CHARACTERISTICS OF SCINTILLATORS*)

R. K. Swank

INTRODUCTION

Several reviews of the development, theory, and applications of scintillation counters have already appeared in print. For the reader’s convenience, some of the most recent and comprehensive reviews are indicated in the bibliography 1–4. In the present paper an attempt is made, as far as possible without repetition, to supplement the preceding data. The following exposition will deal mainly with the scintillators themselves, as well as with the scintillations produced in them by particles of high energy. For convenience of presentation, the scintillators are grouped according to chemical similarity.

The Scintillation Process

In describing the scintillation process it is necessary to consider the magnitude (intensity), spectral composition, and time dependence of the ultraviolet or visible radiation that arises as a result of the absorption, in the scintillator material, of charged particles of high energy. For most particles and energies encountered in experimental nuclear physics, the energy of fast charged particles is spent almost entirely on the excitation of electrons and on ionization in the absorbing material. Since the energy of the particles is very large, all possible excited states are realized, including ionization, with different values of additional kinetic energy. The initial population of the various excited states is determined chiefly by the relative energies of the corresponding transitions from the ground state. This follows from the fact that, apart from direct collision, the field of a charged particle can

*) R. K. Swank, Annual Review of Nuclear Science 4, 111—140, 1954.
Translated by L. G. Eidelman.

be represented in the form of a “white” electromagnetic spectrum, whose shape is described by the Fourier transform for the time-varying field of the fast particle. In monatomic gases at low pressures such excitation would cause the emission of a series of spectral lines corresponding to various transitions from higher to lower levels or to the ground level. In solid or liquid form most materials give only insignificant luminescence when irradiated by charged particles of high energy. Moreover, the emission spectrum of the relatively small number of materials that give intense scintillations corresponds to only one, or at most to a few, transitions from the lower excited states to the normal state. Within the accuracy of the available experimental data, the emission spectra under excitation by elementary particles and under ultraviolet excitation have the same spectral distribution. From this one may conclude that the scintillation process is simply a variety of fluorescence in which excitation is produced by the time-varying field of a moving charge. However, many factors considerably complicate the scintillation process. A calculation carried out by Harrison[^5] showed that the excitation of fluorescence occurring in benzene is many times greater than could have been predicted theoretically on the basis of direct excitation by charged particles. In this case, as probably in many others, the greater part of the fluorescent excitation induced by particles is the result of the decay of higher excited states into the states from which fluorescence occurs. In addition to excitation of the fluorescent state by direct and indirect processes, a particle may also produce an emission process. This may be the result of local effects such as chemical dissociation, heating, electric fields, and mutual quenching by neighboring excited molecules.

Despite the many factors arguing for a separation of the scintillation process and the fluorescence process, it is not hopeless to describe these two phenomena in general expressions. If one temporarily neglects the perturbation of the emission process by low-energy products, the number of photons emitted in scintillation may be expressed as

\[ N=\frac{E_0 q}{w}, \tag{1} \]

where \(E_0\) is the initial energy of the fast particle slowing down in the scintillator, \(w\) is the average energy expended per one transition into the fluorescent state, and \(q\) is the quantum efficiency of fluorescence.

The practical value of equation (1) depends on our ability to modify it in a suitable way for describing the more complex effects mentioned above. In the subsequent discussion some of such modifications will require \(w\) or \(q\) to vary with the energy of the particle.

In this case equation (1) must be written in differential form

\[ dN=-\frac{q'}{w}\,dE, \tag{2} \]

where \(dN\) is the number of photons emitted when the particle energy changes from \(E\) to \(E-dE\).

MEASUREMENT OF SCINTILLATION PROPERTIES

Scintillation efficiency

Most of the data on scintillation efficiency described in the literature are given in terms of the output of a photomultiplier. This method of measurement often leads to an unequal evaluation of different materials because of the dependence of the photocathode efficiency on wavelength. The scintillation amplitude, expressed by the number of cathode photoelectrons, is equal to

\[ \int_0^\infty N \xi(\lambda)\eta(\lambda)\,d\lambda, \]

where \(\xi(\lambda)\) is that part of the emitted photons whose wavelengths lie between \(\lambda\) and \(\lambda+d\lambda\), \(\eta(\lambda)\) is the quantum spectral efficiency of the photocathode, and \(\lambda\) is the wavelength.

Fig. 1. Spectral quantum efficiency of a type 5819 photomultiplier with an S-9 characteristic and the quantum emission spectra of two plastic scintillators. For plastics containing terphenyl and tetraphenylbutadiene, the ratio of light yields is 1.10, while the ratio of the corresponding pulse heights on the photomultiplier is 0.78. The scale of the ordinate axis is arbitrary.

Fortunately, most scintillation-efficiency measurements were carried out with a Cs\(_3\)Sb photocathode. An example of the significance of this effect is shown in Fig. 1. The relative quantum spectral efficiency of a type 5819 photomultiplier*) is plotted on the same figure with the curves of the quantum emission spectrum of two plastic scintillators. From Fig. 1 it may be calculated that the ratio

*) The type of spectral sensitivity shown in Fig. 1 is classified as S-9. The manufacturer has now somewhat changed the spectral sensitivity and designates this type as S-4.

heights of pulses on the photomultiplier for plastic scintillators containing terphenyl and tetraphenylbutadiene is 0.78, whereas the ratio of their light yields is 1.10. If a reflector is used in comparing the properties of scintillators, errors may be caused by a change in the latter’s reflectivity with wavelength. Discrepancies may also arise as a result of differences in the optical purity or in the refractive indices of the samples. These effects are reduced to a minimum if one of the surfaces of the scintillator is in optical contact with the surface of the photocathode.

For comparing the work of different laboratories on measuring the relative efficiency of scintillators, it is necessary to establish a definite standard. The material most often used for such comparative measurements is an anthracene crystal. This choice is somewhat unfortunate, since anthracene is not easy to purify, and the production of perfect crystals of it is rather difficult. Sangster \(^{6}\) showed that, even with the most careful preparation, differences in technique lead to variations in pulse height within the limits of 20%. Determination of the absolute scintillation efficiency from relative measurements, if the absolute efficiency of a standard sample is known, is possible only to the extent that pure standard samples not differing from one another can be obtained. Several investigators have recently measured the absolute efficiency of anthracene. The results of their measurements are given in Table I.

Table I

Absolute scintillation efficiency of anthracene
under excitation by high-energy \(\beta\)-particles

Most scintillators are, at least partially, transparent to their own radiation. This convenient circumstance can be understood from consideration of the fundamental processes of absorption and emission of radiation by a scintillator molecule. The molecule undergoes vibrations about the equilibrium position corresponding

minimum of potential energy. These vibrations are quantized according to the vibrational levels of the ground and excited states. At ordinary temperatures the molecules will be in equilibrium on the lower vibrational levels. In general, the equilibrium position in the excited state will differ from the equilibrium position in the ground state. This fact, together with the Franck–Condon principle, which requires that the coordinates of the nucleus remain fixed during the electronic transition, means that after absorbing a photon the molecule passes to a higher vibrational level of the excited state. Thus the molecule instantaneously leaves thermal equilibrium with the molecules surrounding it, but equilibrium is rapidly established (in \(10^{-13}\)—\(10^{-12}\) sec.) by giving up vibrational energy. Similar thermal equilibration occurs after the emission of a fluorescent photon. Thus the emission spectrum of the molecule is shifted relative to the absorption spectrum toward longer wavelengths. However, the difference between the wavelengths of the absorbed and emitted quanta is a statistical quantity, depending on the initial and final vibrational states of the molecule, and in some cases the emitted quantum may have a shorter wavelength than the absorbed one.

Fig. 2. Schematic representation of the absorption spectrum and the emission spectrum of a scintillator.

In addition, the shape of the energy curve is different for different molecules at each instant of time and for each molecule at different times as a result of thermal fluctuations of neighboring molecules. Thus, although the mean wavelength of the emission spectrum is always greater than the mean wavelength of the absorption spectrum, a partial overlap of these spectra is usually observed. This effect is shown schematically in Fig. 2, where the region \(a\) is proportional to the number of photons emitted during scintillations. As a result of the partial overlap of the spectra, selective self-absorption of short wavelengths occurs. Therefore fewer photons pass through the sample, represented by region \(b\). The absorbed photons will cause excitation of an analogous state in other molecules, and the fraction \(q\) of these absorbed photons

will cause secondary emission. Since thermal equilibrium is established between absorption and emission, the secondary emission will have the same spectral distribution as the primary. Birks and Little\(^7\) showed that the number of photons ultimately emitted can be easily calculated if, for simplicity, it is assumed that the fraction of photons emitted is the same for each subsequent emission. This assumption, connected with neglecting diffusion, is a good approximation for many scintillators, since the number of significant generations of radiation in them is no more than ten, while diffusion from the source of the generations is relatively small. If this assumption is made, then the ratio of the number of observed photons to the number emitted is determined by the formula

\[ \frac{N_{\text{obs}}}{N} = \frac{\dfrac{b}{a}}{1-q\left(1-\dfrac{b}{a}\right)}, \tag{3} \]

and the spectral distribution of the observed scintillations has the same form as the curve \(b\). As might have been expected, this ratio tends to \(b/a\) for infinitely small \(q\), and to unity as \(q\) tends to unity. Thus, a scintillator of great thickness with high quantum fluorescence efficiency may have appreciable self-absorption with only a small loss in pulse height. Self-absorption is much less significant in the case of activated scintillators, since further degradation of the excitation energy occurs only when the excitation is transferred from the base medium to the activation centers. The same is true for scintillators used in “wavelength shifters,” which absorb the primary fluorescent radiation and convert it into longer-wavelength radiation. In three-component scintillators, such as commonly used liquids and plastics, three successive decreases in excitation energy occur. As a consequence, the mean free path for the emitted light in scintillators of this type often reaches several meters.

In measuring relative scintillation efficiency, two methods are usually used. In the first method the scintillator is irradiated by a source of moderate intensity. In this case no attempt is made to observe individual light flashes; instead, the mean value of the emitted light flux is measured. Usually this involves measuring the average value, or the dc component, of the current at the output of the photomultiplier. If, under steady irradiation, an equilibrium value of the current is established, it will be proportional to the mean value of the total light energy emitted during scintillation, irrespective of the time interval between the moment of excitation and the moment at which the process of light emission is completed.

In another method for measuring scintillation efficiency, the amplitude of the light pulses corresponding to the absorption of a single fast particle by the scintillator is measured. If a certain number of pulses is observed per unit time, the observation time of each pulse is necessarily limited. The observation time, or “integration time,” of a pulse recorded by the system is illustrated by Fig. 3. This figure shows a typical anode circuit of a photomultiplier and the usually observed waveforms. The waveform is determined partly by the time constant of the anode circuit \(RC\) and partly by the luminescence characteristic of the scintillator.

Fig. 3. Typical anode circuit of a photomultiplier. \(C\) usually consists of the distributed capacitance of the circuit. Curves \(a\) and \(b\) depict the shapes of the output pulses [equation (6)] for a “fast” and a “slow” scintillator, respectively.

To show this, suppose that at \(t=0\) the scintillator is instantaneously excited by a charged particle of high energy and that the fraction of all fluorescent photons emitted in the time interval from \(t\) to \(t+dt\) can be expressed by the function \(f(t)\,dt\). Then the number of photons emitted for \(t>0\) is equal to \(N f(t)\), and the anode current of the photomultiplier (neglecting the spread of time in the photomultiplier) will be:

\[ I(t)=Ng\bar{\eta}Gef(t), \tag{4} \]

where \(g\) is the fraction of the emitted light collected by the photocathode, \(\bar{\eta}\) is the mean quantum efficiency of the photocathode with respect to the emitted spectrum, and \(G\) is the multiplication coefficient of the photomultiplier. Since the anode current is divided between \(R\) and \(C\), the anode voltage is determined by the solution of the differential equation

\[ I(t)=\frac{V}{R}+C\frac{dV}{dt}. \tag{5} \]

For the simple case in which \(f(t)\) is given by the exponential function \(e^{-t/\tau}\), the voltage pulse will have the form

\[ V(t)=\frac{Ng\bar{\eta}Ge}{C}\left(\frac{RC}{RC-\tau}\right)\left(e^{-\frac{t}{RC}}-e^{-\frac{t}{\tau}}\right). \tag{6} \]

and the pulse amplitude will be:

\[ \left. \begin{aligned} V_{\max} &= \left(\frac{Ng\eta G}{C}\right)\gamma^{\frac{1}{1-\gamma}},\\ \text{where}\qquad \gamma &= \frac{RC}{\tau}. \end{aligned} \right\} \tag{7} \]

Thus, the observed pulse amplitude depends on the scintillator decay time \(\tau\) and on the time constant of the circuit (in the present case \(RC\)). If, in equation (7), \(RC \gg \tau\), then the pulse amplitude does not depend on \(\tau\). However, if this condition (the emission process ends in a short time compared with the time constant of the circuit) is not satisfied, then the scintillation efficiency determined from the pulse amplitude will not correspond to the efficiency measured from the photomultiplier current.

In practice the situation is complicated by the discrepancy between the actual form of the scintillation decay and the simple assumption made above. Often the decay has a short exponential component accompanied by one or several long-lived components. The contribution of such a long-lived component to the pulse amplitude for various values of \(R\) was studied by Kalman^8 and by Bittman, Furst, and Kalman^9.

A new method for studying long-lived components in the scintillation output was proposed by Jackson and Harrison^10. In this method the scintillator, in conjunction with the photomultiplier, is irradiated continuously with X-rays, except for short intervals during which the X-ray tube is switched off. Immediately before the X-ray tube is switched off, the photomultiplier is switched on. In this case the long-lived components come into equilibrium, and from the decay observed during the time in which the X-ray tube is stopped one can calculate the relative contribution of the various components to the total scintillation. Jackson and Harrison^10 and Harrison^11 observed components longer-lived than the initial decay period in most organic crystalline scintillators, as well as in NaI(Tl), but did not find long-lived components in liquid organic scintillators. This suggests that long-lived components in some materials may be detected by comparing their current output and pulse height with the corresponding quantities for a liquid scintillator.

When measuring scintillation efficiency, the choice of a suitable excitation source is important. If it is desired to measure the scintillator output when it is excited by fast electrons, one may use a source of \(\beta\)-rays or of high-energy electrons, or obtain high-energy electrons inside the scin-

irradiated with γ-rays. For scintillators with a small atomic number, irradiation by an external source of “internal-conversion” electrons gives pulses with a sharp peak, so that the pulse height is easily measurable. However, scintillators containing elements with a large atomic number will give strong backscattering of electrons and distort the distribution of pulse heights. In this case an external source of γ-rays is more desirable, since, as a result of photoelectric absorption of γ-rays, sharp peaks are obtained in the pulse-height distribution. A very convenient source is Cs¹³⁷, since it emits both internal-conversion electrons (624 kev) and γ-rays (662 kev). A method is often used in which the current output under excitation by γ-rays is measured. This method can be quite accurate, but under certain circumstances it may also lead to considerable errors. If the scintillator contains only light elements and the γ-ray energy is sufficiently high, only Compton electrons are formed. The absorbing power of a small scintillator in this case is proportional to the number of electrons contained in it. If the walls surrounding the scintillator are also made of a material with a small atomic number, scintillators of several different sizes and densities can be standardized by dividing the counter readings by the number of electrons in the scintillator. If the density and atomic number of the scintillator are very high, while the γ-radiation energy is small, the radiation will be completely absorbed by the scintillator, and then a correction for the solid angle of the scintillator with respect to the source must be introduced into the reading. For intermediate values of energies or atomic numbers the situation is considerably more complicated, since a correction must be introduced into the reading for the energy actually absorbed by the scintillator.

The scintillation efficiency is a function of the temperature of the scintillator. In most cases the efficiency decreases with increasing temperature. Kallmann¹² showed that the efficiency of organic crystals gradually decreases with increasing temperature up to the melting point, at which the efficiency approaches zero. For inorganic scintillators the efficiency depends only weakly on temperature up to a certain critical temperature region, in which the efficiency rapidly falls with increasing temperature. In many cases this sharp decrease in efficiency can be expressed by the formula

\[ N=\frac{N_0}{1+\alpha e^{-\frac{\varepsilon}{kT}}}, \tag{8} \]

where \(N_0\) is the number of photons emitted at low temperature, \(\varepsilon\) is the activation energy associated with quenching, \(k\) is Boltzmann’s constant, and \(\alpha\) is a constant.

Bonanomi and Rossel\(^{13,14}\) showed that the change in scintillation efficiency of certain alkali-metal halides with temperature is accurately described by formula (8). One of the cases leading to this formula is as follows: if a molecule in an excited state (electronic) vibrates with a suitable amplitude, it can reach a point at which the excited and unexcited states differ quantitatively so little that an electronic transition to the ground level is possible with the emission of elastic waves instead of light. The probability of each such event is proportional to \(e^{-\frac{\varepsilon}{kT}}\), where \(\varepsilon\) is the energy required to reach configurational quenching. The competition between this process and the emission process leads directly to an expression of the form of equation (8). Some scintillators, such as calcium tungstate, have a critical region at room temperature. The critical regions of other materials lie below room temperature, and therefore these materials are usually not considered as scintillators.

Scintillation spectrum

Knowledge of the emission spectrum of a scintillator is useful in selecting a suitable photodetector for use with it and in drawing up the specification of the optical system. It is necessary to know, for example, whether a given liquid scintillator should be used in a quartz vessel or whether glass is suitable for it. On the other hand, it is useful to know the emission spectrum in connection with the study of the fundamental principles of the scintillation process. The requirements for measurements of the emission spectrum for these two purposes are quite different. For fundamental studies it is necessary to know the spectrum actually emitted by the molecule. No distortions by selective self-absorption are permissible in this case. For this purpose measurements must be carried out on very thin samples or in dilute solutions. This differs from practical requirements, where it is usually desirable to know the spectrum that is observed at scintillator thicknesses used in scintillation counters. If ultraviolet excitation is used in determining the emission spectrum, the practical spectrum can be reproduced by using “through” excitation, in which the fluorescent radiation passes through the scintillator in order to reach the spectrometer. On the other hand, if “frontal” excitation by ultraviolet light with a wavelength corresponding to the maximum of the absorption band is used, then self-absorption will be small, and the observed spectrum approaches the molecular spectrum. In some cases, in descriptions of spectra, the role of self-absorption is not clear.

Scintillation decay time

The presence of impurities can affect the scintillation decay time of a scintillator just as strongly as it affects its efficiency. An impurity may act as a quencher—in which case the decay time will be shortened—or it may fluoresce; in that case the decay time is characterized by the impurity. In some cases an impurity can capture electrons and lead to phosphorescence.

Secondary self-absorption can change the observed decay time. It is well known that the radiation of monatomic gases can be delayed for a long period of time by secondary self-absorption (see, for example, Mitchell and Zemansky \(^{15}\)). Such a delay is very greatly reduced in solids in accordance with the principles described earlier, according to which the emission spectrum is shifted toward longer wavelengths relative to the absorption spectrum. However, as a result of partial overlap of broad spectral bands, the radiation may nevertheless undergo appreciable self-absorption while passing through a thick specimen. Birks and Little \(^{7}\) showed that, as a result of this effect, the decay time observed in thick organic crystals may be several times greater than the true lifetime of the excited state of the molecule.

Making the same assumptions as in the derivation of equation (3), we find the decay time of a thick scintillator:

\[ \tau=\frac{\tau_{0}}{1-q\left(1-\frac{b}{a}\right)}, \tag{9} \]

where \(\tau_{0}\) is the molecular lifetime, and \(b\), \(a\) are respectively the areas under the curves of the emission spectrum of a thick specimen and of the molecular emission spectrum (both spectra must be normalized so as to coincide in the region of the longest wavelengths). The ratio \(b/a\) is also the probability that an emitted photon will pass through the scintillator while avoiding absorption. For practical application it is important to measure \(\tau\), but for theoretical interpretation it is necessary to determine \(\tau_{0}\).

Almost all measurements of decay time described up to the present have been made with photomultipliers. The large multiplication factor and the broadband frequency characteristic of these devices make possible measurements of scintillation decay time with high accuracy for periods down to \(10^{-8}\) sec. For decay times less than \(10^{-8}\) sec., the influence of the photomultiplier on the observed decay is greatly increased, and for scintillations with duration less than \(3 \times 10^{-9}\) sec.

the principal part of the observed decay time at the output is determined by the characteristics of the photomultiplier.

The time spread introduced by the photomultiplier is, in essence, the spread in the transit time of the electron avalanche. This spread is determined by many factors, such as the number of multiplying emitters, the degree of focusing, the distance between emitters, and the applied voltage. For photomultipliers and operating voltages ordinarily used in a scintillation counter, the spread time (the width of the output pulse at half maximum for an infinitely narrow light pulse) ranges between \(10^{-9}\) and \(2 \times 10^{-8}\) sec.

Since the scintillation arising in each ionization process ejects only several hundred photoelectrons from the photocathode, an exact measurement of the decay time for a single pulse alone is impossible. This problem is analogous to measuring the half-life of short-lived radioisotopes, in which the actual activity is inferred from measurements for several hundred particles. The accuracy of the measurements can be increased by averaging the ordinates of many pulses, by increasing the energy of the ionizing particles, or by using artificial excitation consisting of short flashes containing many particles of high energy.

There are three principal processes used to describe luminescent decay. The first process is fluorescent decay, which follows the law

\[ f(t)=\frac{1}{\tau} e^{-\frac{t}{\tau}} . \tag{10} \]

The decay parameter \(\tau\) does not depend on the temperature or on the excitation density, except for the temperature dependence that may occur at a point with strong temperature quenching.

The second process, known as phosphorescent decay, follows the decay law corresponding to equation (10), but the decay time depends sharply on the temperature, obeying the expression

\[ \left(\frac{1}{\tau}\right)=s e^{-\frac{\varepsilon}{kT}} . \tag{11} \]

The third decay process may be defined as “bimolecular” decay. It is characterized by the fact that the rate of decay is greater the greater the excitation density, and it is described by the expression

\[ f(t)=\frac{a}{(1+at)^2} . \tag{12} \]

The parameter \(a\) is proportional to the excitation density and in some cases also depends on the temperature in the form of equation (11).

A more complete discussion and study of these expressions is given in the works of Randall and Wilkins16 and of Garlick17.

For measuring the scintillation decay time, three methods were used chiefly.

In the first method, the anode pulse (or the pulse of the last dynode) was observed on the screen of a cathode oscilloscope. This method was used most often. The anode time constant \(RC\) may be large in comparison with the decay time; in this case the anode voltage will be proportional to the time integral of the anode current \(I(t)\), which is determined by equation (4); the constant \(RC\) may also be made considerably smaller than the decay time, so that the anode voltage will be proportional to the anode current. Post and Shiren18 considerably improved the time resolving power of the method by applying very high voltages in the photomultiplier, while, to avoid destruction of the instrument, the high voltage was switched on only for a few microseconds. Phillips and Swank19 increased the statistical accuracy by using pulsed X-ray excitation.

In the second method, used by Liebson, Bishop, and Elliott20, the scintillator was excited periodically by a pulsed source of ultraviolet or X-radiation. The exciting ultraviolet radiation was modulated by diffraction in an oscillating quartz crystal. If the number of ultraviolet photons absorbed by the scintillator per second is equal to \(J_0 \sin \omega t\), then, after equilibrium has been established, the number of fluorescent photons emitted per second will be:

\[ F(t)=qJ_0\int_{-\infty}^{t} f(t-t_0)\sin \omega t_0\,dt_0, \tag{13} \]

where the applicability of the superposition principle is assumed. For the simple case in which \(f(t)\) is an exponential function (equation (10)),

\[ F(t)=\frac{qJ_0}{\sqrt{1+\omega^2\tau^2}}\sin(\omega t-\theta), \tag{14} \]

where \(\operatorname{tg}\theta=\omega\tau\). The fluorescent radiation \(F(t)\) will thus pulsate with the same frequency as the exciting radiation, but will be reduced in amplitude and shifted in phase. From the phase difference between the exciting and fluorescent radiations one can find the decay time, if the form of \(f(t)\) is known. This method was modified by Birks and Little7, who used a gas-discharge tube as the excitation source.

The third method for measuring the decay time was described by Elliott et al.^21. The principle of this method is illustrated in Fig. 4. The photomultiplier pulse \(a\) is superposed on its delayed reflection \(b\). The crystal diode passes only the positive part \(v\). Pulse \(v\) enters a low-frequency amplifier, whose output pulse

Fig. 4. Circuit diagram for measuring scintillation decay times by the short-circuited-line method. \(Z_0\) is the characteristic impedance for the given circuit. (After Elliott et al.^21.)

is proportional to the area bounded by curve \(v\), so that the output amplitude (for an ideal diode) will be:

\[ A(t_1)=\int_0^{t_1} f(t)\,dt, \tag{15} \]

where \(t_1\) is the time during which the pulse and its reflection pass along the short-circuited section of the circuit. \(f(t)\) can be found from equation (15) by differentiating with respect to \(t_1\). Elliott et al. assumed an exponential form for \(f(t)\) and measured the change in the time \(t_1\) required to decrease \(A(t_1)\) by a certain number of times. They found that a correction must be introduced for the nonlinearity of the diode, which is relatively constant over the entire region of the decay times studied.

Two other methods were also used which are, to some extent, analogous to the method described above and may be regarded as its variants. The first method, used by Landay^22, consists in determining the decay time of the scintillator when it operates in coincidence circuits. The second method, applied by Bittman et al.^9, consists in determining the amplitude of the anode pulse of the photomultiplier as a function of the shunting resistance \(R\). In this method a qualitative determination of the form of \(f(t)\) was achieved.

ORGANIC SCINTILLATORS

The organic scintillators now known are compounds whose molecules contain one or more benzene rings. They constitute one of the largest and best-known families of fluorescent materials. A complete review of their fluorescent properties is given in Pringsheim’s work^23.

Organic crystals

Organic scintillators form molecular crystals with a small binding energy. The absorption and emission spectra in the crystalline state are only slightly shifted (\(\sim 200\) Å) in comparison with free molecules. The relationship between chemical structure and scintillation efficiency was studied by Kallmann^8, Sangster^6, and Koski and Thomas^24. The authors found no reliable regularity for predicting scintillation efficiency, but several correlations were noted, such as the desirability of symmetric molecules with a large number of conjugated double bonds and the undesirability of steric formations or the presence of sulfur or halogens. The emission spectrum of these compounds extends from 3000 Å for solid benzene to 6000 Å for materials such as pentacene and diphenyloctatetraene. A more or less uniform increase in emission wavelengths occurs as the number of double bonds increases.

Organic scintillators are characterized by their short decay time—of the order of \(10^{-8}\) sec. Recent studies by Jackson and Harrison^10 and Harrison^11 have shown, however, that metastable states are encountered which give secondary components of the afterglow with a duration of about 100 \(\mu\)sec. The decay time of organic scintillators decreases with decreasing temperature. Figure 5 shows the results obtained by Elliott et al.^25 for anthracene and stilbene when measured by the method of a short-circuited line. The effect indicated in the figure is opposite to the corresponding characteristic of phosphorescent afterglow—equation (11). Birks^1 proposed explaining these results by self-absorption—equation (9). The increase of \(\tau\) with increasing temperature may be the result of the fact that the probability \(b/a\) of photon escape decreases with increasing spectral width at high temperatures.

There were considerable disagreements among different investigators concerning the values of the efficiency, emission spectrum, and decay time of various organic crystals. In addition to the effects already described, associated with the thickness of the specimen, the discrepancies were probably determined to a significant extent by the influence of impurities. There are three types of impurity influence on the properties

of an organic crystal: a) by perturbing the fluorescent molecules adjacent to it, the impurity can alter their fluorescent properties; b) the impurity can absorb the radiation emitted by the fluorescent molecules; and c) the fluorescent excitation can migrate without radiation, part of it then being captured by the impurity. The action of mechanism a) alone would require

Fig. 5. Dependence of the scintillation decay time of anthracene and stilbene on temperature. (According to Elliott et al.^25.)

concentrations of the order of 5–10% in order to change the fluorescent properties appreciably, since only the molecules adjacent to the impurity are affected. Therefore, the frequently observed effect on a scintillator of impurities with concentrations of 0.1% or less must be assigned to types b) or c).

A broad investigation of the effect of small amounts of impurities on the fluorescence of organic crystals was carried out by Bowen et al.^26,27,28. It was found that a fluorescent crystal is more sensitive to those impurities that absorb strongly in the region of the fluorescence spectrum; the observations would seem to indicate that the radiation emitted by the crystal is reabsorbed by the impurity. However, as a result of other investigations Bowen came to the conclusion that the excitation energy is capable of diffusing through the crystal and being captured by the impurity, with no radiation being emitted. A theoretical justification of such processes was given by Kallmann and London^29, Frenkel^30, and Förster^31. These conclusions, derived from experiments with ultraviolet excitation, play a very important role in our understanding of the scintillation process. Later experiments with liquid and plastic scintillating solutions confirmed the concept of nonradiative migration of energy in organic scintillators. It must be noted, however, that the validity of Bowen’s conclusions has recently been called into question by Birks^1, who points out that many observations

...which, at first glance, depend on the nonradiative mechanism of transfer, can be equally well explained by the radiative mechanism of transfer.

On the basis of the assumption of nonradiative migration and energy transfer, Bowen derived equations expressing the dependence of the fluorescent yield of the host crystal and, in the case of fluorescent impurities, the dependence of impurity fluorescence on the impurity concentration. Slightly changing Bowen’s terminology, the equations may be written as follows:

\[ q_A=\frac{k_1}{k_1+k_2+k_3c+k_7c}. \tag{16} \]

\[ q_B=\frac{k_3k_4c}{(k_1+k_2+k_3c+k_7c)(k_4+k_5+k_6c)}. \tag{17} \]

where \(q_A\) and \(q_B\) are the quantum efficiencies of the host crystal \(A\) and of the dissolved substance \(B\), respectively, for the radiation absorbed by the host crystal, and

1) \(k_1\) is the probability of the fluorescence process of \(A\);
2) \(k_2\) is the probability of the self-quenching process of \(A\);
3) \(ck_3\) is the probability of the process of excitation transfer from \(A\) to \(B\);
4) \(k_4\) is the probability of the fluorescence process of \(B\);
5) \(k_5\) is the probability of the process of internal quenching of \(B\);
6) \(ck_6\) is the probability of the self-quenching process of \(B\);
7) \(ck_7\) is the probability of quenching of molecules \(A\) by molecules \(B\);

\(c\) is the concentration of \(B\) in \(A\). For small concentrations, process 7) may be neglected, since quenching at small concentrations occurs as a result of process 3), accompanied by processes 5) and 6). Then equations (16) and (17) may be written in the form

\[ q_A=\frac{q_0}{(1+\sigma c)}, \tag{18} \]

\[ q_B=\left(\frac{\sigma c}{1+\sigma c}\right)\left(\frac{q_1}{1+mc}\right), \tag{19} \]

where

\[ q_0=\frac{k_1}{k_1+k_2}, \qquad q_1=\frac{k_4}{k_4+k_5}, \]

\[ \sigma=\frac{k_3}{k_1+k_2}, \qquad m=\frac{k_6}{k_4+k_5}. \]

If the impurity fluoresces, its emission, determined by equation (19), reaches a maximum at \(c=1/\sqrt{\sigma m}\) and then decreases.

If the impurity does not fluoresce \((q_1 = 0)\), then \(q_B = 0\), and quenching \(A\) is determined by equation (18).

A successful application of these principles was found in the use of naphthalene crystals containing small amounts of anthracene as an impurity. The crystals are grown just as easily as pure naphthalene, but give a greater scintillation yield.

As was mentioned above, deviations from the simple linear dependence between the magnitude of the scintillation and the energy of particles stopped in the scintillator, represented by formula (1), may be considered as the result of the interaction of excited molecules with other neighboring excited molecules or with other products created by the scattering of the particles’ energy. Such an effect was first discovered by Kallmann^12, who observed that the light yield of organic crystals per unit of expended energy is considerably smaller for \(\alpha\)-particles than for \(\beta\)-particles. This effect was also confirmed by the results of Hopkins^32, who found that

Fig. 6. Dependence of the ratio of pulse height to energy in anthracene on energy for various particles according to Taylor et al.^33, Frey et al.^34 and Birks^35.

the pulse height upon excitation of anthracene by electrons is proportional to the energy above 125 kev, but deviates from proportionality at lower energy values. Recently the dependence of scintillation efficiency on the energy and nature of the exciting particles has been studied by a number of investigators. The results of Taylor et al.^33, Frey et al.^34 and Birks^35 are combined in the curves shown in Fig. 6. It is easy to see that the ratio of scintillation-

of the efficiency on the energy of the particle being stopped in the scintillator, the smaller the greater the specific energy loss of the particle. This effect is seen more clearly from Fig. 7, where the specific efficiency \(\dfrac{dN}{dx}\) and the differential efficiency \(\dfrac{dN}{dE}\) are shown as functions of the specific energy loss of the particle (according to Taylor et al.). \(\dfrac{dN}{dx}\) is the number of photons emitted per unit length of the particle path (the units in Fig. 7 are arbitrary). It follows from Fig. 7 that the scintillation efficiency of anthracene is a function of the specific energy loss, independently of the mass or charge of the particle. The deviation of the data for electrons

Fig. 7. Specific photon emission \(\dfrac{dN}{dx}\) and differential photon emission \(\dfrac{dN}{dE}\) as functions of the specific energy loss of exciting particles in anthracene. (According to Taylor et al.\(^{33}\).)

with low energy from the curve is explained by Birks\(^{36}\) as a surface effect, which becomes significant when the particle range in the scintillator is less than \(\sim 7\,\mu\). Birks\(^{37}\) derived a theoretical formula for describing the results shown in Fig. 7, based on the assumption of quenching by “impurities” formed when molecules are damaged by irradiation. Applying formula (18) and taking into account that quenchers are formed during the dissipation of particle energy, so that

\[ c = B \frac{dE}{dx}, \]

we obtain:

\[ \frac{dN}{dE}=\frac{q}{w}\left(\frac{1}{1+kB\frac{dE}{dx}}\right). \tag{20} \]

Table II

Organic scintillation crystals

) The photomultiplier output 5819 or 6292 for anthracene is taken as 100.
*) Time during which the intensity decreases by a factor of $e$ from the maximum.

Birks showed that the values of the scintillation amplitude obtained from equation (20) by integration along the particle range give excellent agreement with the experimental data for electrons, protons, deuterons, and \(\alpha\)-particles in anthracene.

Wright\({}^{38}\) developed another theory, which regards quenching as the result of interaction between excited molecules. This theory leads to a bimolecular law of luminescence, which is described by a slowly decreasing exponential and gives, for the scintillation efficiency:

\[ \frac{dN}{dE}=\frac{q}{w}\, \frac{\ln\left(1+M\frac{dE}{dx}\right)} {M\frac{dE}{dx}}, \tag{21} \]

where \(M\) is a constant.

The forms of equations (20) and (21) are not sufficiently different for a choice to be made on the basis of the available experimental data. However, the data of Bittman et al.\({}^{9}\) for the luminescence time testify in favor of Wright’s theory.

The influence of the specific energy loss of the exciting particles on the efficiency of individual scintillators is conveniently determined by comparing the ratio of pulse height to energy for \(\alpha\)-particles of Po \((E_0=5.3\ \text{MeV})\) with the corresponding ratio for high-energy electrons \((E_0 \gg 1.0\ \text{MeV})\); this ratio is often called the “\(\alpha/\beta\) ratio.” It is very close to 0.10 for anthracene and has approximately the same value for other organic scintillators.

Table II gives some properties of commonly used organic crystalline scintillators.

Liquid scintillators

After the report by Reynolds et al.\({}^{39}\) that scintillation pulses comparable with pulses from crystals can be obtained from solutions of \(p\)-terphenyl in xylene, the use of liquid scintillators spread rapidly. An extensive study of these materials was carried out by Kallmann and Furst\({}^{40,41,42}\).

Most of our concepts concerning the basic principles of operation of scintillators of this type are the result of their investigations. They showed that the transfer of excitation energy from the solvent to the dissolved substance occurs in these solutions to a considerable degree analogously to the transfer found by Bowen in crystalline solid solutions. However, in the case of liquids, fluorescence yield was almost not observed for pure substances, i.e. \(q_A=0\). That

the fact that the excitation energy is transferred to the dissolved substance before quenching occurs makes sufficient efficiency possible.

Table III

Liquid scintillators

*) Abbreviations: TP—p-terphenyl; DPH—1,6-diphenyl-1,3,5-hexatriene; αNPO—2-(1-naphthyl)-5-phenyloxazole; PPO—2,5-diphenyloxazole; PBD—2-phenyl-5-(4-biphenyl)-1,3,4-oxadiazole.

**) The output of photomultiplier 5819 or 6292 for an anthracene crystal is taken as 1,00.

***) The time during which the intensity decreases by a factor of \(e\) from its maximum value.

****) Specially purified by Hayes (Los Alamos Scientific Laboratory).

*) Eastman Kodak Co., No. 1502.

Using an analogous analysis, Kallmann and Furst derived an equation of the same form as equation (19), expressing the luminescence yield as a function of concentration. Agreement of this equation with experiment was confirmed for a large number of different solvents and dissolved substances. In addition to the use of

fluorescent soluble substance as activator. Kallmann and Furst found that strongly fluorescing dissolved substances, in very small concentrations, can absorb the fluorescence of the principal dissolved substance and convert it into radiation of longer wavelength. Such secondary dissolved substances, which it is now customary to call “wavelength shifters,” become very useful for obtaining a better match between the scintillator and the spectral sensitivity of the photomultiplier and for reducing self-absorption in the scintillator.

A new series of fluorescent additives for liquid scintillators was found by Hayes[^43]. These compounds, which belong to the phenyloxazoles, are considerably more soluble than p-terphenyl. They are the only known soluble substances that can be successfully used at low temperatures. Various members of this family of compounds are suitable as primary dissolved substances or as wavelength shifters.

Reynolds[^74] studied the yield of liquid scintillators for α-particles. For a solution of 5 g of terphenyl in 1 l of toluene, the yield is very close to that of anthracene. However, the α/β ratio decreases rapidly with decreasing terphenyl concentration. The yield of these solutions for various particles is considered in Harrison’s work[^75].

Liquid scintillators are highly susceptible to deterioration by impurities, in particular organic compounds of sulfur and halogens. A special kind of deterioration by oxygen was studied by Pringle et al.[^44]. Pringle showed that the action of dissolved oxygen is reversible and that the scintillation efficiency can be restored by passing nitrogen through the liquid. The composition and characteristics of a number of liquid scintillation solutions are given in Table III.

Plastic scintillators

Since the report by Schorr and Torney[^45] that scintillations were found in solid solutions of terphenyl in polystyrene, interest in these materials has been concentrated on achieving higher light yield and on investigating the nature of energy-transfer processes.

The spectrum and pulse height of some solid solutions were studied by Kesse[^46]. Pich et al.[^47,^48] developed plastic scintillators containing 1, 1, 4, 4-tetraphenyl-1,3-butadiene, and described the spectra and pulse heights of various solutions, together with experimental results indicating that the scintillation process includes a nonradiative mechanism...

of radiationless energy transfer. Bak and Sveshnikov\(^{49,50}\) studied the pulse height, spectrum, and scintillation time of certain substances dissolved in polystyrene and polyvinyltoluene. It was found that the curves of pulse height versus concentration (Fig. 8) agree very well in character with equations (18) and (19).

Fig. 8. Pulse height as a function of concentration for various plastic scintillators. The solid lines are theoretical curves [equations (18) and (19)] coinciding with the experimental points. (According to data of Sveshnikov and Bak\(^{50}\).)

The study of the passage of energy through a thin film and the measurement of the scintillation time as a function of the concentration of the dissolved substance led to the conclusion that about 20% of the excitation energy of the solvent is transferred to the dissolved substance by radiation, and 80% by a nonradiative mechanism.

A summary of the available data for some plastic scintillators is given in Table IV.

Table IV

Plastic scintillators

) Abbreviations: TP—p-terphenyl; TPB—1,1,4,4-tetraphenyl-1,3-butadiene; DPS—p,p′-diphenylstilbene.
) The photomultiplier output 5819 or 6292 for an anthracene crystal is taken as 1.00.
**) The time during which the intensity decreases by a factor of \(e\) from its maximum value.

INORGANIC SCINTILLATORS

Most of the existing information concerning the behavior of inorganic scintillators comes from earlier studies of the ultraviolet fluorescence and cathodoluminescence of these materials (for reviews see the works of Fonda and Seitz\(^{51}\), Kröger\(^{52}\), Leverenz\(^{53}\), Garlick\(^{17}\), and Pringsheim\(^{23}\)).

Of principal interest are compounds that form ionic crystals. The strong interaction forces between ions cause the individual molecular energy levels of the valence electrons to coalesce into diffuse bands belonging to the entire

crystal. These energy bands are illustrated by the diagram in Fig. 9. In an unexcited crystal the uppermost of the occupied bands is completely filled in accordance with the Pauli exclusion principle. When the crystal absorbs an energy quantum, an electron may pass from the filled band \(F\) into the conduction band \(C\), after which the electron and its hole, which it has left in the filled band, may move independently through the crystal until they are captured by an impurity or by an inhomogeneity center in the crystal.

Fig. 9. Diagram of the energy levels of an activated crystalline scintillator: \(F\)—the highest of the filled bands, \(C\)—conduction band, \(E\)—excitation band, \(T\)—capture levels for electrons, \(L\)—levels of luminescence centers.

There is also the possibility of exciting the crystal by an absorbed quantum without ionization (band \(E\)); in this case the excitation energy is not localized, but rapidly moves through the crystal in the form of excitation waves (Frenkel \(^{30}\), Franck and Teller \(^{54}\)). These excitation waves also exhibit corpuscular properties, and the particle associated with them is described as an exciton. The exciton rapidly diffuses through the crystal, passing by a molecule in a time shorter than the period of vibration of the molecule. It may enter sites of imperfection in the crystal and emit energy in the form of elastic waves, or it may be captured by an impurity, producing an excited state. It may be thought that, owing to the latter process, exciton waves can play an important role in scintillation phenomena.

Alkali-metal halides

These crystals, containing a small amount of thallium halide, are the oldest and most thoroughly studied inorganic phosphors. A survey and explanation of the properties of these phosphors were given by Seitz \(^{55}\). Seitz believes that activation by thallium consists mainly in the substitution, by \( \mathrm{Tl}^+ \) ions, of alkali-metal ions. This introduces new absorption bands with wavelengths greater than those in the fundamental absorption band of the crystal. The observed absorption levels are in a definite relation to the levels in the free thallium atom. Experiments with excitation of \( \mathrm{KCl}(\mathrm{Tl}) \) by ultraviolet radiation showed that: a) Tl fluoresces with high efficiency when excitation is produced by its “characteristic” absorption band...

...but with considerably lower efficiency, when the crystal is irradiated in the “fundamental” absorption band; b) photoconductivity does not arise in either case. Result b) indicates that fundamental absorption must create an exciton rather than a conduction electron, and a) indicates that transfer of exciton energy to the emitting centers is inefficient.

The high scintillation efficiency of NaI(Tl) and KI(Tl) indicates that excitations produced in the lattice must be transferred to the emitting centers with high efficiency. The energy of ionizing particles is considerably greater than the energy of quanta in experiments with ultraviolet light; it may therefore be assumed that most of the particle energy goes into ionization. Emission may thus be the result of recombination of an electron and a hole at the activation center.

Alkali-metal halides activated with thallium give a phosphorescent scintillation glow consisting of one or more components, the form of which is described by equations (10) and (11). The decay time has recently been studied by Bonanomi and Rossel^13,14.

Alkali-metal halides activated with thallium have exceptionally high transparency to their own radiation. The longest absorption wavelength is less than 3000 Å, whereas the emission band in all cases lies almost entirely above 3000 Å and usually above 4000 Å for iodides. The situation is considerably less favorable in the case of activation by Sn or Eu.

The most convenient scintillator among the alkali halides is NaI(Tl). The use of this scintillator has been described by Hofstadter^56,57,58. The greater part of the scintillation energy is emitted in the form of a phosphorescent component having a very short lifetime (0.25 μsec at room temperature). In addition to high efficiency and transparency, a convenient property of this scintillator is that self-quenching by activator ions is very small. As a result, it is possible to obtain optimum efficiency (for electrons) over a wide range of activator concentrations. Harshaw et al.^59 found that, although the thallium concentration can vary by more than a factor of two in a large crystal grown from the melt, the change in pulse height is insignificant. Their data for pulse heights as a function of thallium concentration are shown in Fig. 10.

Studies by Taylor et al. showed that for NaI(Tl) a linear dependence of pulse height on energy is characteristic for electrons and protons over a wide energy range, but that it deviates from linearity for α-particles below 20 MeV. Accordingly, the pulse height per unit energy is the same for protons and electrons,

but less so for \(\alpha\)-particles. In Loubser’s work\(^{60}\), dependences of the relative pulse height on the energy for \(\alpha\)-particles below \(10\) MeV are given. These results are shown in Fig. 11. However, curves similar to those in Fig. 6 cannot be constructed for NaI(Tl), since Eby et al.\(^{61}\) found that the relative yield as a function of energy differs for different thallium concentrations.

Fig. 10. Pulse height for fast electrons as a function of the concentration of Tl in NaI(Tl). (According to the data of Harshaw et al.\(^{59}\).)

Fig. 11. Relative pulse height as a function of \(\alpha\)-particle energy for NaI(Tl). (According to the data of Loubser\(^{60}\).)

Therefore, the work of different investigators cannot be compared unless the activator concentrations are specified.

The detection of slow neutrons by means of the reaction \(\mathrm{Li}^6(n,\alpha)\mathrm{H}^3\) in LiI(Tl) was described by Hofstadter et al.\(^{62}\) Later investigations by Shardt and Bernstein\(^{63}\) showed that these crystals, grown from the melt, exhibit changes in pulse height over the volume of the crystal as a result of large fluctuations in the thallium concentration.

The authors found that Sn mixes more readily and with good homogeneity. Schenck\(^{64}\) obtained a greater pulse height with Eu activation. He found that the pulse height for slow neutrons, divided by the reaction energy, is equal to 95% of the pulse height per unit energy obtained for fast electrons. It was natural to conclude that the efficiency of this scintillator is almost independent of the nature and energy of the exciting particles.

Fig. 12. Proposed shape of the curve of differential efficiency as a function of specific energy loss for LiI(Eu).

Later it was shown that this conclusion was erroneous (Schenck and Neiler\(^{65}\)). It was found that the pulse height per unit energy for protons is greater than for electrons. This and other investigations led to the conclusion that the efficiency for \(\alpha\)-particles is appreciably smaller than the corresponding efficiency for electrons. On this basis one can construct a hypothetical efficiency curve as a function of specific energy loss, similar to that shown in Fig. 12. No explanation of such behavior has yet been found.

The scintillation properties of \(\mathrm{CaI}_2(\mathrm{Tl})\) and \(\mathrm{CsI}(\mathrm{Tl})^{66}\), as well as \(\mathrm{CsF}^{67}\), were described by Van Sciver and Hofstadter. Small transparent crystals of \(\mathrm{NH}_4\mathrm{I}(\mathrm{Tl})\) were grown by Guggenot\(^{76}\). The pulse heights for electrons amounted to only \(1/15\) relative to the pulse height for \(\mathrm{NaI}(\mathrm{Tl})\), and the yield for \(\alpha\)-particles was nonlinear.

Experiments with unactivated CsI crystals at low temperatures were described by Hahn\(^{68}\). At \(77^\circ\mathrm{K}\) these crystals give a large scintillation yield for \(\alpha\)-particles and show a proportionality better than that of \(\mathrm{NaI}(\mathrm{Tl})\) and \(\mathrm{KI}(\mathrm{Tl})\). A summary of data for scintillators made from alkali-metal halides is given in Table V.

Table V

Scintillators of Alkali-Metal Halides

*) The output of 5819 and 6292 photomultipliers with an anode time constant of ~10 μsec for an anthracene crystal is taken as 100.

**) The anode current of the photomultiplier for an anthracene crystal is taken as 100.

***) The time over which the intensity decreases by a factor of e from its maximum value.

****) The pulse height from thermal neutrons, divided by the reaction energy 4.785 MeV, is referred to the pulse height from electrons per unit energy.

Zinc sulfide

Unactivated zinc sulfide gives blue emission immediately beyond the absorption-band edge. Whether this emission is a characteristic of “pure” ZnS or of ZnS activated by excess Zn is unknown. When Ag is introduced as an impurity in amounts on the order of 0.01%, the blue emission is greatly increased and the scintillation efficiency is very high.

ZnS has no pure excitation bands. When irradiated within the first band, photoconductivity appears. Similarly, the absorption of high-energy particles very effectively creates conduction electrons. Luminescence occurs when an electron and a hole recombine at a luminescence center. However, recombination is slowed by the trapping of electrons in the lattice. Bube’s observations\(^{69}\) showed that 16 different trapping levels may be present in the ZnS lattice. Since luminescence occurs upon recombination, the afterglow has a bimolecular character (equation (12)); and since the recombination rate is determined by release from trapping levels, it has a strong temperature dependence.

Although ZnS(Ag) is one of the most effective scintillators now known, and although it has an emission spectrum ideally suited to the best photomultipliers, its use in scintillation counters is very limited for three reasons: a) it is very difficult to make large single crystals; b) the crystal is only partially transparent to its own radiation; and c) a large part of the luminescence energy is emitted too slowly for use in pulse counters. Nevertheless, ZnS(Ag) has been found convenient for counting heavy charged particles, and also for counting fast and slow neutrons.

Kallmann\(^{70}\) found that, whereas the yield of ZnS(Ag) for \(\alpha\)-particles (per unit of absorbed energy) is greater than for electrons, the yield for fission fragments is considerably smaller. This suggests that the general characteristic shown in Fig. 12 may perhaps also be applicable to this scintillator.

Tungstates of the alkaline-earth metals

The tungstates of Mg, Ca, Sr, and Cd all form effective phosphors. Introduction of an activator is not necessary for the fluorescence of these compounds. However, chemically pure powders do not luminesce, and they must be “activated” by heating. This phenomenon was formerly explained by the creation of activator centers when stoichiometric proportions were disturbed. In larger and more perfect crystals, however, heating may simply reduce the number of quenching centers. Kröger’s experiments\(^{52}\) directly indicate that fluorescence

of these compounds is a molecular phenomenon that does not involve the transfer of energy to activator centers.

The observation of scintillations in natural scheelite (CaWO$_4$) by Moon$^{71}$ aroused considerable interest because of the very high sensitivity of these crystals to $\gamma$ rays. Gillette$^{72}$ obtained small synthetic crystals of CaWO$_4$ and CdWO$_4$. Although the high melting point of CaWO$_4$ makes it difficult to grow crystals from the melt, this would probably not be an insurmountable

Table VI

Various inorganic scintillators

) The output of photomultiplier 5819 or 6292 with an anode time constant of $\sim 10$ μsec for an anthracene crystal is taken as 100.
) The anode current of the photomultiplier for anthracene is taken as 100.
) The time in which the intensity decreases by a factor of $e$ from its maximum value.
**) With an external plastic wavelength shifter.

...an obstacle to the manufacture of large crystals. The reduction of technical interest in this material is due not to this difficulty, but to its replacement by the scintillator NaI(Tl), which gives larger pulses with a shorter decay time.

Other scintillators

Scintillations in CaF$_2$ and in other minerals have been described by Moon$^{71}$. The decay time of CaF$_2$ was studied in the work of McIntyre$^{73}$. A summary of data for some scintillators is given in Table VI.

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