the first cascade, and also to use a phosphor with high light output and such a construction for coupling the phosphor to the photomultiplier as would ensure the fullest possible use of the scintillation light. For the latter purpose, photocathodes of large area and light-collecting mirrors are used, and, for penetrating radiation with low ionizing power, transparent phosphors of considerable thickness.

The quality of a scintillation counter intended for measuring radiation energy is conveniently characterized by the ratio of the energy lost by the particle in the phosphor to the number of photoelectrons produced at the photocathode and arriving at the first cascade. This quantity is usually expressed in kiloelectron-volts per photoelectron.

4. RESOLVING POWER OF MULTIPLIERS

One of the most important advantages of multipliers in applications for counting particles is their extremely high resolving power, i.e. the ability to respond separately to pulses separated by very small time intervals. Ultimately, the resolving power of a multiplier is determined by the duration or, if one resorts to cutting off the “tails” of pulses, by the rise time of the pulse caused by a single primary electron. The time itself during which electrons, multiplying at the emitters, pass through the whole multiplier would not limit the resolving power if it were strictly the same for all electrons.

In reality, however, the electrons making up the pulse reach the anode at different times, as a result of which the pulse itself is stretched out in time. According to calculations14, the duration of pulses in a type 931-A multiplier, when a silver-magnesium emitter is used in it and with interstage voltages of 100 V, is equal to \(6 \cdot 10^{-10}\) sec.

Figure 9 presents the energy spectrum of the output pulse of a multiplier due to one primary electron. Along the abscissa axis is plotted the frequency in megahertz (on a logarithmic scale); along the ordinate axis, the root-mean-square value of the current in the pulse per unit frequency interval, in decibels relative to the value at low frequency.

The magnitude of the spread in electron transit times from one cascade to another is affected by: differences in the initial velocities of secondary electrons, differences in the length and shape of the electron trajectories, and also space charge. About 85% of the secondary electrons emitted by modern cesium emitters used in photomultipliers have initial energies from zero to 3 eV. Such a spread of the initial electron energies, at a voltage between multiplier cascades of 100 V, leads to a spread in electron transit times between emitters of the order of \(2 \cdot 10^{-10}\) sec. The spread of times

Fig. 9. Spectral curve of the output pulse of the photomultiplier 931-A.

of electron transit is considerably greater in through-action multipliers (of the “louver” type), where part of the electrons, bypassing the next cascade, moves to the following cascade with an initial velocity corresponding to the inter-cascade voltage.

Thus, in the multiplier 5311, at a supply voltage of 3400 V, the rise time of the pulse from 10 to 90 percent of the amplitude value reaches \(5.0 \cdot 10^{-9}\) sec, and the pulse duration is \(1.0 \cdot 10^{-8}\) sec. At a voltage of 5000 V, which is permissible for a multiplier of this type, the same quantities are respectively \(6.0 \cdot 10^{-9}\) sec and \(1.2 \cdot 10^{-8}\) sec. \({}^{20}\)

For comparison, Fig. 10 gives oscillograms of pulses from scintillations in trans-stilbene, obtained with the photomultiplier 5311 (curves \(a\), \(б\), \(в\)) and with the photomultiplier 5819 (curve \(г\)).

As is seen from the oscillograms, in the photomultiplier 5311 the pulse rise time is approximately twice as long, and the pulse duration 4–5 times longer, than in the photomultiplier 5819. It was found that the spread of electron transit times in a multiplier increases approximately in proportion to the number of cascades. On the other hand, the more

the greater the voltage between the cascades, the smaller is the difference in the initial velocities of the electrons. Therefore, in a multiplier from which a particularly high resolving power is required, it is advantageous to have a small number of cascades and large inter-cascade voltages. The difference in the path lengths of electrons issuing from different points of the emitter also leads to a spread in the electron transit times. In a multiplier with electrostatic focusing of the 931-A type, the greatest difference in electron transit times due to the difference in their trajectories is \(1.7 \cdot 10^{-9}\) sec.\(^6\)

A successful attempt to identify the electron trajectories and thereby to reduce the pulse duration was made in a multiplier with magnetic focusing, intended for operation in the strong magnetic field of an ion accelerator\(^ {49}\) (see § 5). The rise time of the pulse in this multiplier lies within the range \(10^{-11}\)—\(10^{-10}\) sec.

At very large gains, instantaneous currents of large magnitude may be formed at the output of the multiplier. Thus, at a multiplier gain of \(10^9\) and a pulse duration of \(10^{-9}\) sec, one primary electron at the output produces an instantaneous current pulse of

\[ \frac{1.6 \cdot 10^{-19} \cdot 10^9}{10^{-9}} = \]

\[ = 0.16 \text{ ampere}. \]

The space charge formed as a result of such a current can appreciably increase the spread in electron transit times. In a multiplier with smaller gain, the space charge has little effect on the resolving time.

Fig. 10. Oscillograms of pulses from scintillations in transstilbene:
a) FEU-5311, \(U_{\text{oper.}} = 2800\) V;
b) FEU-5311, \(U_{\text{oper.}} = 3500\) V;
c) FEU-5311, \(U_{\text{oper.}} = 4500\) V;
d) FEU-5819, \(U_{\text{oper.}} = 1400\) V.

The duration of pulses from single photoelectrons has been studied experimentally by a number of authors\(^ {21—27}\). In works\(^ {21,27}\) the pulses of the 931-A multiplier were investigated when it was powered by high-voltage pulses. The amplitude of the voltage pulses reached 5 kV, and the duration was up to 2.5 μsec. In this case, in a number of multiplier specimens no breakdowns were observed, while the gain of the photomultipliers increased to \(10^9\). The background of the multiplier was reduced by applying the same high-voltage pulse to the shielding layer deposited on the bulb of the multiplier. The pulses of the multiplier were fed through a coaxial cable directly to the deflecting plates of a high-voltage cathode-ray tube. The duration of the pulses from single electrons emitted by the photocathode was approximately \(5 \cdot 10^{-10}\) sec.

In another work[^25], to determine the duration of pulses, two photomultipliers were used, connected in a coincidence circuit through coaxial cables with characteristic impedances of 100 ohms, used to introduce a delay. By changing the cable length in one of the channels, it was possible to determine the width of the pulses from single photoelectrons. For this quantity a value of about \(10^{-9}\) sec was obtained.

The resolving power of a scintillation counter is limited, in addition to the duration of the pulse in the multiplier, also by the decay time of the phosphor used. However, at present phosphors are known whose decay time is thousandths of a microsecond, and thus the scintillation counter as a whole has a very high resolving power.

5. ELECTRON MULTIPLIERS FOR COUNTING PARTICLES AND QUANTA

In a number of cases, ordinary standard photomultipliers intended for photometry of weak light fluxes prove suitable for use in scintillation counters. It is necessary only to select from batches of instruments those specimens that possess a sufficiently high gain at a low background.

A substantial drawback of such photomultipliers, from the standpoint of their use for counting scintillations, is the small area of the photocathode, which is moreover located deep inside the bulb, as a result of which it is difficult to make effective use of the light from scintillations of large crystals. Especially for scintillation counters, photomultipliers were developed with a flat photocathode of large area deposited on the glass of the bulb[^6],[^30]–[^33].

Thus, the photomultiplier 5819 has a semitransparent photocathode with an area of 11 cm\(^2\), deposited on the flat end surface of the bulb; the photomultiplier 5311 (of the “Venetian blind” type) has the same kind of cathode with an area of 5 cm\(^2\). In newer photomultipliers the area of the photocathode is still larger (60 cm\(^2\) in type H 5037[^32] and 83 cm\(^2\) in type C 7157[^33]; in the latter case the photocathode is deposited on the side surface of the photomultiplier bulb). In all types of photomultipliers for scintillation counters, antimony–cesium photocathodes are used; among all known types of photocathodes they have the greatest sensitivity in the visible region of the spectrum. The sensitivity of semitransparent antimony–cesium photocathodes in photomultipliers is 30–50 \(\frac{\mu\mathrm{A}}{\mathrm{lm}}\). Since part of the radiation of some phosphors lies in the ultraviolet region of the spectrum, it is of interest to extend the spectral sensitivity of photomultipliers toward short wavelengths, which can be accomplished by replacing the glass envelope with a quartz one[^34].

Of great importance from the standpoint of reducing the spread of pulse amplitudes are the uniformity of the photocathode sensitivity and good focusing of photoelectrons from all parts of the cathode onto the first stage. Violation of these requirements leads to the result that scintillations of equal intensity, arising in a large crystal near different parts of the photocathode, will give pulses of different amplitude. In order to ensure collection of photoelectrons from all parts of the cathode onto the first stage, in photomultipliers with large-area photocathodes an electron-optical collecting system, consisting of one or several focusing electrodes, is placed between the cathode and the first stage. To achieve greater uniformity of the photocathode, during its manufacture the antimony layer is deposited from antimony beads located at the center of the photomultiplier bulb[^32]. Nevertheless, as a rule it is not possible to obtain surfaces that are completely uniform in sensitivity. In some specimens of photomultipliers, different parts of the cathode may differ in sensitivity by more than a factor of two. A reduction of the pulse-amplitude spread arising for this reason can be achieved by placing, between the phosphor and the photomultiplier, a lucite layer that acts as a light guide, distributing the light from a scintillation—regardless of the place where it arises in the phosphor—uniformly over the entire surface of the cathode. As was already said above, no less important is the problem of collecting the scintillation light onto the photocathode. Many designs of various kinds of mirrors and reflectors intended for this purpose have been proposed. In particular, good results were obtained by placing large naphthalene crystals (20 mm in diameter and 12.5 mm thick) in a sphere coated on the inside with magnesium oxide[^35]. Often, as a reflector, a layer of magnesium oxide or aluminum foil is used, with which the crystal is covered on all sides except the side facing the multiplier. Some crystals, for example NaJ(Tl), are hygroscopic and require placement in sealed housings, in which, for the entry of radiation, a window closed with thin aluminum foil is left.

Figure 11 shows one of the systems for coupling a phosphor with a photomultiplier[^36].

Large crystals are glued to the multiplier with Canada balsam or with a film of mineral oil having a refractive index intermediate between the refractive indices of the crystal and of the glass of the photomultiplier bulb. This reduces reflection from the lower surface of the crystal, which in crystals with a high refractive index can lead to significant losses[^37].

A good material for gluing phosphors to a photomultiplier is a 25% solution of polystyrene in an aqueous solution of terphenyl[^38]. This composition has a refractive index of 1.58 and does not

possesses any appreciable absorption of light in the visible region of the spectrum. Its use does not require heating the elements being cemented, which is harmful for the multiplier.

In those cases where the counter is intended for registering \(\alpha\)-particles or protons, there should be no barriers between the surface of the phosphor and the source of the particles, such as a layer of varnish, binder, etc. Powdered phosphor is conveniently applied to the envelope of the photomultiplier by simple dusting, after first coating the glass with a very thin layer of a binding substance. To avoid additional spread in the amplitudes of the pulses, the phosphor must be applied in an even, homogeneous layer. In those cases where the radiation being registered is accompanied by neutron radiation, it is desirable that the binder used contain no hydrogen; otherwise the neutrons will cause the appearance of a considerable background. It is possible to apply a phosphor layer without using a binder, by precipitating it from a suspension in absolute ethyl alcohol[^39].

Fig. 11. One of the variants of a system for coupling the crystal to the photomultiplier:
1 — crystal,
2 — casing protecting the crystal from moisture,
3 — reflector (magnesium oxide or aluminum foil),
4 — rubber gasket,
5 — Bakelite ring,
6 — Lucite,
7 — magnetic shield,
8 — photomultiplier,
9 — preamplifier housing.

In those cases where it is necessary to count a very large number of pulses per second or to register processes separated by very small time intervals, the first requirement imposed on the multiplier is a short pulse duration. In addition, since amplifying very short pulses is in itself a difficult problem, requiring the use of amplifiers with distributed constants and other complex apparatus, it is highly desirable to have multipliers with a large amplification coefficient, of the order of \(10^9\), which would give at the output pulses from single photoelectrons that are readily registered without subsequent amplification.

It has already been indicated above that an amplification coefficient of the order of \(10^9\) can be obtained in ordinary photomultipliers when they are supplied with high-voltage pulses (up to \(5000\ \mathrm{V}\)). However, at such a large value the linearity of amplification in ordinary multipliers is disturbed owing to the influence of space-

their charges in the anode part of the multiplier^32,40. The latter can be detected experimentally if one takes into account that the logarithm of the multiplier gain factor, generally speaking, must be a linear function of the logarithm of the cascade voltage.

Indeed, as Luk’yanov^41 showed, the dependence of the coefficient of secondary emission \(\sigma\) of complex emitters on the energy of the primary electrons \(U_n\), in the region of not very high energies, is well described by the formula

\[ \sigma = A u_n e^{-\frac{u_n}{u_M}}, \tag{17} \]

where \(u_M\) is the value of \(u_n\) corresponding to the maximum of \(\sigma\), and \(A\) is a constant.

In accordance with this, the dependence of the gain factor of an \(n\)-cascade multiplier on the inter-cascade voltages can be expressed by the formula

\[ M = \theta \delta^n = \theta A^n u_k^n e^{-n \frac{u_k}{u_M}} \tag{18} \]

(\(u_k\) is the inter-cascade voltage, \(\theta\) is a coefficient taking into account the imperfection of the electron-optical system), whence

\[ \ln M = c + n\left(\ln u_k - \frac{u_k}{u_M}\right), \tag{19} \]

where it is denoted:

\[ c = \ln \theta + n \ln A. \]

For emitters used in multipliers, \(u_M \sim 600\ \text{V}\), while the inter-cascade voltages usually lie within the range from 50 to 200 V. It is not difficult to see that, for such values of \(u_k\) and \(u_M\), the dependence of \(\ln M\) on \(\ln u_k\) is very close to linear (dashed line in Fig. 12).

Fig. 12. Characteristic \(M = f(U_k)\), plotted on a logarithmic scale along both axes. The bending of the characteristic is caused by the influence of the space charge in the anode part of the photomultiplier: 1 — anode voltage 200 V, 2 — anode voltage 100 V.

Experimentally obtained curves \(\ln M = f(\ln u_k)\), however, reveal a considerable deviation from linearity for pulses corresponding to single photoelectrons already at gains of \(10^7\)–\(10^8\), and this deviation is the greater, the smaller the voltage between the last cascade and the anode of the photomultiplier (curves 1 and 2 in Fig. 12).

In order to preserve linearity at higher gains, in the newest designs of photomultipliers the anode is brought closer to the last

cascade in order to increase the field strength between them and to create conditions for the rapid dispersal of space charge. In the photomultiplier 4646 the anode is made in the form of a grid surrounding the last emitter. In another version of this device the anode grid is placed directly in front of the last cascade[^32]. The electrode system of the multiplier 4646 is made in such a way that the trajectories of electrons emerging from different parts of the emitter are identical; owing to this, the spread in the transit times of electrons between emitters is reduced and, with it, the duration of the pulses. The multiplier 4646 has 16 multiplication cascades and, at a supply voltage of 2300 V, has a gain of the order of \(10^9\). The linearity of the gain is preserved up to anode currents of 200 mA (in pulse operation).

At high counting rates it is necessary to take into account yet another property of multipliers that affects the accuracy of the results, namely, the fatigue of the emitters and the associated decrease in the gain coefficient of the multiplier during its operation. Fatigue is a consequence of changes in the emission properties of the emitting surfaces under the action of electron bombardment. It manifests itself to a greater degree the larger the anode current of the multiplier. Fig. 13 shows the change of currents in the various cascades

Fig. 13. Fatigue curves of the last cascades of a photomultiplier under a constant light flux illuminating the photocathode.

of the multiplier 931-A with antimony-cesium emitters at initial anode currents of 10 μA, 100 μA, and 1000 μA[^42]. As is evident from the figure, the emitter of each subsequent cascade fatigues faster and to a greater extent than the preceding one. At initial anode currents of 10, 100, and 1000 μA, its value two hours after switching on the photomultiplier is, respectively, 50, 30, and 12 percent of the initial value.

The decrease in the sensitivity of photomultipliers as a result of emitter fatigue when operating in a scintillation-counter circuit leads to a reduction both in the amplitudes of the recorded pulses and, at a specified discrimination, to a reduction in the counting rate of pulses from

of a source of constant intensity. Thus, in a 5819 photomultiplier operated at a voltage of 900 V with a crystal irradiated by a source of \(\gamma\)-radiation \(Co^{60}\) of 1.04 millicurie, placed at a distance of 36 cm from the crystal, the counting rate of pulses with an amplitude not less than 40% of the maximum decreased in 40 minutes from \(55 \cdot 10^3\) to \(40 \cdot 10^3\) pulses per minute. Then the counting rate became constant. When the counting rate was increased by bringing the source closer to the crystal to a distance of 20 cm, the counting rate again began to fall, decreasing in 20 minutes from \(192 \cdot 10^3\) to \(164 \cdot 10^3\) pulses per minute. The anode current of the photomultiplier in this case was about 2 μA. The fatigue effect in the multiplier became imperceptible at such counting rates when the value of the anode current of the photomultiplier did not exceed 0.1 μA\(^{43}\).

This value of the anode current for multipliers of this kind is apparently the limit above which fatigue substantially interferes with their operation.

A substantial improvement in parameters has been achieved in new domestic photomultipliers\(^{44}\).

Electron multipliers for direct counting of particles (without optical transformation by means of a phosphor) were first constructed by Bay\(^{45}\) and Allen\(^{46,47}\). The electrode system of Allen’s multiplier is shown in Fig. 14a. The electrodes here are given the shape of

Fig. 14a. Electrode system of Allen’s multiplier.

focusing lenses, similar to what was originally proposed by Mekhov*) and described by Lepeshinskaya\(^{48}\). To avoid deflection of the particle beam at the entrance to the multiplier, the latter has an additional electrode at the same potential as the first cascade. Nickel shields 1 and 2 protect the electric field in the region of the first cascades of the multiplier from distortions that might arise under the influence of the potential of the envelope.

The multiplier is placed in a metal envelope with a window; the construction of the latter makes it possible to connect the multiplier to one or another vacuum apparatus in which measurements are to be carried out—

*) Mekhov, author’s application No. 2730 of August 26, 1937.

...apparatus (for example, a mass spectrograph, a β-spectrograph, etc.). The general appearance of a multiplier with the envelope removed is shown in Fig. 146.

In such multipliers, which must allow periodic admission of air, for example when the specimen under investigation is replaced, emitters are used that are stable with respect to the action of air. Such emitters are appropriately treated alloys of silver, copper, aluminum, etc., with beryllium or magnesium. A substantial advantage of these emitters in comparison with emitters containing an alkali metal is their considerably lower susceptibility to fatigue.

Fig. 146. Allen multiplier with the envelope removed.

In a multiplier with such an emitter, intended for recording fast electrons, the window of the envelope is closed by nickel foil 0.02 mm thick. Fast electrons bombard the foil from the outside, causing emission from its inner side of secondary electrons, which are then amplified by the multiplier[^13]. Electron multipliers for direct counting of γ-quanta have an electrode system analogous to that described above. Gold or tantalum surfaces are used in them as cathodes.

In some cases, for example when recording ions in a mass spectrograph, it is necessary to place the multiplier in the region of action of a strong magnetic field. This field, acting on the electron streams in the multiplier, causes them to be defocused and reduces the sensitivity of the multiplier. Sometimes in such cases a photomultiplier is used, placed outside the magnetic field, and the scintillation is transmitted from the phosphor to the photocathode by quartz rods—light guides. This method, however, is not always applicable, since it is associated with a limitation of the resolving time by the duration of the phosphor afterglow; moreover, one has to put up with the comparatively large dark background of photomultipliers and, finally, the photomultiplier, the light guide, and the crystal have to be shielded...

to protect from light, which entails a number of additional inconveniences. It would be expedient to have a multiplier that could operate directly in a strong magnetic field. The design of such a multiplier is shown in Fig. 14b[^49].

A flat plate, the “rail” 1, at ground potential, runs along the entire multiplier. Flat emitters 2 are arranged opposite the “rail” and are fastened to an insulating rod 3 in such a way that the distance between each successive emitter and the “rail” decreases from the first cascade to the anode. The length of the working part of the emitters also decreases successively. Such a design makes it possible to obtain in the multiplier an electric field

Fig. 14b. Electrode system of a multiplier intended for operation in a strong magnetic field: 1—the “rail,” 2—emitters, 3—insulating rod, 4—window, 5—anode.

without sharp disturbances of uniformity. The supply voltage is distributed among the cascades by means of a voltage divider, which consists of 15 half-watt carbon resistors of 1 megohm each. The resistors are placed inside the multiplier. The magnetic field in which the multiplier is to operate is directed perpendicular to the drawing. The number of multiplier cascades is 15. The emitter is copper-beryllium with a 2% beryllium content in copper. The multiplier is intended for the registration of positive ions, for whose entry into its housing there is a window (4) covered with a mesh. Because the electric and magnetic fields in the multiplier are close to uniform, the trajectories of all secondary electrons between two neighboring cascades are close to one another in shape; as a result, on the one hand, good focusing of the electrons is ensured, and on the other, the spread in the transit times of electrons between two neighboring cascades in this multiplier is smaller than in multipliers with electrostatic focusing. Accordingly, the pulse duration in the multiplier described is smaller than in multipliers of other types and, according to the author’s calculations, is about \(1.3 \cdot 10^{-10}\) sec., while the pulse rise time lies between \(10^{-11}\) and \(10^{-10}\) sec. This multiplier also has the further advantage that the positive ions formed in the anode region, owing to the presence of a strong transverse electric field between the emitters,

and “rails” cannot penetrate to the first cascades and produce background pulses. This makes it possible to apply high voltages to the electrodes of the multiplier, up to 8500 V.

Multipliers of this type can operate in magnetic fields with field strengths from 250 to 1100 oersteds at voltages up to 8500 V.

In concluding the present paragraph, let us dwell on the circuit for connecting a photomultiplier and on the choice of its parameters. The supply of the photomultiplier is usually provided by high-voltage batteries or by a stabilized rectifier. The circuit for connecting a photomultiplier is shown in Fig. 15a. The voltage is distributed among the cascades by means of a voltage divider. The magnitude of the divider resistances

Fig. 15a. Circuit for connecting a photomultiplier.

is determined by the maximum value of the anode current at which the photomultiplier will operate. The current in the voltage divider must exceed the greatest anode current of the photomultiplier by not less than a factor of ten, so that when the latter changes there will be no redistribution of voltage among the cascades and no associated changes in the amplification factor. For reasons explained in the preceding paragraph, the voltage between the photocathode and the first cascade is usually chosen to be 3–4 times, and between the first and second cascades 2–2.5 times, greater than the remaining inter-cascade voltages. The voltage between the last cascade and the anode is also desirably made somewhat higher. The anode characteristic of a photomultiplier (Fig. 15b), expressing the dependence of the anode current on the voltage between the last cascade and the anode \(u_a\), at constant voltage on the remaining electrodes, reaches saturation at an anode voltage that is the larger, the greater the magnitude of the photomultiplier current. To avoid nonlinear distortions, it is necessary to choose the anode voltage so that the effective voltage between the last cascade and the anode, equal to the difference between the anode voltage and the voltage of the signal being taken off (Fig. 15b), does not go beyond the horizontal portion of the anode characteristic, which in most types of photomultipliers, at anode currents not exceeding a milliampere, extends from voltages somewhat smaller than the inter-cascade voltage \(u_k\) to a value of the po-

on the order of \(5\)—\(6\,u_k\). With a further increase in the anode voltage, the anode characteristic \(i_a=f(u_a)\) begins to fall slowly because some of the electrons from the next-to-last cascade are deflected to the anode, bypassing the last cascade. The considerable extent of the horizontal portion of the anode characteristic makes it possible to take large-amplitude signals from the anode load of the photomultiplier without the occurrence of nonlinear distortions.

In accordance with the prescribed law of voltage distribution between the electrodes of the multiplier, the ratios between the values of the individual resistances of the voltage divider are chosen. Most often the inter-cascade voltages, apart from the anode voltage, as well as the voltages between the photocathode and the first and second cascades, are chosen to be equal. In the electrode system of a multiplier in which all cascades are similar to one another, this corresponds, for the given supply voltage, to the optimum value of the gain factor. A violation of the uniformity of the voltage distribution between the cascades leads to impaired focusing in the multiplier; therefore the spread in the values of the divider resistances should not be large. Usually the resistances are selected equal to one another with an accuracy of up to 1—2%.

Fig. 156. Anode characteristic of the 931-A photomultiplier.

For carrying out quantitative measurements with a photomultiplier it is necessary to stabilize well the voltage supplying it. From expression (19) it is easy to obtain the dependence of fluctuations of the multiplier gain factor on fluctuations of the supply voltage:

\[ \frac{dM}{M}\simeq n\,\frac{du_k}{u_k}=n\,\frac{du}{u} \qquad (\text{for } u_k \ll u_m), \tag{20} \]

where \(u=u_0-u_a\), \(u_0\) is the total supply voltage.

Thus, in a multiplier with \(n\) stages, a change in the supply voltage by one percent causes a change in the gain factor by approximately \(n\) percent.

In order for the gain factor to remain constant to within \(1\)—\(1.5\%\), it is necessary to stabilize the voltage to an accuracy of up to \(0.1\%\). The dependence of the focusing and, consequently, of the gain factor of the multiplier on the uniformity of the voltage distribution over the stages can be used to reduce the effect of fluctuations of the supply voltage on the gain factor.

For this purpose the multiplier is connected according to the circuit shown in Fig. 16b, ⁵⁰. The voltage on one of the intermediate stages is supplied from a battery and, thus, the potential difference between this stage

Fig. 16. Dependence of the gain factor on voltage when replacing one of the sections of the battery voltage divider.

and the preceding stages is fixed. All the remaining stages are connected to the corresponding points of the voltage divider fed by the rectifier. At the nominal supply voltage, focusing in the region of the stage fed from the battery is somewhat disturbed, as a result of which the gain factor of the multiplier is \(10\)—\(20\%\) lower than the optimum. By an appropriate choice of the battery voltage and the resistance, it is possible to ensure that an increase or decrease of the gain factor due to a change in the supply voltage is compensated, respectively, by a worsening or improvement of the focusing in the region of the separately fed stage. The value of the resistance \(R\) and the battery voltage \(V\), which ensure stabilization of the gain factor, as well as the number of the stage to which the battery is to be connected, are different for different types of photomultipliers. Stabilization of this type is not very critical with respect to the choice of the values \(V\) and \(R\). In Fig. 16 a stabilization curve is given for the photomultiplier 5819, obtained at \(V = 67.5\ \text{V}\) and \(90\ \text{V}\) (dashed curve) and \(R = 1.25\ \text{M}\Omega\). In this case the battery is connected to the 6th stage.

When recording scintillations, the output signal consists of voltage pulses, which may reach 10 volts and more.

for durations of hundredths and thousandths of a microsecond. Owing to the small self-capacitance of the last stages of the photomultiplier, their potential, when such pulses are recorded, does not remain constant, but undergoes sharp step-like changes because the current through the divider does not have time to replenish the charge carried away from the emitter by the secondary electrons. To avoid this, the sections of the voltage divider supplying the last stages of the multiplier are shunted by capacitances of the order of 0.01–0.001 μF, as is shown in Fig. 15a.

Since the rise time of the pulse in the multiplier is very small (see § 4), the amplitude of the pulses at the output is determined not by the load resistance \(R_{\mathrm{n}}\), but by the output capacitance of the multiplier \(C_{\mathrm{out}}\) (except in cases where \(R_{\mathrm{n}}\) and \(C_{\mathrm{out}}\) are so small that \(R_{\mathrm{n}}C_{\mathrm{out}}\) is comparable with the rise time of the pulses in the multiplier). The resistance \(R_{\mathrm{n}}\) determines the discharge time of the capacitance \(C_{\mathrm{out}}\) and, consequently, the duration of the pulses obtained at the output of the multiplier. The choice of \(R_{\mathrm{n}}\) is determined by the conditions of the problem (counting rate) and by the apparatus used for amplification and registration of the photomultiplier pulses.

6. LUMINESCENT SUBSTANCES USED IN SCINTILLATION COUNTERS

A number of requirements are imposed on luminescent substances (phosphors) intended for use in a scintillation counter, arising from the conditions of their operation in the counter.

First of all, the spectral region of the phosphor emission must correspond to the region of maximum sensitivity of the multiplier photocathode. The phosphor must give up a considerable part of the energy lost in it by the particle in the form of light. The fraction of the energy absorbed by the phosphor that is converted by it into light is called the physical efficiency of the phosphor[^51]. Some of the photons produced during the passage of a particle may be absorbed in the bulk of the phosphor itself and not reach the photocathode of the multiplier. Therefore it is important that the luminescent substance be transparent to its own radiation. This is especially necessary when the counter is intended for recording penetrating radiation (gamma and beta rays, X rays). In these cases it is necessary to use luminescent crystals of large thickness in order to absorb an appreciable fraction of the particle energy, and the photons arising in the thickness of the crystal can emerge and reach the photocathode only when the crystal is transparent. (The ratio of the amount of light energy emitted by the phosphor to the amount of energy absorbed in it is called the technical efficiency of the phosphor. This quantity, for one and the same phosphor, may be different depending on the kind of exciter.) For recording radiation with high penetrating power it is also advantageous to use phosphors with a large

with density and high atomic number, since the larger these quantities are, the greater the amount of energy absorbed per unit path length of the particle.

Phosphors in which the scintillation intensity is proportional to the energy of the bombarding particles are of great interest. By using them, one can not only register particles, but also measure their energy.

Finally, a very important characteristic of a phosphor is the duration of individual scintillations. It has already been said above that the resolving power of the multiplier reaches a value of the order of \(0.5 \cdot 10^{-9}\) sec. In order to make use of such high inertia-free operation of the multiplier, which is in principle unattainable in ordinary ionization counters, it is necessary to have luminescent substances with a glow duration of the same order, or at least not greatly exceeding the duration of the pulses in the multiplier. Usually, for each particular case of application, the most suitable luminescent substance is chosen.

Let us briefly consider the characteristics of phosphors that are often used at the present time.

Zinc sulfide activated with silver or copper is used as a screen in the registration of \(\alpha\)-particles. The radiation of these phosphors lies in the blue-green region (see Table II on p. 400). The light output is approximately one photon for every 10 electron-volts of \(\alpha\)-particle energy, which corresponds to a physical efficiency of 28%. For large crystals of \(\mathrm{ZnS}\cdot\mathrm{Cu}\), the scintillation intensity is proportional to the energy of the \(\alpha\)-particles. Powdered and fine-crystalline \(\mathrm{ZnS}\cdot\mathrm{Ag}\), when excited by \(\alpha\)-particles of the same energy, gives flashes that differ very strongly in brightness.

Some authors\(^{52}\) explain the deviation from proportionality between the luminescence intensity and the energy of \(\alpha\)-particles for fine-crystalline \(\mathrm{ZnS}\cdot\mathrm{Ag}\) by different conditions of light scattering at different depths of penetration of the particles into the phosphor. The heavy nuclei produced in the decay of uranium cause in \(\mathrm{ZnS}\cdot\mathrm{Ag}\) scintillations that are considerably brighter than those from \(\alpha\)-particles, although their efficiency is approximately 7 times less than for \(\alpha\)-particles\(^{53}\). The scintillation duration*) in \(\mathrm{ZnS}\cdot\mathrm{Ag}\) is of the order of \(10^{-5}\) sec.

Crystals of \(\mathrm{ZnS}\cdot\mathrm{Ag}\) are transparent for layer thicknesses up to \(80\ \mathrm{mg}/\mathrm{cm}^2\), and \(\mathrm{ZnS}\cdot\mathrm{Cu}\) for thicknesses up to \(200\ \mathrm{mg}/\mathrm{cm}^2\).

Because of its opacity in layers thicker than \(80\ \mathrm{mg}/\mathrm{cm}^2\), zinc sulfide is not very effective for registering \(\beta\)- and \(\gamma\)-rays.

Cadmium sulfide activated with silver scintillates with red light, giving an output of about 20% both for \(\alpha\)-particles and for

*) By the duration of scintillations here and below is meant the time during which the scintillation intensity decreases by a factor of \(e\) from the maximum.

...electrons \(^{55}\). For \(\alpha\)-particles with energies less than \(0.1\) MeV, the scintillations of good CdS·Ag single crystals are proportional to the energy of the \(\alpha\)-particles with an accuracy of up to 5%, which makes it possible to measure the energy of \(\alpha\)-particles \(^{52,54}\). For energies greater than \(0.1\) MeV, the energy yield does not depend on the particle energy. The duration of cadmium sulfide scintillations is \(2 \cdot 10^{-4}\) sec. Very good transparency makes it possible to use crystals of considerable thickness.

Sodium iodide activated with thallium is especially effective for recording \(\gamma\)-rays owing to its high density \((3.67\ \text{g}/\text{cm}^3)\) and comparatively high mean atomic number.

The great hygroscopicity of NaI·Tl makes it necessary to protect it from the action of moisture contained in atmospheric air. NaI·Tl crystals have a high light yield and exhibit a linear dependence of the scintillation intensity on the energy of \(\beta\)- and \(\gamma\)-rays, and also for protons, deuterons \(^{56}\), and \(\alpha\)-particles \(^{57}\). The use of this substance for recording low-energy \(\alpha\)-particles and \(\beta\)-rays is limited by the necessity of keeping it in a quartz ampoule or covering it with an aluminum casing, the walls of which are opaque to these radiations.

The light yield decreases by a factor of 2–5 when the temperature of the crystal is changed from room temperature to \(345^\circ\text{C}\). The pulse duration is \(0.25\ \mu\text{sec}\). When the temperature is changed over the same interval, the pulse duration decreases approximately by a factor of 2 \(^{58}\).

Organic crystals—naphthalene, anthracene, phenanthrene, stilbene, and others—have become widely used in scintillation counters.

High efficiency for \(\beta\)-rays as well as for \(\gamma\)- and X-radiation, the comparative ease of obtaining large transparent crystals, the correspondence of the radiation spectrum to the region of maximum sensitivity of the cesium-antimony photocathode usually used in photomultipliers, and also the very short afterglow duration make these phosphors very convenient for use in scintillation counters.

Powdered naphthalene has a greater physical efficiency than single-crystalline naphthalene, but its technical efficiency is somewhat lower owing to the large scattering of light in the powder. There is evidence that pure naphthalene without an anthracene admixture gives no scintillations \(^{59}\), or, in any case, has very low efficiency. The presence in naphthalene of 1% anthracene as an impurity strongly increases the light yield and shifts the luminescence spectrum of naphthalene toward longer wavelengths. When a naphthalene crystal is cooled to \(-70^\circ\text{C}\), its efficiency increases by a factor of 1.4; when cooled to \(-180^\circ\), by a factor of 2.2 in comparison with the efficiency at room temperature \(^{60}\). Raising the temperature decreases the efficiency, bringing it prac-

tically to zero upon melting. When naphthalene solidifies, the efficiency is restored to half its initial value; however, if the solidified naphthalene is broken up, its physical efficiency is restored completely^[61].

The intensity of scintillations of anthracene, when the temperature is changed from \(+30^\circ\text{C}\) to \(-160^\circ\text{C}\), remains unchanged in measurements with the multiplier 1P28. Measurements with the multiplier 1P21, whose short-wavelength limit of sensitivity corresponds to a longer wavelength than in 1P28, showed an increase in the amplitudes of scintillation pulses upon cooling by approximately \(60\%\). This increase is apparently due to the shift of the anthracene luminescence spectrum upon cooling, to which the 1P21 multiplier responds^[62].

Fig. 17a. Circuit for shaping the pulse of a photomultiplier by means of a short-circuited delay line.

Scintillations of an anthracene crystal under excitation by \(\beta\)-rays are proportional to the energy of the \(\beta\)-particles in the interval from approximately \(0.125\) MeV to \(3.2\) MeV^[63,64].

The duration of scintillations in anthracene and other organic phosphors was determined by a number of researchers^[21–25,65–71]. In doing so, a method was used analogous to that applied for determining the duration of pulses in photomultipliers.

The authors of one of the works^[22] used, for determining the duration of scintillations, the method of shaping photomultiplier pulses by means of a short-circuited delay line (Fig. 17). The pulse from the multiplier and its reflection from the short-circuited tap of the coaxial cable, after rectification by a germanium detector, were fed to a measuring circuit consisting of a preamplifier, a discriminator, and a pulse counter. The addition of the initial and reflected pulses is illustrated in Fig. 17b. The time constant of the amplifier was chosen to be considerably greater than the pulse duration; therefore the amplitude of the pulse at the amplifier output is proportional to the charge, i.e. to the area bounded by the curve in Fig. 17b. It may be considered—

Fig. 17b. Addition of the direct and reflected pulses in the circuit of Fig. 17a.

a — output pulse of the multiplier

b — output pulse and reflected pulse

c — resultant pulse at the amplifier input

...that the decay of the pulse occurs according to the exponential law \(e^{-t/\tau}\), where \(\tau\) is the time during which the pulse amplitude decreases by a factor \(e\) from its peak value. To take into account the nonlinearities introduced by the rectifier and by the entire subsequent circuit, a coefficient \(n\) is introduced into the exponent; this coefficient can be determined from special measurements. Thus, the pulse shape at the output of the circuit has the form described by the function

\[ e^{-\frac{nt}{\tau}} . \tag{21} \]

The amplitude of the pulses at the output will not depend on the length of the short-circuited stub so long as this length is sufficiently large that the initial and reflected pulses are separated in time and do not overlap each other. In this case the magnitude of the signal is proportional to the area under curve \(a\) in Fig. 176, i.e., to the integral

\[ \int_0^\infty e^{-\frac{nt}{\tau}}\,dt=\frac{\tau}{n}. \tag{22} \]

When the length of the stub is decreased, the time required for the pulse to pass in the forward and reverse directions is shortened, and the reflected pulse begins to overlap the initial pulse. By decreasing the length of the stub, it is possible to arrange that the leading edge of the reflected pulse will arrive at the detector at the moment when the magnitude of the initial pulse has decreased by a factor \(e\) from its peak value. This time is obviously equal to \(\tau/n\). The resulting signal in this case must be proportional to the integral of expression (21), taken over the time from zero to \(\tau/n\):

\[ \int_0^{\frac{\tau}{n}} e^{-\frac{nt}{\tau}}\,dt = \frac{\tau}{n}\left(1-\frac{1}{e}\right). \tag{23} \]

The ratio of the pulse amplitudes at the output in the two cases described is

\[ 1-\frac{1}{e}=0.632 . \]

By measuring the number of pulses with a stub of great length and at some bias voltage on the discriminator, the bias is then reduced by a factor of \(0.632\), and such a length of the stub is selected that the number of pulses remains the same. This corresponds to a decrease...

the amplitudes of the pulses by a factor of 0.632. The duration of the pulse, \(\tau\), is found from the formula

\[ \tau = n \frac{2l}{v}, \tag{24} \]

where \(l\) is the length of the tap and \(v\) is the velocity of propagation of the pulse along the cable. The decay time of scintillations in anthracene at room temperature and upon excitation by \(\gamma\)-rays was found to be \(3.4 \cdot 10^{-8}\) sec.; in stilbene, \(1.3 \cdot 10^{-8}\) sec.^22 The character of the decay is exponential.^68 The decay time depends on the temperature of the phosphor. When an anthracene crystal is cooled from \(+20^\circ\) C to \(-268^\circ\) C, the decay time decreases from \(3.2 \cdot 10^{-8}\) sec. to \(0.6 \cdot 10^{-8}\) sec.^65 Scintillations in trans-stilbene at a temperature of \(+27^\circ\) C have a duration of \(6 \cdot 10^{-9}\) sec., and at a temperature of \(-196^\circ\) C about \(4 \cdot 10^{-9}\) sec.^21

The decay time may be different depending on the type of exciting radiation. Thus, upon excitation of naphthalene by \(\beta\)-rays, the decay time is approximately an order of magnitude smaller than upon excitation by \(\alpha\)-particles.^72

In the study of cosmic rays, whose penetrating power is extremely great, it is necessary to use crystals of large thickness. The preparation of large transparent crystals is associated with serious difficulties and is not always successful. Therefore, in studies of cosmic rays, transparent luminescent liquids are often used instead of crystalline phosphors.^73–85 Besides the possibility of preparing phosphors of practically any size with relative ease, liquid phosphors also have the advantage that the duration of scintillations in them is very small. Liquid scintillators have been obtained with luminescence durations down to \(2 \cdot 10^{-9}\) sec.

Liquid luminophors are usually prepared by dissolving solid organic and inorganic luminescent substances in various liquids. Benzene, xylene, toluene, diphenyloxide, phenyldicyclohexane, and many others are used as solvents. The efficiency of liquid luminophors is less than the efficiency of a pure solid phosphor, but not to the extent that would be expected from the low concentration of the dissolved phosphor. Thus, for example, the intensity of scintillations in a solution containing 5 g of terphenyl per liter of solvent (\(m\)-xylene) is only half as great as the intensity of scintillations in solid terphenyl. If the concentration of the phosphor in the solution increases, then the scintillation intensity at first, at low concentrations, increases in proportion to the concentration, and then, as the concentration is increased, begins to decrease. Such a dependence of the scintillation intensity on the concentration of the solution, as well as the scintillation intensity being greater than would be expected from the concentration of phosphor in the solution, is explained by the fact that in the processes of transformation of the energy of particles

light flashes involve solvent molecules[^76][^77]. Apparently, the particles bombarding the liquid initially excite the solvent molecules, and the latter transfer the excess energy to the molecules of the dissolved phosphor. At present a very large number of liquid phosphors are known (see, for example, [^78]). An idea of the scintillation properties of some of them can be obtained from the data of Table I, which gives the number of pulses per second registered by a photomultiplier, in front of whose photocathode a cuvette was placed, filled in turn with the liquids listed in the first column[^75].

Table I

Solution or liquid	Optimal concentration of the solution	Number of pulses in 1 sec.
$\alpha\alpha'$-dinaphthyl in benzene	Saturated	16 400
$n$-terphenyl in benzene	»	15 600
$m$-terphenyl in benzene	»	9 400
Phenyl-$\beta$-naphthylethylene in benzene	2.7	6 700
$\beta$-naphthylethylene in benzene	5.0	5 950
$\alpha$-naphthylamine in benzene	2.8	5 050
$\beta\beta'$-dinaphthyl in benzene	6.0	3 900
$\beta\beta'$-dinaphthylethane in benzene	Saturated	3 200
1,3,5-triphenylbenzene in benzene	»	2 500
$\beta$-naphthol in benzene	1.5	2 200
$\alpha$-naphthol in benzene	2.5	1 700
Naphthamine in benzene	Saturated	1 460
Anthracene in benzene	2.2	1 460
Benzene	—	910
Water (distilled)	—	620
Calcium tungstate (crystalline)	—	12 000
Anthracene (crystalline)	—	37 000

The capacity of the cuvette was 1 ml; the liquids were excited by a Co$^{60}$ $\gamma$-radiation source of intensity 1.5 millicuries, placed at a distance of 6 cm from the cuvette. The data in the table have been corrected for background and for the resolving time of the counter. For comparison, at the end of the table the number of pulses is given which arose under the same conditions when the cuvette was replaced by crystals of calcium tungstate and anthracene of the same dimensions. A convenient form of phosphors is represented by solid solutions of luminescent substances in polystyrene, lucite, paraplex, and other plastics[^86–^92]. Retaining the positive qualities of liquid phosphors, they at the same time possess mechanical strength and therefore, in ease of handling, are not inferior to crystalline phosphors.

Table II gives the characteristics of some frequently used phosphors[^148][^149].

Material	Emission spectrum (in Å)*	Absorption spectrum (crystal color)	Relative light yield for β-particles (light yield of anthracene taken as unity)**	Scintillation duration × 10⁸ sec.***	Dependence on energy [[unclear: visible ending “-ского”]] α
NaJ·Tl	4100 (800)	2930 2340 colorless	2,0	25	approximately linear
KJ·Tl	4100 (900)	2870 2360 colorless	0,5	100	approximately linear
CaJ·Tl	white	colorless	1,5	100	—
LiJ·Tl	blue-green	colorless	1,0	100	—
CdWO₄	5200 green	yellow (onset of absorption from 4500)	2,0	—	—
CaWO₄	4300 blue	colorless, absorption begins from 4000	1,0	600	—
ZnS·Ag	blue	colorless	2,0	1000 decay is non-exponential	approximately nonlinear

Table II

Sensitivity to monochromatic radiation, β	Sensitivity to monochromatic radiation, γ	Light yield per 1 MeV for various particles	Density (g/cm³)	Melting temperature (°C)	Note
linear	linear	$\beta/p = 1{,}0$	3,67	651	Hygroscopic; good crystals are readily obtained
linear	linear	$\beta/\alpha = 1{,}0$ $\beta/p = 1{,}0$	3,13	582	Good crystals are readily obtained
—	—	$\beta/p = 1{,}0$	4,50	621	Good crystals are readily obtained
—	—	—	4,06	446	Very hygroscopic
—	—	—	7,90	1325	Small crystals are readily obtained
—	—	—	6,06	1535	Small crystals are readily obtained
—	—	$\beta/\alpha = 1{,}0$	4,10	1850	Obtained only as a powder or in microcrystalline form

Material	Emission spectrum (in Å)*	Absorption spectrum (crystal color)	Relative light output for β-particles (anthracene light output taken as unity)**	Duration of scintillations × 10⁸ sec.***	Dependence on α-particle energy
Anthracene	4400 (60)	colorless, absorption beginning from 4050	1.0	3.0 ± 0.5 (300° K) 1.2 ± 0.2 (77° K)	nonlinear
Stilbene	4200 weak (360) 4080 strong 100	colorless	0.6	0.6–1.2	—
Phenanthrene	4100 (100) 4300 (100)	colorless	0.3	0.8	—
Diphenyl	3520 3710 3950 weak	colorless	0.6	1.6	—
Terphenyl	3900 4050 4300	colorless	0.65	1.2	—
Naphthalene	3450 (250)	colorless	0.25	6.0	—

*) In parentheses the width of the spectrum at an intensity level equal to [[unclear: continuation cut off]]
**) The values given have not been corrected for spectral sensitivity [[unclear: continuation cut off]]
***) By the duration of scintillation is understood the time during which [[unclear: continuation cut off]]

Continuation of Table II

Sensitivity to monochromatic radiation $\beta$	Sensitivity to monochromatic radiation $\gamma$	Light yield per 1 MeV for different particles	Density (g/cm³)	Melting temperature (°C)	Note
linear in the interval 125–1900 keV	nonlinear	$\beta/\rho = 2.0$ $\beta/\alpha = 8.0$	1.25	217
—	—	not constant	1.16	124	Good crystals are easily obtained
—	—	—	1.03	100	It is very difficult to obtain transparent crystals
—	—	—	1.00	52.5	Good crystals are easily obtained
—	—	$\beta/\alpha \approx 8.0$	1.23	213	Rough; good crystals are easily obtained
—	—	not constant	1.15	80	Summates. Good crystals are easily obtained

with $1/2$ of the maximum.

the photomultiplier sensitivity (5819).

of which the scintillation intensity decreases by a factor of $e$ from the maximum.

Solid luminescent solutions can be obtained either by polymerization of liquid phosphors86, 87, or by dissolving phosphors in a molten polymer88, or, finally, by melting a mixture of phosphor and powdered plastic under pressure89, 90. As an example, we shall describe the process of preparing a phosphor by the last of these methods90. Polystyrene powder is mixed with organic fluorescent agents—terphenyl, fluorene, or others. To shift the luminescence spectrum into the region of maximum sensitivity of the photomultiplier (the emission spectrum of terphenyl includes wavelengths of 3900 Å, 4050 Å, and 4300 Å, whereas most photomultipliers with semitransparent photocathodes on glass have a sensitivity maximum in the region of 4800 Å), it is advisable to add a small amount of diphenylhexatriene to the mixture. Typical compositions of the mixture are: 50 g of polystyrene powder, 1.5 g of terphenyl, and 10 mg of diphenylhexatriene, or 50 g of polystyrene powder, 5 g of fluorene, and 10 mg of diphenylhexatriene. A high purity of all the components being mixed is necessary. The mixture is thoroughly mixed, poured into a mold, and heated at first under a pressure of 50–150 kg/cm². The polystyrene gradually softens. When the mixture reaches a temperature of 90–105°C, the pressure is raised to 500–700 kg/cm² and heating is continued. If terphenyl is used, whose melting temperature is 212°C, then the maximum temperature to which the melt must be brought is 230°C; in the case of fluorene, the maximum temperature is 150–160°C. The melt is then slowly cooled under pressure. To avoid the occurrence of sharp temperature gradients, the mold must be wrapped in a layer of heat-insulating material. After cooling, the phosphor is ready for use.

The efficiency of a cylinder 4 cm long, made from a solid solution of p-terphenyl (5%) in polystyrene, determined from coincidence measurements using a 5819 photomultiplier, proved to be 23–28% for Co60 γ-rays. Phosphors containing anthracene and stilbene have lower efficiency.

7. OPERATION OF MULTIPLIERS IN COINCIDENCE CIRCUITS

The high resolving power of counters with multipliers makes it possible to use them successfully in various kinds of coincidence circuits. Circuits registering double, multiple, or delayed coincidences are used to eliminate the multiplier background, to study the half-life periods of short-lived radioactive substances, to determine the direction and velocity of particle motion, and so on.

In the work already mentioned9, in order to reduce the effect of photomultiplier background pulses, a simple differential coincidence circuit on crystal diodes was used, exploiting the nonlinearity

characteristics of the diodes. The circuit operates satisfactorily if the photomultiplier pulses are of the order of tenths of a volt.

In this circuit (Fig. 18, a) the anodes of two photomultipliers operating from one phosphor are connected together and connected to the negative pole of the diode, the other pole of which goes to the pulse recorder. The last stages of each of the multipliers, through two other diodes, also go to the pulse recorder. If a pulse arises in only one multiplier, then at the input of the recorder there will arrive simultaneously a pulse from the anode and, equal to it but opposite in sign, a pulse from the last stage. As a result the pulse will not be recorded. If, however, pulses arise simultaneously in two photomultipliers, then after passage through the diodes two positive pulses from the last emitters, \(a' + a' = 2a'\), will arrive at the measuring instrument, and (from the anodes connected together) a doubled negative pulse \(a''\). Owing to the nonlinearity of the diode characteristics, the doubled pulse from the photomultiplier anodes after passage through the diodes will be greater than the sum of two single pulses from the emitters. The difference \(a'' - 2a'\) (Fig. 18, b) is different from zero, and the indicator records a signal.

Fig. 18. a) Coincidence circuit using crystal diodes. b) To explain the operation of the circuit in Fig. 18, a.

Another coincidence circuit, also using crystal detectors, is shown in Fig. 19a \(^{24}\).

Here the photomultiplier currents flow through resistances \(R_1\) and \(R_2\). Approximately \(1/10\) of the current of each multiplier passes through diodes \(D_1\) and \(D_2\) and the resistance \(R_3\), from which the output voltage is taken. Resistances \(R_5\) and \(R_6\) serve to regulate the gain of the multipliers, while potentiometer \(R_4\) balances the drop

of the voltages across the resistances \(R_1\) and \(R_2\). In Fig. 19b are shown experimentally obtained curves of the output voltage \(V_g\) as a function of the currents in the resistances \(R_1\) and \(R_2\) in the static regime. The dependence of \(V_g\) on \(I_1\) and \(I_2\) retains its form also when the circuit operates in the pulse-registration regime.

Suppose that, in the absence of pulses in the photomultipliers, the currents \(I_1\) and \(I_2\) are equal to \(0.1\) mA. The voltage \(V_g\) is then equal to \(0.9\) V. If in one of the photomultipliers, for example \(L\)-1, a pulse arises, then the potential of point \(B\) (Fig. 19a) will fall and the current through diode \(D_1\) will decrease.

Fig. 19a. Coincidence circuit with crystal diodes, allowing the counting of two-, three-, and higher-fold coincidences.

Since, however, \(R_3 \gg R_2\), the decrease in the potential \(V_g\) will be insignificant (point \(y\) in Fig. 19b). If, on the other hand, pulses arise simultaneously in two photomultipliers, both diodes will be blocked at the same time and the potential \(V_g\) will become considerably smaller than the initial value (point \(z\) in Fig. 19b). By using a discriminator, it is easy to separate the coincident large pulses from the small pulses produced by each multiplier separately.

The magnitude of the amplitudes of the photomultiplier pulses capable of triggering the circuit is substantially affected by the parasitic capacitances shunting the resistances \(R_1\), \(R_2\), and \(R_3\). The resolving time of this circuit, according to the authors’ estimate, is \(0.15\ \mu\text{sec}\). In the authors’ opinion, with a corresponding reduction of the resistances entering into the circuit, the resolving time of the circuit can be reduced by a factor of 100 or more. With the aid of the described circuit, coincidences can be registered not only in two but also in a larger number of photomultipliers. For this purpose several branches (according to the number of multipliers), identical to the two shown in Fig. 19a, are connected into the circuit.

A coincidence circuit with high resolving power, operating into an oscilloscope, is shown in Fig. 20[^93]. Here the pulse from the first photomultiplier starts the triggered sweep and at the same time blanks the oscilloscope beam. The pulse from the second multiplier, after amplification, is applied to the vertical plates of the oscilloscope. In order that the sweep should begin somewhat earlier than the vertical deflection of the beam begins, a delay line is inserted in the channel circuit through which

Fig. 19b. To explain the operation of the circuit of Fig. 19a. The curves determine the relation of the currents \(I_1\) and \(I_2\), at which the output voltage remains constant.

the second pulse is transmitted. The oscilloscope screen is covered by a mask in which a rectangular window is cut. The oscilloscope beam is observed through the window only in the case when it is deflected by a pulse. The sweep line is covered by the mask.

Light from the image of the pulse on the screen is collected by a lens into an aperture in chamber \(G\), inside which a photomultiplier is placed, and produces in the latter current pulses which, after amplification, are recorded by a counter.

Background pulses of photomultiplier \(I\) start the sweep, part of whose light penetrates into the window of the mask and produces false pulses in photomultiplier \(A\). However, with a window width of \(1\) mm the pulse from the signal exceeds by a factor of \(3.5\) the pulses due to illumination of photomultiplier \(A\) by the false sweep or due to the intrinsic noise of the oscilloscope tube. To increase the sensitivity very much

it is desirable to reduce the background of multiplier \(A\) by cooling. When working with 1P21 photomultipliers with stilbene as the scintillator, with a window width \(B\) from 50 to 1 mm and a sweep speed of \(0.08\ \mu\text{s}\) per 2.5 cm, a resolving time, respectively, from \(1.6\cdot10^{-7}\) to \(3.2\cdot10^{-9}\) sec was achieved. The authors indicate that by increasing the sweep speed or decreasing the window width \(B\), the resolving time can be reduced by several more times.

At a background intensity of 1000 pulses per second in the first channel and 2000 pulses per second in the second, a source can be measured which gives only 0.2–1.0 pulse per second. In other works\({}^{94}\) a similar method is used for recording triple coincidences. The sweep and beam modulation are triggered in them by separate channels with separate photomultipliers. In such circuits the number of recorded background pulses is millions of times smaller than the number of background pulses in one photomultiplier.

Fig. 20. Coincidence circuit with high resolving power.

Some of the existing circuits make it possible to register coincident pulses separated by a time interval not exceeding, in order of magnitude, \(10^{-10}\) sec. One of such circuits is shown in Fig. 21, \(a\)\({}^{95}\). Here \(D_1\) and \(D_2\) are crystal diodes, \(C_1\) and \(C\) are capacitors of 100 micromicrofarads. The circuit has two inputs: \(A\) and \(Б\). If a pulse (of negative polarity) arrives only through channel \(A\), then capacitors \(C_1\) and \(C_2\) are charged to the same potential. At the output terminals \(B_1\) and \(B_2\), no potential difference arises in this case. A pulse that has arisen only in channel \(Б\) does not charge the capacitors, since it is not passed by the reverse-connected diodes. If, however, negative pulses arise simultaneously in both channels, then capacitor \(C_1\) is charged by the entire pulse, while pulses of the same polarity arrive at both plates of \(C_2\). As a result, capacitor \(C_2\) turns out to be ...

is charged to a lower potential than \(C_1\), and at the output of the circuit a potential difference arises between points \(B_1\) and \(B_2\). For convenience in further amplification of the signal, the diode \(D_2\) and capacitor \(C_2\) can be interchanged; then the output signal can be taken from the slider of a potentiometer \((R \simeq 10^6\ \Omega)\), connected between points \(B_1\) and \(B_2\). This modification of the circuit eliminates the need to use an amplifier with a differential input. To investigate the operation of the circuit, a delay line (a piece of coaxial cable) was inserted into one of the channels, and the number of coincidences was measured as a function of the delay time. The source of pulses was an electron multiplier excited by \(\gamma\)-radiation from \(\mathrm{Co}^{60}\). The corresponding curve is shown in Fig. 21,b, where the abscissa is the delay time, and the ordinate is the number of coincidences, in percent of the number of coincidences in the absence of delay. With a multiplier gain of at least \(1.6 \cdot 10^8\), the circuit registers pulses from single primary electrons if they are separated by a time interval not exceeding \(2.95 \cdot 10^{-10}\) sec.

Fig. 21. a) Coincidence circuit using crystal diodes with a resolving power of the order of \(10^{-10}\) sec. b) Dependence of the number of coincidences of pulses, simultaneously fed to both arms of the circuit of Fig. 21a, on the delay time in one of the channels.

8. COUNTING ALPHA PARTICLES

The features that must be taken into account in constructing alpha-particle counters are the short range of alpha particles in matter and their large specific ionization.

In a scintillation counter for alpha particles there is no need to use phosphor crystals of great thickness, since the penetration depth of an \(\alpha\)-particle into the phosphor is very small. Even the fastest \(\alpha\)-particles give up all their energy in the surface layer of the phosphor, only \(3\)—\(5\ \mathrm{mg}/\mathrm{cm}^2\) thick, and it is useless to make screens of greater thickness. Moreover, with increasing screen thickness

absorption of \(\gamma\)-rays, often emitted by the source together with \(\alpha\)-particles, is increased, which leads to an increase in the number of pulses not belonging to \(\alpha\)-particles, i.e., to an increase in the background. In those cases where this is possible, it is best to place the \(\alpha\)-particle source in the same volume as the phosphor and the multiplier, so that there are no barriers between the source and the phosphor. If, because of the operating conditions, this cannot be done and the multiplier with the phosphor has to be protected from external light by some screen, this screen must be made sufficiently thin and of such a material that \(\alpha\)-particles can penetrate through it. If the \(\alpha\)-particles bombard the phosphor from the side opposite the photocathode, then the phosphor must be transparent to its own radiation.

Most often, silver- or copper-activated zinc sulfide, as well as cadmium sulfide, are used as phosphors for scintillation \(\alpha\)-counters. Individual light flashes in silver-activated zinc sulfide for \(\alpha\)-particles of one and the same energy differ greatly in intensity. The flashes are more uniform in cadmium sulfide, but here too the spread of intensities lies within \(\pm 25\%\).

Fig. 22. Circuit of a scintillation counter for \(\alpha\)-particles.

A simple circuit for registering \(\alpha\)-particles by means of telephones or a mechanical counter is shown in Fig. 22\(^{96}\). The zinc-sulfide screen is applied to the bulb of a 931-A multiplier. The multiplier is powered from batteries at a voltage of 1100 V through a potentiometer, each section of which has a resistance of 10 megohms. The voltage on the multiplier is regulated by a variable resistance \(R = 10\) megohms connected in series. A crystal detector is used in the circuit. When switch \(K_2\) is open, the pulses from the multiplier, pro-

passing through the transformer, actuate the telephones \(T\) connected into its secondary winding. The impedance of the transformer must be sufficiently high that the voltage drop across the series-connected inductance of 60 millihenries is small in comparison with the voltage across the transformer.

The dark current of the multiplier creates in the telephones a background, which appears as a steady whistle. Against this background the sharp clicks from \(\alpha\)-particles are clearly audible. A rectifier connected in parallel with the transformer considerably improves the contrast between the background and the pulses from \(\alpha\)-particles.

The circuit makes it possible to measure the intensity of \(\alpha\)-rays with the aid of a microammeter. For this purpose the switch \(K_2\) is closed and the pulses from the multiplier charge the capacitance \(C\) (the distributed capacitance of the output of the multiplier and of the circuit with respect to ground), which then discharges through the instrument. The values of \(L\) and \(R\) are chosen so that the discharge of the capacitance takes place sufficiently slowly. The readings of the microammeter are proportional to the number of pulses.

In another type of scintillation counter, photomultipliers 931-A and 1P21 with a zinc-sulfide screen of blue

Fig. 23. Variant of an \(\alpha\)-particle counter circuit.

luminescence were used. The counting circuit consisted of an inverter, a discriminator, a second inverter, and a multivibrator (Fig. 23)\(^{97}\). The photomultiplier operated at a total voltage of 600 V, uniformly distributed among the stages. The load resistance of the photomultiplier was chosen equal to 20 megohms. The negative pulses from the photomultiplier change sign in the inverter and are applied to the grid of the discriminator. The discriminator bias is chosen so that the pulses of the dark current, considerably smaller in amplitude than the pulses from

α-particles are not passed by the discriminator. The third cascade again inverts the pulses, after which they are fed to the grid of the multivibrator.

A positive pulse arriving at the grid of the multivibrator brings it into operation, as a result of which capacitor \(C\), shunting the instrument, is charged to a definite potential. The time during which the capacitor is charged and, together with it, the value of the potential is determined by the magnitude of the grid resistance and the connected capacitance. Capacitor \(C\) is discharged through a resistance of \(25\,000\ \Omega\) and the microammeter. The time constant of the instrument circuit ensures proportionality of the current passing through the instrument to the number of pulses.

The bias on the grid of the discriminator was set so that the background did not exceed one pulse in 10 minutes. At each pulse the pointer of the microammeter is deflected by 1 division and then slowly returns to zero. The time constant of the instrument is equal to 18 seconds, so that one minute was quite sufficient for the pointer of the instrument to return to zero.

The probability that in the course of one minute more than one background pulse will arise, at an average number of pulses of 1 in 10 minutes, calculated from Poisson’s law, is only \(0.5\%\). This means that if the pointer of the instrument is deflected by more than one division, then this deflection must almost certainly be attributed to scintillations, and not to the background.

The probability of the occurrence of two or more pulses per minute is \(95\%\) if the average number of pulses is 4.74 per minute. If it is assumed that the efficiency of the counter is equal to \(30\%\), then a source sending into the window of the multiplier

\[ \frac{4.74}{0.3} \simeq 16 \]

α-particles per minute will give each subsequent pulse in the microammeter before the pointer has time to return to zero. Thus, a source of 16 α-particles per minute can be detected by the counter. The average value of the maximum readings for a source giving 16 α-particles per minute into the window of the multiplier is \(3.3 \pm 0.9\) microamperes.

The instrument provides a set of capacitances for the grid circuit of the multivibrator; by switching them it is possible to vary the sensitivity of the counter. The upper counting limit is 50,000 counts per minute.

The counter is only slightly sensitive to γ-rays. A source of \(10\ \mathrm{mg}\) of radium, brought directly up to the screen, did not cause an increase in the readings of the microammeter.

As was already stated, flashes in ZnS phosphor under excitation by α-particles of the same energy differ greatly in brightness. At the same time, however, it turns out that the total intensity of the flashes, measured by the steady photocurrent, is proportional to the energy of the α-particles, if coarse-crystalline ZnS is used \(^{52,54}\). Польз—

relying on this, one can measure the energy of α-particles. The proportionality between the energy and the intensity of scintillations is violated if the phosphor is taken in powder form, which, apparently, is explained by the different conditions of scattering of the luminescence excited at different depths by α-particles with different energies.

The spread of scintillation intensities from monochromatic α-rays in CdS single crystals is considerably smaller than in zinc sulfide, and lies within ±25%, while for very good CdS·Ag crystals it does not exceed 5%. Good proportionality between the energy of α-particles and the intensity of flashes makes it possible to use CdS·Ag crystals successfully for measuring the energy of α-particles up to 0.1 MeV. At higher energies a significant deviation from proportionality is observed.

Among other phosphors in which proportionality is observed between the mean intensity of flashes and the energy of α-particles, one may mention copper-activated zinc sulfide and natural transparent scheelite.

The scintillation intensity in a NaI·Tl crystal is proportional to the energy of α-particles only for energies exceeding 10 MeV^57.

Fig. 24. Dependence of the amplitudes of photomultiplier pulses on the energy of α-particles for counters with different crystals.
1—anthracene, 2—stilbene, 3—NaI·Tl.

Organic crystals—stilbene, anthracene—show a nonlinear dependence of scintillation intensity on α-particle energy (Fig. 24).

In direct counting of α-particles with a multiplier having copper–beryllium emitters, the counting efficiency is close to 100% and remains constant over a wide range of α-particle energies. Each α-particle causes the emission of about 10 secondary electrons from the surface of the copper–beryllium emitter. The method of registering protons and deuterons is essentially no different from that for α-particles of similar energies^98.

9. COUNTING ELECTRONS

Scintillation counters are successfully used for counting fast electrons. As luminescent substances, organic phosphors are usually employed—anthracene, stilbene, and others, from which large transparent crystals can be prepared comparatively easily. The light output of most organic phosphors is proportional to the energy of the electrons. This makes it possible to construct “scintillation spectrometers” for measuring the energy of β-particles. For this purpose a circuit with a differential pulse analyzer is used, which makes it possible to count pulses whose magnitude lies within a specified interval and thereby to determine the distribution of β-particles in energy.⁵⁹˒⁹⁹

In Fig. 25, a, b, c, and d are shown the magnitudes of pulses from scintillations in anthracene, stilbene, and NaI·Tl as functions of the energy of the recorded electrons. If the ordinate scale of curves a, b, and d is multiplied by \(6.73 \cdot 10^{-3}\), the same scale as in Fig. 24 is obtained. It is seen from the graphs that the characteristics of the organic crystals—anthracene and stilbene—are nonlinear for electrons with energies below 100 kev and linear for electron energies from 125 kev to 3.5 Mev.

In a scintillation counter with an anthracene crystal, for every 2.5 kev of energy lost by a β-particle in the crystal, one photoelectron is emitted by the photocathode of the multiplier. If it is assumed that the efficiency of the antimony-cesium photocathode is 10% (1 photoelectron for every 10 photons), then the efficiency of conversion of β-particle energy into light energy is 1–2%.

In studying β-spectra by means of scintillation methods, it should be borne in mind that some high-energy β-rays are scattered out of the phosphor, losing in it only part of their energy. To avoid the errors associated with this, one may split a large crystal in half and place the β-ray source between its two halves.¹⁰⁰ With sufficiently large crystal dimensions the absorption of β-rays in it will be complete. Such a method, however, is inapplicable in cases where the β-radiation is accompanied by strongly converting γ-rays, since in this case, in addition to β-rays, internal-conversion electrons will also be recorded. If a diaphragm is placed between the source and the crystal so that the β-rays can fall only on the bottom of a conical hole drilled in the crystal (Fig. 26), then complete absorption of the β-rays incident on the crystal will be ensured, while at the same time the registration of conversion electrons will be excluded.¹⁴⁷

Electron multipliers are also used for the direct counting of electrons. In this case the electron beam under investigation is directed directly onto the first emitter of the multiplier.

Fig. 25. Dependence of the amplitudes of photomultiplier pulses on the energy of β-particles.
a, b — anthracene; c — stilbene; d — NaJ·Tl.

a)
- Pulse magnitude (arbitrary units), curve 1
- Energy in keV, curve 1
- Energy in keV, curve 2
- Pulse magnitude (arbitrary units), curve 2

b)
- Number of pulses
- Electron energy in keV

c)
- Pulse magnitude (arbitrary units)
- Energy in keV

d)
- Pulse magnitude (relative units), curve 1
- Energy in keV, curve 1
- Energy in keV, curve 2
- Pulse magnitude (relative units), curve 2

Such a method is especially convenient in those cases where it is necessary to register electrons with relatively small (less than 100 kev) energy.

The efficiency, i.e., the ratio of the number of registered pulses (after subtraction of the background) to the number of primary electrons, was studied by Allen\[^47] with the aid of an electrostatic electron spectrometer (Fig. 27). The electrons, whose source was a heated tungsten filament, were accelerated by a voltage applied between the filament and target \(A\), then passed between the deflecting plates \(I\) and \(II\), were separated according to velocity, and through a diaphragm entered the multiplier. During the measurements the beam was alternately centered either on slit \(D\), or on another, larger slit \(E\), behind which there was a collector connected to the input of a direct-current amplifier. Knowing the relative transmission of slits \(D\) and \(E\) for electrons (it had been determined beforehand and proved to be independent of the electron energy) and measuring, with the aid of the direct-current amplifier, the current passing through slit \(E\), it was possible to determine the magnitude of the current passing through slit \(D\) into the multiplier. To determine the counting efficiency, the number of pulses per second registered by the counter was compared with the magnitude of the current entering the multiplier. The curves of Fig. 28 illustrate the counting efficiency (expressed as the number of counts per minute referred to unit current) as a function of electron energy. The departure of the curves into the region corresponding to an efficiency above 100% for electrons with energy 300 ev is explained by the insufficient (\(\pm 10\%\)) accuracy of the calibration of the slits. The decrease in efficiency with increasing electron energy may be explained by the fact that the relative number of secondary electrons with small velocities, emitted by the first emitter, decreases as the energy of the primary electrons increases. Electrons possessing large velocities, however, are poorly focused in the electrode system of the multiplier. This explains the increase in counting efficiency for fast electrons.  **Fig. 26.** Arrangement of the source of \(\beta\)-radiation and the shape of the crystal, ensuring complete absorption of the energy of \(\beta\)-rays in the crystal. \(1\) — source, \(2\) — diaphragm, \(3\) — crystal.  **Fig. 27.** Electrostatic electron spectrometer. <!-- source-page: 053 --> with increasing gain of the amplifier placed after the multiplier, which makes it possible to register a larger number of small pulses (see the upper curve in Fig. 28, for which the amplifier gain is twice that for the lower one). Fig. 29 illustrates the dependence of the number of counts on the voltage on the multiplier cascades. At a voltage of 450 V per cascade the number  Fig. 28. Dependence of the electron-counting efficiency of a multiplier with copper-beryllium emitters on electron energy. The pulses of the multiplier were amplified by an amplifier. The upper curve was taken at an amplifier gain twice as large as the lower one. of counts reaches its greatest value and thereafter does not change with increasing voltage. In experiments with a type 931-A multiplier with beryllium emitters, the electron-counting efficiency reached 23% at a voltage of 300 V per cascade. For electrons with an energy  Fig. 29. Dependence of the number of pulses on the voltage on the multiplier cascades. of 1 MeV the counting efficiency was 5–10%. Multipliers in which the first electrode is made of a heavy metal, for example tungsten or platinum, exhibit a greater electron-counting efficiency than multipliers with the first emitter made of a metal of low atomic number. In the multiplier described above for counting β-particles, in which a thin (0.02 mm) nickel plate operating “in transmission” served as the cathode,¹³ the counting efficiency for β-particles from a uranium source was 4.9%, and from a strontium source, 6.0%. <!-- source-page: 054 --> ## 10. REGISTRATION OF γ-RAYS The study of the distribution of pulse amplitudes from gamma scintillations showed that there is a continuous distribution of scintillation brightness from zero to some maximum value. This is consistent with the continuous energy distribution of Compton electrons arising in the phosphor when γ-rays pass through it. By determining the end point of the pulse distribution curve, corresponding to pulses of maximum magnitude, one can determine the energy of the γ-rays. This method is used in the already mentioned “scintillation spectrometer”[^59]. It gives, however, very unreliable results when nonmonochromatic γ-spectra are being studied. In this case it is convenient to make use of the circumstance that, in phosphors consisting of elements with high atomic number, under γ-irradiation a large number of photoelectrons arise, which should give maxima at the corresponding positions of the pulse-amplitude distribution curve[^102]. These maxima can be easily found when recording the scintillation-intensity distribution curve by means of a photomultiplier and a multichannel pulse-amplitude analyzer.  **Fig. 30.** Distribution of scintillation intensity in NaI·Tl; for Na²⁴ maximum 1 corresponds to a γ-ray energy of 1.4 MeV, maximum 2—2.8 MeV. Figure 30 shows the scintillation-intensity distribution curve in NaI·Tl for Na²⁴, recorded with an IP21 photomultiplier and a 10-channel pulse analyzer. The two maxima on the curve correspond to γ-ray energies of 1.4 MeV and 2.8 MeV.  **Fig. 31.** Calibration graph of a scintillation γ-spectrometer with a crystal. Figure 31 gives the calibration graph of the instrument, obtained using γ-sources with known spectra; <!-- source-page: 055 --> The accuracy of determining the energy of γ-rays by this method is 2–3%. The counting efficiency of γ-quanta when working with the NaI·Tl phosphor is of the order of 10%. This means that, on the average, each of 10 γ-quanta passing through the phosphor produces a recorded scintillation. With an anthracene crystal about 1 cm thick, an efficiency of 5 to 8% was achieved. When measuring γ-radiation of high intensity (of the order of 10 roentgens per hour and above), the use of a phosphor is limited by the output currents of the multiplier. In such cases the γ-rays may be directed directly onto the photomultiplier. Fig. 32 gives the dependence of the anode current of the 1P21 photomultiplier on the intensity of γ-rays for a radium source[^103]. The multiplier exhibits maximum sensitivity for γ-rays with an energy of the order of 65 effective kilovolts. In Fig. 33, *a* and *b*, are shown the directivity curves of the sensitivity of the photomultiplier when the γ-radiation source is moved along a circle of radius 40 cm in the plane containing the axis of the photomultiplier (Fig. 33, *a*), and in the plane perpendicular to this axis (Fig. 33, *b*).  **Fig. 32.** Dependence of the anode current of the 1P21 photomultiplier on the intensity of rays from a radium source acting directly on the photocathode of the photomultiplier.  **Fig. 33.** Directivity curves of the sensitivity of the 1P21 photomultiplier to γ-radiation. In those cases where it is necessary to have a radiation meter varying over wide limits, one may use a simple and convenient instrument, the circuit of which is shown in Fig. 34[^10]. The instrument includes a single-tube circuit with negative feedback, supplied from the same voltage source as ... <!-- source-page: 056 --> photomultiplier. The cathode resistance of the tube is provided by a resistor with a microammeter connected in series, slightly shunted by a voltage divider feeding the photomultiplier. A change in the intensity of the radiation acting on the photomultiplier changes, owing to the presence of feedback, the current in the resistance \(R_3\), and with it the voltage applied to the photomultiplier. When working with the 931-A photomultiplier and with the circuit parameters indicated in Fig. 34, a change in radiation intensity by \(10^4\) times causes  Fig. 34. Logarithmic radiation meter. Fig. 35. Calibration graph of the instrument according to the circuit of Fig. 34. a change in the voltage on the photomultiplier from 1150 to 300 V. At the same time the change in the anode current of the photomultiplier amounts to only 8%. The value of the voltage applied to the photomultiplier, measured by the instrument \(M\), serves as a measure of the radiation intensity. Fig. 35 presents the calibration graph of the instrument. The described circuit with a 931-A photomultiplier and an anthracene crystal of volume \(2\ \mathrm{cm}^3\) had a maximum sensitivity to \(\gamma\)-rays of 1 milliroentgen per hour and a full scale of \(10^4\) milliroentgens per hour. Scintillation counters are also used for recording X-radiation \(^{101,\ 103}\). With the aid of a NaI·Tl crystal measuring \(12 \times 6\ \mathrm{mm}\) and a 5819 photomultiplier, quanta of X-radiation with energies from 5 keV to 80 keV were recorded with an efficiency close to 100%. For X-rays with ener- <!-- source-page: 057 --> gies from 2 to 5 keV the efficiency was from 50 to 80%. In the energy interval from 2 keV to 1000 keV, proportionality was observed between the energy of the X-rays and the intensity of the scintillations. In the direct counting of X-rays and γ-quanta in multipliers, cathodes made of heavy metals are used, for example of gold  *Axis labels in the figure:* ordinate—“number of pulses per 1000 quanta”; abscissa—“wavelength,” Å. **Fig. 36.** Dependence of the number of pulses per each thousand quanta on the wavelength of X-rays in an electron multiplier with a tantalum cathode. or tantalum ^14, 105. The dependence of the counting efficiency on the wavelength of γ-radiation in a multiplier with a tantalum cathode is shown in Fig. 36. ## 11. COUNTING PHOTONS OF VISIBLE LIGHT A photomultiplier with an appropriate counting circuit can be used directly for counting photons of visible light. It is obvious that in this case there is no need to use any radiation converters. Rodionov and Oshorovich ^7 used, for counting light quanta, a Kubetskii secondary-electron tube with an antimony–cesium photocathode. To reduce the dark current, the authors placed the tube, mounted in a sealed fixture, in a Dewar vessel filled with liquid air, which had a transparent window for the passage of light. To protect against moisture, a dryer with a moisture absorbent was placed inside the fixture. Immediately near the multiplier there was a preamplifier, which amplified the voltage pulses arising at the output of the multiplier by approximately a factor of 10. The pulses were then amplified by the main amplifier (at medium frequencies by approximately a factor of 600). <!-- source-page: 058 --> consisting of two three-tube feedback loops. The entire setup, together with the power supplies, was carefully shielded. The output of the amplifier was connected through a scaling circuit to a mechanical counter and, for visual observations, to an oscillograph. The multiplier operated at a voltage of 1300 V and had a gain of \(2.8 \cdot 10^5\). The sensitivity of the photocathode at \(-180^\circ\text{C}\) was, for a wavelength \(\lambda = 5000\,\text{\AA}\), \(4.6 \cdot 10^{-2}\) coulombs per calorie, or \(9 \cdot 10^{-3}\) electrons per quantum. The temperature of the multiplier reached \(-183^\circ\text{C}\) after 1.5–2 hours of cooling. The background count at this temperature ranged from 12 to 45 pulses per minute. The standard luminous flux from the radiophosphor gave, according to the authors’ calculation, \(7 \cdot 10^4\) quanta per second (reduced to the wavelength \(\lambda = 5000\,\text{\AA}\)) in the window of the photomultiplier. This luminous flux produced 12,000 pulses per minute at the output of the device. Thus, the photon counter described reacted with one pulse to each \[ \frac{7 \cdot 10^4}{200} = 3500 \]

quanta of light. Measurements of the electronic yield of the photocathode at the same temperature, in the direct-current regime and at a considerably larger luminous flux, gave, within the experimental error, a value of the same order. The circuit described operated with sufficient stability.

For counting infrared photons, a photomultiplier with an oxygen–cesium photocathode and emitters was used, subjected to deep cooling \(^{107}\).

The sensitivity of the setup was determined by recording black-body radiation. To protect the cathode from heating, the heat rays were absorbed by a water filter placed between the photomultiplier and the light source.

From the spectral characteristic of the black-body radiation, given by Planck’s formula, the known absorption curve of water, and the actual spectral characteristic of the Ag · Cs\(_2\)O · Cs surface, it was found that in the region of maximum cathode sensitivity \((8000\,\text{\AA})\), the sensitivity of the counter was \(1/75\) electron per photon.

An electron multiplier with a copper–beryllium photocathode and emitters was used for counting photons in the ultraviolet region of the spectrum \(^{108}\).

12. REGISTRATION OF COSMIC-RAY PARTICLES. “CHERENKOV COUNTER”

In recent years scintillation counters have also begun to be used for the investigation of cosmic radiation. Since the intensity of cosmic radiation in the earth’s atmosphere is small, for its registration it is necessary to use scintillators of large area and, accordingly, photomultipliers with a large photocathode surface.

In one of the works\(^{109,110}\), in which the distribution of pulses from cosmic rays by amplitude was studied, the scintillating substance (naphthalene, anthracene) was poured in the form of a layer about \(0.5\) cm thick onto the bottom of a glass cuvette 11 cm in diameter; the photomultiplier was placed at a distance of 8 cm from the cuvette and was cooled with dry ice in order to reduce the background. The measurements were carried out at an altitude of 3500 m above sea level.

The authors investigated the relative efficiency (i.e., in the given case, the relative magnitude of the pulses) of a scintillation counter with various scintillators for cosmic rays.

Their data are given in Table III; the efficiency of naphthalene is taken as 100.

Table III

Scintillating substance	Efficiency
Crystals:
Naphthalene	100
Anthracene	250
\(\mathrm{CaF}_2\)	40
Liquids:
Anthracene in benzene	10
Naphthalene in benzene	15
Terphenyl in xylene	75

Investigation of the proportionality of pulse amplitudes to the energy of cosmic rays showed that such proportionality is preserved for \(\mu\)-mesons of cosmic rays up to hundreds of millions of electron-volts\(^{111}\).

The electron multiplier makes it possible to use the phenomenon discovered in 1934 by the Soviet physicist P. A. Cherenkov\(^{112–114}\) for the detection of fast charged particles and for determining their velocities\(^{115–119}\). The Cherenkov phenomenon consists in the appearance of radiation when charged particles pass through a substance with velocities exceeding the phase velocity of light in the given medium. This radiation has a sharply expressed directionality, and the angle of emission \(\theta\) is connected with the refractive index of the medium \(n\) and the ratio of the particle velocity to the velocity of light in vacuum by the relation

\[ \cos \theta = \frac{1}{\beta n}. \]

For water \(n = 1.33\), and for fast particles \((\beta \to 1)\) \(\theta = 37^\circ\). The successful experience of using the Cherenkov phenomenon for the registration of \(\mu\)-mesons

consisted in the following1. A cylindrical cuvette with silvered walls (to reduce light losses) was filled with distilled water. From above the cuvette was covered with black paper, and below there was a light-collecting cone enclosing the photocathode of an 11-stage multiplier of type 5311 (Fig. 37).

The pulses from the multiplier were fed to an amplifier with a small time constant, equal to \(3.2\cdot 10^{-8}\) sec, after which they went to a discriminator and a recording device. The small time constant of the amplifier ensured good separation of the recorded pulses from the background pulses of the photomultiplier. Indeed, owing to the fact that the probability of emission by the antimony-cesium photocathode of the multiplier of more than one thermoelectron in a time \(3.2\cdot 10^{-8}\) sec is very small, the background pulses due to thermoelectronic emission of the photocathode corresponded each to one electron from the photocathode, whereas pulses from scintillations were produced by a large number of photoelectrons.

Fig. 37. Scheme of the experiment for recording \(\mu\)-mesons with a Cherenkov counter.

To prove that the recorded pulses were due to cosmic particles, the counter described was connected into a coincidence circuit with a group of Geiger counters placed in the path of the particles. The total effective area of the Geiger counters was \(120\ \text{cm}^2\). The experiment consisted in counting coincidences of pulses in the multiplier and the Geiger counter. When the discriminator was shifted by \(5\ \text{V}\), the number of coincidences per minute (after subtracting random coincidences) was about 4, and when the discriminator was shifted by \(15\ \text{V}\), 2.54. For control, the multiplier was set in another position, so that its photocathode was at point \(K\) and the light of the Cherenkov radiation could not fall on it. In this case the number of coincidences was, respectively, 0.47 and 0.15 per minute and corresponded to the number of random coincidences, which could be calculated in advance. Distilled water was chosen as the medium in order to avoid recording scintillations of non-Cherenkov origin.

The decisive proof that the observed scintillations were caused by Cherenkov radiation is the detected av-

by the effect of the directionality of the radiation, which is in agreement with the properties of this radiation.

Very recently a Cherenkov counter was described,^119 in which a 7157 photomultiplier with a photocathode area of \(95 \text{ cm}^2\) was used, while the radiator was a lucite block \(6 \times 10 \times 20 \text{ cm}^3\) in size. The efficiency of cosmic-particle counting in this instrument was \(100\%\). The dependence of the limiting angle of radiation on the particle velocity makes possible a direct determination of particle velocities by means of Cherenkov counters. An important property of such a counter is also its extremely fast response \((\sim 10^{-9}\ \text{sec})\). The volume of the working liquid—in the case described, water—may be made sufficiently large in order to increase the counting efficiency. Still another advantage is its low sensitivity to \(\gamma\)-rays, which in a number of cases are present as background. In a certain energy interval a Cherenkov counter can also be used to separate the meson component from protons.

13. REGISTRATION OF NEUTRONS

The scintillation method is successfully used for the registration of both fast and slow neutrons.^120–124, 84, 125–136

Slow neutrons are most often registered by means of phosphors containing, in their composition or as an impurity, light elements—lithium, boron—with which neutrons enter into nuclear reactions accompanied by the emission of charged particles. The latter produce scintillations in the phosphor.

Quite suitable for the registration and counting of slow neutrons are^134–136 LiI crystals with an admixture of Tl or Tll. When a neutron is captured, the nucleus disintegrates into an \(\alpha\)-particle \((\mathrm{He}^4)\) and a triton \((\mathrm{H}^3)\), with a total energy of about \(4.79\) MeV, which produce a light flash in the crystal. The cross section for the neutron-capture reaction by a lithium nucleus is large (about \(900 \cdot 10^{-24}\ \text{cm}^2\)); therefore the efficiency of a counter with a LiI crystal for slow neutrons is also large. With a thickness of \(1\) cm the LiI · Tl crystal captures about \(60\%\) of all thermal neutrons passing through it. The neutron-counting efficiency of a counter with such a crystal is about \(50\%\). The luminescence color of LiI · Tl crystals is blue-green; the afterglow time is about \(1.2\ \mu\text{sec}\). The magnitude of the pulses in them is ten times smaller than the magnitude of the pulses in NaI · Tl under the action of ionizing particles of the same energy.

The pulses from the background of \(\gamma\)-rays and electrons are several times smaller than the pulses from \(\alpha\)-particles and tritons; therefore the latter can easily be selected by means of a discriminator.

Approximately the same efficiency for thermal neutrons was possessed by a counter in which a thin layer of powdered \(\mathrm{B}_2\mathrm{O}_3\), immersed in a solution of terphenyl in toluene, was used. Pow-

The $B_2O_3$ layer was prepared from pure colorless $B_2O_3$ glass, obtained by heating $H_3BO_3$ for several hours to $500^\circ$C. The use of thin layers was necessary in order to reduce the background from $\gamma$-rays. To reduce light losses due to reflection from the $B_2O_3$ layer, the refractive index of the liquid was chosen equal to the refractive index of $B_2O_3$.

For the detection of slow neutrons, use is also made of the $\gamma$-radiation arising as a result of the neutron-capture reaction by nuclei$^{122, 123, 137}$ when neutrons pass through boron, cadmium, samarium, or indium. A scintillation counter with an anthracene crystal or NaI·Tl is used to register the $\gamma$-radiation.

The counting efficiency with an anthracene counter when boron was used was 1%, and when cadmium and samarium were used it was 4%.

To register fast neutrons, hydrogen-containing crystalline or liquid phosphors are used. Passing through them, fast neutrons transfer their energy to recoil protons, which produce scintillations.

In one of the works, for the registration of fast neutrons, a solution of terphenyl in xylene was used (concentration—2 grams of terphenyl per liter of solution$^{138}$). The solution was poured into a brass tube 6 cm long and 4 cm in diameter, closed on one side (the photomultiplier side) by a quartz window and on the opposite side by a thin duralumin plate. The inner surface of the tube was lined with aluminum foil, which served as a light reflector. To reduce reflection of light from the quartz–photomultiplier-window boundary, mineral oil was poured between the quartz window and the surface of the photomultiplier, with a refractive index intermediate between those of quartz and the glass of the photomultiplier bulb.

The average efficiency of such a counter for neutrons with energies from 1 to 10 MeV proved to be 50%, and the distribution of pulse amplitudes corresponded to the energy spectrum of the neutrons.

It was found that changing the concentration of terphenyl in xylene within the range 0.5–5% produces no appreciable differences for neutrons with an energy of 14 MeV$^{139}$.

For detecting fast neutrons, organic crystals may be used, for example anthracene, in which recoil protons are produced under neutron irradiation$^{140, 141}$.

However, with a strong $\gamma$-ray background, the use of such counters is difficult, since organic crystals give more intense scintillations under the action of the electrons arising during $\gamma$-irradiation than under the action of the protons liberated by neutrons. For the same flux of neutrons and $\gamma$-rays of the same energy ($\sim 2.5$ MeV), incident on an anthracene crystal, and with zero bias on the discriminator, the number of neutron pulses exceeded the number of $\gamma$-ray pulses by only a factor of 2.2$^{132}$. With an increase

…of the bias on the discriminator, pulses from neutrons whose amplitude is smaller than the pulses from $\gamma$-rays cease to be counted, while the background from $\gamma$-rays is still registered. Thus, in the presence of a strong $\gamma$-ray background, counting neutrons by means of an anthracene crystal is practically impossible. In such cases one may use inorganic crystals (in which the intensities of the flashes from recoil protons and from electrons are approximately the same) in the form of a powder of small grains suspended in a hydrogen-containing liquid. Thus, a mixture consisting of small NaI · Tl crystals, each about 10 microns in size, suspended in $\alpha$-bromonaphthalene ($\mathrm{C}_{10}\mathrm{H}_{7}\mathrm{Br}_{2}$), with cuvette dimensions of $2\ \mathrm{cm}$ in height and $2\ \mathrm{cm}$ in diameter, made it possible to register neutrons with an energy of $2.5\ \mathrm{MeV}$ with an efficiency of 5% relative to the number of neutrons absorbed in the mixture. The background from $\gamma$-rays of the same intensity and energy as the neutrons amounted to only 10% of the number of pulses due to neutrons.

14. COUNTING POSITIVE IONS

Slow (up to $10\ \mathrm{keV}$) positive ions cannot be registered by means of luminescent crystals, since their range in the substance is extremely small and the intensity of the scintillations is very weak. Therefore, for counting slow ions the method of direct registration by an electron multiplier is used.

For most metallic surfaces the coefficient of secondary emission under bombardment by positive ions considerably exceeds unity. For ion energies from 0 to $4\ \mathrm{keV}$ the coefficient of secondary emission increases with the energy of the ions. For ion energies greater than $4\ \mathrm{keV}$ the coefficient of secondary emission remains constant. Figure 38 gives curves characterizing the dependence of the number of pulses on the energy of singly charged lithium ions for a 13-stage multiplier$^{2,142}$. Each curve was taken at a constant voltage $V_g$ on the discriminator (indicated on the graph). A counting rate of 375 pulses per minute (with a scale-of-256 counting factor) corresponded to 100-percent counting efficiency. The high efficiency of ion counting permits

Fig. 38. Dependence of the number of multiplier pulses on ion energy.

Fig. 39. Schematic of a mass spectrometer with an electron multiplier:
A — ion source, Б — magnet, В — electron multiplier.

Graph labels: ordinate — Anodic ion current in units; abscissa — Mass number; peak label — Cerium; annotation — $\times 40$.

Fig. 40. Mass spectrum of cerium obtained with the aid of an electron multiplier. On the right, a portion of the curve is shown separately, enlarged by a factor of 40 along the ordinate axis.

...successfully use the multiplier in mass spectrography. For this purpose the multiplier is mounted with a mass spectrograph, and its output is connected to a counting circuit or an electrometer. In measurements of the output current, the use of a multiplier has the advantage of a larger signal-to-noise ratio (as compared with amplifiers) when the ion current is less than \(10^{-13}\) a.

Figure 39 schematically shows a mass spectrometer with an 11-stage multiplier, by means of which the mass spectra of Rb, Nb, and \(\mathrm{Ce}^{143}\) were studied. Figure 40 shows the mass spectrum of cerium obtained in this way. In this case the multiplier current was measured by a direct-current amplifier. At the point corresponding to mass 140, this current is equal to \(10^{-8}\)–\(10^{-9}\) a. There are mass spectrometers in which the multiplying system is mounted as a single unit together with the device that separates the ions.

The use of electron multipliers for the registration of slow ions played an essential role in the development of the theory of \(\beta\)-decay\(^{144-146}\), making it possible, in particular, to measure the neutrino momentum directly.

References Cited

1. Z. Bay, Rev. Sci. Instr. 12, 127 (1941).
2. J. S. Allen, Proc. I. R. E. 38, 346 (1950).
3. G. A. Morton and J. A. Mitchell, RCA Rev. 9, 632 (1948).
4. A. Drigo, Nuovo Cim. 7, 267 (1950).
5. C. Taylor, Journ. phys. rad. 10, 255 (1949).
6. G. A. Morton, RCA Rev. 10, 525 (1949).
7. S. F. Rodionov and A. L. Shorvits, DAN 74, 461 (1950).
8. R. W. Engstrom, Journ. Opt. Soc. Am. 37, 420 (1947).
9. G. A. Morton and R. W. Robinson, Nucleonics 4, 25 (1949).
10. R. J. T. Herbert, Nucleonics 10, No. 8, 37 (1952).
11. T. N. Godfrey, F. B. Harrison and J. W. Kenfel, Phys. Rev. 84, 1248 (1951).
12. R. J. Lanter and R. W. Corwin, Rev. Sci. Instr. 23, 507 (1952).
13. R. Stone, Rev. Sci. Instr. 20, 935 (1949).
14. K. P. Meyer, E. Baldinger, P. Huber, Helv. Phys. Acta 23, 121 (1950).
15. K. P. Meyer, P. Huber, E. Baldinger, Helv. Phys. Acta 21, 188 (1948).
16. F. Sauter, Zeits. f. Naturforsch. 4a, 682 (1949).
17. R. C. Hoyt, Rev. Sci. Instr. 20, 178 (1948).
18. R. Westöö and T. Wiedling, Ark. Fys. T. I, Nr. 10, 269 (1949).
19. R. D. Sard, Journ. Appl. Phys. 17, 768 (1946).
20. J. S. Allen and T. C. Engelder, Rev. Sci. Instr. 22, 401 (1951).
21. J. M. R. F. Post and N. S. Schiren, Phys. Rev. 78, 80 (1950).
22. J. O. Elliot, S. H. Liebson, R. D. Meyers and C. F. Ravilious, Rev. Sci. Instr. 21, 631 (1950).
23. G. Papp, Rev. Sci. Instr. 19, 568 (1948).
24. W. C. Elmore, Rev. Sci. Instr. 21, 649 (1950).
25. A. Landby, Phys. Rev. 80, 477 (1950).
26. O. Martinson, P. Isaacs, H. Brown and J. W. Roderman, Phys. Rev. 79, 179 (1950).
27. R. F. Post, Nucleonics 10, No. 5, 46 (1952).

1. R. F. Post and L. G. Schiff, Phys. Rev. 80, 1113 (1950).
2. F. Seitz and D. W. Muller, Phys. Rev. 78, 605 (1950).
3. A. Sommer and W. E. Turk, Journ. Sci. Instr. 27, 5 (1950).
4. P. S. Farago, Nature 161, 60 (1948/1).
5. M. H. Greenblatt, M. W. Green, P. W. Davison, G. A. Morton, Nucleonics 10, No. 8, 44 (1952).
6. J. Winckler and K. Anderson, Rev. Sci. Instr. 23, 765 (1952).
7. L. Dunkelman and C. Lock, Journ. Opt. Soc. Am. 41, 802 (1951).
8. R. Batchelor, J. W. Smith and L. Blackmore, Nature 165, 688 (1950).
9. R. K. Swank and J. S. Moenich, Rev. Sci. Instr. 23, 503 (1952).
10. W. A. Schurkliff and R. C. Jones, Journ. Opt. Soc. Am. 39, 912 (1949).
11. R. L. Shipp, Rev. Sci. Instr. 23, 773 (1952).
12. D. O. Coldwell and J. R. Armstrong, Rev. Sci. Instr. 23, 508 (1952).
13. J. F. Raffe and E. J. Robins, Proc. Phys. Soc. B 65, 320 (1952).
14. C. Yu. Lukyanov, ZhTF 6, 1256 (1936).
15. F. H. Marshall, J. W. Coltman and L. P. Hunter, Rev. Sci. Instr. 18, 504 (1947).
16. L. Reiffel, C. A. Stone and A. R. Branner, Nucleonics 9, No. 6, 13 (1951).
17. ZhTF 22, 178 (1952).
18. Z. Bay, Nature 141, No. 3563, 284 (1938).
19. J. S. Allen, Phys. Rev. 55, 10 (1939).
20. J. S. Allen, Rev. Sci. Instr. 18, 739 (1947).
21. V. N. Lepeshinskaya, Izv. el.-prom. slabogo toka No. 12, 2 (1938).
22. L. G. Smith, Rev. Sci. Instr. 22, 166 (1951).
23. R. Scherr and J. B. Gerhart, Rev. Sci. Instr. 23, 770 (1952).
24. H. Kallmann, Phys. Rev. 75, 623 (1949).
25. J. Broser and H. Kallmann, Ann. d. Phys. 3, 317 (1948).
26. J. Broser and H. Kallmann, Ann. d. Phys. 4, 85 (1948).
27. J. Broser and H. Kallmann, Ann. d. Phys. 4, 61 (1948).
28. H. Kallmann and R. Warminsky, Ann. d. Phys. 4, 57 (1948).
29. Taylor, Remely, Jentschke and Kruger, Phys. Rev. 83, 169 (1951).
30. R. H. Lovberg, Phys. Rev. 84, 852 (1951).
31. W. C. Elmore and R. Hofstadter, Phys. Rev. 75, 203 (1949).
32. W. H. Jordan and P. R. Bell, Nucleonics 5, 30 (1949).
33. R. S. Classen and R. W. Boom, Phys. Rev. 75, 331 (1949).
34. L. Herforth and H. Kallmann, Ann. d. Phys. 4, 231 (1949).
35. G. G. Kelley and M. Goodrich, Phys. Rev. 77, 138 (1950).
36. J. F. Norton, Phys. Rev. 77, 759 (1950).
37. J. I. Hopkins, Phys. Rev. 77, 406 (1950).
38. S. H. Liebson and J. O. Elliot, Phys. Rev. 78, 65 (1950).
39. J. O. Elliot, S. H. Liebson and C. F. Ravilious, Phys. Rev. 79, 393 (1950).
40. R. F. Post, Phys. Rev. 79, 735 (1950).
41. G. B. Collins, Phys. Rev. 74, 1543 (1948).
42. C. F. Ravilious, J. O. Elliot and S. H. Liebson, Phys. Rev. 77, 851 (1950).
43. R. Hofstadter, S. H. Liebson and J. O. Elliot, Phys. Rev. 78, 81 (1950).
44. UFN 44, 447 (1951).
45. J. Broser, H. Kallmann and C. Reuver, Zeits. f. Naturforsch. 5a, 79 (1950).
46. G. T. Reynolds, Nucleonics 6, No. 5, 68 (1950).

1. E. H. Belcher, Nature 167, No. 4243, 314 (1951).
2. G. T. Reynolds, Harrison and Salbini, Phys. Rev. 78, 621 (1950).
3. H. Kallmann and M. Furst, Phys. Rev. 79, 857 (1950).
4. H. Kallmann and M. Furst, Phys. Rev. 81, 853 (1951).
5. H. Kallmann and M. Furst, Nucleonics 8, 32 (1951).
6. C. F. Ravilious, Rev. Sci. Instr. 23, 760 (1952).
7. S. A. Colgate, Rev. Sci. Instr. 22, 346 (1951).
8. G. T. Reynolds, Nucleonics 6, No. 5, 68 (1950).
9. M. Ageno, Phys. Rev. 79, 720 (1950).
10. C. F. Ravilious, J. O. Elliot and S. H. Liebson, Phys. Rev. 77, 851 (1950).
11. C. O. Muchlause and G. E. Thomas, Phys. Rev. 85, 926 (1952).
12. R. F. Post, Phys. Rev. 79, 735 (1950).
13. R. N. Klopper and M. L. Widenbeck, Rev. Sci. Instr. 23, 446 (1952).
14. W. S. Koski, Phys. Rev. 82, 230 (1951).
15. M. G. Schorr and F. L. Torney, Phys. Rev. 80, 474 (1950).
16. J. L. Horwood, G. G. Eichholz, Phys. Rev. 83, 886 (1951).
17. G. G. Eichholz and J. L. Horwood, Rev. Sci. Instr. 23, 305 (1952).
18. L. Pichat, Y. Lochin, Journ. chim. phys. 48, No. 5–6, 225 (1951).
19. M. G. Schorr and E. C. Farmer, Phys. Rev. 81, 891 (1951).
20. R. Hofstadter and J. A. McIntyre, Rev. Sci. Instr. 21, 52 (1950).
21. H. Kallmann and C. A. Accardo, Rev. Sci. Instr. 21, 48 (1950).
22. Z. Bay, Rev. Sci. Instr. 22, 397 (1951).
23. R. Scherr, Rev. Sci. Instr. 18, 10 (1947).
24. A. S. Goldin, E. R. Rohrer and R. J. Macklin, Rev. Sci. Instr. 21, 554 (1950).
25. W. Franzen, Phys. Rev. 79, 742 (1950).
26. J. S. Hopkins, Rev. Sci. Instr. 22, 29 (1951).
27. B. H. Kettele, Phys. Rev. 80, 7581 (1950).
28. R. E. Bell and R. L. Graham, Rev. Sci. Instr. 23, 301 (1952).
29. S. A. E. Johansson, Nature 165, 396 (1950).
30. J. D. Graves and G. E. Koch, Rev. Sci. Instr. 21, 304 (1950).
31. H. I. West, W. E. Meyrhof and R. Hofstadter, Phys. Rev. 81, 141 (1951).
32. M. Ter-Pogossian and W. B. Ittner, Rev. Sci. Instr. 22, 646 (1951).
33. J. S. Allen, Rev. Sci. Instr. 12, 484 (1941).
34. Z. Bay, Zeits. f. Physik 117, No. 3–4 (1941).
35. A. H. Morrisch, G. W. Williams and E. K. Darby, Rev. Sci. Instr. 21, 884 (1950).
36. D. D. and C. G. Montgomery, Phys. Rev. 82, 284 (1951).
37. UFN 45, 630 (1951).
38. F. X. Rose and T. Bowen, Phys. Rev. 82, 284 (1951).
39. P. A. Cherenkov, DAN 2, 451 (1934).
40. S. I. Vavilov, DAN 2, 457 (1934).
41. UFN 44, 443 (1951).
42. UFN 46, 413 (1952).
43. R. L. Mather, Phys. Rev. 84, 181 (1951).
44. J. Marshall, Phys. Rev. 81, No. 2 (1951).
45. J. R. Winckler, Phys. Rev. 85, 1054 (1952).
46. J. R. Winckler and K. Anderson, Rev. Sci. Instr. 23, 765 (1952).
47. J. Moulton and Scherwin, Rev. Sci. Instr. 20, No. 11 (1949).
48. H. B. Frey, Rev. Sci. Instr. 21, 886 (1950).
49. J. Broser, H. Kallmann and R. Warminsky, Research 2, 87 (1949).
50. J. C. Duckworth, A. W. Merrison and A. Whitteker, Nature 165, 69 (1950).
51. K. H. San and W. E. Shopp, Rev. Sci. Instr. 21, 395 (1950).

1. D. E. Alburger, Rev. Sci. Instr. 23, 765 (1952).
2. N. D. Malloy, F. L. Hereford, R. E. Garreta, B. S. Slope, Rev. Sci. Instr. 23, 769 (1952).
3. J. Schenk, Nucleonics 10, No. 8, 54 (1952).
4. R. F. Mozley and F. C. Shoemaker, Rev. Sci. Instr. 23, 569 (1952).
5. G. R. Keepin and R. H. Lovberg, Rev. Sci. Instr. 23, 483 (1952).
6. W. F. Hornyak, Rev. Sci. Instr. 23, 264 (1952).
7. G. L. Guernsey, G. R. Mott, B. K. Nelson and A. Roberts, Rev. Sci. Instr. 23, 476 (1952).
8. G. N. Harding, Nature 167, No. 4246, 437 (1951).
9. D. E. Alburger, Rev. Sci. Instr. 23, 769 (1952).
10. J. E. Draper, Rev. Sci. Instr. 22, 543 (1951).
11. R. Hofstadter, J. A. McIntyre, H. Roderick and H. Y. West, Phys. Rev. 82, 749 (1951).
12. W. Bernstein and A. W. Schardt, Bull. Am. Phys. Soc. 26, 15 (1951).
13. B. Hamermesh and V. Hummel, Phys. Rev. 83, 663 (1951).
14. P. S. Jastram, A. H. Benade, M. R. Cleland and A. L. Hughes, Phys. Rev. 81, 327 (1951).
15. C. E. Falk, H. L. Posa and C. L. Lune, Phys. Rev. 83, 176 (1951).
16. W. G. Cross, Phys. Rev. 83, 873 (1951).
17. G. E. Owen, J. H. Neiler and W. Ray, Phys. Rev. 83, 675 (1951).
18. A. H. Morrish and J. S. Allen, Phys. Rev. 74, 1260 (1948).
19. A. A. Choen, Phys. Rev. 63, 219 (1943).
20. J. S. Allen, Phys. Rev. 61, No. 11—12, 692 (1942).
21. J. S. Allen, Pamth and A. H. Morrisch, Phys. Rev. 75, 170 (1949).
22. Scherwin, Phys. Rev. 75, 1799 (1949).
23. P. R. Bell and J. M. Cassidy, Phys. Rev. 77, 301 (1950); 77, 409 (1950).
24. R. Hofstadter, Nucleonics 21, 294 (1950).
25. W. H. Jordan, Annual Rev. Nucl. Sci. 127 (1952).

1. visible footnote marker in the source text; footnote text is not present on this page. ↩