PHOTOGRAPHIC PLATES FOR NUCLEAR PHYSICS

D. H. Webb*)

In 1896 Becquerel showed that uranium salts emit radiation that causes a photographic plate to darken.

In the early work on radioactivity, the radiation of these newly discovered substances was detected only by means of photographic plates. Later, however, when a number of quantitative studies had been carried out on the radiation associated with radioactivity, other methods of measurement became widely used.

In 1911 Wilson proposed a chamber, an instrument by means of which the tracks of individual charged particles could be seen.

At about the same time it was first shown that photographic plates could also record the tracks of individual charged particles.

In 1910 Kinoshita¹ demonstrated that the grains of a photographic emulsion can be activated by alpha particles and, moreover, that the action of a single alpha particle is sufficient to form in a grain a latent image capable of development.

In 1912 Reinganum² showed that the path traversed by an alpha particle in an emulsion is marked by a line of developable grains. From the time of this discovery, scientists have used photographic plates for recording and studying individual nuclear processes. Among the pioneers in this field, special mention should be made of Mysovsky**), Zhdanov**), Blau and Wambacher, and Wilkins. The work carried out up to 1941 is summarized in Shapiro’s excellent review³.

In their ability to record individual nuclear processes, photographic plates resembled the Wilson chamber, but they provided neither a fine distinction between the tracks of different particles nor, still less, the possibility of recording the deflections of charged particles in a magnetic field, as is done in the Wilson chamber.

*) Phys. Rev. 74, 511 (1948).
**) Translator’s insertion.

In the Wilson chamber one observes alpha particles, protons, deuterons, positrons, electrons, and mesons. It is highly desirable to bring the development of photographic plates to such a level that they too would record the tracks of all these particles over a wide range of energies.

Photographic plates satisfying these requirements, with their high stopping power and their ability to continuously record incident particles, will be an exceptionally important instrument for the study of nuclear physics.

The purpose of the present article is to show how far work in this direction has advanced, what properties modern plates possess, and what the prospects are for the future. An account is given of the mechanism of the action of charged particles on photographic plates, the composition and structure of modern nuclear plates are discussed, and a method is given for calculating the stopping power of an emulsion of known composition. The distribution of grains and the factors on which it depends are also considered; finally, certain questions of latent-image formation are discussed in connection with the number of ion pairs required to cause the development of an individual grain. In discussing all these questions an attempt has been made to show that the ideas presented are in agreement with practical results. The author does not seek to report new, unusual experimental results. (While this work was in press, two papers on the same subject appeared—by Demers^4 and by Lattes, Fowler, and Cuer^5. These papers contain considerably more experimental data on nuclear plates than the present work, and we recommend them in every way to the reader. A beautifully illustrated book has been published by Powell and Occhialini^6*.) Rather, the questions considered and the experimental data cited are intended as a guide for understanding the role and action of photographic plates when they are used as an instrument for investigating nuclear processes.

SPECIFIC ENERGY LOSSES AND RANGE–ENERGY CURVES OF CHARGED PARTICLES IN AIR

Fig. 1 shows the dependence of the energy loss per 1 cm of path when a proton passes through air. This curve gives the energy loss in MeV per 1 cm of path in air as a function of the proton energy, expressed in MeV, and was constructed on the basis of Smith’s theoretical data^7, using the following equation^8–10 for

) See Usp. Fiz. Nauk 35*, 213, 384 (1948).

PHOTOGRAPHIC PLATES FOR NUCLEAR PHYSICS

of the mean energy loss per unit thickness of the stopping material:

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

where \(ze\) is the charge of the incident particle; \(v\) is the velocity of the incident particle; \(N\) is the number of atoms in \(1\ \mathrm{cm}^3\) of the stopping material; \(Z\) is the atomic number of the stopping material; \(I\) is the mean ionization potential of the stopping material; \(m\) is the mass of the electron; \(\beta=v/c\) (\(c\) is the speed of light); \(C_k\) is a correction term which must be applied in the case when \(v\) is comparable with the velocity of a \(K\)-electron of the stopping substance, but is much greater than the latter for electrons of other shells.

Fig. 1. Theoretical curve of the dependence of the energy loss per \(1\ \mathrm{cm}\) path in air on the energy of a proton.

The main part of the energy loss experienced by charged particles passing through matter goes into the formation of ions in the interaction of the bombarding particles with the electrons of the stopping substance. The energy loss varies directly as the square of the charge \((ze)^2\) of the incident particle, inversely as the square of the velocity \(v\) of the particle, and directly as the number of electrons in a cubic centimeter of the stopping substance \((NZ)\). The quantity

\[ B=Z\ln\left(2\frac{mv^2}{I}\right) \tag{2} \]

is denoted as the stopping number of an atom of the stopping substance, and the ratio of \(B\) for a given substance to \(B_0\) for air is called the relative stopping power of an atom of this substance:

\[ S_a=\frac{B}{B_0}. \tag{3} \]

The curve of the dependence of the range on the energy of a charged particle in air can be obtained from integral (4), containing the rate of energy loss:

\[ R=\int_0^E \frac{dE}{\left(\dfrac{dE}{dx}\right)}. \tag{4} \]

The range–energy curve for protons in air, according to Smith, is shown in Fig. 2. From the curves of energy loss and range for a given type of particle, characterized by definite values of charge and mass, one can determine the energy loss and range curves of other particles with various values of \(z\) and \(M\) by means of equations (5) and (6). As an example let us consider alpha particles and protons.

Fig. 2. Theoretical curve of the dependence of range on energy for protons in air.

If an alpha particle and a proton have equal velocities, then

\[ \left(\frac{dE}{dx}\right)_{\alpha,v} = \left(\frac{z_{\alpha}}{z_{\mathrm H}}\right)^2 \left(\frac{dE}{dx}\right)_{\mathrm H,v}, \]

\[ R_{\alpha}(v) = \left(\frac{z_{\mathrm H}}{z_{\alpha}}\right)^2 \frac{M_{\alpha}}{M_{\mathrm H}}\,R_{\mathrm H}(v), \tag{5} \]

or, since particles having equal velocities have energies proportional to the values of their masses, equation (5) may be expressed in terms of particle energies:

\[ \left(\frac{dE}{dx}\right)_{\alpha,E} = \left(\frac{z_{\alpha}}{z_{\mathrm H}}\right)^2 \left(\frac{dE}{dx}\right)_{\mathrm H} \left(\frac{M_{\mathrm H}}{M_{\alpha}}E\right), \]

\[ R_{\alpha}(E) = \left(\frac{z_{\mathrm H}}{z_{\alpha}}\right)^2 \left(\frac{M_{\alpha}}{M_{\mathrm H}}\right) R_{\mathrm H}\left(\left(\frac{M_{\mathrm H}}{M_{\alpha}}\right)E\right). \tag{6} \]

Equations (5) and (6) are very convenient in those cases when, starting from known energy loss and range values for one particle, one passes to another, with differing values of \(z\) and \(M\).

In Fig. 3 are shown the curves of energy loss, in MeV per 1 cm of path in air, for alpha particles, deuterons, protons, mesons (with mass equal to 0.1 of the proton mass), and electrons. The proton curve is the same as that given in Fig. 1. Relative corrections have been introduced up to an energy value of 400 MeV. The curves for alpha particles, deuterons, and mesons were derived from the proton curve by means of equation (6) and are no more accurate than the proton curve. The curve of energy loss for electrons is shown on an enlarged scale in the right-hand part of Fig. 3.

Fig. 3. Theoretical curves of energy loss in MeV per 1 cm of path in air for α-particles, deuterons, protons, mesons, and electrons.

The energy-loss curves are presented in the present work because they are directly related to the mechanism that imparts to the photographic grain the capacity to be developed when charged particles act upon it, and therefore serve as material for discussion of this question below.

THRESHOLD OF SENSITIVITY OF PHOTOGRAPHIC LAYERS TO CHARGED PARTICLES

The threshold of sensitivity of plates used for investigations in nuclear physics can best be expressed by the minimum value of the specific energy loss at which the path of a particle will still be recorded as a distinguishable line of grains.

On the best modern nuclear plates it has been found that this limit is reached at an energy equal to approximately 100 MeV for deuterons and about 50 MeV for protons. Thus, on Ilford NTB plates irradiated in the cyclotron of the University of California with deuterons of energy 190 MeV, individual tracks are observed under the microscope over a length of about 2 cm from the point at which they stop in the emulsion. If the stopping power of the emulsion is taken to be 2000, then this range is equivalent to a range in air of 40 m, which corresponds precisely to an energy for the deuteron equal to 100 MeV. The end of such a track, corresponding to the maximum values of the energy, consists of sparse and irregularly arranged grains. It must be assumed that at

at such energy values, only grains with maximum sensitivity acquire the ability to be developed.

A direct illustration of the sensitivity of Ilford NTB nuclear plates is given by the photographs shown in Fig. 4. In the upper photograph a plate is shown that was irradiated with deuterons of energy 190 MeV in the cyclotron of the University of California. During irradiation the plate was placed edge-on to the deuteron beam. The deuterons struck a glass plate on which an emulsion layer had been deposited, penetrated into the glass and then into the emulsion. The tracks arising in the emulsion layer correspond to ener-

Fig. 4. Photographic plate irradiated with deuterons of energy 190 MeV. At the top—the plate irradiated with 190 MeV deuterons. Below—microphotographs of deuteron tracks at different distances from the end of the range.

deuterons at the given point. The dark part at the bottom of the photograph corresponds to the most intense part of the deuteron beam. It is noticeable that the blackening of the plate is small if the range of the particles is more than 6.9 cm, and then increases near the ends of the tracks in accordance with the Bragg ionization curve. It is interesting to note that the range of a deuteron with an energy of 190 MeV in glass is 6.9 cm, and in the emulsion—6.4 cm, if the stopping power of the emulsion is taken as 2000. It follows from this that the stopping powers of glass and of photographic emulsion are quite close.

In order to determine how deuterons with different energies are recorded on Ilford NTB plates, microphotographs were made of tracks from a plate subjected to a longer exposure than the preceding one, at points corresponding to 0, 0.5, 1.0, 2.0, 4.0, and 6.0 cm from the end of their range in the emulsion. These tracks are shown in the lower part of Fig. 4. Only parallel tracks were considered, since diagonal ones arise from deflected or secondary particles having lower velocity. From the photographs it follows that dense tracks are obtained at positions 0.0 and 0.5 cm (about 45 MeV), less dense tracks at position 1.0 (64 MeV), rare but still distinguishable tracks at position 2.0 (95 MeV). At position 4.0 (about 138 MeV) the tracks become quite rare and, finally, at position 6.0 (185 MeV) they are already only barely indicated by very sparsely located grains. From the photographs examined it follows that, with increasing energy of the recorded particles, no sharp decrease in the sensitivity of the photographic layer is observed. However, when the tracks are examined under the microscope, it is seen that the quality of the tracks deteriorates noticeably at energies above 100 MeV.

From the deuteron curve shown in Fig. 3 it follows that an energy of 100 MeV corresponds to a value of the energy loss in air of 0.013 MeV per 1 cm of range. Taking this value of the energy loss as threshold, i.e., such that a still sufficient number of grains will give distinguishable tracks, one can derive the following limiting energy values for other particles, irradiation with which will produce tracks of comparable quality:

Particle	Limiting energy
deuterons	100 MeV
protons	50 MeV
alpha particles	400 MeV
mesons ($200\,m_e$)	5 MeV
electrons	0.022 MeV

It is interesting to note that Ilford NTB plates irradiated in a cyclotron with alpha particles of energy 380 MeV record particles with this energy. The entire track (about 3.2 cm long), corresponding to particles of this energy, cannot be recorded in a thin emulsion layer. It has likewise never been observed that the beginnings of tracks of alpha particles with such energy were recorded.

Tracks of protons with high energy were recorded on Ilford Halftone plates by Wambacher.^11 One of these tracks had a length in the emulsion of 2 cm. If the value of the stopping power for the emulsion used is taken as 1300 relative to air, then in air the range of such a particle will be 26 m, which corresponds to an energy of 57 MeV.

Many authors^12–17 have published experimental work on the recording of meson tracks in photoemulsions. Lattes, Muirhead, Occhialini, Powell, and others^12 pointed out the circumstance that, probably because of insufficient sensitivity, mesons with energies above 5 MeV cannot be detected by Ilford C-2 plates. In a later work, Lattes, Occhialini, and Powell^16 analyzed meson tracks with various residual ranges. From the range the energy of the meson can be determined if some value is adopted for its mass; for example, if the mass is taken as equal to 200 electron masses, then the observed tracks correspond to mesons with an energy of 4.1 MeV. These results are cited as evidence that particles having energies between zero and the upper limits indicated can produce distinguishable tracks in nuclear plates.

Fig. 5. Microphotograph of an Eastman NTB plate irradiated with electrons of energy 30 KeV. The tracks have 4–5 grains.

Up to now it has not yet been possible to obtain entirely reliable tracks of electrons in emulsions. However, Demers^4 found that on very sensitive plates of his own manufacture complex tracks consisting of a small number of grains are observed, which he attributed to electrons. After Demers, workers of the Kodak research laboratory in England obtained electron tracks on highly sensitive proton plates.^18 Recently, electron tracks have been observed on Eastman NTB plates. A microphotograph of the tracks is shown in Fig. 5. The plate was exposed to electrons with an energy of 30 KeV in an RCA electron microscope; the electron beam was directed perpendicular to the plate. The photograph shows that these tracks are short and wavy, and each track consists of a few grains. From the electron energy-loss curve shown in Fig. 3 it follows that the limiting energy of electrons capable of producing a visible manifestation

grains, equal to 0.022 MeV. Electrons with such energy will have a range in air equal to 0.7 cm. If the stopping power of the emulsion is taken as 2000, this will correspond to a range in the emulsion of 3.5 μ. Therefore only a few grains at the end of the electron range (3 or 4) may prove capable of development. The action of electrons on the grains of the emulsion here is also in complete agreement with what is expected on the basis of energy-loss data.

It may also be concluded from this that in nuclear emulsions manufactured at present only a small fraction of the grains will be excited by particles whose energy-loss value is less than 0.013 MeV per 1 cm of air. This limit, somewhat arbitrary, is based on the assumption that the emulsion contains some fraction of grains with very high sensitivity and that a particle with such a value of energy loss will be recorded as a noticeable line of grains.

It is of interest to compare the value 0.013 MeV per 1 cm with the minimum value of the energy loss on the curves of Fig. 3, in order to see the present state of affairs with the registration of particles of the highest energies. It should be pointed out that all the energy-loss curves shown in Fig. 3 pass through a shallow minimum, almost equal in value for all types of particles, of approximately 0.0022 MeV per 1 cm. It follows that an emulsion with a sensitivity threshold 5–6 times lower would be suitable for registering particles of any energy value. Although this goal is hardly attainable, a study of the curves of Fig. 3 shows that every small improvement in the sensitivity threshold will reduce the disproportion in the energy values of the different particles that can be recorded. Taking into account the fact that nuclear plates have been seriously studied only quite recently, there is reason to hope that their sensitivity can be raised to a value corresponding to an energy loss of 0.0022 MeV per 1 cm.

RANGE–ENERGY CURVES FOR CHARGED PARTICLES IN PHOTOGRAPHIC EMULSIONS

To illustrate the range–energy relation for nuclear plates with a high content of silver bromide, Figs. 6 and 7 give curves of the dependence of the range in the emulsion (in microns) on the energy (in MeV), respectively for alpha particles and protons. The curves for alpha particles in Fig. 6 are constructed on the assumption that the stopping power does not depend on the energy and is equal to 1800 relative to air. This value was chosen on the basis of the average results obtained on NTA and NTB emulsions exposed to alpha particles with energies below 9 MeV, emitted by natural radioactive substances such as thorium, polonium, and uranium. Each batch of Ilford plates gave standard—

... results upon irradiation with polonium alpha-particles (5.3 MeV) with ranges between 21 and 22 microns, in good agreement with the value of the stopping power 1800.

The data published by Lin, St. John, Chestelet, Faraggi, and Vigneron\(^ {19}\) for alpha-particles recorded on Ilford Halfton plates are given in the table on p. 87.

These data indicate that there is a drop in the value of the stopping power when going over to lower energies. Below, the question of the stopping power of emulsions will be considered in more detail, and a method will be given for calculating this quantity with allowance for the stopping power of the atoms entering into the composition of the emulsion, for a specified composition.

For energies above 10 MeV, so few measurements have been made of the ranges of alpha-particles in emulsion as a function of energy that for this region it is impossible to construct an experimental curve. Therefore, until a sufficient number of measurements has been made for energies above 10 MeV, the curve for this region shown in Fig. 6 must be regarded as approximate.

Fig. 6. Curves of the dependence of the range in emulsion on the particle energy for the case of \(\alpha\)-particles. The emulsion contains a high percentage of AgBr. The stopping power is taken to be 1800.

Fig. 7. Curves of the dependence of the range in emulsion on the energy of protons. The emulsion contains a high percentage of AgBr. The stopping power is taken to be 2000.

The vertical arrow in Fig. 6 indicates the track of fission fragments of \(U_{235}\) and corresponds to the range obtained by many authors\(^{20–22}\) who used photographic plates for recording fission fragments.

The range (25 μ), indicated by the arrow, corresponds to the full length of the track of two fragments. One of such tracks, obtained on an Ilford NTC plate, is shown in Fig. 19. It should be noted that the greatest grain density is observed in the middle part of the track. The large charge of the particles immediately after the decay causes a large initial

Stopping power of the emulsion for α-particles

	\(E\) (in MeV)	Range in the emulsion (in microns)	Stopping power relative to air
ThC′	8.77	46.1	1860
ThC	6.05	26.2	1810
Po	5.29	21.4	1790
UI	4.71	18.8	1710
UII	4.15	15.6	1700

ionization, despite the high velocity of the particles. Since the fragments rapidly lose velocity, the ionization increases. However, the loss of charge by the fragments more than compensates for the loss of velocity, and as a result a decrease of ionization is noticeable along the track, as indicated by the decreasing grain density at the end of the track. It is of interest to determine the mean effective charge of a fragment from the observed ranges of uranium fission fragments; applying equation (6):

\[ R_{\text{frag}}(E)=\left(\frac{z_{\mathrm H}}{z_0}\right)^2 \left(\frac{M_0}{M_{\mathrm H}}\right) R_{\mathrm H}\left(\frac{M_{\mathrm H}}{M_0}E\right). \]

Substituting a fragment mass equal to 117 proton masses and a charge value equal to 10, we obtain, for an energy of 160 MeV for both fragments:

\[ R_0(160)=\left(\frac{1}{100}\right)117 R_{\mathrm H}(1.36)=4.68\ \text{cm of air}, \]

or, for the range in the emulsion, taking the stopping power as 1800,

\[ R_0=26\ \mu. \]

Thus, if the mean charge for the fission fragments is taken to be 10, the value of the range is in good agreement with experiment.

On the scale of Fig. 6 the cross section of an emulsion \(25\mu\) thick is shown in comparison with the length of tracks. It is clear from the figure that the thickness of an emulsion layer of \(25\mu\) is sufficient for recording tracks of alpha particles with moderate values of energy. However, for energy values above 15 MeV, plates with a greater thickness of the emulsion layer, reaching 50 and \(100\mu\), are necessary. In Fig. 7 the curve of the dependence of range on energy is given for protons with energies up to 40 MeV. The curve was constructed for a constant value of the stopping power of the emulsion relative to air, taken as 2000, instead of the value 1800 adopted in constructing the curves for alpha particles. This value was chosen as a result of tests of Ilford NTB plates irradiated with protons with energies below 10 MeV. Ilford NTB plates were regularly tested by irradiating them with protons of 7 MeV energy on the cyclotron of the University of Rochester. The average value of the ranges for such protons in the emulsion is equal to \(300\mu\). Comparing this range with the range in air for such protons, equal to 60 cm, gives the relative stopping power of the plates, equal to 2000. In fact, the stopping power of the emulsion does not have a constant value independent of the energy of the particles, but increases rather sharply with increasing particle energy in the region of low energies and levels off into a flat curve at higher energies, as shown in Fig. 9. From this figure it follows that the flat region of the stopping-power curve is reached at considerably lower energy values for protons than for alpha particles, and this is in agreement with the higher value of the stopping power (2000) used in constructing the curves of Fig. 7.

Owing to the absence of experimental data on the stopping power of the plates at energies above 10 MeV, and also owing to the sharp change of stopping power at low energies, the range–energy curves shown in Figs. 6 and 7 should be regarded only as a fairly reliable guide in considering these relationships.

In Fig. 7 the cross section of emulsions \(25\), \(50\), and \(100\mu\) thick is given for the purpose of comparing these values with the lengths of tracks of protons of various energies. Commercial emulsions at the present time have layer thicknesses up to \(100\mu\). In recording protons with energies above 10 MeV, it is required that the greater part of the beam fall within the small angle defined by the thickness of the emulsion layer.

For completeness, in Fig. 8 the range–energy curves for mesons and deuterons are presented. Both curves were constructed for a constant stopping power of 2000; it was also assumed that the mass of the meson is \(1/10\) of the mass of the proton.

It follows from the foregoing that, for recording particles with high energy, plates with an emulsion-layer thickness many times exceeding \(100\mu\), i.e. up to several milli-

meters thick. Unfortunately, a number of circumstances hinder the use of plates with such a great thickness of the emulsion layer. The casting of gelatin emulsions with thicknesses above 100 μ is extremely difficult. A 100-micron coating of the support (film) will cause it to bend. If, however, the casting is done on glass, the gelatin layer will peel off and be destroyed owing to the fact that the tensile forces arising in the gelatin are sufficient to destroy the surface of the glass on which the emulsion layer has been deposited.

In addition, great difficulties are encountered in processing thick layers. Both processes—development and fixing—depend on the diffusion of chemical reagents into the emulsion layer and of reaction products out of the layer. Since the chemical agents are exhausted inside the layer, a properly proceeding process of exchange diffusion is necessary for complete development and fixing of the layer. Even in plates with a layer thickness of 100 μ, development and fixing are carried out with difficulty, and sometimes the process proceeds unevenly at different depths of the layer. Finally, it should be pointed out that the thickness of the emulsion layer which can be examined with a microscope is limited by the working distance of the objective used. When using an objective with oil immersion, a focal length of 1.8 mm, and 97-fold magnification, the maximum working distance in the emulsion without a cover glass is 300 μ.

Fig. 8. Curves of the dependence of range on energy for mesons (A) (0.1 proton mass) and deuterons (B). The emulsion contains a high percentage of AgBr. The stopping power is taken as equal to 2000.

FACTORY PLATES FOR NUCLEAR PHYSICS

The plates considered here for research in nuclear physics are manufactured by the Ilford and Kodak firms in England and by the Eastman firm in America.

The Ilford Research Laboratory has issued a brochure describing its plates for recording the tracks of charged particles, giving the photographic characteristics and the composition of the emulsions. The following table and description of the plates are given:

Type B-2 is a fine-grained and the most sensitive emulsion, giving good tracks of alpha particles and protons with energies of 2–4 MeV.

Type C-2 is a finer-grained emulsion than B-2; it gives more distinguishable tracks of alpha particles and protons. It is specially prepared for recording proton tracks suitable for measurement.

Type E-1 has a finer grain than C-2; it gives alpha-particle tracks of improved quality, suitable for precise measurement of their ranges. Proton tracks are poor and differ noticeably from alpha-particle tracks.

Type D-1 is finer-grained than E-1; it gives poor alpha-particle tracks; proton tracks are not recorded at all. It is suitable for recording tracks of fission fragments. These plates may be considered obsolete, but are produced for special purposes.

Type B-1. The emulsion has grains similar to those in emulsion B-2, and a sensitivity similar to that of emulsion C-2. Usually, emulsions B-2 or C-2 are chosen for work.

Type C-1 is similar to E-1, but with a coarser grain and greater sensitivity. It gives poor discrimination between tracks of alpha particles and protons with low energy.

The standard thickness of emulsion layers is 50–100 microns. All emulsions, except C-1 and D-1, can be loaded with lithium, boron, or beryllium; plates can also be manufactured with a lower content of silver halide in the gelatin.

All these plates, manufactured according to the standard, have the same chemical composition. Under normal atmospheric conditions, one cubic centimeter of emulsion contains: Ag — 1.87 g, H — 0.056 g, Br — 1.36 g, O — 0.24 g, J — 0.053 g, S — 0.014 g, C — 0.33 g, N — 0.083 g; Ca, P, Cr, Si, Na — traces.

The Ilford company has also published tables of the dependence of ranges on energies, based on range measurements in the energy interval from 0 to 10 MeV, and has extrapolated these values to energies from 10 to 35 MeV, both for alpha particles and for protons.

The range values as a function of energy published by Ilford differ little from those given in Figs. 6 and 7 for alpha particles and protons with energies below 10 MeV; however, for the energy region above 10 MeV there is some difference. This occurs because the curves of Figs. 6 and 7 are constructed at a constant stopping power of the emulsion for all energy values. In the next chapter the question of stopping power is considered in more detail, and curves are given for the dependence of range on energy for different values of the stopping power.

The Kodak company has recently begun to produce plates for nuclear research under the name NTP-2. These are highly sensitive plates, specially recommended for recording fast particles with low ionizing power. At the experimental stage there are the first plates for recording electrons. The plates are issued in the size \(2.5 \times 7.5\) cm and with emulsion thickness ...

PHOTOGRAPHIC PLATES FOR NUCLEAR PHYSICS

of a layer of 50 μ. In sensitivity, stopping power, and physical characteristics these plates are similar to Ilford NTB plates. They are described below.

Table I

Nuclear plates of the Ilford firm

		Type NTA	Type NTB *)	Type NTC
Sensitivity	To charged particles	α-particles up to 200 MeV Protons up to 20 MeV Deuterons up to 20 MeV	α-particles up to 400 MeV Protons up to 50 MeV Deuterons up to 100 MeV Mesons up to 5 MeV	Fragments
Sensitivity	To light, γ-rays and β-rays	Low	Medium	Very low
Development	For showing ionization losses with energy	2 min at 20° C in D-19	2 min at 20° C in D-19	Special instructions
Development	For obtaining tracks for counting	2 min at 20° C in D-8 diluted 2:1	2 min at 20° C in D-8 diluted 2:1	Special instructions
Recommended fixing	Recommended fixing	F-5 or 30% hyposulfite	F-5 or 30% hyposulfite	F-5 or 30% hyposulfite
Emulsion thickness	Emulsion thickness	from 25 to 100 μ	50 and 100 μ	25 μ
AgBr content (% in dry emulsion)	AgBr content (% in dry emulsion)	83%	83%	65%
Grain size (diameter)	Grain size (diameter)	0.2–0.4 μ	0.2–0.3 μ	0.1–0.4 μ

*) Recommended in all cases for recording particles with high energy and low ionizing power.

At present the Ilford firm produces three main types of plates for nuclear research: NTA, NTB, NTC. The principal properties of these plates and the recommended conditions for their photographic processing are given in Table I.

Samples of tracks of various nuclear particles registered on such plates are shown in Figs. 16–19. It should be mentioned that NTA and NTB plates may be used with fillings of boron, lithium, and beryllium; the amount of the filling substances is expressed in milligrams per \(1\ \mathrm{cm}^2\) for each plate number. There is a special instruction for the use and processing of these plates.

For a number of problems it is desirable for the physicist to know exactly the composition of the photographic plates. For Ilford plates the following data are given. All emulsions are mixtures of gelatin with silver bromide. The composition of gelatin in weight percent is:

Element	Weight percent
carbon	50.0
hydrogen	6.7
nitrogen	18.0
oxygen	25.0

Nuclear plates have a relatively high percentage of silver bromide in comparison with ordinary plates. Emulsions

Table II

Composition of Ilford plates

Element	NTA and NTB: weight percent	NTA and NTB: atomic ratio	NTC: weight percent	NTC: atomic ratio
Ag	47.1	1.0	38.0	1.0
I	1.49	0.027	1.24	0.027
Br	33.9	0.97	27.4	0.979
C	8.47	1.62	16.2	3.83
H	1.17	2.68	2.25	6.38
N	3.06	0.50	6.84	1.17
O	4.80	0.69	9.09	1.62
Relative humidity in %	Moisture impurity in dry emulsion	Moisture impurity in dry emulsion	Moisture impurity in dry emulsion	Moisture impurity in dry emulsion
50	2.2	2.2	4.5	4.5
70	4.0	4.0	8.0	8.0

Ilford NTA and NTB contain about 83% silver halide and 17% gelatin. NTC plates have about 65% silver and 35% gelatin.

Table II gives the composition of NTA, NTB, and NTC plates in weight percent and in atomic concentrations. The composition was determined by chemical analysis of the dry emulsion. For exact work the values of the atomic composition must be corrected for the moisture content according to the lower part of Table II.

STOPPING POWER OF PHOTOGRAPHIC EMULSIONS

It appears possible to give a calculation of the stopping power of a photographic emulsion, based on the latest data on the atomic stopping power of the substances entering into the composition of the emulsion.

The method for calculating the stopping power of chemical compounds, when the atomic stopping power of the elements composing the compound is known, has been set forth by many authors\(^{23—24}\). We shall give a survey of the method for calculating the stopping power of a chemical compound before applying it to the case of photographic emulsions. The relative atomic stopping power of one substance in comparison with that of another substance taken as a standard can be determined by the relation

\[ \frac{R_0}{R}=\frac{N}{N_0}\frac{S}{S_0}, \tag{7} \]

where \(R_0\) is the range of a charged particle in air, \(R\) is the range in the substance being determined, \(N_0\) is the effective number of atoms per \(1\ \mathrm{cm}^3\) of air under normal conditions, calculated from the mean atomic weight, and \(N\) is the number of atoms in \(1\ \mathrm{cm}^3\) of the substance under investigation. The quantity \(S/S_0\) is the atomic stopping power of the substance relative to air.

As Koehr has indicated, the quantities usually measured in experimental work are not \(R_0/R\), but the relative differential ranges for small energy intervals, \(\Delta R_0/\Delta R\). Therefore we shall modify relation (7):

\[ \frac{\Delta R_0}{\Delta R}=\frac{N}{N_0}\frac{S}{S_0}. \tag{8} \]

or, since \(S_0\) for air is taken equal to unity,

\[ \frac{\Delta R_0}{\Delta R}=\frac{N}{N_0}S. \tag{9} \]

If we replace the quantities \(N\) and \(N_0\) by their equivalent values expressed through density and atomic weight, i.e. \(N = kd/A\) and \(N_0 = kd_0/A_0\), we obtain the expression

\[ \frac{\Delta R_0}{\Delta R}=\frac{dA_0}{d_0A}S. \tag{10} \]

Bragg established the fact that the stopping power of a chemical compound consisting of different types of atoms is an additive quantity. Consequently, for a compound we may write:

\[ \frac{\Delta R_0}{\Delta R}=\frac{n\left(N_1S_1+N_2S_2+N_3S_3+\ldots+N_iS_i\right)}{N_0}, \]

where \(N_1, N_2,\) etc. are the numbers of atoms of each type in the molecule, and \(n\) is the number of molecules of the compound in \(1\ \mathrm{cm}^3\). Since

\[ N_0=\frac{n d_0}{A_0} \]

and

\[ n=\frac{d}{N_1A_1+N_2A_2+\cdots+N_iA_i}, \]

we find:

\[ \frac{\Delta R_0}{\Delta R} = \frac{dA_0}{d_0} \left( \frac{N_1S_1+N_2S_2+\cdots+N_iS_i} {N_1A_1+N_2A_2+\cdots+N_iA_i} \right) = \frac{dA_0S}{d_0M}. \tag{11} \]

where \(M\) in equation (11) is the molecular weight and \(S\) is the molecular stopping power. For calculation purposes it is more convenient to write (11) in the form*):

\[ \frac{\Delta R_0}{\Delta R} = \frac{dA_0}{d_0} \left( \frac{N_1A_1S_1}{A_1\sum_j N_jA_j} + \frac{N_2A_2S_2}{A_2\sum_j N_jA_j} +\cdots+ \frac{N_iA_iS_i}{A_i\sum_j N_jA_j} \right). \]

This relation can be simplified:

\[ \frac{\Delta R_0}{\Delta R} = \frac{dA_0}{d_0} \left( \frac{p_1S_1}{A_1} + \frac{p_2S_2}{A_2} +\cdots+ \frac{p_iS_i}{A_i} \right), \tag{12} \]

where \(p_i=N_iA_i/\sum_j N_jA_j\) represents the relative weight of each element in the compound.

A photographic emulsion is not a chemical compound in the sense of a homogeneous chemical combination of atoms or identical molecules. It is a highly dispersed mixture of two compounds—gelatin and silver bromide. Gelatin is the medium in which silver bromide is suspended in the form of small crystals. The physical characteristics of the emulsion for which the stopping power calculations are given are presented in the following table:

Characteristic	Value
density of the emulsion	\(3.64\ \mathrm{g/cm^3}\)
weight percentage of silver bromide in the dry emulsion	\(85.0\%\)
weight percentage of gelatin	\(15.0\%\)
density of silver bromide	\(6.47\ \mathrm{g/cm^3}\)
concentration of silver bromide in the emulsion	\(3.09\ \mathrm{g/cm^3}\)
mean grain diameter	\(0.3\ \mu\)
mean grain mass	\(0.92\cdot10^{-13}\ \mathrm{g}\)
number of grains per \(1\ \mathrm{cm}^3\) of emulsion	\(3.36\cdot10^{13}\) grains/\(\mathrm{cm^3}\)
impurity content (in % of dry emulsion)	\(3.35\%\)

If we assume that such a mixture of grains of silver bromide and gelatin can be regarded as a chemical compound of

*) This formula was used by Coer\(^{24}\) for calculating the stopping power of emulsions.

of the various atoms, we can calculate the relative stopping power of the emulsion from equation (12), assuming that the atomic composition of the emulsion and the atomic stopping powers of the atoms entering into it are known. To illustrate this, we give the following calculations of the stopping power of the emulsion as a function of energy*).

An emulsion containing 85% silver bromide contains 3.35% impurities relative to the dry weight of the emulsion, and gelatin consisting of 50% carbon, 6.7% hydrogen, 18% nitrogen, and 25% oxygen. The atomic composition of the emulsion is given in Table III.

Table III

Composition of the emulsion

(iodide is not taken into account in the calculation, since it has little effect on the stopping power; for the calculation, iodide is replaced by bromide. The composition of the emulsions, as well as their stopping power, is the same for Ilford NTA and NTB plates and Ilford plates)

Element	Number of atoms per AgBr molecule	Weight per AgBr molecule	\(p_i\) (weight %)	\(\dfrac{p_i}{A_i} = \dfrac{\text{fraction of total weight}}{\text{atomic weight}}\)
Ag	1.0	107.88	47.20	0.004375
Br	1.0	79.92	34.95	0.004373
C	1.39	16.70	7.30	0.006083
H	3.06	3.08	1.35	0.013410
N	0.43	6.02	2.64	0.001886
O	0.932	14.90	6.53	0.004081

A table of atomic stopping powers for the elements hydrogen, carbon, aluminum, copper, silver, and gold as a function of the energy of alpha particles and protons was published by Bethe and Livingston\(^{25}\). In constructing curves relating stopping power and atomic weight, one can obtain from these values interpolated values of the atomic stopping power for bromine, nitrogen, and oxygen. Table IV gives the published values, as well as data obtained by interpolation.

The stopping power of the emulsion relative to air was calculated for each energy value appearing in Table IV,

*) The method for calculating the stopping power of a heterogeneous emulsion follows directly from the method developed by A. [[unclear: name]], to whom the author expresses deep gratitude (not published).

with the application of equation (12) and the following values of the constants: the mean atomic weight of air \(A_0=14.5\), the density of air \(d_0=0.001205\,\text{g}/\text{cm}^3\);

Table IV

Values of the stopping power of atoms

Energy (in MeV)	Energy (in MeV)	Atomic stopping power	Atomic stopping power	Atomic stopping power	Atomic stopping power	Atomic stopping power	Atomic stopping power	Atomic stopping power
\(E_\alpha\)	\(E_{\mathrm{H}}\)	\(S_{\mathrm{Ag}}\)	\(S_{\mathrm{Br}}\)	\(S_{\mathrm{C}}\)	\(S_{\mathrm{H}}\)	\(S_{\mathrm{N}}\)	\(S_{\mathrm{O}}\)	\(S_{\text{air}}\)
2.07	0.52	2.25	2.07	0.94	0.260	1.02	1.10	1.0
4.66	1.17	3.08	2.68	0.932	0.224	1.02	1.10	1.0
8.30	2.09	3.43	2.94	0.921	0.209	1.01	1.10	1.0
12.95	3.26	3.64	3.10	0.914	0.200	1.01	1.09	1.0
18.60	4.70	3.76	3.19	0.908	0.194	1.00	1.09	1.0
33.20	8.36	3.93	3.30	0.899	0.186	1.00	1.08	1.0
51.90	13.06	4.04	3.38	0.892	0.181	0.99	1.08	1.0
Extrapolated	Extrapolated	Extrapolated	Extrapolated	Extrapolated	Extrapolated	Extrapolated	Extrapolated	Extrapolated
80.0	20.0	4.12	3.44	0.850	0.170	0.98	1.07	1.0

the density of the emulsion \(d=3.64\,\text{g}/\text{cm}^3\); the atomic stopping powers \(S_i\) are given in Table IV.

The values of the relative stopping power \(\Delta R_0/\Delta R\), obtained in this way for alpha particles and protons of various energies, are given in Table V. In Fig. 9 the integral stopping power \(R_0/R\) for protons and alpha particles is plotted as a function of the energy expressed in MeV.

Fig. 9. Dependence of the integral stopping power of the emulsion on energy for protons (A) and \(\alpha\)-particles (B).

The values for constructing this curve were obtained as follows. The differential values of the range in air in a narrow energy interval (2 MeV) were divided by the stopping-power values from Table V, and the corresponding values of the range in the emulsion were obtained. These quantities were then summed to obtain the integral value of the range in the emulsion. The quotient obtained by dividing the integral values of the range in air by the value of the range in the emulsion,

gave the integral value of the stopping power of the emulsion for a given energy. The points shown in Fig. 9 are the experimental values of the stopping power, published by Lattes, Fowler, and Coer^26 for Ilford B-1 emulsion. The content

Table V

Stopping power of the emulsion

Energy MeV $E_\alpha$	$E_{\mathrm{H}}$	$\Delta R_0/\Delta R$
2.07	0.52	1511
4.66	1.17	1764
8.30	2.09	1868
12.95	3.26	1930
18.60	4.70	1964
33.20	8.36	2009
51.90	13.06	2040
Extrapolated	Extrapolated	Extrapolated
80	20	2065

of silver halide in these emulsions, according to the Ilford data cited earlier, is equal to 81%. The content of silver bromide in the emulsion (with 3.5% moisture), according to Table III, is equal to 82.05%. Since the silver halide content in the emulsion is very close in both cases, the experimental points agree well with the values of the theoretically calculated stopping power*).

In Figs. 10 and 11 the transformed curves are presented and the dependence of the range in the emulsion (in microns) on the stopping power is shown.

*) The theoretical curve of stopping power (Fig. 9) for alpha particles agrees well with the data of Chin San-chang, Nester, Faraggi, and Vigneron^19 for Ilford Halftone plates. Peck^38 made measurements of stopping power on Eastman NTB plates for protons with energies of 2–9 MeV. He found a constant value of the stopping power in this energy interval, equal to 2050. However, his measurements showed a sharp increase of the stopping power below 4 MeV, reaching at 2.4 MeV a value of 2820. This result is at present unclear, but since it is in sharp contradiction with the theoretical and experimental data of other authors, there must have been some unusual conditions in the experimental work or in the emulsion that led to such a result. This problem can be clarified only by further careful work in this direction.

In Fig. 12 are given theoretically calculated curves of the dependence of the range in the emulsion on the energy of alpha particles and protons, taking into account the values of the stopping power presented in Fig. 9.

It is of interest to present the result of calculating the stopping power as a function of energy for pure silver bromide. Using equa-

Fig. 10. Curve of the dependence of the calculated integral stopping power on the range in the emulsion for α-particles.

Fig. 11. Curve of the dependence of the calculated integral stopping power on the range in the emulsion for protons.

tion (12) and the values of the stopping power for silver and bromine atoms from Table IV, one can obtain the value of the stopping power for silver bromide. These values are approximately 50% higher than for the emulsion.

DENSITY OF PHOTOGRAPHIC GRAINS IN TRACKS OF CHARGED PARTICLES

The question of the density of developed grains in the track of a charged particle recorded in a photographic emulsion is of great importance for physicists using the photographic method for recording charged particles. From the distance between grains it is often possible to determine the type of particle under investigation. For example, from the distance between grains and from small scattering angles one can unmistakably distinguish the track of a meson from the track of a proton[^13][^16]. It may be assumed that the distance between grains depends on the energy loss (the curves are shown in Fig. 3). For the same points on the curve with the same energy loss, the distance between grains on the tracks of different particles will be the same. This result is valid, since the activity of a particle in forming the latent image depends on the number of ions arising in the grain. From this point of view, the process of latent-image formation under the action of charged particles does not differ in essence from that under the action of light.

Fig. 12. Curves of the dependence of range in emulsion on energy for protons (A) and α-particles (B). The stopping power changes according to the curve in Fig. 9.

It is now well established[^27]–[^29] that, under the action of light, an individual grain of the emulsion acts as a whole. Light quanta strike a silver bromide crystal, and each quantum, being absorbed in the crystal, raises the energy state of an electron associated with a bromine ion. An electron located at an energy level corresponding to the conduction level can move freely in the crystal and can be displaced under the action of an electric field. This phenomenon has been well demonstrated by experiments on photoconductivity in silver bromide crystals. The free electron will move in the crystal until it comes into contact with the so-called sensitivity center of the grain (some impurity or disturbed surface of the crystal), where it is captured at the lowest energy level, situated below the conduction band. The electron captured in this way will be surrounded by an electrostatic field that will attract any positive silver ion located nearby. Since, in general, mobile silver ions are always present in a silver bromide crystal (as has been shown by the study of the ionic conductivity of these crystals at

at room temperature), these ions will move toward charged centers, where they will combine with electrons, forming silver atoms. This process is repeated until an amount of silver sufficient for development has been formed. It seems probable that exposed grains may contain many inclusions of silver of various sizes; however, grains acquire the capacity for development only when they acquire a sufficiently large, properly situated inclusion.

Fig. 13. Diagram illustrating the impulse imparted to an electron when a charged particle passes.

In the case of irradiation of grains by fast charged particles, as the particle passes through the grain, electrons arise in it. The electrons liberated in this way will in general be similar to the electrons produced by the action of light and may serve for the formation of the latent image. However, one distinction must be pointed out: under the action of particles with high energy, electrons are formed inside the grain in a very short interval of time. Thus, when irradiated by alpha particles with an energy of 5 MeV and with a grain size of \(0.3\,\mu\) in diameter, all electrons are liberated in \(2\cdot 10^{-14}\) sec. This rapidity of electron liberation may lead to the ineffectiveness of the photographic process, first, because the positive and negative ions formed by the particle lie along a straight, narrow track inside the grain. The ions will tend to recombine, and therefore some of them will be lost for the process of formation of the latent image.

Secondly, it is well known that, for a short exposure to light, less than \(10^{-3}\) sec., the exposure is not very effective because of a violation of the reciprocity law of the photochemical process of latent-image formation. In order for the formation of the latent image to proceed successfully, the electrons must be liberated at a rate comparable with the rate of motion of silver ions and must be neutralized immediately after capture. If too short an exposure is given, the silver of the latent image tends to disperse throughout the grain, which leads to ineffectiveness of the process.

The preceding brief description of the theory of formation of the latent image will serve as the basis for explaining the fact that the distances between grains in a photographic track, when irradiated by particles with different charges but with the same velocity, and when irradiated by identical particles having different velocities, are not the same.

In Fig. 13 the rotation of an electron around an atom of the stopping substance and the passage of a charged particle with charge \(ze\) and velocity \(v\) past this electron at a distance \(p\) are shown schematically.

The force experienced by the electron when the charged particle is in its vicinity has order of magnitude

\[ F=\frac{ze^2}{p^2}. \]

The impulse experienced by the electron is given by the product of the force \(F\) and the time \(t\) during which the particle is in the vicinity of the electron. To a first approximation this time may be taken as equal to

\[ t=\frac{2p}{v}. \]

Thus, the impulse is equal to

\[ Ft=\frac{ze^2}{pv}. \tag{13} \]

Now let us consider the impulse imparted to the electron in two cases: 1) when a proton passes by, 2) when an alpha particle with the same range passes by. It is known that an alpha particle and a proton of equal range have equal velocities. This follows from the fact that an alpha particle, having four times the energy of a proton, loses it four times faster than the proton, owing to its double charge, as is readily seen from equation (1). If we now equate the impulses in these two cases, we shall find that

\[ \frac{2e^2}{p_\alpha v}=\frac{e^2}{p_{\mathrm H}v}, \]

whence

\[ \left(\frac{p_\alpha}{p_{\mathrm H}}\right)^2=4. \]

It is easy to see that \(p_\alpha\) and \(p_{\mathrm H}\) determine the diameters of cylinders in which the actions of the alpha particle and the proton, respectively, are equal. The number of atoms contained in such cylinders will be proportional to the value \(p^2\). Thus, one may expect that, at equal velocities, an alpha particle will ionize approximately four times as many atoms as a proton.

Similarly, it is well known that protons and deuterons of the same range have velocities related by the ratio \(v_{\mathrm H}=1.25v_{\mathrm D}\). The ratio of the values of \(p\), since the charges are the same, will be equal to 1.25. Therefore deuterons will produce \(1.25^2\), i.e. 1.56 times more ions than a proton of the same range.

The sensitivity threshold of the photographic grain must depend, to a first approximation, on the number of ion pairs formed in the grain. On the basis of this fundamental assumption, the diagram shown in Fig. 14 can schematically explain the inequality of the distances—

... between grains under the action of various particles. Let us suppose, for example, that a charged particle with a given range passes along the path indicated by the arrow in Fig. 14. Its path passes through different thicknesses in different grains, which are distributed irregularly in space. Let us suppose that the incident particle is a proton having such a velocity that it can create a sufficient number of ion pairs for the formation of a latent image only in those cases when it passes through the entire diameter of a grain. Then, since such a path passes only through two marginal grains, only these grains will acquire the capacity for development. A deuteron with the same range, having a lower velocity and therefore a somewhat higher ionizing power, will possibly activate grains 1, 3, 4. An alpha particle with the same range, having the same velocity and thus a four times greater ionizing power as compared with the proton, will activate on its path all the grains from the first to the fourth.

Fig. 14. Diagram illustrating the passage of a charged particle through randomly arranged emulsion grains.

The distances between grains in the tracks of alpha particles, deuterons, and protons for equal residual ranges were measured by Wilkins and St. Helens \(^{30}\), and it was found that the grain density in proton tracks was about one half of that for alpha particles, and that the grain density for deuteron tracks lies between the densities for alpha-particle and proton tracks.

When charged particles, such as alpha particles (with energies less than \(10\ \mathrm{MeV}\)) and protons (with energies less than \(3\ \mathrm{MeV}\)), have very low velocities, they ionize strongly and will activate practically every grain with which they come into contact. Under these conditions the grain density in the track will approach the maximum value corresponding to the grain density in an unexposed emulsion. From this point of view it is interesting to give the maximum grain density as a function of the concentration of silver bromide \(C\) and of the grain diameter \(d\) for an emulsion of a given type. If it is assumed that all grains are spherical and have diameter \(d\ \mathrm{cm}\), then a simple calculation shows that the number of grains which will be struck by a particle traveling along a straight path of length \(\lambda\) will be equal to the total number of grains whose centers lie inside a cylinder of diameter \(d\) and length \(\lambda\). This number is easily found by dividing the concentration of silver bromide in the emulsion, \(C\ \mathrm{g/cm^3}\), by the mass of one grain and multiplying by the volume of a cylinder of diameter \(d\) and length \(\lambda\). The final expression will be:

\[ n=\frac{3}{2}\frac{C\lambda}{d\rho}\ \text{grains per }1\ \mathrm{cm}, \tag{14} \]

in which \(\rho\) is the density of silver bromide in \(\text{g}/\text{cm}^3\). If we take \(\lambda\) equal to \(1\ \text{cm}\) and \(\rho\) equal to 6.47, then for the maximum grain density we obtain the expression

\[ n = 0.23\,\frac{C}{d}\ \text{grains}/\text{cm}. \tag{15} \]

This relation was first given and verified by Zhdanov\({}^{31}\) and later by Demers\({}^{4}\). Zhdanov, using several emulsions with different values of \(C\) and \(d\), verified equation (15) by measuring the relative distance between grains \(\Delta\). If we put

\[ \Delta = \frac{1}{n} = \frac{d}{0.23\,C}, \tag{16} \]

then

\[ \frac{\Delta_1}{\Delta_2} = \frac{d_1}{d_2}\,\frac{C_2}{C_1}. \]

This relation between the values of \(\Delta\) for different emulsions proved to be valid with satisfactory accuracy. Demers also checked equation (16) on a number of factory-made and special experimental emulsions and found that the minimum distance between grains \(\Delta_0\) for alpha particles near the end of their range is in good agreement with the theoretical minimum distance between grains \(\Delta\), calculated from (16).

It is interesting to calculate the value \(\Delta_0\) for the emulsion for which calculations of stopping power were made earlier in this work. Using the values \(C = 3.09\ \text{g}/\text{cm}^3\) and \(d = 0.3\,\mu\), we find that

\[ \Delta_0 = \frac{d}{0.23\,C} = 0.435\,\mu . \]

Fig. 15. Curves of the dependence of grain density on the distance to the end of the track of a charged particle.

In Fig. 15 are shown experimental data for the density of grains, expressed as a function of the residual range, obtained by Brock and Gardner\({}^{32}\) for Ilford NTA plates. The points show the numbers of grains per \(0.1\ \text{mm}\) of path length for different residual ranges of alpha particles and deuterons. It can be seen that the grain density for deuterons is smaller than for alpha particles of the given

path. In the case of alpha particles, for the shortest measured residual path the grain density is approximately 1.5 grains per micron, corresponding to a value of 0.6 $\mu$.

Lattes, Occhialini, and Powell$^{16}$ developed a useful method for determining the relative masses of two types of particles with the same value of charge from the grain density. It is well known (see equation 5) that the rate of energy loss of a charged particle having a fixed value of charge is a function only of the particle velocity and does not depend on its mass. Therefore the rate of energy loss may be written as

\[ \frac{dE}{dR}=f(v). \tag{17} \]

Since the photographic effect depends on the rate of energy loss, it may be assumed that the grain density along the track will also be a function of the velocity, and thus

\[ \frac{dN}{dR}=f(v). \]

From equation (5) it can be seen that the length of the residual range $R$ of a particle with a given velocity $v$ and fixed charge is proportional to its mass $M$. Thus, the grain density may also be written as a function of the residual range divided by the mass:

\[ \frac{dN}{dR}=f\left(\frac{R}{M}\right). \tag{18} \]

Integrating, we find that

\[ N=M\int_{0}^{R/M} f\left(\frac{R}{M}\right)\,d\left(\frac{R}{M}\right). \tag{19} \]

Since the integral on the right will have a definite value, starting from that point of the track where the velocity has a specified value (a specified value of $R/M$), then for two different particles having different masses, the total numbers of grains $N_1$ and $N_2$ on the residual ranges $R_1$ and $R_2$ will be in a ratio equal to the ratio of the masses $M_1$ and $M_2$. Thus,

\[ \frac{R_1}{R_2}=\frac{N_1}{N_2}=\frac{M_1}{M_2}. \tag{20} \]

If it is required to compare the masses of two particles by counting grains, then the procedure consists in finding points along two trajectories for which the grain densities are equal. Then the ratio of the masses of the two particles will be equal to the ratio of two residual ranges, or to the ratio of the total number of grains in two residual ranges (for which $\frac{N_1}{R_1}=\frac{N_2}{R_2}$).

ANALYSIS OF TRACKS OF CHARGED PARTICLES AND CALIBRATION OF PLATES

In analyzing tracks of charged particles in a photographic emulsion, the experimenter must be sure of the measurements of the recorded residual range of the particle in the emulsion, the small scattering angles along the track, and the grain density along the track. The true range of the particle and the small scattering angles will depend on the composition of the emulsion, and it may be expected that they will remain constant on going from one emulsion to another. However, the recorded range of the particle and the distance between grains at the beginning of the track will depend on the sensitivity of the individual grains of the emulsion, which is very difficult to reproduce accurately. Consequently, if a photographic plate is used for quantitative purposes, for example to determine the properties of a particle by measuring the range and the distance between grains, it is essential that the plates used be subjected, in the same experiments, to control irradiation by particles with known characteristics, for example protons or alpha particles of known energies, and be processed in a definite manner. All plates coated with emulsion from the same emulsion batch should give similar results, provided that before exposure they were kept under proper conditions of temperature and humidity and that they had proper standard processing conditions.

It is extremely desirable that emulsions be constant from batch to batch, so that the smallest possible calibration by irradiation would be required. In the manufacture of nuclear plates, much effort is expended to achieve this goal. However, even now experimental work is still needed to improve these plates, to increase their sensitivity to particles of high energy, to lower the background density, and to reduce the degree of fading of the latent image that takes place between irradiation and development.

As was established earlier in this work, successive batches of Ilford NTA plates give standard results when irradiated by polonium alpha particles with an energy of 5.3 MeV, and NTB plates when irradiated by protons with an energy of 7 MeV. These characteristics are used for control measurements and the subsequent rejection of those emulsions that do not give the established tolerance in the values of the recorded range and distances between grains in the track. It should be pointed out, however, that such a test does not indicate what results will be obtained when the plates are irradiated by particles with an energy much greater than that used in the control irradiations. For example, it was found that nuclear plates which gave identical distances between grains on passing from one emulsion to another when tested with protons of medium energy may give different results when irradiated with particles of higher energy, corresponding approximately to the sensitivity threshold of the pla-

particles. At higher energies, when the density of grains in the track becomes small, the distance between grains depends ever more sharply on the sensitivity threshold of the individual grains, and even a small difference in sensitivity becomes measurable. In the near future a new cyclotron will go into operation, and it will then become possible to carry out standard tests with protons over a broader spectrum of energies.

Fig. 16. Tracks of polonium α-particles obtained on Ilford NTA plates.

At present the only reliable procedure that can be recommended to a worker in this field consists in calibrating the plates of each new batch of emulsion with particles of those energies for which these plates will be used. It follows from this that, if a prolonged investigation is being carried out, it is necessary to use plates with the same emulsion number throughout and to keep them continuously at a reduced temperature.

EXAMPLES OF NUCLEAR TRACKS IN PHOTOGRAPHIC EMULSIONS

In Figs. 16–19 are shown photographs of tracks obtained on factory-made Ilford plates. The tracks shown in Fig. 16 were obtained on Ilford NTA plates by irradiation with a weak polonium source—

…source of alpha particles, which was practically in contact with the plate. The polonium alpha particles have an energy of 5.3 MeV and, consequently, a range in the emulsion of about 22 μ.

The star in Fig. 17 consists of four tracks of alpha particles emitted in the successive decay of a thorium atom. The plate

Fig. 17. Tracks of four α-particles from a thorium atom, decaying successively: ThX (5.68 MeV), Tn (6.28 MeV), ThA (6.78 MeV), and ThC′ (8.78 MeV).

NTA Eastman was impregnated with a solution of thorium nitrate, dried, kept for several days, and then washed and processed. On the plate treated in this way, stars are visible, formed by alpha particles emerging from a single center and corresponding to the successive decay of the thorium nucleus. The four tracks shown in the photograph correspond to four successive alpha decays of thorium X (5.68 MeV), thoron (6.48 MeV), thorium A (6.78 MeV), and thorium C′ (8.78 MeV). In Fig. 18 the track of a proton with an energy of 7 MeV on an NTB Eastman plate is shown. The distances

between the grains along the whole track is almost constant. This circumstance indicates that the maximum possible grain density along the whole track was obtained. The direction of motion of the proton is from top to bottom, as is indicated by the scattering through a small angle at the lower end of the track. Scattering occurs when the velocity of the proton is small.

Fig. 19 shows the tracks of two fission fragments of a uranium-235 atom. The Ilford NTC plate was impregnated with uranyl acetate and irradiated with slow neutrons. The fission of uranium-235 occurs near the center of the track, and the track itself is produced by two fragments with large charge, flying apart with a total energy of about 160 MeV. The large charge of the fragments is established from the relatively short range of the particles (about 25 μ for both fragments). It must also be pointed out that the grain density is greatest near the center of the track and decreases in the direction toward its two ends, since the charge of the fragments and, consequently, also the ionizing power decrease.

IONIZATION AND THE FORMATION OF THE LATENT IMAGE

In concluding this article it is advisable to make a few remarks on the mechanism of formation of the latent image under irradiation by charged particles[^33]. By analogy with the action of light on a photographic grain it seems probable that the action of charged

Fig. 18. Track of a proton with an energy of 7 MeV on an Ilford NTB plate. The track ends in the lower part of the figure.

particles in the formation of the latent image in the photographic grain is determined by the appearance of free conduction electrons, just as in irradiation by light. However, a certain difference should be pointed out.

In irradiation by light, quanta are absorbed at random points over the surface of the entire grain and usually at a moderate rate, so that all the quanta absorbed by one grain are absorbed by it over a time greater than \(10^{-3}\) sec. However, as we indicated earlier, in the case of the action of a charged particle of average energy, all pairs of ions arise along a straight line passing through the grain in a time less than \(10^{-13}\) sec. Under these conditions the formation of a latent image is ineffective because of recombination of ions and violation of the reciprocity law. For both these reasons it should be expected that, in order to impart to the grain the ability to be developed under the action of a charged particle, it is necessary to liberate more electrons in the grain than under irradiation by light.

Fig. 19. Tracks of fragments of \( \mathrm{U}_{235} \) on Eastman NTC plates, obtained by impregnating the emulsion with uranium oxide and bombarding it with slow neutrons.

Figure 20 gives a curve showing the dependence on energy of the number of ion pairs formed per \(1\,\mu\) of path of an alpha particle in air. The data for constructing the curve are taken from the literature \(^{34}\). This curve has the same course as the energy-loss curve shown in Fig. 3. Therefore, for comparison, on the right-hand side of Fig. 20 a scale is given expressing the energy loss in MeV per \(1\) cm of path. In air it is necessary to expend about \(35\) eV to form one ion pair, regardless of whether the incident particle is an electron, a proton, or an alpha particle.

D. H. WEBB

The formation of ion pairs when a charged particle passes through a solid substance will likewise proceed in accordance with a curve analogous to that shown in Fig. 20. However, this quantity is not as easy to measure for a solid as for a gas, and there are very few data on the value of the energy required for the formation of one ion pair in solids. Experiments with the now available open crystalline counters, in which silver chloride crystals are used as a solid ionization chamber for registering charged particles of high energy, make it possible to obtain average values of the energy required for the formation of an ion pair in silver chloride. Since silver chloride is very similar to silver bromide, the value obtained in this way may also be applied to the photographic case. Van Heerden[^35], who developed a counter made from a silver chloride crystal, found that, for the formation of each ion pair under the action of fast beta particles passing through a silver chloride crystal, \(7.6\ \mathrm{eV}\) is required. Later Hofstadter, Milton, and Ridgway[^36], working with a counter made from a silver chloride crystal and using high-energy electrons, found a series of energy values for the formation of an ion pair in various crystal specimens. The smallest of the values obtained was \(13\)—\(16\ \mathrm{eV}\). The authors believe that this value is higher than the true one because of defects in the crystal, which, as is known, limit photoconductivity currents. At the present time, apparently, the most probable value of the energy required for the formation of an ion pair in silver chloride is the value \(7.6\ \mathrm{eV}\) found by Van Heerden, which is the one we adopt for the calculation.

Fig. 20. Curve of formation of ion pairs as a function of energy for \(\alpha\)-particles in air.

From the curve in Fig. 20 it follows that, for alpha particles with an energy of \(18\ \mathrm{MeV}\), one ion pair is formed per micron of path in air, and the magnitude of the energy lost is approximately \(0.35\ \mathrm{MeV}\) per \(1\ \mathrm{cm}\) of path in air. If, for the value of the sensitivity threshold of a photographic grain, one adopts \(0.013\ \mathrm{MeV}\) per \(1\ \mathrm{cm}\) of air, corresponding to a deuteron with an energy of \(100\ \mathrm{MeV}\), then the number of ion pairs formed will be \(0.037\) ion pairs per micron of air, since the formation of ion pairs is proportional to the loss of energy. The maximum number of ion pairs formed in a grain by particles with the same value of energy loss can be found by multi-

by multiplying the number of ion pairs formed per micron of air by the stopping power of silver bromide relative to air (about 3000), by dividing this quantity by the ratio of the energy required to form a pair of ions in silver bromide (electron-volts in silver bromide) to that for a pair of ions in air (electron-volts in air), and by multiplying the result by the diameter of the grain (0.3 $\mu$). Then we find that the number of ion pairs per AgBr grain is equal to $0.037 \cdot 3000 \cdot (35/7.6)\cdot 0.3 = 153$.

Fig. 21. Electron tracks on plates of the NTV System. The plates were exposed to X-rays with an energy of 180 KeV.

The result gives an approximate value for the minimum number of ions necessary to impart developability to a photographic grain with a diameter of 0.3 $\mu$. This value should be regarded as very approximate, since its exact value cannot be established for a particle of high energy that makes the grain developable. If the beginning of the tracks

deuterons with an energy of 100 MeV consists of rare and irregular grains, this means that we have reached the limit at which a sufficiently small fraction of grains acquires the capacity for development.

It is interesting to compare the value—153 ions per grain—with the number of light quanta needed to impart to a grain the capacity for development, as determined in recent work with single-layer plates[^37][^38]. In these works it was established that, on average, a grain must absorb 40 quanta in order to acquire the capacity for development.

Meanwhile, between the writing of the present article and its publication the sensitivity of nuclear plates has increased considerably. Emulsions of the highest sensitivity now record electron tracks up to 20–30 μ long, which corresponds to energies of 30–70 KeV.

In Fig. 21 electron tracks are shown, obtained on Ilford NTB plates irradiated with X-rays of energy 180 KeV. In this case the traces of photoelectrons knocked out by the X-rays are recorded. The longest recorded tracks have a length of 20 μ, which corresponds approximately to an energy of 50 KeV. This plate was developed for two minutes with developer D-8, diluted in the ratio 2:1. Electron tracks provide such a convenient and sensitive method for determining the threshold sensitivity of plates that this method is now used for testing Ilford NTB plates.

In Fig. 22 a meson track is shown, obtained on Ilford NTB plates. The irradiation was carried out with mesons generated in the cyclotron of the University of California. The track has a length of 400 μ and corresponds to a negative meson with mass \(313\,m_e\) and energy approximately 3.6 MeV. As can be seen, the meson track ends with the formation of a star as a result of a nuclear reaction caused by the meson.

Fig. 22. Track of a negative meson (mass \(= 300m_e\)) on an Ilford NTB plate. Range in the emulsion—400 μ.

References

1. S. Kinoshita, Proc. Roy. Soc. (London) 83 A, 432 (1910).
2. M. Reinganum, Physik. Zeits. 10, 1276 (1911).
3. M. Shapiro, Rev. Mod. Phys. 13, 58 (1941).
4. P. Demers, Can. J. Research 25, 223 (1947).
5. C. M. Lattes, P. H. Fowler and P. Cüer, Proc. Phys. Soc. 59, 883 (1947).
6. C. F. Powell and G. P. S. Occhialini, Nuclear Physics in Photographs (Oxford University Press, London, 1947); UFN 35, 213, 384 (1948).
7. J. H. Smith, Phys. Rev. 71, 32 (1947).
8. M. S. Livingston and Bethe, Rev. Mod. Phys. 9, 263 (1937).
9. B. Rossi and K. Greisen, Rev. Mod. Phys. 13, 249 (1941).
10. J. Wheeler and R. Ladenberg, Phys. Rev. 60, 761 (1941).
11. H. Wambacher, Sitz. Akad. Wiss. in Wien, Math. Naturwiss. Klasse, Abteilung II, 149, Heft 3—4, 157 (1940).
12. C. M. H. Lattes, H. Muirhead, G. P. S. Okkialini and Powell, Nature 159, 694 (1947).
13. D. M. Bosé and B. Choudhuri, Nature 148, 259 (1941).
14. D. H. Perkins, Nature 159, 126 (1947).
15. G. P. S. Okkialini and C. F. Powell, Nature 159, 186 (1947).
16. C. M. G. Lattes, G. P. S. Okkialini and C. F. Powell, Nature 160, 453 (1947).
17. C. M. G. Lattes, G. P. S. Okkialini and C. F. Powell, Nature 160, 486 (1947).
18. R. W. Berriman, Nature 161, 432 (1948).
19. Tsien San-Tsiang, H. Faraggi and L. Vigneron, Comptes rendus 223, 571 (1946).
20. P. Demers, Phys. Rev. 70, 974 (1946).
21. K. Klark-Horovitz and W. A. Miller, Phys. Rev. 59, 941 (1946).
22. L. L. Green and D. L. Livesey, Nature 153, 272 (1946).
23. H. R. Traubenberg, Zeits. f. Physik 5, 396 (1921).
24. P. Cüer, Comptes rendus 223, 1121 (1946).
25. H. Bethe and M. S. Livingston, Rev. Mod. Phys. 9, 272 (1937).
26. C. M. G. Lattes, P. H. Fowler and P. Cüer, Proc. Phys. Soc. 59, 883 (1947).
27. R. W. Gurney and N. F. Mott, Proc. Roy. Soc. 164 A, 151 (1938).
28. J. H. Webb, J. App. Phys. 11, 18 (1940).
29. W. F. Berg and K. Mendelsohn, Proc. Roy. Soc. 168 A, 168 (1938).
30. T. R. Wilkins and H. J. St. Helens, Rev. Mod. Phys. 11, 35 (1940); Phys. Rev. 54, 783 (1938).
31. A. Zhdanov — DAN, 28, 110 (1940). de phys. et. rad. 6, 283 (1935).
32. R. L. Brock and E. Gardner, Rev. Sci. Instr. 19, 299 (1948).
33. P. Cüer, Sci. et. Ind. Phot. 18, 321 (1947); 18, 353 (1947).
34. J. B. Hoag, Electron and Nuclear Physics (D. Van Nostrand Comp.) N.-Y., 1938, 2nd ed., p. 461.
35. P. H. Van Herden, N. V. Noord-Hollandsche Uitgevers Maatschappij (Amsterdam, 1945).
36. A. R. Hofstadter, J. C. D. Milton and S. L. Ridgeway, Phys. Rev. 72, 977 (1947).
37. J. H. Webb, J. Opt. Soc. Am. 38, 312 (1948).
38. R. A. Peck, J. Phys. Rev. 72, 1121 (1947).