NEW INSTRUMENTS AND METHODS OF MEASUREMENT

COUNTERS WITH HIGH RESOLVING POWER

V. M. Kharitonov

In nuclear physics and in cosmic-ray physics, the measurement of very small time intervals is encountered in measuring the lifetimes of various particles; the measurement of very small time intervals could also be used for the direct determination of particle velocities. The limits within which the time intervals to be measured in various problems lie are very broad. Thus, for example, the lifetime of the meson is equal to 2.15 μsec; the lifetimes of individual kinds of varitrons are apparently of the order of \(5 \cdot 10^{-8}—10^{-7}\) sec. For the direct measurement of particle velocities it is necessary to measure time intervals of the order of \(10^{-8}—10^{-9}\) sec, with an accuracy of up to several ten-thousandths of a microsecond. For the measurement of such small time intervals, exclusively radio-engineering methods are used.

All the problems mentioned above reduce to the fact that we must measure the interval of time between the moments when a particle passes through two specified points in space. Every such problem is divided into two, to a certain extent independent, problems.

The first of them consists in obtaining, when a particle passes through a specified point in space, an electrical pulse whose beginning would coincide sufficiently accurately with the moment at which the particle passes through this point. More precisely, it is necessary to have a device registering the particles in which the fluctuations of the time interval between the moment of passage of the particle and the moment when the pulse at the output of the device reaches a specified magnitude would be smaller than the minimum time interval that we intend to measure. The second problem consists in measuring the time between the beginnings of two such pulses and is, properly speaking, purely a radio-engineering one.

The present article is a review, compiled from data published in the current literature, chiefly during the last-

... a year and a half. It is devoted only to the first of the indicated tasks—the consideration of the proposed recording devices from the point of view of speed of operation. In doing this we have tried to set out, as fully as possible, the factual experimental material and the methodology of the work, so that it may be clear what has actually been achieved in this direction and what may be expected on the basis of practical, and not merely theoretical, considerations.

1. DELAY OF PULSES IN A GEIGER–MÜLLER COUNTER

The question of the delay of pulses in Geiger–Müller counters arose in the very first experiments on determining the lifetime of cosmic-ray mesons. In the first work in which the existence of such a delay was established[^1], non-self-quenching Geiger–Müller counters of diameter \(1\ \mathrm{cm}\) and length 15 and \(20\ \mathrm{cm}\), filled with a mixture of 94% argon and 6% oxygen at total pressures of 9 and \(15\ \mathrm{cm}\) of mercury, respectively, were used for the registration of particles. Figure 1 shows a diagram of the apparatus. The idea of the experiment is as follows: a meson, slowed down in plate 1 and striking one of the counters \(A\), comes to rest in plate 2 and decays; the decay electron enters one of the counters of group \(B\). If we now measure the time interval between the beginnings of the corresponding pulses in counters \(A\) and \(B\), we thereby find the lifetime of the meson.

Fig. 1. Schematic of the apparatus on which the delay of pulses in Geiger–Müller counters was discovered.

Having carried out the corresponding experiments, the authors found that a noticeable number of delayed pulses is observed even without the lead plate 2, with delay times up to 5 microseconds. This delay is evidently introduced by the counters themselves, and therefore such counters are unsuitable for measuring small time intervals.

Let us consider first of all what accounts for the delay of discharges in Geiger–Müller counters of the usual construction. Such a counter consists of a thin-walled conducting cylinder along whose axis a thin metal wire is stretched (Fig. 2). The space

between the wire and the cylinder is filled with a working mixture, usually consisting of argon with an admixture of organic vapors. A potential difference is applied between the wire and the cylinder—positive to the wire, negative to the cylinder. When a charged particle passes through the counter, positive ions and free electrons are formed along its path; the latter, under the action of the electric field in the counter, begin to move in the direction of the wire. As they approach the wire, the electrons enter regions with ever greater field strength (the field strength varies as \(1/r\), where \(r\) is the distance from the center of the wire), and the energy acquired by an electron between two successive

Fig. 2. Circuit diagram for connecting a Geiger–Müller counter.

collisions with atoms of the working mixture increases all the time. The development of the discharge (avalanche) begins when the energy acquired by the electron between two successive collisions with atoms of the working mixture proves sufficient to ionize these atoms. Under the operating conditions of the counter (in order that a discharge, once arisen, should cease), the potential difference between the wire and the cylinder cannot be made such that avalanche development could begin at any point of the working space of the counter: avalanche development begins only immediately near the wire. Since usually the operating voltage of the counter is 10–20% higher than the threshold voltage, the radius of the region in which avalanche development can begin consequently exceeds the radius of the wire by only 10–20%. Thus, the greater part of the volume of such a counter serves only for the formation of primary electrons, and in order for a discharge to begin in the counter, this electron must move from the place where the ion was formed into the region adjacent to the wire. The time required for this is the minimum interval between the moment the particle enters the counter and the moment the development of the discharge in the counter begins, i.e. the minimum response time of the Geiger–Müller counter. In addition, the response time of the counter depends on the cutoff voltage at which the circuit operates, since a finite time is required for the pulse on the counter to reach a definite magnitude.

Let the diffusion velocity of the electrons be determined by the relation

\[ v = kE^{n}, \tag{1} \]

where \(k\) is the mobility, and \(E\) is the field strength in volts per centimeter:

\[ E=\frac{V}{\ln \frac{R}{r_0}}\,\frac{1}{r} \]

(\(V\) is the potential difference on the counter, \(R\) and \(r_0\) are the radii of the cathode and the wire, respectively, and \(r\) is the distance from the point under consideration to the axis of the counter). Substituting this value of \(E\) into the expression for the electron velocity and integrating \(\frac{1}{v}\) with respect to \(r\) from \(r\) to \(r_0\), we find the time of displacement of the electron from the point under consideration to the wire. If \(r_0 \ll r\), then, neglecting the second term, we obtain\(^2\):

\[ t=\frac{r^{n+1}}{(n+1)k}\left(\frac{\ln\left(\frac{R}{r_0}\right)}{V}\right)^n . \tag{2} \]

To determine the mobility of electrons in a Geiger–Müller counter, measurements were made\(^2\) of the delay of discharges in a counter 70 mm in diameter, filled with a mixture of argon (90 mm Hg) and alcohol (10 mm Hg), as a function of the distance from the wire at which the beam of cosmic particles passed, selected by two thin counters 12 mm in diameter (Fig. 3). For the delay time, a quadratic dependence on \(r\) was obtained, whence it follows that \(n\) in (1) and in (2) is equal to unity:

Fig. 3. Diagram of the apparatus for determining the mobility of electrons in a Geiger–Müller counter.

\[ v=kE;\qquad t=\frac{r^2}{2k}\cdot\frac{\ln\frac{R}{r_0}}{V}. \tag{3} \]

For the mobility \(k\) the authors found

\[ \frac{k}{p}=1.56\cdot 10^6\ \text{cm/sec per volt/cm} \tag{4} \]

at a pressure of 1 mm of mercury. This value was obtained from a delay of 2 μsec for a counter 70 mm in diameter; the accuracy of the measurements was \(\pm 10\%\), \(\pm 0.1\ \mu\text{sec}\). For a counter 20 mm in diameter at an operating voltage of 1000 V, formula (3) gives a delay of 0.2 μsec. Approximately such a delay was established by Rossi.

and Nereson in their work on determining the decay constant of the meson⁴ (approximately Gaussian distribution of delay times with rms delay of 0.2 μsec for counters 25 mm in diameter, filled with a mixture of argon (10 cm Hg) and alcohol (1 cm Hg), at an operating voltage 120 V above threshold). Formula (3) should be valid for values of \(\frac{E}{p}\) of the order of 0.6–2 volts/cm per 1 mm of pressure.

Shervin³ measured the mobility of electrons in a counter filled with a mixture of 92% argon and 8% amyl acetate at a total pressure of 100 mm Hg. A narrow beam of \(\beta\)-particles, selected by slits, was directed near the wire of one counter and at a specified distance from the wire of another, and the maximum drift time between the pulses from these two counters was measured; the accuracy of the delay measurement was of the order of \(10^{-8}\) seconds. For the radial velocity of the electrons Shervin obtained the following expression:

\[ v = k \left( \frac{E}{p} \right)^{\frac{1}{2}} \ \text{cm/sec}, \tag{5} \]

which corresponds to the formula for the delay time in the form

\[ t = \frac{2r^{\frac{3}{2}}}{3\left(\frac{k}{p}\right)} \cdot \left( \frac{\ln\left(\frac{R}{r_0}\right)}{V} \right)^{\frac{1}{2}} . \tag{6} \]

The constant \(k\) for the indicated mixture is equal to \(4.5 \cdot 10^6\), with \(E\) expressed in volts per cm and \(p\) in mm of mercury. The value of \(\frac{E}{p}\) is here of the same order as in the preceding work². For a small counter diameter, formulas (3) and (6) give noticeably different results: thus, for a counter diameter of 5 mm, a wire diameter of \(50\,\mu\), a mixture pressure of 300 mm Hg, and an operating voltage of 850 V, from (3) we obtain a delay time of \(2.8 \cdot 10^{-8}\) sec, and from (6), \(11 \cdot 10^{-8}\) sec. The difference in the results may be connected with the different composition of the working mixture.

The triggering delay of the circuit, in addition to the finite electron drift time, is also caused by the finite rise time of the pulse. The magnitude of this delay depends on the shape of the pulse front on the counter and on the circuit bias voltage.

The rise time of the pulse in a Geiger–Müller counter is determined by the velocity of propagation of the discharge along the wire. This velocity has been measured by a number of authors⁵–⁸. The values they obtained for the velocity of discharge propagation along the wire lie within the range from 4 to 40 cm/μsec and depend strongly on the composition of the working mixture and on the overvoltage on the counter. To measure the propagation velocity, counters of special design are used. The measurement scheme in works⁶˒⁷ is presented...

on Fig. 4. The counter is provided with two diaphragms, to which pulses from a square-wave generator with a frequency up to 30 Mc/s are applied, and the

Fig. 4. Schematic of the setup for measuring the propagation velocity of the discharge along the counter wire \(^{6,7}\).

Fig. 5. One of the curves obtained with the setup shown in Fig. 4.

number of discharges in the last section is counted. Figure 5 presents one of the curves obtained in \(^{7}\). At the maxima the propagation time of the charge

between the diaphragms is equal to an integral number of periods of the generator, and at the minima to a half-integral number of periods. Knowing the corresponding frequencies of the sine generator, it is easy to find the propagation velocity. In \(^{8}\) two methods were used: in the first of them a counter with a divided cathode was used (Fig. 6), and the time interval between

Fig. 6. Diagram of a counter with a divided cathode, used in \(^{8}\) for measuring the propagation time of the discharge along the filament.

the appearance of pulses in the end sections was measured; the maximum time interval corresponded to a pulse arising in one of the end sections and reaching the other, and made it possible to determine the propagation velocity. The length of the central section was \(30\ \mathrm{cm}\); the propagation time, depending on the composition of the working mixture, lay

Fig. 7. Diagram of the apparatus for measuring the propagation time of the charge along the filament of the counter, used in \(^{9}\). \(G\)—generator, \(4\ \mathrm{MHz}\), quartz-stabilized; \(P\)—scaling circuit; \(C\)—mechanical counter.

within the range from \(5.7\) to \(8.9\ \mu\mathrm{sec}\); when the content of the quenching admixture (ethyl alcohol) was increased from 6 to 30%, the propagation velocity fell from \(5.4\) to \(3.5 \cdot 10^{6}\ \mathrm{cm/sec}\) (at a total pressure of the mixture of \(10\ \mathrm{cm}\ \mathrm{Hg}\)); the diameter of the counter was \(1\ \mathrm{cm}\). In the second method, small platinum probes were used in the form of rings made of wire \(0.46\ \mathrm{mm}\) in diameter, with an internal ring diameter of \(1.4\ \mathrm{mm}\); the rings encircled the counter filament and were placed at a distance of \(28\ \mathrm{cm}\) from one another. In-

time intervals in both experiments were measured by means of the Rossi and Nereson circuit[^4].

In[^9] the velocity of charge propagation in a counter filled with pure hydrogen was measured. The experimental arrangement is shown in Fig. 7. The pulse from the first section of the counter unlocked circuit \(A\), which began to pass pulses from the generator to the scaling circuit; the generator frequency was \(4\) Mc, with quartz stabilization. The pulse from section III locked circuit \(A\). The number of pulses counted by the scaling circuit determined the time of propagation of the discharge through section II; moreover, for calculating the discharge-propagation velocity only those cases were taken which gave the maximum delay. The dimensions of the counter were as follows: diameter of the tungsten wire \(0.076\) mm, diameter of the copper cathode \(19.2\) mm, length of section II—\(1\) and \(2\) m. The following table gives the values of the discharge-propagation velocity obtained for two different fillings of the counter and at different overvoltages:

It is evident from the table that the propagation velocity of the discharge in a counter without a quenching additive is considerably higher and that, in addition, the value of the propagation velocity depends strongly on the overvoltage.

The dependence of the pulse-delay time on the overvoltage on the counter was also observed by Shervin[^3]: in one of his experiments, when the primary \(\beta\)-particles passed directly near the wire of the second counter, the delay time varied from \(1\) to \(20 \cdot 10^{-8}\) sec as the overvoltage on this counter was decreased from \(240\) to \(0\) V.

The shape of the pulses on the counter wire as a function of the discharge-propagation velocity and of the dimensions of the counter is calculated in[^10]. The spread in delay time associated with the finite rate of rise of the pulses is due to the dependence of the steepness of the pulse front on the point in the counter at which the pulse began. Thus, according to the calculations given in[^10], if there is a counter for which the propagation time of the pulse from one end to the other is \(1\) μsec, then a pulse beginning at one of the ends of the counter will require \(0.3\) μsec in order to reach \(0.1\) of its maximum value, whereas a pulse beginning in the middle of the counter will require only \(0.15\) μsec for this; the spread in

the delay time will thus be 0.15 μsec. The magnitude of this spread will obviously be the smaller, the lower the cutoff voltage of the circuit: if in the example given above the circuit is triggered by a voltage equal to 0.01 of the pulse amplitude, then the delay will be of the order of 0.04 μsec, and the spread only about 0.02 μsec.

Thus, in conclusion we may say that in the Geiger–Müller counters in common use at the present time the delay time of the pulses is 0.1–0.2 μsec. One may try to reduce this time by increasing the voltage at which the counter operates, and by reducing the diameter of the counter, as well as by selecting the best composition of the mixture. In this way one may hope to reduce the delay time to 0.02–0.04 μsec; in addition, it is possible to admit particles only through the central part of the counter and thereby further reduce the maximum delay time of the pulses. The limit for Geiger–Müller counters apparently lies around 0.02 μsec.

The diffusion of electrons to the filament and the finite velocity of propagation of discharges along the filament explain small delay times of the order of 0.1–0.3 μsec. Large delay times of the order of a microsecond and more, observed, for example, in ¹, are explained by the fact that the electrons formed during the passage of the primary particle through the counter adhere to atoms of the mixture and form negative ions. In this case, instead of the comparatively rapid motion of electrons, we have the slow diffusion of heavy ions, and several microseconds may pass before the negative ions enter regions with a large field strength: here the energy acquired by them between collisions proves sufficient for ionization, free electrons are formed, and a discharge begins in the counter. In ¹, the adhesion of electrons was favored by the presence of oxygen, which has a great affinity for electrons. The hypothesis of electron adhesion to oxygen atoms as the cause of large delays was confirmed by experiments ¹¹, ¹². In the work ¹¹, carried out with counters filled with pure oxygen at a pressure of 19 cm Hg, the mean pulse delay was of the order of \(10^{-5}\) sec.

Large delay times are sometimes also encountered in ordinary counters filled with argon with an admixture of organic vapors. Thus, for example, in the measurements ¹³ the number of cases with a delay exceeding 1 μsec was equal to one per 5000 discharges; apparently these cases should be explained by the adhesion of electrons to the atoms of gases making up the working mixture, or else by the presence of impurities in the counters. In interpreting experimental data, the indicated circumstance (the presence of large delays) can sometimes have substantial significance. In order to avoid these unpleasant cases of prolonged delay, one may place two counters directly one above the other and, for the moment when the particle passes through the counters, take the beginning of the first of the pulses.

2. CRYSTAL COUNTERS

The principle of operation of the crystal counter is described in detail in \({}^{10}\). The counting properties of crystals were investigated by Shpetter, Haub and Dzhenschke \({}^{21}\), who tested a number of substances without obtaining successful results. Successful results were obtained by Van Heerden \({}^{14}\) with silver chloride, independently of \({}^{21}\) (see UFN, vol. XXXI, p. 586, 1947). Van Heerden tested crystals of silver chloride cooled to the temperature of liquid nitrogen, and a number of other crystals, including diamond. He found counting properties only in specially prepared crystals of silver chloride.

The appearance of conductivity in a crystal when a fast charged particle passes through it is completely analogous to the phenomenon of photoconductivity and consists in the fact that, when passing through the crystal, the fast particle interacts with the electrons of the crystal and transfers some of them into the conduction band; under the action of the applied field these electrons begin to move, and a current pulse appears in the external circuit. The theoretical form of the pulses in a crystal counter and the dependence of the pulse magnitude on the trajectory of the particle are considered in \({}^{14}\) (see also \({}^{10}\)). The principal advantages of the crystal counter should be: the rapid rise of the pulse, determined by the electron collection time, and negligible dead time; since the mobility of electrons in the conduction band is several thousand cm/sec per volt/cm, and the operating voltage is of the order of 2–5 thousand volts/cm, the collection time should be of the order of \(10^{-8}\) sec.

Up to the present, the following crystals have been successfully investigated:

Silver chloride \({}^{14-19}\).
Thallium chloride \({}^{20}\).
Diamonds \({}^{21-26, 10}\).
Crystals with cadmium \({}^{28}\) (see also \({}^{53}\)).
Zinc sulphide \({}^{29}\).

Let us consider the experimental data available concerning the applicability of these crystals as counters.

a) Silver chloride, thallium chloride

In order that a silver chloride crystal may serve as a counter, it is subjected to the following treatment \({}^{17}\) (see also \({}^{10}\)): after the electrodes have been applied by platinization, the crystal is annealed for several hours at a temperature of \(400^\circ\)C, cooled over the course of a day to room temperature, and placed in a holder, and then slowly cooled to the temperature of liquid nitrogen; the electrodes may also be applied to the crystal after annealing, for example by reducing silver on the surface of the crystal with some developer.

However, even after the indicated treatment one cannot be certain that the crystal will operate satisfactorily as a counter.

The pulse front in some cases was less than \(1.5\cdot 10^{-7}\) sec and was determined by the parameters of the amplifier; in other cases it was more than one microsecond \(^{16,17}\). The following table gives data obtained in \(^{17}\) (silver chloride):

The saturation potential is, in \(^{16}\), 5000 volts/cm; in \(^{19}\), 2000 volts/cm. Useful pulses exceed the harmful background by from several times to several tens of times, depending on the ionizing power of the particles.

In \(^{14,16—18}\) the operation of silver-chloride crystals under irradiation by \(\gamma\)-rays was investigated; in \(^{18}\) it was established that, in a neutron beam, pulses 20 times larger than under irradiation by \(\gamma\)-rays are observed.

For satisfactory operation of a crystal counter it is apparently necessary that it be a sufficiently ideal crystal, without noticeable disturbances of the crystal lattice and without internal stresses; however, it cannot be asserted that this

is indeed necessary. From the table given above, it would seem that at considerable internal stresses the crystal operates poorly. On the other hand, Hofstadter[^20] investigated the counting properties of a polycrystal consisting of 40% thallium chloride and 60% thallium iodide and, under irradiation with $\gamma$-rays, found pulses exceeding the background by a factor of five (the pulse magnitude reached $0.2$ mV). The pulse front was $0.4$ μsec.

The role of space charge in a crystal counter was studied in [^18]. The authors established that after 10 thousand pulses the magnitude of the pulses in the counter falls noticeably, and after 50 thousand pulses amounts to only a few percent of the initial value; the space charge persists for up to 48 hours. If the voltage is removed from a polarized crystal and the electrodes are grounded, then pulses of the initial magnitude and of opposite polarity are observed; these gradually decrease until the space charge disappears; this cycle can be repeated many times.

In one of the most recent works with silver chloride, the results obtained were satisfactory and stable only in the case when the crystals were cooled with liquid nitrogen immediately after annealing and were not subjected to excessively strong irradiation; the saturation voltage was $2000$ volts/cm. Crystals kept for several days at room temperature required a considerably higher voltage for saturation. The authors indicate that the counting properties of the crystal can be improved by irradiation with $\gamma$-rays at low temperature and without a field; they explain this by the filling of local levels.

b) Diamonds

The ability of diamonds to “count” charged particles was established already in the first work of Shte[t]ter, Habra, and Dzhenchke[^21]. In this work, the possibility of registering $\alpha$-particles by alkali-halide crystals, zinc sulfide, and diamonds was investigated. In the alkali-halide crystals and in zinc sulfide no effect was found. In two examined diamond specimens $0.4$ mm thick, possessing good photoconductivity, pulses from individual $\alpha$-particles were observed in a field of $3000$ volts/cm. Despite the homogeneity of the $\alpha$-particles, the pulses differed greatly from one another; special experiments showed that this difference was not connected with a difference in path length from the place of formation of the electrons to the collecting electrode. Sometimes pulses larger than those from a single $\alpha$-particle were observed.

Vulgridzh et al.[^22] observed pulses from $\alpha$-particles in thin diamond flakes ($0.5$ mm) with the electrodes placed on one and on opposite sides of the flake at an operating voltage of about $2000$ volts/cm. Upon removal of the field they observed pulses of the opposite sign, caused by the accumulation of space charge. Of one hundred industrial

[[unclear: beginning of word]] diamonds of \(1/4\) carat, only two gave good results when irradiated with \(\gamma\)-rays ^{23}; in this case the pulses exceeded the background by a factor of 10. Testing about two hundred large diamonds weighing from one to two carats, of various quality, including precious ones ^{10}, showed that 30 of them counted, and no correspondence was established between the quality of the diamonds and their counting properties; the magnitude of the pulses depended on the specimen. (The paper does not state whether the diamonds were irradiated with \(\gamma\)-rays or with \(\alpha\)-particles.)

Friedman, Birks, and Gauvin ^{25}, and Hofstadter ^{26}, drew attention to the fact that the counting properties of diamonds with respect to \(\gamma\)-rays are directly connected with their internal structure. Counting properties are possessed by the so-called type 2, transparent in the ultraviolet down to 2250 Å and in the infrared region at \(8\,\mu\), and having a layered structure with layer thicknesses from 10 to \(100\,\mu\). Type 1, opaque to the far ultraviolet \((\lambda < 3000\ \text{Å})\) and to infrared radiation with \(\lambda = 8\,\mu\), is unsuitable for counters. According to Raman’s theory, type 1 has a microcrystalline structure consisting of two analogous modifications. At the same time, in ^{27} it is asserted that type 1 is the best of the known approximations to an ideal crystal, and that comparison of good crystals shows that X-ray diffraction in type 1 is several times less intense than in type 2; absorption in a divergent beam of X-rays is not observed at all in type 1 and is clearly noticeable in type 2. Crystals of type 2 are considerably rarer than those of type 1, but type 1 in pure form is also encountered very rarely. Real crystals most often represent a mixture of the two types.

As counters of \(\alpha\)-particles, crystals of both types are apparently suitable. In ^{22}, when irradiated with \(\alpha\)-particles, all diamonds counted. In ^{43} a special comparison was made of the counting properties of diamonds with respect to \(\alpha\)-particles with the type of crystal, determined by transparency in the ultraviolet and by X-ray diffraction ^{44}. The data obtained are given in the following table:

It is evident from the table that all opaque crystals and all type-I crystals count. In the author’s opinion, it is possible that conductivity appears in the transparent regions of crystals, which, generally speaking, constitute a mixture of both types. In the present work the pulses in different crystals differed greatly in magnitude, and even in different places of one and the same crystal very different pulses were obtained. This difference in the pulses may also be explained by the mixed structure of the crystals, but it may possibly also be explained by the nonuniform localization of foreign inclusions. Under irradiation by $\alpha$-particles from polonium (5 MeV) and with a system capacitance of $30\,\mu\mu\mathrm{F}$, the maximum pulse magnitude was $2700\,\mu\mathrm{V}$. Diamonds were not irradiated with $\beta$-particles. The steepness of the pulse front in diamonds has likewise not yet been measured.

c) Crystals with cadmium

Frerichs $^{28}$ found that in artificial cadmium crystals CdS, CdSe, CdTe, obtained by the reaction of cadmium vapors with $\mathrm{H}_2\mathrm{S}$, $\mathrm{H}_2\mathrm{Se}$, and $\mathrm{H}_2\mathrm{Te}$, respectively, conductivity can be excited not only by irradiation with light, but also by X-, $\gamma$-, $\alpha$-, and $\beta$-rays. In that work, not separate pulses were observed, but a general conductivity current produced by sufficiently intense irradiation of the crystals. In a note $^{53}$ that appeared quite recently, the observation in cadmium sulfide crystals of pulses from individual particles is reported (there references are also given to $^{54}$ and $^{55}$; concerning the mechanism of conductivity in cadmium crystals, see also note $^{56}$). All these reports are still preliminary.

d) Zinc sulfide

In $^{29}$ the testing of zinc sulfide crystals under irradiation with $\alpha$-particles is described.

The electrodes were arranged, as in $^{22}$, either on one and the same side or on different sides of the crystal. When the electrodes were arranged on one and the same side of the crystal and with a gap between them of $0.003\,\mathrm{cm}$, conductivity pulses were observed at a voltage between the electrodes of $30\,\mathrm{V}$; with plates on different sides of a crystal about $1\,\mathrm{mm}$ thick, at a voltage of $100\,\mathrm{V}$. Pulses were observed in all samples available to the author. The number of pulses and their height were smaller than in the best diamonds investigated by the same author.

The samples used in the work were natural cubic crystals of zinc blende (sphalerite). Spectrochemical analysis of one of the samples showed up to 0.1% of foreign inclusions, chiefly germanium. In the other samples there were impurities of the order of 0.01% of one or several of the following

elements: gallium, mercury, cadmium, magnesium. The author of the work notes that these crystals count, despite the fact that they are contaminated considerably more strongly than diamond crystals, of which some nevertheless did not count.

3. ELECTRON MULTIPLIERS

An electron multiplier for registering individual γ-quanta was used by Baye^30. Allen^31 used a multiplier for registering ions, α-particles, protons, and electrons. More detailed data concerning the construction of Allen’s multiplier have been published in ^32. For an analysis of the operation of the multiplier and the literature, see ^10 (see also ^33).

The possibility of using the multiplier as a fast-acting counter is determined by the magnitude of the spread in the time of passage of the electron from the first electrode to the last, or, in other words, by the width of the pulse produced by a single electron. This width is, in order of magnitude, \(10^{-9}\) sec. (see ^48). In addition, uncertainty in the magnitude of the delay may also result from unequal magnitudes of the pulses at the output of the multiplier.

The disadvantages of the multiplier as a counter are:

1) the relative complexity of manufacture and operation, which makes it difficult to use several multipliers at once;

2) the necessity of cooling the multiplier with dry ice or liquid air in order to increase the ratio of the useful-signal magnitude to the background;

3) different magnitudes of the pulses at the output of the multiplier (see ^10); a large spread in pulse magnitudes often leads to a considerable loss of intensity;

4) low efficiency with respect to fast electrons and γ-quanta (of the order of 0.5–1%).

To increase the efficiency of the multiplier, Coltman and Marshall^34 proposed directing the particles not directly onto the first electrode of the multiplier, but onto a fluorescent screen; then the task of the multiplier would be only to register scintillation flashes, the light from which can be focused by an optical system onto the first electrode of the multiplier. According to the authors’ data, an X-quantum with an energy greater than 25 keV can already be distinguished against the background of the multiplier; β-particles with an energy of 1.7 MeV give pulses 10 times greater than the background, and α-particles with an energy of 5 MeV—50 times greater than the background. For α-particles, protons, and electrons the efficiency of such a device is 100%; for γ-rays it decreases with increasing quantum energy because of the reduced absorption of γ-quanta. The phosphor of the counter can be made with boron and, in this way, a counter for slow neutrons can be obtained.

The efficiency of the phosphor—multiplier combination was also determined in [49]. Zinc sulfide was used as the phosphor. Multiplier 931-A was connected to the input of an ordinary amplifier with a gain of 500; the background of the multiplier was 300 pulses per minute. In the work the efficiency was determined for slow protons, deuterons, and $\alpha$-particles; it turned out that pulses from protons with an energy of 80 keV could be completely distinguished from the background; pulses from protons with energies down to 17 keV were recorded.

However, since we wish to have a fast counter, such a combination of a phosphor with a multiplier will not always operate sufficiently satisfactorily, since the phosphor decay time may be of the order of $10^{-6}$ sec. (see Section 5).

4. CHERENKOV COUNTERS OF FAST PARTICLES

A number of authors have proposed using the Cherenkov effect for the registration of fast particles. For this purpose the flux of particles under investigation must be passed through some optically dense transparent substance, for example Lucite or Plexiglas.

The angle $\theta$ at which coherent radiation is emitted is determined by the relation

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

where $n$ is the refractive index of the medium; the intensity of the radiation of a given frequency is proportional to $\sin^2\theta$.

The possibility of using Cherenkov radiation for the registration of individual fast particles was first pointed out by Getting [35]. According to Getting’s calculations, 212 photons in the near-ultraviolet region, for which Lucite is quite transparent, should be emitted per 1 cm of path in Lucite. For a path length in Lucite of 20 cm this gives 4000 photons. If, with the aid of a suitable optical system, they are collected on the electrode of a photomultiplier, then with a multiplier efficiency of 1.2% (factory data for the RCA 931-A multiplier) and a gain of $10^6$ we obtain at the output a pulse with a charge of $8 \cdot 10^{-11}$ coulomb. With an output capacitance of 20 cm this will give a voltage pulse of 0.4 V, which can be registered in the usual way.

The photon collection time is determined by the length of the path traversed by them and will be $(5—10)\cdot 10^{-10}$ sec. The total duration of the leading edge of the pulse after the multiplier will be $10^{-9}$ sec. According to Getting’s calculations, the multiplier background should be no more than 0.3—0.4%.

The first experimental attempt to verify these calculations was undertaken by Jelley [36]. Cosmic particles passed through a Geiger–Müller counter and a Lucite rod. During 4500 hours of operation of the instrument no pulses were found that could be attributed to Cherenkov radiation.

In Fig. 8 a diagram is shown of Dike’s second series of experiments. These experiments differ from those of the first series in the focusing of the Cherenkov radiation from lucite, and also in that artificial \(\beta\)-particles were used in them. A lead block with an aperture served as a collimator. In the control experiments a shutter made of blackened cardboard was placed between the lens and the photomultiplier. The results of Dike’s second series of experiments are presented in Fig. 9.

Fig. 8. Diagram of the apparatus for checking the possibility of using Cherenkov radiation for particle counting.

Labels in the diagram: trajectory of a fast electron; lead; \(\beta\)-rays from betatron; lens; lucite rod; Cherenkov radiation; photomultiplier; 1P28.

In this graph (curve \(A\)) the number of pulses (vertical scale) greater than a given magnitude (horizontal scale) is plotted.

Curve \(B\) is obtained from \(A\) by subtracting the background of the multiplier, obtained with the betatron switched off; curve \(C\) is obtained from \(B\) by subtracting the background from X-rays, obtained in control experiments with the cardboard shutter. Curve \(C\) corresponds to the energy spectrum of electrons generated in lead by the bremsstrahlung of electrons with an initial energy of 20 MeV. The magnitude of the largest pulse corresponds to approximately 5 photoelectrons, which is 4 times less than the calculated maximum if one uses the manufacturer’s data for the efficiency of the photomultiplier. In Dike’s opinion, his results agree with the supposition that the corresponding pulses were produced by Cherenkov radiation. The author also considers that, although from geometrical considerations it is unlikely that fluorescence played a noticeable role—

Fig. 9. Results obtained with the apparatus shown in Fig. 8.
\(A\)—total number of pulses, \(B\)—total number of pulses after subtraction of the dark background, \(C\)—photonic pulses (total number of pulses minus dark background, minus background from X-radiation). Circles—data obtained from experiments with a lower intensity of irradiation.

Axis labels in the graph: vertical—number of pulses exceeding the corresponding value; horizontal—pulse magnitude.

...an important role; however, it cannot be asserted that it is entirely insignificant.

The possibility of detecting the Cherenkov radiation of cosmic particles was also tested by Weiss and Andersen[^37]. A special Geiger–Müller counter, sensitive to ultraviolet radiation in the range 2000–3000 Å, was placed in a vessel of water, which served as the medium in which the radiation arose (Fig. 10). In control experiments the water was replaced by a 1% solution of hydroquinone, opaque to ultraviolet. The efficiency of the counter was \(5 \cdot 10^{-3}\). In pure water the number of counts per minute was 249; in the hydroquinone solution this number fell to 219. The authors of this work also point out that attention must be paid to the possible role of radiation from excited atoms.

Labels in Fig. 10: Counter with a mesh cathode of glass transparent to ultraviolet. Pure water or water with an ultraviolet absorber.

Fig. 10. Schematic of an apparatus for detecting the Cherenkov radiation of cosmic particles.

Furry[^38] proposed using measurements of the intensity of Cherenkov radiation directly to determine the velocity of cosmic particles. So far, however, the possibility of using Cherenkov radiation for the registration of individual fast particles requires further investigation.

5. SCINTILLATION COUNTERS

The idea of a scintillation counter is that fast particles are registered by flashes of scintillation, amplified by a photomultiplier (see Section 3). The disadvantage of ordinary inorganic phosphors, such as zinc sulfide and others, is that they are opaque to their own radiation, and therefore only radiation from the surface layer can reach the receiver; thus only an insignificant part of the energy of the fast particle, converted into fluorescence energy, is used.

However, some organic phosphors, in particular naphthalene, are quite transparent to their own radiation[^39][^40][^41]. Because of this it is possible to obtain very large pulses upon absorption of \(\beta\)-particles and \(\gamma\)-quanta. In order that pulses caused by slow electrons should not be masked by the background of the multiplier, the latter must be cooled; when the multiplier is cooled with dry ice to \(-40^\circ\)C, the background becomes sufficiently weak. It was established that scintillation pulses in naphthalene are very short, considerably shorter than in other commonly used phosphors. On the other hand, according to[^39] and[^41] naphthalene apparently is not sensitive to \(\alpha\)-particles.

For work with a naphthalene counter, the standard multiplier RCA 931-A proved quite suitable. The leading edge of the pulses was shorter than 0.1 μsec. If a naphthalene block \(1/2\) inch thick covers the entire sensitive area of the multiplier, then the efficiency of such a device for \(\gamma\)-rays is 20%.

To eliminate the background, the naphthalene block may be placed between two multipliers connected in a coincidence circuit \({}^{39}\). Satisfactory results are then obtained even at room temperature. The energy of \(\beta\)- and \(\gamma\)-rays can be determined from the magnitude of the pulses.

R. Moon \({}^{42}\) investigated a whole series of inorganic phosphors in the form of crystals. Selected 1P28 and 1P21 multipliers cooled with dry ice were used to record the scintillations. At the anode load of the multiplier (10 thousand cm) pulses up to 50 mV were obtained; pulses of less than 1 mV were not recorded. The pulse shape in this work was apparently determined by the parameters of the circuit rather than by the properties of the phosphors: the rise of the pulses ended in 0.5 μsec, and the duration was of the order of 1 μsec. Some crystals scintillate even without irradiation (for example, pure CaF\(_2\) crystals, both natural and artificial). When these crystals are irradiated with ultraviolet light, visible phosphorescence is observed, and on the following day they still give up to 200 pulses per second; on cooling this number decreases to 20. Crystals exposed in this way give thermal luminescence when heated to \(100^\circ\)C; with prolonged heating the crystals “burn out,” and if the burned-out crystal is cooled to room temperature, spontaneous flashes are no longer observed. Below is a table of the substances tested by Moon.

The best substance proved to be scheelite—at the same weight it is three times more effective than naphthalene. Kalman tested calcium tungstate but detected no pulses; this is probably explained by the fact that he used powder rather than crystals.

A whole series of organic substances was also tested by various authors. For work with the 1P21 multiplier, anthracene proved even more convenient than naphthalene \({}^{45}\): \(\gamma\)-rays from Co\({}^{60}\) give three times larger pulses than with naphthalene; a polonium-beryllium neutron source gives pulses five times larger and an intensity five times greater than with naphthalene. Special investigations with absorption in lead and cadmium showed that these pulses are caused by fast neutrons; the efficiency of such a counter for fast neutrons is estimated at 10–15%.

In order for a scintillation counter to be usable as a fast-acting one, it is necessary that within a short interval of time after the passage of the particle and the excitation of the phosphor a noticeable number of photons should be emitted—then the pulse at the multiplier output will have a sufficiently steep leading edge, and it will be possible

will register small time intervals between two pulses. The number of photons emitted by the phosphor during a given small initial interval of time is determined by the burn-out time of the phosphor; the change in the amount of light energy emitted by the phosphor after the beginning of emission is determined by the exponential law of decay:

Counting properties of inorganic phosphors

\[ I = I_0 e^{-t/\tau}, \]

where $\tau$ is the burn-out time of the phosphor. For the majority of inorganic phosphors the burn-out time is of the order of $0.1$–$1$ μsec.

In$^{46}$ the burn-out time of organic phosphors—naphthalene, anthracene, and phenanthrene—was measured. In the measurements the multiplier output was connected directly to the deflecting plates of a micro-oscillograph (see$^{47}$); oscillations from a standard generator with a frequency of 130 Mc/s were used as time marks.

When observing without a phosphor and without an irradiator at room temperature, small pulses were detected with a front duration of about $2 \cdot 10^{-9}$ sec, apparently corresponding to the release of one (or several) electrons from the first electrode of the multiplier; the observed duration of the front proved to be considerably

greater than the value \(6\cdot 10^{-10}\) sec calculated by Sard\({}^{48}\). It is possible that this comparatively slow rise is due to constants of the output circuit of the multiplier, as is evidently indicated by the damped oscillations with a frequency of 200 Mc/s accompanying each such pulse.

When cooled with liquid nitrogen, such pulses (without a phosphor) were observed only when the multiplier was irradiated.

The following table gives the burn-out times of the phosphors tested:

The complete picture of scintillation is as follows: an electron with an energy of 1 MeV, passing through any of the phosphors tested, gives enough light to liberate several (of the order of ten) electrons from the photocathode. This emission occurs within an interval of \(2\cdot 10^{-9}\) sec. Then the amount of emitted energy changes according to the decay law given above, in accordance with the value of the burn-out time.

The experiments described also showed that commercial naphthalene and carefully purified naphthalene have \(\tau\) of the same order.

6. PLANE-PARALLEL COUNTER

The idea of a plane-parallel counter is that the region of possible avalanche development in a Geiger–Müller counter is extended over the entire volume of the counter; such a counter design would make it possible to avoid the delay of pulses associated with the drift of electrons to the counter wire.

In order for an avalanche to be able to begin at any point in the counter volume, it is necessary that the field in this volume be as uniform as possible. The most suitable for this purpose is a counter with flat electrodes. Such a counter is described in \({}^{50}\) and \({}^{51}\).

In \({}^{50}\), copper plates with an area of 35 cm\(^2\) were placed at a distance of 2.4 mm; the counter was filled with a mixture of argon (\(1/2\) atm) and xylene (6 mm Hg) and operated at a voltage of 1500 V; the plateau of the counter was 1500 V; quenching was carried out by a multivibrator with a period of 0.05 sec; the leading edge of the pulse from the counter was measured by means of a special circuit described in \({}^{52}\), and was equal to \(5\cdot 10^{-9}\) sec.

In \({}^{51}\), copper foil 0.003 inch thick was stretched over rings 2 inches in diameter; the distance between the plates was equal to…

1 mm; the counter was filled with a mixture of 90% argon and 10% \(N\)-butane at a total pressure of 2 atm; quenching was carried out by the Neher–Pickering circuit with a period of \(10^{-2}\) sec. The counter operated at a voltage of 3000 V; the plateau was 900 V. The pulses were transmitted by a line with a characteristic impedance of 70 ohms and were equal (without amplification) to 600 V. The leading edge of the pulses was shorter than \(10^{-8}\) sec. In agreement with the preceding author, the delay of the pulses in the plane-parallel counter was measured by comparison with a Geiger–Müller counter; in this case the plane counter triggered a horizontal sweep of duration 0.5 μsec, while the Geiger counter gave the vertical deflection. Within the accuracy of the experiment (0.1 μsec) no delay of the pulses of the plane counter relative to the Geiger–Müller counter was detected.

The recovery time of the counter was of the order of 0.01 sec, and the efficiency for fast electrons was 10%.

A more careful measurement of the delay of pulses from a plane counter was made by Keuffel \(^{57}\) with the aid of a 10-detector Nedermeijer “chronograph” (see \(^{52}\)). The relative delay of pulses from two plane-parallel counters was measured. With an overvoltage on the counters of 500 V, half of the pulses were delayed by less than \(12 \cdot 10^{-9}\) sec; with an overvoltage of 1000 V, half of the pulses were delayed by less than \(4 \cdot 10^{-9}\) sec. The author believes that the large delay is possibly connected with insufficient parallelism of the electrodes.

According to the observation of the author of the present work, the lifetime of a plane-parallel counter at an overvoltage of 1000 V is of the order of a month.

The shape of the pulse of a plane-parallel counter must differ appreciably from the shape of the pulse of a Geiger–Müller counter or of a proportional counter (see \(^{10}\)). In the initial stage of the development of the discharge, the growth of the pulse is determined by the velocity of propagation of the streamer, produced by the primary electron and traversing the anode–cathode gap with a velocity of the order of \(4 \cdot 10^{8}\)—\(10^{9}\) cm/sec; for a counter with a spacing between plates of 2.4 mm we obtain \((2—6)\cdot 10^{-10}\) sec; during this time only a small part of the pulse voltage should appear. As soon as the streamer closes the discharge gap, breakdown occurs, and within a very small interval of time, determined by the external circuit, the pulse reaches its full value—several hundred volts. The leading edge of the pulse of the plane-parallel counter observed by Keuffel (\(5 \cdot 10^{-9}\) sec) is possibly determined by the parameters of the output circuit.

Instead of a plane-parallel counter construction, which is very inconvenient for practical realization, one may use two coaxial cylinders whose diameters differ by only 15–20%. Such a counter should operate practically like a plane-parallel one, while the manufacture of such a counter and its adjustment are considerably simpler.

V. M. KHARITONOV

7. CONCLUSION

Among the fast-acting counters currently being developed, the most promising should be considered to be crystal counters, scintillation counters, and plane-parallel counters (or counters operating on the plane-parallel principle). The latter immediately give pulses suitable for triggering the measuring circuit, which favorably distinguishes them from counters of other types. However, the scintillation counter will apparently be no less fast-acting. Crystal counters are very attractive because of the simplicity of their construction, but apparently much still remains unclear in their operation.

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