Mechanism of the Photographic Action of Ionizing Particles

A. L. Kartuzhanskii

1. Introduction

More than 40 years have passed since a photographic layer was first used for the registration of ionizing particles. However, only in the last decade has the photographic method become widely used in nuclear physics, and photographic emulsion has acquired the possibility of successfully competing with such widely used instruments as the Wilson chamber or ionization counters. This success of the photographic method is due, above all, to the development of new types of photographic layers distinguished by great thickness, a high concentration of silver halide, high sensitivity, and a number of other necessary properties. In the development of these emulsions, great credit belongs to the Soviet scientists L. V. Mysovskii, A. P. Zhdanov, and others.

Despite such great progress, the improvement of methods for preparing and using photographic emulsions has in many respects proceeded “blindly,” since even now the question of the mechanism of the photographic action of ionizing particles cannot be considered fully clarified; consequently it is still not entirely clear by what means manufacturers and users of photographic layers should achieve the best results.

As is known, a photographic layer is an aggregate of very small crystals of silver halide salts, most often AgBr with a small admixture of AgJ, suspended in gelatin. The passage of a particle through such a layer makes the crystals affected by it—or at least some of them—capable of development, i.e. of reduction to metallic silver under the action of a developer solution; an analogous result is also produced by the incidence of light on the layer. The passage of a charged particle through matter is accompanied by numerous acts of ionization of the atoms or molecules constituting this

substance. It is therefore natural to suppose that the photographic action of a particle is determined precisely by its ability to produce ionization in the emulsion crystals, with the formation in them of free conduction electrons. The list of ionic crystals in which the passage of particles gives rise to the appearance of various electronic processes (luminescence, photoconductivity, etc.) is sufficiently extensive, and a number of crystals from this group have found application in such instruments of nuclear physics as, for example, scintillation counters and crystal counters. Nevertheless, only the silver halides have proved suitable for the purposes of photographic registration of particles, and for the same reasons for which these substances proved to occupy an exceptional position as the basis for registering the action of light.

Under the action of light, as under the action of particles, crystals of silver halides undergo a definite photochemical change, consisting in the formation of extremely small particles of metallic silver—the so-called latent image (see the review by P. V. Meiklyar ¹). These products of the photochemical reaction are distinguished by a comparatively high stability in time and by the ability to catalyze the reduction reaction of silver halide in the developer, which makes the changes that have occurred in the crystals directly visible. The combination of these features places the silver halide salts in an exceptional position among photosensitive substances, as well as among substances used for the registration of particles. Thus, the foundation of the photographic method in nuclear physics consists equally of the specific properties of silver halides and of the ability of particles to produce ionization along their path. The considerations set forth inevitably had to lead, and did lead, to the idea of transferring to the case of the action of particles everything that is known concerning the mechanism of the photographic action of light. How fruitful such an approach to the question proves to be, and to what extent it may be considered justified, we shall see from what follows.

Our review will concern two principal questions: the passage of ionizing particles through matter, a special case of which is the passage of particles through a photographic layer, and the nature of the processes in the photographic layer that ultimately lead to its development. The second question, being closer to the subject of the review, will accordingly be set out in greater detail. Particular attention will be paid to the behavior of an individual emulsion crystal of silver halide, since the basis of photographic registration of particles—regardless of whether the result of the action of the particles is an individual track or a continuous blackening—is formed by the processes occurring in an individual crystal.

2. PASSAGE OF CHARGED PARTICLES THROUGH MATTER, IN PARTICULAR THROUGH A PHOTOGRAPHIC LAYER

On entering some medium and moving through it, a particle possessing a certain velocity, and consequently kinetic energy, continuously interacts with the atoms of the substance constituting this medium. If the particle has an electric charge, then the chief role is played by the electrical interaction of the particle with the atomic nuclei and with the electrons of the outer shell. Each such act of interaction causes a change in the particle’s velocity both in direction and in magnitude, generally speaking in the direction of decrease; as a result of this the kinetic energy of the particle is gradually expended and passes to the atoms of the substance. The change in velocity in direction is due mainly to interaction with the nuclei and does not play any appreciable role for fast particles, whereas the change in velocity in magnitude is determined chiefly by the Coulomb interaction with the electron shells, above all with the outer shell, and is the principal means by which the particle transfers energy to the substance.

In the case of ionic crystals of interest to us, which include all silver halides, the most widespread case of interaction is the removal of one valence electron from an anion; double ionization and ionization of higher orders occur very rarely. If for each ion encountered by the particle there is one liberated electron, then from this follows a proportionality between the ionizing power of the particle and its photochemical action; this regularity will be useful later. In silver halides the products of ionization of a singly charged halide ion are an electron and a neutral halide atom. Such a pair is customarily called an ion pair, by analogy with other cases of the ionizing action of particles, although as applied to the present case such a name is rather unfortunate.

Unlike light energy, where the quantum is indivisible and is necessarily absorbed as a whole, the energy of a particle is almost always absorbed in portions; the magnitude of such portions depends on the electrical properties of the substance. As it advances through the substance the particle loses velocity and interacts more and more often with atoms, until in the end it comes to rest, if the thickness of the layer of substance is sufficient for this. Therefore the loss of energy per unit path depends not only on the substance but also on the velocity of the particle. The loss of energy, generally speaking, increases with decreasing velocity according to the formula derived by Bethe and Livingston and having the form:

\[ -\frac{dE}{dx}=4\pi(ze^2)^2\,\frac{N}{mv^2}\left\{Z\left[\ln\frac{2mv^2}{I(1-\beta^2)}-\beta^2\right]-c_k\right\}. \tag{1} \]

Here \(ze\) is the charge of the particle, \(v\) is the velocity of the particle, \(m\) is the electron mass, \(N\) is the number of atoms in \(1\ \mathrm{cm}^3\) of the stopping substance, \(Z\) is the atomic number of the stopping substance, \(I\) is the mean ionization potential of the stopping substance, \(\beta=\dfrac{v}{c}\) (\(c\) is the speed of light), and \(c_k\) is a correction for the case when \(v\) is comparable with the velocity of a \(K\)-electron of the stopping substance.

From this, in principle, one can calculate the range of a particle with energy \(E\) in a substance in the form of the integral

\[ R=\int_E^0 \frac{dE}{\left(-\dfrac{dE}{dx}\right)} =\int_0^v \frac{Mv\,dv}{\dfrac{dE}{dx}}, \tag{2} \]

where \(M\) denotes the mass of the particle. However, direct calculation of the integral is possible only in rare cases, for example for fast cathode rays, for which the expression in braces changes with velocity considerably more slowly than all the other quantities; in this case the range is proportional to the fourth power of the velocity. For \(\alpha\)-particles\(^2\) the range already varies according to the law \(v^3\), and for canal \(H\)-rays according to the law \(v^{3/2}\).

If the corrections in formula (1) are neglected, then the expression in braces becomes \(Z\ln \dfrac{2mv^2}{I}\); this quantity, which for brevity we shall denote by \(B\), is called the stopping number of an atom of the stopping substance and is an important characteristic of the stopping substance with respect to the particles passing through it. If for air this number is equal to \(B_0\), then the quantity \(S=\dfrac{B}{B_0}\) may be called the relative stopping power of an atom of the stopping substance. The range of an \(R\)-particle is, evidently, inversely proportional to the number of electrons in \(1\ \mathrm{cm}^3\) of the stopping substance (\(NZ\)) or, using the quantities just introduced, to the relative stopping power of the substance (\(NS\)).

Comparing the given substance with air, we obtain the formula important for what follows

\[ \frac{R_0}{R}=\frac{N}{N_0}\cdot\frac{S}{S_0}. \tag{3} \]

Continuing to analyze formula (1), one can also verify that, for a given stopping substance, the interaction of a particle with the substance is determined by its charge and velocity. We shall characterize a particle passing through a substance by its ionizing ability, by which we shall mean the number of ion pairs formed by the given particle in passing through a layer of substance of such thickness that there is \(1\ \mathrm{g}\) of substance per \(1\ \mathrm{cm}^2\) of area. Taking into account the relativistic corrections, we obtain from formula (1),

that the least interaction with matter is exhibited by singly charged particles with velocity \(v \simeq 0.87c\). With the aid of formula (2) it is easy to see that, at this velocity, the range of particles in matter is inversely proportional to their masses. Consequently, the relativistic electron (or positron) has the least ionizing ability and the greatest range in the stopping substance. Some idea of the passage of various particles through air at the same initial energy is given by Table I, borrowed from Meidinger\(^2\).

Table I

Let us turn to the case when the role of the stopping substance is played by the photographic layer, i.e. the combination of silver halide and gelatin. If we were dealing with a chemical compound consisting of \(k\) different atoms, then in this case the following formula\(^3\), representing a generalization of formula (3), would be valid:

\[ \frac{R}{R_0}=\frac{d}{d_0}A_0\sum_{i=1}^{k}\frac{p_i S_i}{A_i}. \tag{4} \]

Here \(d\) is the density of the substance (the subscript “0,” as before, refers to air), \(A_i\) is the atomic weight, \(p_i\) is the weight fraction, and \(S_i\) is the relative stopping power of the atoms of the \(i\)-th component. The application of this formula to a photographic layer is, strictly speaking, not legitimate; nevertheless, calculations made on its basis have led to unexpectedly good results. This is apparently connected with the very high degree of dispersion of the silver halide and with its large concentration—about 50% by volume—which makes it possible to regard the emulsion layer as a kind of compound of the form \(\mathrm{AgHal}\cdot\mathrm{Gel}\).

The quantity \(\dfrac{R}{R_0}\), called the stopping power of the photographic layer relative to air, is not a constant quantity: it depends on the energy of the particles through the quantities \(S_i\). Therefore the result of the calculation by formula (4) is usually expressed in the form of curves of the dependence of \(\dfrac{R}{R_0}\) on energy. For emulsions with a silver halide content by weight of 80–85%, the stopping power is about 2000, decreasing sharply (to \(\sim 1500\) and less) in the region of low energies. For pure silver bromide the stopping power, calculated by formula (4), exceeds 3000.

The stopping power of emulsions gives us the possibility of determining the length of the particle range in the photographic layer. In this connection, for photographic recording of the particle range, only its passage through the emulsion crystals is of significance. It must be taken into account, however, that development of all the crystals encountered by the particle will be possible only if, from the moment the particle enters the layer, it loses in each crystal at least some minimum portion of energy corresponding to the sensitivity threshold of the crystals of the given emulsion. If this condition is not fulfilled, development of the crystals, even those traversed by the particle, does not occur. The sensitivity threshold indicates what minimum number of ionization events is required to be produced in a crystal in order to render it developable. But the number of such events over the extent of a single crystal also depends on the properties of the particle (charge, velocity), which determine its ionizing ability, or \(\dfrac{dE}{dx}\). Therefore the correspondence or noncorrespondence between the characteristics of the particle and of the layer, i.e. between the ionizing ability and the sensitivity threshold, is the criterion for the possibility of photographically recording the particle range. The particle range in the layer, determined by the stopping power of the layer, may not correspond to the length of the photographically recorded track, and only in the case of sufficient sensitivity of the layer are the length of the track and the length ...

the range coincide. In the remaining cases the length of the track is always less than the range for the following quite obvious reason: if a particle, on entering the layer, possesses a knowingly greater energy and, consequently, a smaller ionizing power than is required for its registration by the given layer, then its visible photographic action will begin from the moment when, as a result of its preceding passage through the layer, it has expended part of its energy and its ionizing power has come into correspondence with the sensitivity of the layer. It is precisely this residual part of the range that will be registered by the layer in the form of a track, and the length of the track for one and the same particle will be the smaller, the more inappropriate in sensitivity the layer was.

In reality the relationship between the properties of the particle and of the layer is somewhat more complicated than indicated above. It must be taken into account that no technological process for manufacturing an emulsion is capable of ensuring complete homogeneity of the crystals with respect to size and sensitivity. The number of acts of ionization produced by one and the same particle in different crystals may differ by 20–30% and more solely on account of differences in the sizes of the crystals^47. If this number of acts is at the limit of the sensitivity of the layer, then some part of the crystals struck by the particle will not acquire the capacity for development. The connection between the number of acts of ionization and the length of the path of the particle in the crystal may also manifest itself in the form of a different capacity for development in crystals struck by the particle along an edge and in crystals pierced by the particle along a diameter. Given complete homogeneity of the crystals in size and equality of the paths traversed in them by the particle, nonuniformity of the crystals with respect to the threshold of sensitivity may, in turn, have a substantial effect, and one and the same number of acts of ionization will impart developability not to all crystals. As a result, even with sufficient, on the average, sensitivity of the crystals, the track of the particle after development will, possibly, include not all crystals struck by the particle. If such a phenomenon occurs at the beginning of the track, then the eye may see the beginning of the track not where the first crystals struck by the particle and developed are situated, but where the distance between the struck crystals becomes sufficiently small; in this case the length of the track will be less than the range, despite sufficient sensitivity of the layer.

In the most favorable case, when all the crystals struck by the particle without exception become developable, and the range and the track of the particle in the layer are equal, one can, from simple geometrical considerations, find the number of crystals contained in the track. Such a calculation leads to the well-known formula of Zhdanov^4

\[ n = \frac{3}{2}\,\frac{c\lambda}{pd}, \tag{5} \]

where \(\lambda\) is the particle range, \(d\) is the diameter of the crystal, \(\rho\) is the density of the silver halide (for AgBr \(6.47\ \mathrm{g/cm^3}\)), and \(c\) is the concentration of silver halide in the emulsion (also in \(\mathrm{g/cm^3}\)). The considerations set forth above are formally taken into account by introducing a factor \(P<1\), indicating the probability that crystals will be developed under the action of the given particle; the number of crystals in the track will then be \(n' = nP\).

It is now necessary to determine, at least roughly, the number of acts of ionization produced in a single crystal by an ionizing particle. For this it is necessary to know two quantities: first, the loss of energy by the particle over the length of one crystal and, second,

Fig. 1.

the expenditure of energy on a single act of ionization in a silver-halide crystal. To obtain the first quantity we shall first confine ourselves to the case of a particle with the minimum ionizing power and turn to the curves of Fig. 1, constructed on the basis of formula (1). As can be seen, the curves for all singly charged particles have one and the same minimum value of \(\left(-\dfrac{dE}{dx}\right)\), although, of course, at different values of the corresponding abscissa. This value, equal for air to \(2.2\ \mathrm{keV/cm}\), must be multiplied by the stopping power of AgBr, which we shall take as equal to 3000, and by the diameter of the emulsion crystal, which for most nuclear emulsions is about \(0.3\mu\). The result obtained—\(0.2\ \mathrm{keV}\)—is the loss of energy by the particle in one crystal for the case, least favorable from the photographic point of view, of the passage of a relativistic singly charged particle. As for the second quantity, the data available here are not very reliable. First of all, these data refer not to bromide but to chlori-

silver, recently widely used in crystal counters. The most significant shortcoming of these data should be considered their disagreement among different authors: 13–16 eV per one act of ionization according to Hofstadter, Milton, and Ridgway^5, 7.6 eV according to van Heerden^6, and 6.6 eV according to Wightman and Streit^64. A critical examination of these values, as well as certain considerations expressed by Mott^7, compel one to regard van Heerden’s data as more reliable. Taking into account the close similarity of silver chloride and silver bromide, we shall use them for our calculation. Then we find that the least photographically effective particles create, in one crystal,

\[ \frac{200}{7.6}=26 \]

pairs of ions, i.e., 26 conduction electrons and the same number of neutral bromine atoms. Berriman^63, by a somewhat different route, obtained a similar value—22 pairs of ions. Such a minimal number of electrons must participate in the formation of the latent image and thereby lead to development of the crystal.

It is of interest to compare the value obtained with data on the minimum number of photoelectrons formed in an emulsion crystal under the action of light. To be sure, the available data of three different authors—Webb^8, Meiklar^9, and Herlin^10—give us not the number of photoelectrons, but the number of silver atoms in the latent image; however, since two of the authors^89 obviously worked under optimal illumination conditions, when each photoelectron corresponds to the formation of one silver atom, the available data are also applicable to photoelectrons. All three works give an astonishingly coincident value—eight electrons per crystal; with very prolonged development this number may be still smaller^9. Data^10 are also available for the action of hard X-rays (0.06 Å): in this case the liberation of more than 200 electrons is required. The latter value, however, should rather be compared with the values obtained for various particles and given below; it is also necessary to make a correction for the large sizes of the crystals in X-ray films (on the average about \(1\,\mu\)).

If we pass from relativistic particles to singly charged particles of lower energies, then the number of ion pairs created in one crystal must increase considerably. Demers^7, on the basis of his measurements for protons with an energy of 12 MeV, estimates this number roughly at 50–100 ion pairs; the curves of Fig. 1 make it possible to take this number as equal to at least 500. If, however, we pass to multiply charged particles, the values obtained increase by a factor of \(z^2\) at equal energies. For example, the \(\alpha\)-radiation of naturally radioactive elements, whose energy does not exceed 8–9 MeV, must create in one crystal, in any case, several thousand ion pairs; thus, for the \(\alpha\)-radiation of Po\(^{210}\) with an energy of 5.3 MeV one may expect the formation of about \(10^4\) ion pairs per

crystal. This value is in agreement with the measurement of the number of silver atoms formed in a bromo-silver layer by an α-particle with energy \(5.5\) MeV, carried out by Noddaq (see ²); he found that 50,000 atoms are formed in 10–15 crystals. For fission fragments of nuclei the number of ion pairs may reach \(10^6\) per crystal.

It should not be forgotten that 26 ion pairs per crystal is a threshold value, and moreover only in the case of the most highly sensitive layers, which register relativistic singly charged particles; the remaining layers have a higher sensitivity threshold and therefore will not register such particles, while at the same time registering particles of lower energies or of greater charge. This makes it possible, by photographic means, to separate particles of different nature or of different velocities, if one creates a set of layers differing in sensitivity threshold. The available data on the production of the firms Ilford, Kodak, etc. ¹¹ show that the whole variety of layers they manufacture is just such a set. Table II gives the sensitivity characteristics of Ilford plates ¹¹; here we also give, calculated by us from the curves of Fig. 1, data on the sensitivity threshold of these layers.

Table II

The sufficient constancy of the magnitude of the sensitivity threshold in each vertical column once again shows that, for the registration of particles, the decisive significance is not the nature of the particle, but the number of ionization acts produced by it in the crystal of the photographic layer.

We must now establish the further fate of the products of ionization—the conduction electron and the bromine atom, po-

since the manner of their occurrence in the crystal has already been considered. For this it is first necessary to give a brief account of the mechanism of formation of the latent image in an individual emulsion crystal.

3. FORMATION OF THE LATENT PHOTOGRAPHIC IMAGE

According to present-day views, the process of formation of the latent photographic image breaks down into two independent stages—an electronic and an ionic one, the first of which is very short in duration compared with the second. The original version of the theory of latent-image formation, first put forward by Gurney and Mott ^12 and covering only the action of light on photographic layers, contained a detailed description of each of the two stages, based on the facts known at that time. Although in recent times a number of new facts have been established, which has led to a considerable modification of the original theory, all proposed variants of the mechanism of latent-image formation ^13, ^14, ^15, ^16 necessarily include the two-stage Gurney–Mott scheme and merely represent in different ways the concrete form of each of the two stages.

The first stage—the electronic one—begins with the appearance of a photoelectron in the conduction band. Earlier ^12 it was assumed that this electron is liberated from a halide ion upon absorption of a light quantum according to the reaction $\mathrm{Hal}^{-} + h\nu = \mathrm{Hal} + e^{-}$, i.e., by exactly the same route as in the case of the action of particles. There are now convincing data ^15 in favor of the view that light liberates electrons not from halide ions, but from so-called $F$-centers, which should be regarded as electrons fixed in the crystal lattice at vacant anion sites, i.e., at the positions of missing halide ions. In one way or another, as a result of the primary photochemical act a free electron arises, capable of moving through the crystal until it is captured by some “trap” (in the energetic sense), in other words, by a level possessing a certain “depth” relative to the lower edge of the conduction band. Such traps may be any disturbances of periodicity in the crystal, but the effective ones among them are only those for which the depth of the corresponding levels is greater than the energy of thermal motion. Among them the most important role belongs to the so-called sensitivity centers, deliberately created in the crystals during the process of manufacture of the emulsion. These centers are, ^17 in all probability, particles of metallic silver located on the surfaces of the crystals, and they are the most effective traps, so that other traps can play a noticeable role either if the sensitivity centers were not created in the process of manufacture of the emulsion, or when these centers are filled (see

further). With the capture of the electron in the trap, for example at a sensitivity center, the electronic stage ends.

The product of the primary act is also a neutral bromine atom or a positive hole (in the case of an \(F\)-center). The bromine atom easily leaves the crystal because of its neutrality. The hole follows the electron to the place where it is captured, but this already belongs to the next stage. The second stage—the ionic one—begins from the moment of electron capture and consists in the formation of one neutral silver atom at the site of electron capture. For this it is necessary to neutralize a silver ion by the reaction
\(\mathrm{Ag}^{+} + e^{-} \to \mathrm{Ag}\). Gurney and Mott, considering it proved\(^{18}\) that in an AgHal lattice the only type of defects are interstitial cations \(\mathrm{Ag}^{+}\), assumed that this reaction proceeds by the Coulomb attraction of mobile \(\mathrm{Ag}^{+}\) ions to the sites of electron capture. However, the nature of structural defects in silver halides is at present a subject of discussion (see the collection\(^{19}\)), and for the neutralization process another mechanism has been proposed\(^{13,14}\), based on the relay departure of a halide ion from the site of electron capture, or, what is the same thing, on the displacement of an anion hole to the capture site. In any case, under any mechanism the ionic stage proceeds relatively slowly; to determine its duration, data on the ionic (dark) conductivity of AgHal may be used. The corresponding calculations\(^{1}\) give for the neutralization time a value of the order of \(10^{-5}\) sec. in the case of AgBr and \(10^{-4}\) sec. in the case of AgCl; this is at least 4–5 orders of magnitude greater than the duration of the electronic stage.

The difference in the rates of the two stages of the process of latent-image formation leads to very substantial consequences. A simple calculation\(^{1}\) shows that electrostatic repulsion does not allow other electrons to approach the capture site of one of the electrons before its neutralization. Therefore, if during a time shorter than that required for electron neutralization other electrons are released in the crystal, they are forced to be captured at other sites of the crystal. A latent-image center that imparts developability to the crystal consists of a group of atoms numbering not fewer than 8–10, as was already said above. Consequently, the emergence of new centers of latent-image formation instead of the continuous growth of one and the same center prevents the crystal from acquiring developability; in order for at least one latent-image center to attain the necessary dimensions, under these conditions the release of a larger number of electrons is required, part of which is used photographically ineffectively. The more slowly neutralization occurs, the greater the number of centers among which the latent image is distributed.

The described phenomenon for the case of the action of light is expressed in the form of the so-called deviations from the reciprocity law under short-time and intense illumination, i.e., a drop in the light-sensitivity of the layer when the illumination time is reduced\({}^{20}\); the reduction in the duration of illumination means the formation of the same number of photoelectrons over a shorter interval of time\({}^{20}\). Experiment shows\({}^{21}\) that the fall in sensitivity when the illumination time is reduced occurs down to \(10^{-5}\) sec., after which the sensitivity is stabilized, since neutralization does not occur at all during illumination, and a further decrease in illumination time no longer affects the sensitivity. Consequently, the losses of photoelectrons due to lagging of the ionic process may be characterized by the magnitude of the change in sensitivity when the illumination time is changed from \(10^{-5}\) sec. to the optimum time, i.e., such an illumination time for which the time interval between the formation of two successive electrons is approximately equal to the neutralization time. The change in sensitivity in such an interval of illumination times for most layers is of the order of two- or threefold. Consequently, if under optimum conditions (and such were the conditions in the works\({}^{8,9}\)) the formation in it of 8–10 electrons may prove sufficient for development of a crystal, then at very short illumination times 20–30 electrons are required for this purpose. If we now recall that in the case of the action of particles approximately the same number was required—no fewer than 26 electrons per grain—then such a coincidence can in no way be regarded as accidental.

The time required for a particle to pass through a crystal is usually \(10^{-13}\)–\(10^{-14}\) sec. During this time the formation of conduction electrons in the crystal also takes place; photographically, however, as we have already said, the times \(10^{-13}\) and \(10^{-5}\) sec. are equivalent owing to fulfillment of the reciprocity law in this interval. The agreement obtained is clear evidence that the formation of the latent image by ionizing particles proceeds analogously to its formation under the action of short-time intense illumination.

A similar idea has been expressed more than once: a number of authors\({}^{3,7,11,22,63}\) directly call deviations from the reciprocity law the cause of the photographic inefficiency of the action of particles, in the sense in which this is set forth here. There are also direct experimental data\({}^{23}\) showing that all possible factors associated with the processes of manufacture and development of photographic layers and responsible for the quantitative change in deviations from reciprocity under the action of short-time illumination cause an analogous change in the sensitivity of these layers to particles. It seems to us that the calculation presented above, which gave good agreement of the two quantities, still more convincingly confirms the validity of the analogy under consideration.

The data with which we operated for the number of photoelectrons were obtained on layers of high light sensitivity in one case and of high sensitivity to particles in the other. Layers of lower sensitivity require, for the manifestation to appear, a considerably larger number of photoelectrons per crystal. For the action of particles this number can be found from Table II by multiplying the sensitivity thresholds given there by \(\frac{1000}{7.6}=130\); for the action of light this number may likewise be of the order of hundreds \(\left(105\right.\) according to one set of data \(^{10}\), \(220\)—according to another \(^{24}\)). Such an increase is connected with the growth in the number of photoelectrons lost for the latent image owing to the lower effectiveness of the sensitivity centers in low-sensitivity crystals, as well as other causes considered below. However, all these causes should reduce to the same extent the sensitivity both to light and to particles. Therefore, at first glance it appears paradoxical that the well-known fact holds: all nuclear emulsions, including those sensitive to particles with minimal ionizing power, have very low light sensitivity.

The explanation of this contradiction apparently lies in recognizing the primary role of \(F\)-centers in the absorption of light by emulsion crystals. The number of \(F\)-centers, even in a crystal of an emulsion highly sensitive to light, is very small in comparison with the number of halide ions; but these centers are characterized by a relatively large number of electrons liberated per unit of absorbed energy, and their presence in the crystal substantially affects the light sensitivity. In the case of the action of ionizing particles, however, \(F\)-centers and halide ions, considered as electron donors, are equivalent, and the relative role of \(F\)-centers is determined primarily by their concentration—a quantity which, as has already been said, is very small. Moreover, \(F\)-centers may even lower the sensitivity to particles, since they possess not only donor but also acceptor functions. Consequently, methods for increasing the sensitivity of emulsions to light and to particles may be fundamentally different, and sometimes directly opposite. Thus, to increase the sensitivity of layers to hard radiations \(^{25}\), the introduction of PbBr\(_2\) and CdBr\(_2\) impurities into the solid phase of the emulsion is used; at the same time, according to Meiklar, these impurities lower the concentration of \(F\)-centers and cause a decrease in the photochemical and photographic \(^{26}\) sensitivity of silver bromide to light. Therefore the absence of parallelism*)

*) This absence of parallelism in no way contradicts the fact that the sensitivity to short-term intense illumination always changes in the same direction as the sensitivity to particles, since in the latter case only the relative inefficiency of short-term illumination is involved.

between photosensitivity and sensitivity to particles may serve as an additional indication of the important role of \(F\)-centers in the process of latent-image formation. The identity of the behavior of electrons liberated by light from \(F\)-centers and by a particle from halide ions at all subsequent stages of latent-image formation is beyond doubt; as an analogy let us recall that electrons liberated by light of various wavelengths (both in the region of intrinsic sensitivity and in the region of sensitization) also behave subsequently in a completely identical manner\(^{27}\). This makes it possible to present the subsequent material (not always sufficiently investigated in the part concerning particles) on the basis of data established for light.

The question that must now be considered concerns the distribution of silver atoms among the individual centers of the latent image. Since the time required for a particle to pass through a crystal is many orders of magnitude shorter than the duration of the ionic process, during the passage of a particle each possible fixation center—whether a sensitivity center or any other trap—can capture only one electron, since all subsequent electrons will be repelled by it. After the neutralization time has elapsed (\(10^{-5}\) sec. for AgBr), as many latent-image centers (each consisting of one atom) may appear in the crystal as there were electrons liberated during the passage of the particle. However, some of the electrons may recombine\(^{7}\) with bromine atoms, again forming ions, or with anion holes, forming \(F\)-centers. In any case, all centers arising as a result of the passage of the particle would have to consist of one atom and could not impart developability to the crystal. Consequently, subsequently some additional processes of regrouping of the latent image must occur, as a result of which some centers are supplemented at the expense of others and attain the dimensions required for development of the crystal. Such processes, in the case of the action of short-duration intense illumination, have in fact been observed\(^{20}\); they proved to be identical with the process of relaxation of photoconductivity\(^{28}\) and have a duration of the order of \(10^{-4}\) sec. It may be assumed that in the case of the action of particles an analogous phenomenon takes place. During regrouping, the special significance of sensitivity centers among the other traps present in the crystal is fully manifested; it is precisely at these centers that the concentration of the photolytically formed silver occurs first of all, whereas the other traps, with the possible exception of the deepest ones, tend to free themselves of silver atoms. This explains the low sensitivity of crystals in which such sensitivity centers were not created during the preparation of the emulsion.

A. L. KARTUZHANSKII

The described regrouping of the latent image should lead to the formation of at least one center of sufficient size (8–10 atoms in the best case), and then development of the crystal will become possible. But one can imagine a case in which, owing to the low sensitivity of the crystals, i.e., the insufficient effectiveness of the sensitivity centers present in them, regrouping will not lead to the appearance of centers that cause the onset of development, despite a sufficient number of photoelectrons released in the crystal. At the same time, along with atomic centers, one will observe the formation of stable groups consisting of several atoms—analogues of what was found in the case of the action of short-term intense illumination and was given the name subcenters \(^{29}\). The number of atoms in subcenters, according to some data \(^{8,9}\), is only two; i.e., any center larger than an atomic one must be thermally stable.

The probability that, by means of regrouping, a center consisting of some specified number of atoms will be formed must be determined by two factors: first, by the number of single-atom centers created in the crystal, which in turn depends on the number of released electrons, i.e., ultimately on the ionizing power of the particle; and, second, by the ability of the sensitivity centers present in the crystals to concentrate the latent image on the basis of the regrouping mechanism set forth above, i.e., by the properties of the photographic layer. The action of the second factor is most easily traced with the aid of the so-called method of double exposures \(^{30}\), and we shall have occasion to discuss this in detail in Section 5. As for the first factor, we shall confine ourselves to considering the following, in our view indisputable, proof of the connection between the ionizing power of a particle and the sizes of the centers it creates.

One may expect that the formation of large centers is more probable under the action of a particle of high ionizing power than of low ionizing power; subcenters, on the contrary, should have greater significance under the action of weakly ionizing particles. The presence of subcenters can readily be established \(^{30}\) from curves [[unclear: line continues into obscured/rotated text]].

Fig. 2.
Axis label: Exposure; vertical label: Density.

Fig. 3.
Axis label: Number of \(\alpha\)-particles per cm\(^2\); vertical label: [[unclear: vertical axis label]].

[[rotated text visible at bottom]]

and \(C\) is a constant related to the number of crystals struck by the particles. The coincidence of the curve in Fig. 3 (both the calculated and the experimental one \(^{2}\)) with curve II in Fig. 2 is obvious, all the more so since from formula (6) the slope of the curve in Fig. 3 must be maximal at the origin:

\[ \frac{dD}{dp} = \frac{Np}{C D^{\,m-?}}, \qquad \left.\frac{dD}{dp}\right|_{D=0} = N^{?}. \]

[[unclear: remaining rotated line fragment]]

…of $\alpha$-particles, which have a high ionizing ability ($\sim 10^4$ ion pairs per crystal), the dependence of the blackening density on the exposure is described by Kinoshita’s formula$^{31}$

\[ D = D_m(1 - e^{-cN}), \tag{6} \]

where $N$ is the number of $\alpha$-particles per $1\ \mathrm{cm}^2$ of the layer, $D_m$ is a constant characterizing the maximum value of $D$ attained in the given layer, and $c$ is a constant associated with the number of crystals struck by the particles. The agreement of the curve in Fig. 3 (both calculated and experimental$^2$) with curve II in Fig. 2 is obvious, all the more so because, from formula (6), the slope of the curve in Fig. 3 must be maximal at the origin of coordinates:

\[ \frac{dD}{dN} = cD_m e^{-cN}, \qquad \left.\frac{dD}{dN}\right|_{N=0} = cD_m. \]

Fig. 2.

Fig. 3.

Such a result means that each $\alpha$-particle makes the crystal it strikes developable (this has also been confirmed by direct experiment$^{65}$), since it forms centers in it, not subcenters. In the case of proton action$^{32}$, the blackening density is no longer described by a simple exponential function, and the form of the corresponding curve, when plotted in the same coordinates as in Fig. 2, is similar to a curve of type I. This peculiarity of the initial section is even more noticeable in the curves obtained for electrons$^{33}$, if, again, they are replotted in coordinates $D=f(I)$, where $I$ is the intensity. In the latter case the electrons in question have energies of $100\ \mathrm{keV}$ and higher, liberating in each crystal fewer than a hundred secondary electrons (as against $10^4$ electrons liberated by an $\alpha$-particle) and giving a probability of development considerably below unity$^{67}$.

A. L. KARTUZHANSKII

Thus, the form of the initial portion of the curves expressing the density of blackening as a function of exposure definitely indicates that the formation of subcenters is more probable under the action of weakly ionizing particles, and that particles with high ionizing power make developable all the crystals affected by them, although the centers of the latent image initially created by them consist of a single atom, as should be the case for any ionizing particle. The connection between the ionizing power of a particle and the formation of subcenters can also be traced by studying the kinetics of development. The data cited in Section 5 make it possible to confirm fully the conclusions just drawn.

Quite recently, the first data have appeared on the results of electron-microscopic investigation of the dispersity and topography of the latent image formed by $\alpha$-particles with an energy of $5.3$ MeV, by X-rays with energies from $30$ to $65$ keV, and by light of optimal or very low intensity1. These data show that the dispersity of the latent image is greatest in the case of the action of $\alpha$-particles and least in the case of the action of light; X-rays occupy an intermediate position in this respect. Thus, an increase in the dispersity of the latent image as the ionizing power of the radiation decreases has been directly demonstrated.

The centers of the latent image may differ not only in magnitude, but also in their position with respect to the surface of the crystal. The development reaction of a crystal always begins at its surface, and if the developer does not contain, in sufficient quantity, solvents of silver halide (for example, sodium sulfite), then the reaction is entirely confined to the surface layer of the crystal. Therefore the formation of large latent-image centers is effective, from the point of view of the developability of the crystal, only if it occurs on the surface of the crystal, since otherwise the crystal will not be developed despite the presence in it of the corresponding centers. Even when working with developers that dissolve AgHal, the efficiency of development of crystals containing only internal centers is reduced because of the delay in the initial stage of the development reaction. Here we again encounter the special significance of sensitivity centers, since they are created precisely on the surface of crystals after the stage of emulsion manufacture associated with crystal growth has ceased. These centers not only serve as deep traps capable, to the greatest extent, of retaining electrons captured in them (directly or as a result of rearrangement), but are also topographically situated in the most advantageous way.

Under conditions of a very brief action of radiation on the crystal, whether light of high intensity or a particle, in the crys-

in the crystals a high instantaneous concentration of photoelectrons is produced, as a result of which possible defects both on the surface and in the depth of the crystal become sites of fixation. Deep traps can draw to themselves part of the electrons, and to a greater extent the higher the electron concentration. For the case of light of high intensity it was shown by a direct experiment^34 that in the total amount of photolytic silver a substantial fraction is accounted for by the latent image formed inside the crystals. However, recently the unambiguity of this experiment has been called into question^35. In the case of the action of $\alpha$-particles there is also experimental evidence that the internal latent image constitutes the principal mass of the entire latent image^36, although these results too are not free from objections. It must also be taken into account that the concentration of photoelectrons in the crystal arising during the passage of $\alpha$-particles with an energy of $5.3$ Mev (such were the conditions of experiment^36) considerably exceeds the concentrations produced in most cases by particles, and thereby especially favorable conditions are created for the occurrence of a latent image inside the crystal. Nevertheless, there is no reason to doubt that, to a certain extent, an internal latent image actually arises whenever a particle passes through a crystal. This is also supported by the fact that electrons are liberated along the whole path of the particle in the crystal, including its deep part; and although the electrons have the possibility, by a relay process, of reaching the surface from any point in the depth of the crystal (according to indirect data^37, from all points lying less than $0.2\,\mu$ from the surface; recall that the diameter of the crystal is $0.3\,\mu$), the probability of their capture by internal defects is great. From this point of view the electron-microscopic observations already mentioned^37 of the latent image produced by particles and by light were of great interest; however, they revealed mainly differences in dispersity, adding in favor of the existence of a deep latent image only some, for the most part indirect, data.

It is necessary to emphasize the difference between the dispersity of the latent image, on the one hand, and the efficiency of utilization of photoelectrons, on the other. This can best be explained by an example. A relativistic singly charged particle produces $26$ photoelectrons per crystal. If recombination is neglected, all these electrons will be neutralized; the result will be $26$ silver atoms, from which subsequently there must form at least one center consisting of a minimum of $8$ atoms. Thus the efficiency (if one may so express it) in this case is

$$ \frac{8}{26} \simeq 30\%. $$

At the same time an $\alpha$-particle produces about $10^4$ photoelectrons, of

of which, again, a center of no fewer than 8 atoms must be formed. On the basis of a number of experiments connected with the manifestation and regression of the latent image, it is known that in this case in each crystal there is one or several centers considerably larger—say, of 100 atoms; the coefficient of useful action here will amount to only 1%. This is, perhaps, too crude an estimate, but in any case the coefficient of useful action is far from 30%. Consequently, although under the action of α-particles the sizes of the centers formed are considerably larger than under the action of relativistic particles, and the developability of the crystals is correspondingly higher, the photoelectrons are used less effectively.

This picture has an analogue also in the case of the action of light^[37]: light of low intensity forms a less disperse latent image than light of optimal intensity, although the efficiency of use of photoelectrons in the second case is tens of times greater than in the first.

Thus, the problem of creating, from all the metallic silver formed as a result of the passage of a particle, such centers as ensure the developability of the crystal, i.e. groups of 8–10 atoms, is readily solved only when the number of liberated electrons is many hundreds or, at least, tens of times greater than the number of electrons effectively used. If, however, the number of liberated electrons is small, as, for example, in the passage of a relativistic singly charged particle, then, owing to the relatively high dispersity of the photolytic silver formed and its distribution throughout the whole volume of the crystal, and not only over the surface, the problem becomes very complicated. Obtaining sufficient sensitivity of the crystals in this case depends especially strongly on the ability to create in them highly effective sensitivity centers. Unfortunately, the theory of this question belongs among the least investigated sections of photographic science, and the totality of the data available here has scarcely gone beyond a simple collection of facts. It is precisely this circumstance that compels one to speak “blindly,” about insufficient knowledge of the mechanism of the photographic action of particles.

Among methods for increasing the sensitivity of fine-grained emulsions (and, together with others, all nuclear emulsions are such), a special place is occupied by sensitization with gold salts, which has given excellent results both for light^[38] and for harder radiations—X-rays and gamma rays and secondary electrons^[2]. Although it is quite beyond doubt^[2] that the result of such sensitization is the formation of sensitivity centers possessing very high effectiveness as traps for electrons, there is no satisfactory explanation of the chemical essence of the action of gold salts.

4. DESTRUCTION OF THE LATENT PHOTOGRAPHIC IMAGE

The relatively high stability of the latent image—much greater than that of analogous products of photochemical reactions in crystals of other substances—by no means excludes the possibility of its destruction. The causes of destruction may be of two kinds: first, chemical reactions of metallic silver, as a result of which the composition of the centers of the latent image changes, and, second, the departure of electrons and ions from the center of the latent image owing to energy supplied from outside; the latter case is of particular interest to us.

The best-known form of destruction is the so-called regression, which consists in the gradual loss of developability by emulsion crystals as the interval of time between irradiation and development increases, or, in other words, the inability of the exposed layer to withstand prolonged storage. It is known also for light^39, but is expressed much more clearly for particles. It is now considered proven^40, ^41 that, in the main (according to some data^41, by 90%), regression is caused by chemical factors and, above all, by the reaction of the centers of the latent image with moisture and with atmospheric oxygen. However, some fraction of regression must be ascribed to the thermal dissipation of centers^42. This process should be conceived as the reverse of the process of formation of the latent image: owing to the energy of thermal motion, electrons are liberated from the centers of the latent image. The electrons pass into the conduction band and, as a result of subsequent processes, for example recombination, are lost for the latent image. After the electrons, the excess positive charges remaining at the center depart, and the centers decrease in size, passing into subcenters or dissipating completely. The probability of dissipation naturally increases with increasing storage time of the layer, and the degree of regression depends on the storage time \(t\) according to the law \((1 - e^{-\alpha t})\).

Thermal dissipation can explain a number of regularities of regression. Thus, regression is enhanced as the ionizing ability of the particle decreases; this is expressed, on the one hand, in the form of a dependence of regression on the type and energy of the particles^40, and, on the other hand, in the form of greater regression at the beginning of a track as compared with its end. This phenomenon is the basis of a method for distinguishing tracks of particles with not very different ionizing ability. With a sufficient storage time the tracks of tritons, for example, regress much more strongly than the tracks of \(\alpha\)-particles, and the distinction is made without error, whereas before storage the tracks of these particles are almost indistinguishable^65. It follows from the preceding section that a lower ionizing ability of a particle corresponds to a more

high dispersity of the latent image. Since the activation energy required for the liberation of an electron from a latent-image center increases with the growth of the center itself9, the probability of thermal destruction of a latent-image center increases as its dimensions decrease. From this it is easy to pass also to the temperature dependence of regression. If the activation energy is denoted by \(U\), then the probability of liberation should be characterized11, as usual, by \(e^{-\frac{U}{kT}}\). It is precisely this temperature dependence of regression that was established experimentally43; this is an indirect argument in favor of the mechanism set forth here for the dissipation of the latent image and, consequently, also of the reverse mechanism of latent-image formation.

Thermal dissipation can be observed not only for formed centers or subcenters, but also for individual silver atoms formed during photolysis. In the case of the action of light, such a phenomenon is well known and is the cause of the failure of the reciprocity law under prolonged and weak illumination20. In the case of the action of particles this phenomenon has not been observed directly, but, in Kovner’s opinion44, it manifests itself indirectly in the following way. In checking the fulfillment of the reciprocity law for photographic layers irradiated with electrons of energy 30–80 kev in an electron microscope, it turned out that one and the same exposure imparted to the layer at different irradiation durations gives the same photographic effect in the case when the time interval between the arrivals in the crystal of two successive electrons is much less than 1 sec. With an interval of the order of a second or more, the photographic effect decreases considerably, and this indicates the existence in the crystal of some phenomenon that prevents the formation of the latent image and has a duration of the order of a second; judging from the data available for the case of the action of light20, the process of thermal dissipation of atomic centers satisfies these requirements. However, under the action of light, the dissipation of atomic centers is characteristic of low illuminations, which are very unlike in their action to particles, especially to particles as weakly ionizing as electrons. At high illuminations, whose action is similar to irradiation with electrons23, atomic centers undergo rearrangement (see Section 3), having a duration of \(\sim 10^{-4}\) sec, before dissipation occurs. True, the rearrangement itself is also connected with thermal dissipation (since it is activated by thermal motion), but in a somewhat different manner. It is not yet possible to explain the discrepancy between Kovner’s data and the point of view presented here.

The described mechanism of dissipation is also valid for the destruction of the latent image by means of an additional action—

...exposure to long-wavelength light of such a spectral composition that it cannot itself form a latent image, but is absorbed by an already existing latent image. Absorption of a light quantum releases an electron from a center or subcenter, after which an excess positive charge remains. This phenomenon, called the Herschel effect, has recently been used^45 as a means of removing the fog produced in photographic plates by $\gamma$-radiation, without simultaneously destroying the tracks of $\alpha$-particles. Centers of the smallest size are most susceptible to the Herschel effect, as also to thermal fading; for the action of light this was shown by direct experiment^30. Therefore, for a latent image produced by $\gamma$-rays, the destructive action of additional nonactinic exposure is much greater than for a latent image produced by particles of appreciable ionizing power, in particular $\alpha$-particles. With respect to the tracks of particles of low and minimal ionizing power, the described method of fog removal is unlikely to have any value, since the number of electrons released by a $\gamma$-quantum in one crystal^25 proves to be of the same order as the number of electrons released by such a particle; consequently, the Herschel effect should be more or less the same for the fog and for the tracks.

Consideration of the chemical destruction of the latent image is not part of our task, although methods based on this principle (treatment with chromic acid^46, treatment with water vapor^43) are widely used in nuclear physics to remove undesirable tracks. It is only necessary to note that all these methods are associated with destruction of the surface latent image, and the subsequent fate of the crystal—development or nondevelopment—depends on the quantity and state of the internal latent image, and this in turn is determined by the ionizing power of the particle. Without assuming the existence of a surface and a deep latent image, it is impossible to explain the selective action of chemical agents with respect to the tracks of different particles; therefore the methods named serve as yet another proof of the high degree of dispersity of the latent image formed by particles, and of its tendency to be distributed throughout the entire volume of the crystal.

5. THE INFLUENCE OF DEVELOPMENT CONDITIONS, TEMPERATURE, AND ADDITIONAL EXPOSURE ON THE SENSITIVITY OF THE PHOTOGRAPHIC LAYER

All the factors listed in the heading are grouped together for the reason that the action of each of them is directly connected with the mechanism of formation of the latent image, in particular with the formation of subcenters under the action of particles. Their consideration will allow us to confirm and supplement the data presented earlier.

The mechanism of the development process can at present be set forth on the basis of the same ideas as the mechanism of formation of the latent image. According to the viewpoint of Gurney and Mott12, subsequently developed by Berg29, an ion of the developing substance gives up its electron to the center of the latent image. With the appearance of a charge on the center in the crystal, all the phenomena occur that accompanied the trapping of an electron in the formation of the latent image. Each such electron will therefore be neutralized by one of the silver ions in the crystal, with the formation of one silver atom at the center; as a result of repeated recurrence of this process, all the silver contained in the crystal is deposited at the center, forming a large metallic particle (most often in the form of filaments) accessible to direct observation.

The viewpoint set forth here corresponds to the following scheme of energy levels (Fig. 4), borrowed from Berg48. The level occupied by the electron in the ion of the developing substance must be higher than the levels of the latent-image center. In turn, the levels of the latent-image center are situated higher than those of the particle of metallic silver formed as a result of the growth of the latent-image center, i.e., in this scheme the growth of the silver particle is expressed by a lowering of the levels. The levels of the subcenter, not shown separately in Fig. 4, must occupy the highest position among the levels of the latent image, and their depth relative to the developer level is so small that an electron which has passed from the developer to a subcenter can easily leave it before neutralization begins, i.e., in the present case before development begins. If, however, neutralization occurs (and there is some probability of this), then the level to which the next electron passes will be located somewhat lower, and the probability of neutralization increases. Repetition of such a process is accompanied by an ever greater lowering of the levels and an ever greater probability of neutralization of the electron—what, in the language of chemistry, should be called the autocatalytic character of the development reaction. Naturally, development of the latent-image center proceeds in the same manner as that of the subcenter, with the difference that the levels of the center are located below the levels of the subcenter, and the probability of neutralization is comparatively greater.

Fig. 4.

relatively large already for the first electron transferred from the developer. Therefore there is every reason to believe that the distinction between centers and subcenters is not as sharp as, for simplicity, was assumed in Section 3: one cannot say that subcenters do not impart developability to the crystal at all. But the development process caused by subcenters is extremely extended in time, and if the development time is not sufficiently long, then we ascertain the absence of developability, although with a greater duration we could observe the development of crystals having only subcenters. Meiklyar showed\(^{9}\) that between the number of atoms \(N_0\) in a center or subcenter and the time \(t\) required for the development of a crystal containing such a center there exists the relation

\[ \frac{1}{N_0}=at+\beta; \]

with very prolonged development, developability of crystals with \(N_0=4\) (instead of 8—10) was observed.

Along with crystals containing a latent image, some crystals not affected by light or particles, which form photographic fog, also have the capacity for development. Their development is due to the presence of excessively large sensitivity centers, which do not require supplementation at the expense of photolytic silver in order to impart developability to the crystal. This case corresponds to the deepest levels of the sensitivity center in Fig. 4, located at the same depth as the lowest levels of the latent-image center. The formation of fog centers in crystals is highly undesirable, and it is desirable to stop the growth of sensitivity centers in the process of preparing a photographic emulsion at the moment when they correspond to the highest levels in Fig. 4, lying above the subcenter levels. Then the crystal will be capable of developing if it contains a center or even a subcenter of the latent image, but without exposure it will not develop. The technology of emulsion manufacture still makes it possible neither to stop the growth of sensitivity centers with sufficient accuracy nor to ensure complete uniformity of the crystals in sensitivity; therefore the appearance of fog during development is as yet unavoidable. Nevertheless, the best samples of the available photographic layers already combine high sensitivity with low fog.

In connection with the scheme of Fig. 4, one should mention another scheme, proposed by Keuer\(^{22}\) and having gained some currency in works devoted to the photographic action of particles. According to Keuer, the electron level in the developer occupies an intermediate position between the center levels and the subcenter levels; the levels of the fog center may be either above or below the electron level in the developer, but always below the subcenter levels. Then the developer can give up its electron to the latent-image center, and possibly also to the fog center; the subcenter, however, must itself give electrons to the developing substance. This means that the developer will

reduce to metallic silver crystals containing centers of the latent image and, perhaps, fog crystals, but will always destroy (i.e., oxidize) subcenters; consequently, according to Koehler’s scheme, development in the presence in the crystal of only subcenters is excluded. Meanwhile there is, in our opinion, indisputable evidence that development of a latent image dispersed to the state of subcenters is possible, and differs only in the kinetics of the reaction.

Grenishin2 obtained kinetic curves for the development of photographic layers of different sensitivity irradiated by electrons with an energy of 50 kev (Fig. 5). The course of these curves shows that development is the more extended in time, the lower the sensitivity of the layer or the effectiveness of grouping of the photolytic silver, i.e., in other words, the more probable the formation of subcenters instead of centers. It must be taken into account that the curves given were obtained for continuous blackenings, in producing which multiple hits of particles in one and the same crystal are possible; in this case there is the possibility of supplementing subcenters formed by preceding particles at the expense of electrons liberated by subsequent particles. Therefore, in the formation of blackening under the action of a flux of particles, subcenters have a somewhat lesser significance than in the formation of a track under the action of a single particle. Nevertheless, the curves in Fig. 5 definitely show the presence of subcenters, especially if they are compared with the kinetic curves of development of a latent image produced by light of different intensity. In Fig. 6 such curves are given for an exposure of low intensity and long duration (a) and of high intensity and short duration (b); the similarity of curve a to the curve for the action of electrons on a high-sensitivity layer and of curve b to the curve for the action of electrons on a low-sensitivity

Fig. 5.

... layer is quite obvious. Let us recall that, for light of high intensity, the existence and predominant significance of subcenters has been proved experimentally ^30,50. The point of Gurney’s work ^49 consists precisely in applying the same experimental methods to the case of the action of particles, with the aim of detecting identity or difference in the action of particles and of light; and the curves of Fig. 5 are one

Fig. 6.

of the proofs obtained by him (for others see below) of the similarity of the action of both radiations, in particular of the formation of subcenters under the action of particles.

There is also other evidence of a connection between the dimensions of the latent-image center and the kinetics of the development reaction. Thus, the differing developability of crystals subjected to the action of different particles served as the basis for developing a method of distinguishing tracks ^65. The same principle underlies the method of “controlled underdevelopment” ^52, which makes it possible to obtain sufficiently developed tracks of particles with greater ionizing power, without developing, in the same layer, the tracks of particles with lower ionizing power. Further evidence is provided by the well-known fact ^51 of the development of particle tracks from the end, i.e., beginning with those crystals in which the ionizing power of the particle was greatest and the latent image created by it was least dispersed. The same phenomenon is observed in the development of partially regressed tracks: as is known ^51,65, the development of such tracks requires a more vigorous or longer action of the developer, corresponding to the presence in the crystals of latent-image centers considerably smaller than immediately after the passage of the particle through these crystals. The latter, incidentally, serves as yet another indication that some part of the regression must be attributed not to the chemical action of the surrounding medium.

The facts set forth could to some extent be explained by the dissolving action of the developer, as a result of which the latent image located in the depth of the crystal begins to play an essential role. Indeed, when a particle with a high ionizing power passes through, when several thousand silver atoms are formed in a single crystal, a significant part of it is deposited inside the crystal owing to the limited capacity of the surface. However, for particles with a low ionizing power (and such, for example, are the electrons with which Grenishin worked) the latent image may be, to a considerable degree, a surface one, and for the action of light this is undoubtedly so. Moreover, the dissolving action of ordinary technical developers is too small^48 to explain the invariably observed difference^53 in the development kinetics of a latent image with clearly different dispersity, especially in the initial stage. Therefore, a more convincing explanation of the peculiarities of the development of the latent image formed by the action of particles seems to be, above all, its high dispersity, in complete agreement with the mechanism of its formation described here, and only to some extent the topographical features of its distribution in the crystal; the latter also does not contradict the mechanism set forth here.

The role of temperature in the process of formation of the latent image for the action of light has been elucidated quite fully (see review^20); for the action of particles there are only scattered experimental data^54,^55, which we shall now consider, using analogies between the action of particles and of light. It was shown^54 that, in the temperature interval from \(-78^\circ\) to \(+20^\circ\mathrm{C}\), the sensitivity of a whole series of nuclear emulsions with respect to protons of energy \(\sim 10\) MeV increases monotonically. With respect to \(\alpha\)-particles, a monotonic increase in sensitivity, estimated from the number of crystals in a track, was observed in the temperature interval from \(-185^\circ\) to \(+20^\circ\mathrm{C}\)^2,^55. Such an effect for the action of brief intensive exposure has long been known^56,^57 and is explained by a slowing of the ionic stage of the process of latent-image formation in connection with the decrease of ionic conductivity when the temperature is lowered. As a result, with decreasing temperature the dispersity of the latent image increases (see Section 3), this being further intensified by the fact that the rearrangement of the latent image, which requires thermal activation, also becomes less probable. There is every reason to believe that the observed dependence of sensitivity to particles on temperature has the same origin.

At the same time, at temperatures above \(20\)–\(30^\circ\mathrm{C}\) the sensitivity of layers to particles passes through a maximum and, at

with a further increase in temperature falls somewhat. A decrease in sensitivity with increasing temperature is also known for the action of light\(^{56,57}\), but only in the case of weak illumination of long duration, when thermal dissipation of the latent image is of substantial importance (see Section 4). The action of particles on highly sensitive layers\(^{49}\), when the centers formed in the crystals are relatively large and less subject to dissipation, should be similar to the action of light of low intensity. Beiser\(^{11}\) showed that the temperature behavior of the sensitivity of various nuclear plates, estimated from the number of crystals in the track of one and the same particle, is well described over a wide interval by the formula

\[ n = Ae^{-\frac{\varepsilon_1}{kT}}\left(1 - ae^{-\frac{\varepsilon_2}{kT}}\right), \tag{7} \]

where \(\varepsilon_1\) is the activation energy of ionic conductivity, and \(\varepsilon_2\) is the activation energy of thermal dissipation. The constants \(A\) and \(a\) depend on the sensitivity of the emulsion; \(A\), moreover, depends on \(\frac{dE}{dx}\). Thus, formula (7) takes into account both types of influence of temperature on sensitivity; following the explanation given above, one may expect that the factor in parentheses will differ noticeably from unity only for highly sensitive layers. Unfortunately, data on the magnitude of the coefficient \(a\) for different layers are lacking. In any case, the experimental results\(^{11,55}\) concerning the action of temperature on crystals affected by particles are exhaustively explained\(^{11,22}\) by means of the same two-stage Gurney–Mott scheme on the basis of which the temperature behavior of photosensitivity was also explained\(^{12,57}\).

A number of interesting data on the state of the latent image can be obtained by the so-called “double-exposure method,” based on the use of an additional fogging exposure of the photographic layer. First proposed by Webb and Evans\(^{38}\) and improved by Burton and Berg\(^{39}\), this method proceeds from the assertion that the combined action on a photographic layer of two fogging exposures, of which the first is brief and intense and the second long and weak, is characterized by a high photographic efficiency—in any case, always greater than with the reverse order of action of the same fogging exposures. The first of the listed fogging exposures creates a large number of subcenters, and the second supplements them to the size of centers, i.e., sharply increases developability\(^{39}\). The reverse order of the fogging exposures does not give the same effect because the prolonged weak fogging exposure by itself creates a small number of large centers, and the reasons why it may prove ineffective (thermal destruction at the initial stage of center formation) are not eliminated by the second fogging exposure.

Proceeding from the analogy between the action of light, especially of high intensity, and the action of particles, Grenishin\(^{49}\) applied the method of double exposures to the blackening produced on various photographic layers by a beam of electrons with an energy of 50 keV. It turned out that the action of light of low intensity after irradiation with electrons gave greater blackening than the reverse order of action, but only on layers of low sensitivity to electrons, where, as is assumed, the latent image exists in the form of subcenters. On layers with high sensitivity to electrons, where the latent image is grouped in the form of centers, the result proved to be the same for both orders of exposure. The action of an additional short-term and intense illumination did not lead to an increase in blackening on any of the layers, irrespective of their sensitivity. Both results fully correspond only to the explanation of the role of additional illumination set forth above.

The action of additional illumination can also be observed directly, without comparing the direct and reverse orders of action; such illumination, like development, is selective, since it acts on crystals containing a latent image, without affecting crystals without a latent image. Thus, the blackening produced by the β-radiation of RaE (maximum energy 1.17 MeV) on NT-2a plates can be increased by a factor of 1.5–2\(^{49}\) by means of an additional weak illumination, which by itself produces on this layer a barely noticeable fog \((D < 0.1)\). Since in this case the recorded radiation is, to a considerable extent, relativistic and has minimal ionizing power, while the plates used are intended for β-radiation with energies up to 0.1 MeV\(^{11}\), possessing at least twice as great an ionizing power, then on the basis of the preceding discussion one should expect the formation mainly of subcenters, and the enhancing action of the second illumination is quite natural.

The enhancing action of additional illumination depends on its spectral composition\(^{49}\); if experiments are carried out with spectrally dispersed light, then the positions of the enhancement maxima turn out to be the same as in the enhancement of the photographic action of short-term illumination\(^{50}\). On passing to increasingly longer-wavelength radiation in the second exposure, a point should be reached at which the enhancement is replaced by weakening as a result of the appearance of the Herschel effect (see Section 4). In this case, however, the boundary of the indicated phenomenon depends on the sensitivity of the photographic layer\(^{50}\), i.e., ultimately on the dispersity of the latent image; in this connection one should also recall the selectivity of the Herschel effect with respect to the photographic action of different radiations\(^{45}\), as was already discussed earlier.

On some layers, an “anomalous Herschel effect” was observed,^60 consisting in an enhancement of the action of particles (in this case, protons) under additional illumination with red light, instead of the expected weakening. It is characteristic that, in the same layers, a similar anomaly was also observed with respect to the action of an extremely brief exposure. Layers possessing this feature must consist of crystals with a comparatively high sensitivity to particles and to brief illumination. In such crystals, as Meiklyar showed,^61 red light does not so much destroy as create (or supplement) the latent image, whereas under the same conditions in low-sensitivity crystals this light is capable only of weakening the previously created latent image.

The “anomalous Herschel effect” is also noteworthy in that it helps to reduce the regression of a latent image that has undergone its intensifying action.^60 This can be explained by a decrease in the probability of thermal scattering of the latent-image center as it grows. The decrease in regression is especially noticeable in the initial period of storage of the irradiated layer; it may be thought that the physical causes of regression—and only they are eliminated by additional exposure—play an important role precisely in the initial period of storage, whereas subsequently chemical regression plays the predominant role.

In conclusion, let us touch upon one more question closely connected with the dispersity of the latent image—the nonobservance of the reciprocity law for blackenings produced by the action of particles. The reciprocity law must be fulfilled where each particle, having passed through any crystal, makes it developable, i.e., creates latent-image centers in it. If, however, a particle creates subcenters in the crystals (even if not in all of them), then the crystals cease to be physically identical, and the prerequisites for a violation of reciprocity appear. In addition, one must take into account the existence in crystals of processes of growth and destruction of the latent image after the end of the particle’s action (see Sections 3 and 4), whose duration is commensurable with the time between the passage of two particles through one and the same crystal. The very widespread earlier opinion that the reciprocity law is unconditionally fulfilled for any particles is explained by the comparatively small particle energies with which the experiments confirming this opinion were performed. Most often alpha (more rarely beta) particles of natural origin were used, and the limits of variation of the beam intensity were small. As the range of experiment widened, deviations from the reciprocity law were established for electrons,^44,62 and protons,^32 i.e., particles with relatively low ionizing power, which create the most dispersed latent image; violations of this

of the law under the action of $\alpha$-particles, which on average create larger centers, are known\(^2\) only for very low-sensitivity layers, where the crystals do not have effective sensitivity centers. Here we find yet another proof of the connection between the character of the particle and the state of the photolytic silver formed by it; this connection, let us recall, follows directly from the mechanism described above for the formation of the latent image under the action of particles.

If the exposure is of long duration, and the radiation is characterized by low ionizing ability (for example, in the case of $\beta$-radiography), then deviations from the reciprocity law, as was shown\(^ {33}\), can be partly attributed to regression during irradiation, which again is directly connected with the high dispersion of the latent image produced under these conditions.

6. CONCLUSION

In all the material set forth, the similarity between the photographic action of particles and the photographic action of light has been noted so many times that a natural question arises: is there in fact any difference at all between the action of the two kinds of radiation?

We have seen that absorption of the energy carried by either of these radiations gives rise in emulsion crystals to the same processes, proceeding in exactly the same sequence, but at the same time the absorption of energy itself occurs differently for particles and for light. For a definitive answer it is useful once again to recall all the differences we have established.

First of all, the centers of energy absorption under the action of light are mainly $F$-centers, whereas under the action of particles the energy is absorbed in the overwhelming majority of cases by halide ions in the lattice. This difference is of essential importance for the choice of methods for increasing the sensitivity of crystals, but it has no influence on the processes accompanying the act of energy absorption, beginning with the very first of them—the transition of a free electron into the conduction band.

Next, the energy of a particle is absorbed along a narrow “channel” in the crystal, corresponding to the path of the particle in it; this “channel” intersects the surface of the crystal at the points of entry and exit of the particle, while in the remaining, larger part it is located in the interior of the crystal, where absorption of the main part of the energy takes place. Light energy, however, is absorbed uniformly throughout the whole volume of the crystal, or—owing to the sharp increase in the absorption coefficient on passing to ever shorter wavelengths—uniformly in the surface and subsurface layer of the crystal. A consequence of such a difference may be the neodi-

topography of the latent image in an individual crystal and, in particular, the predominance of the internal image under the action of particles and of the surface image under the action of light.

Further, the time during which the particle is in the crystal is about \(10^{-13}\) sec., which is 6–7 orders of magnitude less than the shortest exposures encountered in photography. Therefore the instantaneous concentration of photoelectrons liberated in the crystal by the absorbed energy, in the case of the action of particles, may be extremely large in comparison with that in the case of the action of light. This promotes the formation of a highly dispersed latent image, on the average more dispersed than for light, although the processes of regrouping, growth, and dissolution of the latent image after the end of irradiation contribute to no small extent to smoothing out the differences in the dispersity of the latent image produced by particles and by light.

Finally, in the absorption of a light quantum, even from the ultraviolet region, the absorbed energy is sufficient only for the liberation of a valence electron and its transfer to the conduction band. The energy lost by a particle in the crystal is at least 2–3 orders of magnitude greater, and along with the liberation of valence electrons there may occur the liberation of electrons from deeper shells—\(K\), \(L\), etc.; however, the subsequent behavior of such electrons may in no way differ from the behavior of photoelectrons. At the same time, large portions of the energy of the particles may be imparted to individual electrons in the form of kinetic energy, and such electrons acquire the ability to traverse distances large in comparison with the diameter of the crystal. Thus secondary electrons arise, producing independent tracks and recently given the name \(\delta\)-electrons. The number of such secondary particles, which play an essential role in the identification of nuclei, especially in cosmic radiation, is determined by the ratio

\[ \frac{z^2}{v^2} \]

for the primary particle; if the charge of the primary particle is \(z \leqslant 2\), as was the case in the phenomena considered by us, and the velocities are not too small, then secondary particles practically do not arise at all. Moreover, secondary electrons, in forming their tracks, act on the crystals in the same way as any primary electron of the same energy, and therefore according to the mechanism set forth above. Thus, the possibility of simultaneous absorption in the act of ionization of a large amount of energy (as compared with a light quantum) does not entail the appearance of any essentially new phenomena.

All the differences listed in the photographic action of light and particles proved possible to explain without resorting to the supposition of the existence of any fundamentally new processes,

which would compel us to speak of a special mechanism for the formation of the latent image, inherent only in the action of particles. Under the action of light, by an appropriate choice of the photographic layer and illumination conditions, it is also possible to obtain a highly dispersed, to a considerable extent atomized, latent image, and moreover predominantly in the depth of the crystal. Many effects supposedly connected with the specificity of the action of particles are in fact a direct consequence of the two-stage Gurney–Mott mechanism under conditions of an extremely short exposure, impossible for light, and of the liberation of a considerably larger number of electrons in the crystal than under the action of light. All this represents differences of a quantitative, not a qualitative, character. Therefore, to the question posed at the beginning of this section one should answer that the mechanism of the photographic action of light and particles is the same, and the results of the action coincide to the extent to which the exposure conditions may be regarded as the same.

It will not be superfluous to point out that the peculiarities of the action of particles—especially when development is involved—are often attributed to phenomena which are in fact connected with the peculiarities of the layers used, namely, with the high concentration of silver halide and the great thickness of the emulsion layer. Since these peculiarities do not concern the mechanism of formation, or even the mechanism of development, of the latent image, we do not consider them here.

CITED LITERATURE

1. P. V. Meiklyar, UFN 38, 43 (1949).
2. W. Meidinger, Fortschritte der Photographie, Lpz., 1944, vol. 3, p. 245.
3. J. H. Webb, UFN 38, 77 (1949).
4. A. P. Zhdanov, J. de phys. et radium 6, 233 (1935).
5. A. Hofstadter, J. Milton and S. Ridgeway, Phys. Rev. 72, 977 (1947).
6. P. J. van Heerden, Dissertation, Utrecht, 1945.
7. See P. Demers, in the collection The Photographic Method in Nuclear Physics, IL, 1952, p. 77 ff.
8. J. H. Webb, JOSA 40, 3 (1950).
9. P. V. Meiklyar, ZhETF 23, 217 (1952).
10. H. Herlin, in the collection Radiography, IL, 1952, p. 24 ff.
11. A. Beiser, Rev. Mod. Phys. 24, 273 (1952). (For the translation see this issue.)
12. R. W. Gurney and N. F. Mott, Proc. Roy. Soc. 164A, 151 (1938).
    N. Mott and R. Gurney, Electronic Processes in Ionic Crystals, IL, 1950, ch. VII.
13. P. D. Dankov, ZhFKh 23, 1025 (1949).
14. P. V. Meiklyar, Usp. nauchn. fot. 1, 149 (1951).
15. P. V. Meiklyar, DAN 77, 391 (1951).
16. J. M. Hedges and J. W. Mitchell, Phil. Mag. 44, 357 (1953).

1. K. V. Chibisov, A. A. Titov and A. A. Mikhailova, DAN 54, 713 (1947).
2. C. Tubandt, Handb. Exper. Physik 12, 1 (1932).
3. Collection, “Physical Foundations of Photographic Sensitivity,” IL, 1953, part I.
4. A. L. Kartuzhanskii, UFN 51, 161 (1953).
5. A. L. Kartuzhanskii and P. V. Meiklyar, ZhETF 21, 532 (1951).
6. P. Koer, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 7–33.
7. A. L. Kartuzhanskii, ZhETF 22, 768 (1952).
8. K. Mees, Theory of the Photographic Process, Moscow—Leningrad, 1949, p. 227.
9. H. Hering and F. Müller, collection “Radiography,” IL, 1952, pp. 61–72.
10. S. Fujisawa et E. Mizuki, Sci. ind. phot. 23, 179 (1952).
11. M. Biltz and J. H. Webb, JOSA 38, 561 (1948).
12. P. V. Meiklyar, ZhETF 21, 42 (1951).
13. W. F. Berg, Trans. Farad. Soc. 39, 115 (1943).
14. P. C. Burton and W. F. Berg, Phot. J. 86B, 2 (1946).
15. S. Kinoshita, Proc. Roy. Soc. 83A, 432 (1910).
16. P. Brix und H. G. Demmelt, Zeits. f. Physik 126, 35 (1949).
17. R. C. Ray and G. W. W. Stevens, Brit. J. Radiol., 26, 362 (1953).
18. W. F. Berg, A. Marriage and G. W. W. Stevens, Phot. J. 81, 413 (1941).
19. P. Koer, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 33–50.
20. L. Winand, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 106–108.
21. F. A. Hamm and J. J. Comer, J. Appl. Phys., 24, 1495 (1953); H. Hoerlin and F. A. Hamm, J. Appl. Phys., 24, 1514 (1953).
22. R. Koslowsky, Zeits. wiss. Phot. 46, 65 (1951).
23. A. Otto, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 50–54.
24. J. Albu and G. Faraggi, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 124–132.
25. K. Mazer, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 140–143.
26. A. Beizer, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 132–133.
27. G. Faraggi, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 143–145; G. Faraggi and J. Albu, collection “Photographic Registration of Ionizing Radiations,” IL, 1953, pp. 223–231.
28. I. A. Kovner, ZhETF 20, 401 (1950).
29. A. M. Goldstein and C. H. Sherman, Rev. Sci. Instr. 23, 267 (1952).
30. N. A. Perfilov, Journ. of Phys. USSR 10, 1 (1946).
31. E. Pickup, Canad. J. Phys. 31, 898 (1953).
32. V. F. Berg, collection “Chemistry of Photographic Processes,” IL, 1951, pp. 122–123.
33. S. G. Grenishin, ZhTF 22, 33 (1952).
34. P. V. Meiklyar, DAN 69, 23 (1949).
35. G. Igoda, collection “Radiography,” IL, 1952, pp. 97–292.
36. G. Stevens, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 115–117.
37. P. de Vaucouleur et R. Viollet, Sci. ind. phot. 18, 97 (1947).
38. E. Dollmann, collection “The Photographic Method in Nuclear Physics,” IL, 1952, pp. 120–123.
39. T. R. Wilkins and R. N. Wolfe, JOSA 23, 324 (1933).
40. J. H. Webb, JOSA 25, 4 (1935).
41. A. L. Kartuzhanskii and P. V. Meiklyar, ZhETF 21, 693 (1951).

1. J. H. Webb and C. H. Evans, JOSA 28, 431 (1938).
2. K. Zuber, Nature 170, 669 (1952).
3. E. Schopper, S. Magun und W. Braun, Zeits. Naturforsch. 6a, 338 (1951).
4. P. V. Meiklyar, ZhFKh 19, 441 (1945).
5. B. von Borries und M. Knoll, Phys. Zeits. 35, 279 (1934).
6. R. W. Berriman, Phot. J. 89A, 121 (1949).
7. W. L. Whitemore and J. C. Street, Phys. Rev. 76, 1786 (1949).
8. C. Dilworth, G. Occhialini, and L. Vermezen, collection Photographic Registration of Ionizing Radiations, IL, 1953, pp. 128—129.
9. J. H. Webb, JOSA 38, 312 (1948).
10. D. Okrent and A. Solomon, collection Photographic Registration of Ionizing Radiations, IL, 1953, pp. 48—65.

2. Grenishin. ↩