Artificial Production of Radioactive Elements

A. I. Alikhanov and A. I. Alikhanyan, Leningrad

In the artificial disintegration of nuclei, regardless of the kind of particles with which the nucleus is bombarded, at the moment of collision heavy particles are emitted (protons, α-particles, and neutrons). As typical nuclear transformations one may cite the well-studied reactions observed when nitrogen, beryllium, and aluminum are bombarded with α-particles:

\[ \mathrm{N}_{7}^{14} + \mathrm{He}_{2}^{4} = \mathrm{O}_{8}^{17} + \mathrm{H}_{1}^{1}; \tag{1} \]

\[ \mathrm{Be}_{4}^{9} + \mathrm{He}_{2}^{4} = \mathrm{C}_{6}^{12} + \mathrm{n}_{0}^{1}; \tag{2} \]

\[ \mathrm{Al}_{13}^{27} + \mathrm{He}_{2}^{4} = \mathrm{Si}_{14}^{30} + \mathrm{H}_{1}^{1}. \tag{3} \]

In the cases cited, as a result of the reaction, simultaneously with the formation of a new nucleus either a proton or a neutron is emitted. But never before, in the disintegration of nuclei, had the emission of light particles, i.e. electrons, been observed.

Only after the discovery of the positron did Curie and Joliot discover a phenomenon which, at first glance, appeared to be the first case of emission of a light particle (a positron) in nuclear disintegration. Subjecting a sheet of aluminum, placed in a Wilson chamber, to the action of α-particles, Curie and Joliot¹ observed, along with the well-known emission of protons in this case (reaction 3), also an intense emission of positrons (according to the authors’ data, one positron is emitted for \(1–2 \cdot 10^{6}\) α-particles bombarding aluminum). In Fig. 1 a Wilson photograph is presented, in which both the path of a proton (a straight, thick path) and the paths of positrons are visible,

Fig. 1. Paths of a proton and positrons

The Wilson chamber in the experiments of Curie and Joliot was placed in a magnetic field, which curved the paths of the electrons and thereby made it possible to determine the sign of the charge and the energy of the electrons. Emission of positrons of a similar kind was observed when boron was bombarded with \(\alpha\)-particles.

Usually the transformations in aluminum and in boron when they are bombarded with \(\alpha\)-particles are accompanied by the emission of protons.

\[ \mathrm{B}^{10}_{5}+\mathrm{He}^{4}_{2}=\mathrm{C}^{13}_{6}+\mathrm{H}^{1}_{1}; \tag{4} \]

\[ \mathrm{Al}^{27}_{13}+\mathrm{He}^{4}_{2}=\mathrm{Si}^{30}_{14}+\mathrm{H}^{1}_{1}. \tag{3} \]

However, after the discovery of the neutron it was shown that bombardment of these two elements with \(\alpha\)-particles is also accompanied by the emission of neutrons. This circumstance gave Curie and Joliot grounds to suppose that, in part, the interaction of \(\alpha\)-particles with the nuclei of boron and aluminum may proceed according to the following reactions:

\[ \mathrm{B}^{10}_{5}+\mathrm{He}^{4}_{2}=\mathrm{C}^{13}_{6}+\mathrm{n}^{1}_{0}+\mathrm{e}^{+}; \]

\[ \mathrm{Al}^{27}_{13}+\mathrm{He}^{4}_{2}=\mathrm{Si}^{30}_{14}+\mathrm{n}^{1}_{0}+\mathrm{e}^{+}. \]

As a result of these reactions we obtain the same products: the nuclei \(\mathrm{C}^{13}_{6}\) and \(\mathrm{Si}^{30}_{14}\), while the proton proves to be, as it were, split into its constituent elements—a neutron and a positron. On this basis, Curie and Joliot came to the conclusion that the proton is a composite particle consisting of a neutron and a positron closely bound to one another.

However, this explanation very soon had to be abandoned. Investigating how the number of positrons emitted by aluminum depends on the energy (range) of the \(\alpha\)-particles, Curie and Joliot\(^2\) found that even if the source of \(\alpha\)-particles (Po) is completely removed from the aluminum plate, the emission of positrons from it continues, weakening with time according to an exponential law. This experiment undoubtedly led the authors to the conclusion that, under the action of the \(\alpha\)-particles of polonium on aluminum (or boron), nuclei of some new radioactive substance are formed, which emits positrons in its decay. Instead of reactions (3) and (4) for boron and aluminum, Curie and Joliot proposed the following reactions:

\[ \mathrm{B}^{10}_{5}+\mathrm{He}^{4}_{2}=\mathrm{N}^{13}_{7}+\mathrm{n}^{1}_{0}; \]

\[ \mathrm{Al}^{27}_{13}+\mathrm{He}^{4}_{2}=\mathrm{P}^{30}_{15}+\mathrm{n}^{1}_{0}, \]

in which \(\mathrm{N}^{13}_{7}\) and \(\mathrm{P}^{30}_{15}\) are those new radioactive substances which decay with the emission of positrons.

It is important to note here that neither the isotope \(\mathrm{N}^{13}\) nor the isotope \(\mathrm{P}^{30}\) occurs in nature. This is now entirely understandable, since they are radioactive and their half-lives are short. According to Curie and Joliot, the half-life of radioactive nitrogen is 14 min., and that of radioactive phosphorus is 3 min. In addition to radioactive nitrogen and phosphorus, Curie and Joliot obtained a radioactive isotope of silicon by bombarding magnesium with \(\alpha\)-particles. In Fig. 2 are shown the cur-

…decay curves for radioactive nitrogen, phosphorus, and silicon, first obtained by Curie and Joliot. Along the abscissa axis is plotted the time in minutes, and along the ordinate axis—the logarithm of the number of particles over a certain interval of time.

Subsequently Curie and Joliot, and also Alikhanov, Alikhanyan, and Dzelepov³, showed that magnesium, when bombarded with α-particles, emits a larger number of negative electrons, and that the reaction proceeds as follows:

\[ \mathrm{Mg}_{12}^{25}+\mathrm{He}_{2}^{4}=\mathrm{Al}_{13}^{28}+\mathrm{H}_{1}^{1}. \]

In this case the radioactive element is \(\mathrm{Al}_{13}^{28}\), which decays with the emission of electrons:

\[ \mathrm{Al}_{13}^{28}\longrightarrow \mathrm{Si}_{14}^{28}+\mathrm{e}^{-}. \]

To prove the correctness of the above reactions, Curie and Joliot showed by chemical analysis that the radioactive element produced when boron is bombarded—

Fig. 2. Radioactive decay curves

Curve I—boron (radio-nitrogen); curve II—aluminum (radio-phosphorus); curve III—magnesium (radio-aluminum and radio-silicon)

—with α-particles is indeed nitrogen, and in the case of aluminum—phosphorus. For example, boron nitride (BN), after exposure to α-particles, was treated with hot alkali; in this process all the nitrogen, both the active nitrogen produced from boron and the inactive nitrogen contained in the boron nitride, was released in the form of ammonia. The gas was collected in a thin-walled glass tube, and then the activity of the gas and the activity of the precipitate were measured with a Geiger–Müller counter with a thin window. All the activity proved to be concentrated in the glass tube in which the gaseous reaction products had been collected. The chemical reaction con—

took only 5 min in all, and during this time the activity did not have time to weaken appreciably (half-life 14 min).

After the discovery of artificially produced radioactivity, the list of new radioactive isotopes of light elements began to grow very rapidly. Bombarding nitrogen with high-energy α-particles (5 cm range), Wertenstein⁴ obtained a radioactive isotope of fluorine, \(F_{9}^{17}\), with a half-life of 1.2 min.

For this case the reaction may be written in the following form:

\[ N_{7}^{14}+He_{2}^{4}=F_{9}^{17}+n_{0}^{1}; \]

\[ F_{9}^{17}\to O_{8}^{17}+e^{+}. \]

Nitrogen is contained in large quantity in the air, and therefore all elements subjected to the action of α-particles in air may give an activity with a half-life of 1.2 min, since the atoms of radioactive fluorine, having high velocities, can reach the surface of the substance being bombarded and settle on it. This circumstance should always be borne in mind in investigations of artificial radioactivity.

Frisch⁵ showed that sodium and phosphorus, when bombarded with \(\alpha\)-particles of ThC′ of very high energy (8.5 cm range), give radioactive elements with half-lives of 7 sec and 40 min, respectively. The reactions may be written as follows:

\[ Na_{11}^{23}+He_{2}^{4}=Al_{13}^{26}+n_{0}^{1}; \qquad Al_{13}^{26}\to Mg_{12}^{26}+e^{+}; \]

\[ P_{15}^{31}+He_{2}^{4}=Cl_{17}^{34}+n_{0}^{1}; \qquad Cl_{17}^{34}\to S_{16}^{34}+e^{+}; \]

In the latter case Frisch showed by chemical analysis that the radioactive element is chlorine. Meitner⁶ found in a Wilson chamber that lithium, upon direct bombardment by the α-particles of polonium, emits positrons, which apparently corresponds to the formation of the radioactive element boron \(B_{5}^{9}\), having a very short half-life.

In all the cases listed, α-particles served as the “exciters” of radioactivity. The same radioactive isotopes (and also a number of new ones) can be obtained by using other charged particles—protons and deuterons—as “exciters,” as well as neutrons. Cockcroft and Walton⁷ obtained radioactive nitrogen \(N_{7}^{13}\), produced by bombarding boron with α-particles, by bombarding carbon with protons of energy 600 kV. Lauritsen and Crane⁸ obtained the same radioactive nitrogen by bombarding carbon with deuterons. In fact, as a result of these two reactions

\[ C_{6}^{12}+H_{1}^{1}=N_{7}^{13}; \tag{5} \]

\[ C_{6}^{12}+H_{1}^{2}=N_{7}^{13}+n_{0}^{1} \tag{5a} \]

we apparently obtain the same radioactive nitrogen, but, as experience showed, with somewhat different properties. Namely, the period

the half-life of radioactive nitrogen obtained from carbon proved to be 10.3 min, instead of 14 min for radioactive nitrogen obtained from boron. It should also be noted that the proton-capture reaction

\[ \mathrm{C}_6^{12} + \mathrm{H}_1^1 = \mathrm{N}_7^{13} \]

is theoretically very improbable. Indeed, just as in the atom, the energy states of the nucleus are quantized.

Evidence of this is provided by the strict discreteness of the energies of \(\alpha\)-particles emitted in \(\alpha\)-decay, and the strict discreteness of the wavelengths of \(\gamma\)-rays emitted by excited nuclei. In the case when the splitting of a nucleus is accompanied by the emission of some particle (\(\alpha\)-particle, proton, or neutron), the greater part of the energy released in the reaction, according to the laws of conservation of energy and momentum, is transferred to this particle. The energy released in the reaction is the difference between the energies of the initial nucleus and the bombarding particle and the energies of the product nucleus and the emitted particle. In the case of a reaction with proton capture, among all the protons falling on the target and having different velocities inside the target, only those can take part in the formation of a new nucleus whose energy, together with the energy of the capturing nucleus, is equal (within the width of the level) to the energy of the product nucleus.

Meanwhile, as we have already noted, the width of the nuclear energy levels is very small, and therefore only a very small fraction of the incident protons will satisfy the stated conditions. In actual fact, Cockcroft’s experiments show that reaction (5), at the same particle energy as in the case of reaction (5a), occurs only 10 times less often. It might be supposed that before capture the proton emits the excess energy in the form of a \(\gamma\)-quantum. However, the probability of emission of a \(\gamma\)-quantum in so short a time as the collision time is theoretically very small. We shall return to this question in the chapter on the artificial production of radioactive elements by bombardment with neutrons (neutron capture). In addition to radioactive nitrogen, Lauritsen and Crane obtained radioactive carbon \(\mathrm{C}^{11}\) in two ways: by bombarding boron with protons and deuterons:

\[ \mathrm{B}_5^{11} + \mathrm{H}_1^1 = \mathrm{C}_6^{11} + \mathrm{n}_1^1; \]
\[ \mathrm{B}_5^{10} + \mathrm{H}_1^2 = \mathrm{C}_6^{11} + \mathrm{n}_0^1; \qquad \mathrm{C}_6^{11} \longrightarrow \mathrm{B}_5^{11} + \mathrm{e}^{+}. \]

In Lawrence’s laboratory, Livingston and McMillan\(^9\) obtained radioactive oxygen by bombarding nitrogen with deuterons of energy 2000 kV:

\[ \mathrm{N}_7^{14} + \mathrm{H}_1^2 = \mathrm{O}_7^{15} + \mathrm{n}_0^1; \]
\[ \mathrm{O}_8^{15} \longrightarrow \mathrm{N}_7^{15} + \mathrm{e}^{+}. \]

In the same laboratory Lawrence^10 obtained radioactive sodium \( \mathrm{Na}_{11}^{24} \), emitting negative electrons:

\[ \mathrm{Na}_{11}^{23}+\mathrm{H}_{1}^{2}=\mathrm{Na}_{11}^{24}+\mathrm{H}_{1}^{1}, \]

\[ \mathrm{Na}_{11}^{24}\longrightarrow \mathrm{Mg}_{12}^{24}+e^{-}. \]

Probability of Formation of Radioactive Atoms as a Function of the Energy of \(\alpha\)-Particles

As was indicated above, the number of nuclei of radioactive phosphorus atoms obtained from aluminum by bombardment with polonium \(\alpha\)-particles (range 3.85 cm), according to Curie and Joliot, is of the order of 1–2 per \(2\cdot 10^{6}\) \(\alpha\)-particles. In reality, according to Ellis and Henderson,^11 and also Alikhanov, Alikhanyan, and Dzhelepov,^12 this number obtained by Curie and Joliot is too large. The authors mentioned investigated the dependence of the probability of formation of radioactive atoms on the energy of the \(\alpha\)-particles and showed that for \(10^{8}\) \(\alpha\)-particles with a range of 3.85 cm one atom of radioactive phosphorus is obtained. Since the penetration of \(\alpha\)-particles into the nucleus increases with increasing energy, the number of atoms of radioactive phosphorus formed will be the greater, the greater the energy of the \(\alpha\)-particles. For example, in the case of \(\alpha\)-particles of RaC′ with an energy of \(7.2\cdot 10^{6}\) kV, one atom of radioactive phosphorus is obtained already per \(10^{6}\) \(\alpha\)-particles. If, as a source of \(\alpha\)-particles, one takes a thin-walled ampoule containing radium emanation in an amount of 300 mC, then it is possible to obtain 150,000 atoms of radioactive phosphorus, which in the first minute will give \(3\cdot 10^{4}\) positrons, which will be equivalent to an extremely weak radioactive source.

Considerably more intense sources can be obtained by using artificially accelerated charged particles—protons and deuterons. For example, Cockcroft, having a beam of deuterons accelerated to 600 kV, obtained a preparation of radioactive carbon emitting \(10^{6}\) positrons in one minute, while Lawrence, using his method of multiple acceleration of deuterons in a magnetic field, obtained a preparation of radioactive sodium emitting \(1.8\cdot 10^{9}\) electrons per minute. As an example we shall give Cockcroft’s data for the yield of radioactive atoms. Thus, in the case of bombardment of boron by deuterons with an energy of 550 kV, one atom of radioactive carbon is obtained per \(4\cdot 10^{8}\) deuterons, while in the case of bombardment of carbon by deuterons with an energy of 600 kV, one atom is obtained per \(5\cdot 10^{8}\) deuterons.

The probability of formation of a radioactive nucleus depends on a large number of factors. If the energy of the particle is sufficient for the reaction to be energetically possible, then the principal factor on which the probability of disintegration depends is the penetration of the particle through the potential barrier of the nucleus. After the particle has penetrated through the barrier, it is necessary that it be captured by the nucleus, and this is the second factor condi-

…determining the probability of the reaction. Finally, when the particle has been captured by the nucleus, the reaction may proceed along different paths, as for example

\[ \mathrm{Al}_{13}^{27}+\mathrm{He}_{2}^{4}=\mathrm{Si}_{13}^{30}+\mathrm{H}_{1}^{1}; \]

\[ \mathrm{Al}_{13}^{27}+\mathrm{H}_{2}^{4}=\mathrm{P}_{15}^{30}+\mathrm{n}_{0}^{1}, \]

where the second reaction is 20–40 times less probable than the first.

Fig. 3. Positron yield from aluminum as a function of the range of α-particles

The probability of penetration of a particle through the potential barrier is determined by Gamow’s well-known formula:

\[ C=e^{-\frac{2\pi e^{3}}{h}\sqrt{\frac{2m}{E^{*}}+\frac{zZ}{\sqrt{E}}\,(2u-\sin 2u)}} , \]

where

\[ \cos^{2}u=\frac{r_{0}E^{*}}{zZe^{2}}, \qquad E^{*}=\frac{mM}{m+M}E . \]

Here \(M\) and \(Z\) are the mass and charge of the bombarded nucleus, \(m\) and \(z\) are the mass and charge of the bombarding particle, and \(E\) is its energy; \(r_{0}\) denotes the nuclear radius.

The probability of capture of a particle that has already penetrated into the nucleus must depend on the energy released, on the spins of the various intranuclear particles, on the distribution of angular momenta among the particles …

...after disintegration and on the probability that the particle leaving the nucleus will penetrate through the barrier. In the present state of the theory, most of these factors can be estimated only qualitatively.

Figures 3, 4, and 5 give the experimental curves for the dependence of the formation of radioactive nuclei on the energy of the $\alpha$-particles in the case of aluminum, boron, and magnesium. An experimental study of the yield of radioactive atoms as a function of the energy of the $\alpha$-particles was carried out by Ellis and Henderson¹¹, and also by Alikhanov, Alikhanyan, and Dzhelepov¹², in the following manner. Thin mica plates, which slowed the $\alpha$-particles, were inserted between the target being bombarded and the source of $\alpha$-particles.

Fig. 4. Yield of positrons from boron as a function of the range of the $\alpha$-particles

Then the target was brought up to the window of a Geiger–Müller counter, and the number of positrons was counted over a certain interval of time. Since the thicknesses of the targets used in the experiments were greater than the range of the $\alpha$-particles, $\alpha$-particles of different ranges, from the given one down to zero, took part in the formation of atoms. Therefore, in order to obtain the true curve, the experimental yield curve must be differentiated with respect to the range. Figures 6, 7, and 8 give the curves after differentiation. From these curves one can draw a number of conclusions. Thus, for example, it is seen that the dependence on energy is the steeper, the larger the atomic number of the substance being bombarded, as is to be expected, since the height of the potential barrier increases with increasing atomic number.

The dependence of the yield on the energy of the $\alpha$-particles in boron (atomic number 5) is much weaker than in aluminum (atomic number 13). From the figure

it is evident that the curve becomes flatter at large ranges of the \(\alpha\)-particles. This indicates that the energy of the \(\alpha\)-particles reaches or exceeds the height of the potential barrier of the boron nucleus. Naturally, this saturation in boron occurs earlier than in aluminum, which has a greater height of the potential barrier. On the curve for the transformation in the magnesium nucleus it is interesting to note a maximum at an \(\alpha\)-particle energy of \(5000\ \mathrm{kV}\), corresponding to the resonance penetration of \(\alpha\)-particles into the magnesium nucleus.

Production of Radioactive Elements by Bombardment with Neutrons

The production of radioactive elements by bombardment with charged particles (\(\alpha\)-particles, protons, and deuterons) has one essential limitation. Charged particles can act only on elements with small atomic numbers and accordingly yield only light radioactive elements. The larger the atomic number of the nucleus being bombarded, the higher the potential barrier around it and the less probable the penetration of a charged particle into the nucleus. In fact, by bombardment with charged particles it has so far been possible to activate only about ten elements, up to the element with atomic number 15 (phosphorus). If, however, nuclei are bombarded with neutrons, then it could be expected that it would be possible to obtain new radioactive substances with a larger atomic number.

Fig. 5. Electron yield from magnesium as a function of the range of \(\alpha\)-particles.

It is true that the neutron sources now available are much weaker than sources of \(\alpha\)-particles, protons, and deuterons. But this must in part be compensated by the greater probability of neutron penetration into the nucleus. The experiments undertaken by Fermi and his collaborators[^13] brilliantly confirmed these considerations. Of sixty elements subjected to the action of neutrons, more than forty showed noticeable activity appearing after irradiation. Fermi’s discovery sharply increased the number of new radioactive ele-

Fig. 6. Positron yield curve from aluminum, obtained by differentiating the experimental curve of Fig. 3

Fig. 7. Positron yield curve from boron, obtained by differentiating the experimental curve of Fig. 4

ments and made it possible to obtain radioactive substances with almost any atomic number. As a source of neutrons Fermi and his collaborators used a glass tube containing beryllium powder and radium emanation in an amount of 800 millicuries. As is known, when beryllium is bombarded with α-particles, neutrons are emitted with energies ranging from zero to 10–14 million volts, and hard γ-rays with an energy of about \(7 \cdot 10^{6}\) kV. Here the source of α-particles is the radium emanation and the RaA and RaC′ in equilibrium with it. With the above-mentioned amount of emanation (800 mC), such a source emits about \(8 \cdot 10^{5}\) neu-

Fig. 8. Curve of the yield of electrons from magnesium, obtained by differentiating the experimental curve of Fig. 5

trons per second. The substance subjected to the action of neutrons, usually in the form of a plate 1–2 mm thick, is placed against the neutron source and then, after a certain exposure time, is brought to a Geiger–Müller electron counter. The walls of the counter were so thin (0.1 mm of aluminum) that electrons could pass into the counter without a large loss in their number; there is no point in making the thickness of the irradiated plate greater than 1–2 mm, since electrons arising at a greater depth will in any case be unable to escape from there and enter the counter.

The sources of radioactive substances obtained in this way have a considerably lower intensity in comparison with the intensity obtained in experiments with α-particles, protons, and deuterons. First of all, this is explained by the fact that the available neutron sources are extremely weak. In addition

in experiments of this kind, of the total number of neutrons falling on the target, only that part is effective which produces new nuclei at a depth of no more than 1–2 mm, from which the β-particles can still emerge. In practice, in experiments, radioactive sources obtained by neutron bombardment give about 500–1000 counts per minute in a Geiger–Müller counter, whereas with α-particle bombardment we had more than 10,000 positrons per minute. By counting the number of counts in the counter as a function of time, it is possible to measure the half-life of the radioactive substance obtained. By placing filters of various thicknesses between the counter and the activated plate, it was possible to determine roughly the mean energy of the electrons emitted by this radioactive element. If the counter is covered with a thick filter so that the electrons cannot penetrate into it, then it is possible to determine whether this substance emits γ-rays. In this case the thickness of the irradiated plate could be much greater (of the order of several centimeters), owing to the fact that γ-rays pass through such thicknesses without any appreciable weakening of intensity.

Fig. 9. Motion of electrons in a nonuniform field

To determine the sign of the electrons emitted in the decay, Fermi and his collaborators used the method of electron deflection in a nonuniform field (the method of Willard and Tibo[^14]), which consists in the following. If a source of electrons is placed in a nonuniform magnetic field with a sharp gradient of the field along the radius of the magnet poles (Figs. 9 and 10), then all electrons, irrespective of the magnitude and direction of their velocity, will, moving in spirals, be displaced to the point \(P\). In this case negative electrons will be displaced along one side of the semicircle, and positive electrons along the other. Using only one semicircle, one can, near the point \(P\), collect, for a given direction of the magnetic field, only negative electrons, and with the reverse field—only positive ones. The convenience of this method lies in the fact that the greater part of the electrons emitted

Fig. 10. Apparatus for magnetic deflection of electrons

ARTIFICIAL PRODUCTION OF RADIOACTIVE ELEMENTS

at the point \(S\), can be collected near the point \(P\). If the window of a Geiger counter is placed at the point \(P\), then a rather large number of discharges can be observed in it, even if there is a comparatively weak source at the point \(S\). All the radioactive elements obtained by Fermi and his collaborators under neutron bombardment, as magnetic analysis showed, emit negative electrons.

To determine the sign and energy of the electrons, one may also use the method of a Wilson chamber placed in a magnetic field. In Fig. 11a there is shown a Wilson photograph obtained by Kurchatov and Latyshev. In the photograph one can see the path of a negative electron emerging from a plate covered with a layer of bromine activated by neutrons.

Fig. 11a. Path of a negative electron

Let us now turn to the description of several concrete cases. Aluminum, after bombardment by neutrons, acquires a fairly strong activity. From the decay curve it was possible to conclude that aluminum activated by neutrons has two half-life periods—12 min. and 15 hr., which indicates the presence of two different radioactive substances. Since aluminum has no isotopes, it follows from this that several radioactive elements can be obtained from one and the same nucleus. Chemical analysis showed that the substance with a half-life of 15 hr. behaves in a chemical reaction like sodium. On this basis, the nuclear reaction may be written as follows:

\[ \mathrm{Al}_{13}^{27} + \mathrm{n}_{0}^{1} = \mathrm{Na}_{11}^{24} + \mathrm{He}_{2}^{4}, \]

i.e., upon the capture of a neutron by the Al nucleus, the latter emits an \(\alpha\)-particle and is transformed into the radioactive isotope of sodium \(\mathrm{Na}^{24}\). Subsequently its nucleus emits an electron and is transformed into the stable isotope of magnesium:

\[ \mathrm{Na}_{11}^{24} \to \mathrm{Mg}_{12}^{24} + \bar e. \]

The radioactive substance having a half-life of 12 min., according to

by all indications is the isotope of magnesium \(Mg^{27}\), i.e., the reaction in this case proceeds as follows:

\[ Al^{27}_{13}+n^{1}_{0}=Mg^{27}_{12}+H^{1}_{1}. \]

Radioactive magnesium, decaying with the emission of an electron

\[ Mg^{27}_{12}\to Al^{27}_{13}+e^{-}, \]

passes into the original isotope of aluminum \(Al^{27}_{13}\). Thus, as a result of this type of reaction we shall always return to the initial substance, and all transformations are reduced, as it were, to a disintegration of the neutron extended in time.

Fig. 11b. Tracks of an \(\alpha\)-particle and \(H^{3}_{1}\).

Silicon, after bombardment with neutrons, also acquires considerable activity with a half-life of about 3 min. Chemical analysis showed that the nuclear reaction most probably proceeds in the following way:

\[ Si^{28}_{14}+n^{1}_{0}=Al^{28}_{13}+H^{1}_{1}. \]

The radioactive isotope of aluminum, emitting an electron

\[ Al^{28}_{13}\to Si^{28}_{14}+e^{-}, \]

is transformed into the initial substance—into \(Si^{28}_{14}\).

Let us note that this same radioactive aluminum was obtained from magnesium by bombardment with \(\alpha\)-particles. This same radioactive isotope, apparently, can also be obtained from phosphorus by bombarding it with neutrons. Phosphorus activated by neutrons exhibits two half-lives: one—3 min, and the second—3 hours.

Chemical analysis leads to the conclusion that the half-life of 3 hours must be assigned to \(Si^{31}\)

\[ P^{31}_{15}+n^{1}_{0}=Si^{31}_{14}+H^{1}_{1}. \]

If, however, in the splitting an \(\alpha\)-particle is emitted instead of a proton, then we again obtain radioactive aluminum, having a half-life equal to 3 min.

\[ P^{31}_{15}+n^{1}_{0}=Al^{28}_{13}+He^{4}_{2}. \]

Analogous nuclear reactions also occur in heavier nuclei. For example, in the case of iron, cobalt, manganese, and vanadium

neutron capture is accompanied by the emission either of a proton or of an α-particle, with the subsequent formation of radioactive nuclei according to the reactions:

\[ {}^{56}_{26}\mathrm{Fe}+{}^{1}_{0}\mathrm{n}={}^{56}_{25}\mathrm{Mn}+{}^{1}_{1}\mathrm{H}, \]
\[ {}^{59}_{27}\mathrm{Co}+{}^{1}_{0}\mathrm{n}={}^{56}_{26}\mathrm{Mn}+{}^{4}_{2}\mathrm{He}, \]

and so on.

It is especially necessary to note the reactions in which neutron capture is not accompanied by the emission of a heavy particle (proton, α-particle), the so-called “capture reactions.” Bromine irradiated with neutrons gives strong activity with half-lives of 30 min. and 6 hr. Fermi and his collaborators attempted, by chemical analysis, to determine the radioactive substances formed in this case. If, in the formation of radioactive elements from bromine, α-particles or protons were emitted according to the reactions

\[ {}^{79}_{35}\mathrm{Br}+{}^{1}_{0}\mathrm{n}={}^{79}_{34}\mathrm{Se}+{}^{1}_{1}\mathrm{H}; \]
\[ {}^{79}_{35}\mathrm{Br}+{}^{1}_{0}\mathrm{n}={}^{76}_{33}\mathrm{As}+{}^{4}_{2}\mathrm{He}, \]

then in chemical reactions these radioactive substances should have behaved as selenium and arsenic. The analysis was carried out as follows: arsenic and selenium were added to active bromine \((\mathrm{NH}_4\mathrm{Br})\); then the first was separated in the form of sulfide, and the second—electrochemically. In both cases the separated substances showed no noticeable activity. On obtaining bromine from ammonium bromide in the form of AgBr, the authors found strong activity in the precipitate and concluded that the radioactive substances obtained from bromine are isotopes of bromine and are formed as a result of the reaction:

\[ {}^{79}_{35}\mathrm{Br}+{}^{1}_{0}\mathrm{n}={}^{80}_{35}\mathrm{Br}; \]
\[ {}^{81}_{35}\mathrm{Br}+{}^{1}_{0}\mathrm{n}={}^{82}_{35}\mathrm{Br}. \]

Similar experiments were carried out with iodine, and it was shown that in this case also the radioactive element obtained is an isotope of iodine. Recently Szilard and Chalmers[^15] developed a very simple method for separating radioactive bromine (iodine) from activated bromine (iodine). This method is based on the following considerations. When a neutron collides with a bromine nucleus, the bromine atom, owing to recoil, will be torn from the molecule of the compound (ethyl bromide) and will remain in the free state. By combining it with silver, all the radioactive bromine, together with a small amount of specially added bromine, can be precipitated as a thin layer on a surface of \(1\ \mathrm{cm}^2\). In practice, by this method one can obtain preparations enriched 10–20 times. We shall not list here all the reactions and radioactive elements obtained by Fermi and his collaborators, but at the end of the article we shall give a table of all radioactive elements obtained as a result of bombardment of various elements by α-particles, protons, neutrons, and deuterons.

On the basis of this rich experimental material one can draw a number of general conclusions.

1. Most elements, irrespective of their atomic number, can be activated by bombardment with neutrons.

2. The collision cross section of neutrons with the nucleus, for elements that are activated by neutrons, is of the order of the geometrical cross section of the nucleus; in other words, the majority of neutrons that enter the nucleus take part in the reaction and form active atoms.

3. The radioactive elements obtained are either isotopes of the original atoms, or their atomic numbers are smaller by one (the case of proton emission) or by two (the case of $\alpha$-particle emission) units. In this respect a certain difference between light and heavy elements should be noted. For light elements, reactions of the second and third type predominate (emission of a proton or an $\alpha$-particle), whereas in the case of heavy elements the radioactive element is almost always an isotope of the original element. Reactions with the emission of charged particles ($\alpha$-particles, protons) are more probable in light elements, since in heavy elements the potential barrier is much higher, which sharply decreases the probability of emission of heavy positively charged particles.

4. All radioactive elements obtained by neutron bombardment emit negative electrons. The latter circumstance supports Heisenberg’s considerations on the stability of nuclei. Heisenberg, regarding nuclei as consisting of protons and neutrons, assumed that the principal forces of interaction between the particles in the nucleus are exchange forces between neutrons and protons, and from this obtained a general condition for nuclear stability. Namely, it turned out that the binding energy reaches its maximum value in the case when the number of protons is equal to the number of neutrons.

Under neutron bombardment, radioactive elements always have an excess of neutrons in comparison with their stable isotopes. The process of emission of a negative electron restores the proper ratio of the number of neutrons to the number of protons and leads to the formation of a stable isotope. Conversely, all radioactive elements that emit positrons have, in comparison with their stable isotopes, a deficiency of neutrons. Therefore, here the emission of a positive electron can restore the proper ratio of the number of neutrons to protons. Particular difficulties arise when attempting to interpret theoretically reactions with the “sticking” of neutrons.

We have already indicated that in the case of bombardment of boron by protons, radioactive nitrogen nuclei are formed, and the reaction proceeds without the emission of a heavy particle (“sticking” of the proton). The difficulties of which we spoke there apply entirely to the case of the “sticking” of a neutron. A neutron can be captured by a nucleus in the case when it approaches the nucleus to a distance

of the order of \(10^{-12}\) cm. It follows from this that a neutron having an energy of the order of several million volts will interact with a nucleus during a time of the order of \(10^{-21}\) sec. Since a neutron will be captured by a nucleus only in the case when it has a strictly definite energy, during this time (\(10^{-21}\) sec.) the excess of its energy must be emitted in the form of a \(\gamma\)-quantum. Meanwhile, theory gives a very small probability for radiation within so short a time interval. In order to avoid these difficulties, the following hypothesis was put forward: a neutron, passing near a nucleus, excites it, losing part of its energy. Subsequently the excited nucleus, emitting a neutron and a \(\gamma\)-quantum, passes into a radioactive isotope of the original element with its atomic weight decreased by one unit. This hypothesis, however, contradicts Fermi’s latest experiments. Bombarding aluminum with slow neutrons, Fermi and his collaborators\({}^{17}\) found, in addition to the previously observed activity with a half-life of 12 min., another activity with a half-life of 3 min., which can be ascribed only to radioactive aluminum \(\left(\mathrm{Al}_{13}^{28}\right)\). But since aluminum has only one isotope, \(\mathrm{Al}_{13}^{27}\), it follows from this that \(\mathrm{Al}_{13}^{28}\) can be obtained in this case only as a result of the “sticking” of the neutron.

Probability of the Formation of Radioactive Atoms as a Function of the Energy of Neutrons

If it were possible to vary the energy of neutrons, then, as in experiments with \(\alpha\)-particles, it would be of interest to study the formation of radioactive nuclei at different neutron energies. At the present time, however, there is no good method for changing neutron velocities. The only method usually employed is the following. If a beam of neutrons is passed through light substances, then, as a result of collisions with the nuclei of this substance, the neutrons that have passed through will on average have a smaller energy. It is obvious that the smaller the atomic weight of the nucleus with which the neutrons collide, the more strongly the velocities of the neutrons will change, and the maximum loss of energy will occur in the case of collisions of neutrons with hydrogen. The inconvenience of this method consists, first, in the fact that only a small fraction of neutrons undergoes collisions in comparatively thick filters (2—3 cm), and, secondly, in the fact that as a result of collisions the neutrons acquire the most varied velocities. A substantial difficulty in studying the dependence of the probability of formation of radioactive atoms on neutron energy is the absence of monochromatic sources of neutrons.

Some conclusions can be drawn on the basis of experiments with artificial sources of neutrons. As is known, when lithium, beryllium, and deuteron are bombarded with deuterons, intense emission of neutrons is observed. Bjerge and Westcott\({}^{16}\), using-

using these neutron sources for activating fluorine, silicon, phosphorus, and silver, compared the activity obtained as a result of bombardment by neutrons from a Be + Em source with the activity obtained under bombardment by neutrons from Li + D, Be + D, and D + D. Their results are given in Table 1, where the last four columns give the relative intensities of emission of β-particles, calculated for the same number of neutrons.

TABLE 1

Concerning the energies of the neutrons from these four sources, the following may be said. The energy spectrum of neutrons from Be + Em and Li + D is not monochromatic and extends from zero to 15 million electron-volts. The Be + D source is less rich in neutrons of high energies than the two preceding sources. Finally, the D + D source emits neutrons with an energy of about 2 million electron-volts.

From this table one may conclude that, for the cases studied, the smaller the neutron energy, the smaller the probability of formation of a radioactive nucleus. As we have already indicated, from phosphorus, under bombardment by neutrons, two radioactive elements are obtained: radioactive aluminum \( \mathrm{Al}^{28}_{13} \) (half-life about 3 minutes) and radioactive silicon (half-life about 3 hours). From the table it is evident that the yield of radioactive aluminum depends much more sharply on the neutron energy than does the yield of radioactive silicon. In the first case an α-particle is emitted in the reaction, in the second—a proton. The greater the energy of the neutrons bombarding phosphorus, the greater the energy of the α-particles and protons emitted in the reaction. But the probability that an α-particle will pass through the potential barrier of the nucleus depends much more strongly on its energy than does the corresponding probability for a proton. It is possible that this is precisely what explains the different dependence of the yield of these two radioactive elements on the neutron energy.

Extremely interesting results have recently been obtained by Fermi and his collaborators¹⁸, who used as a neutron source an ampoule with radium emanation filled with beryllium. They varied the velocities of the neutrons by the method described above, surrounding the neutron source with filters made of be-

substances containing hydrogen (paraffin, water). It turned out that in cases of reactions with the emission of an $\alpha$-particle and a proton, a decrease in the energy of the neutrons leads to a decrease in the yield of radioactive atoms. Conversely, in the case when the reaction is accompanied by capture of a neutron, a decrease in the energy of the neutrons leads to a sharp increase in the number of radioactive atoms formed.

These experiments were carried out in the following way. At some distance from the neutron source, a plate of the substance to be activated (usually silver) was placed, and after irradiation its activity was measured. Usually, at large distances from the source (10–15 cm) the activity proved to be negligibly small. Then the plate was again placed at the same distance from the source, but this time was surrounded by a thick layer (10–15 cm) of a substance containing hydrogen (water, paraffin). The activity of the plate irradiated by neutrons under these conditions proved, depending on the geometrical conditions, to be tens and even hundreds of times greater. Surrounding the activated plate with substances not containing hydrogen does not appreciably increase its activity. As has already been noted, this phenomenon is observed only in those cases when the reaction proceeds by pure neutron capture, i.e., without emission of a heavy particle.

In the two other types of reactions (emission of a proton, emission of an $\alpha$-particle), the presence of such a layer of water diminishes the activity of the irradiated object. As a possible explanation of this phenomenon the authors proposed the following hypothesis. Neutrons, when passing through a layer of water or paraffin, undergo repeated collisions with hydrogen nuclei and sharply reduce their speed. If one assumes that the probability of collision of a neutron with a proton increases strongly as the neutron speed decreases, then it may be expected that some neutrons, once they have reduced their speed as a result of several collisions, will now very often collide with hydrogen nuclei and, losing more and more of their speed, will diffuse scatter in the water, analogously to molecules diffusing in a gas. Ultimately, as a result of numerous collisions, the speed of some of the neutrons may reach thermal speeds, and in the substance containing hydrogen there will be a neutron gas.

An activated plate placed in this gas may be traversed several times by one and the same neutron, whereas under irradiation by a beam of unscattered neutrons each neutron traversed it only once. Obviously, this circumstance increases the possibility of capture of a neutron by a nucleus. But it is unlikely that the whole effect is due only to this circumstance. In addition, evidently, the probability itself for a slow neutron to be captured by a nucleus is much greater than for a fast one.

From this point of view it is clear why only hydrogen-containing substances possess the property of very strongly increasing the activity. As we have already noted above, owing to the practical equal-

…owing to the masses of the neutron and the proton, the neutron loses velocity most of all in a collision with a proton.

By direct experiments Fermi and his collaborators[^18] were able to show that, indeed, the probability of capture of slow neutrons is in some cases very great. These experiments were carried out in the following, extremely simple, manner. The plate to be activated, immersed in water, was first tightly covered with the substance in which it was desired to determine the probability of absorption of slow neutrons. After irradiation with neutrons, this substance was removed from the plate and its activity was measured. Comparing this activity with the activity obtained from the same plate when irradiated with neutrons in water, but without the absorbing layer, one can determine the absorption coefficient of slow neutrons in this substance and thence calculate the cross section for capture of these neutrons by the nuclei of the absorber. It proved to be especially large for boron and lithium.

The authors give the value of the cross section for lithium as \(0.16 \cdot 10^{-21}\), for boron \(3 \cdot 10^{-21}\), for rhodium \(0.4 \cdot 10^{-21}\ \text{cm}^2\), etc.

A very thin layer of boron (\(20\,\mu\)) proves sufficient to reduce the intensity of the transmitted flux of slow neutrons by a factor of two. At the same time, large thicknesses of lead (\(1\text{—}2\ \text{cm}\)) do not noticeably attenuate the intensity of the flux of slow neutrons. This means that slow neutrons are not captured by the lead nucleus at all. A large absorption coefficient of slow neutrons by no means yet implies the presence of great activity. For example, boron, lithium, and other substances are not activated by neutrons at all. Apparently, having captured a neutron, these elements turn into stable isotopes, or else disintegrate with the emission of heavy particles.

Investigating the capture of slow electrons by lithium, Chadwick[^20] found that in this capture there occurs disintegration of the lithium nucleus with the emission of an \(\alpha\)-particle and the hydrogen isotope \(\mathrm{H}_1^3\):

\[ \mathrm{Li}_1^6 + n_0^1 = \mathrm{He}_2^1 + \mathrm{H}_1^3. \]

Kurchatov and Latyshev showed the same by the Wilson chamber method. In Fig. 11b it is seen how, from a thin lithium plate placed inside a Wilson chamber irradiated with neutrons slowed down in water, two particles fly out simultaneously in opposite directions. One of them, giving a short track, judging by the character of the ionization, is an \(\alpha\)-particle, and the second is \(\mathrm{H}_1^3\). An analogous splitting of the nucleus is observed when a slow neutron is captured by a bromine nucleus.

Thus the new discovery of Fermi and his collaborators not only makes it possible to study the interaction between neutrons and such nuclei as subsequently become radioactive, but also makes it possible, by measuring the absorption coefficient, to study the same questions also for nuclei that do not subsequently yield radioactive isotopes.

Moreover, thanks to this discovery, they succeeded in obtaining a number of radioactive elements, which previously had been produced only by reactions with the emission of a proton or an $\alpha$-particle, by means of a reaction of pure neutron capture. For example, aluminum, which after irradiation with fast neutrons has an activity with a half-life of 12 min., after exposure to neutrons in water revealed yet another activity with a half-life of 3 min., which may be attributed, as we have already noted, to $\mathrm{Al}_{13}^{28}$. In exactly the same way, sodium revealed a new period of about 15 hours. In chlorine a new period of 50 min. was found, etc.

Distribution of Electrons and Positrons in $\beta$-Decay by Energies

Every $\beta$-emitting element is characterized by the sign of the emitted particle, the decay constant, and, in addition, by the energy spectrum of the emitted particles. As is known, in $\beta$-decay the emitted electrons have all possible energies, beginning from 0 and ending with a certain energy, quite definite for each substance. The fact that the spectrum of the emitted $\beta$-particles is continuous is in sharp contradiction with the law of conservation of energy and still remains the most obscure point in the problem of $\beta$-decay. Recently Pauli put forward a hypothesis according to which, simultaneously with the $\beta$-particle, one more light particle—the neutrino—is emitted in the decay. This particle must have a mass of the order of the electron mass, but have no charge, and as a consequence must possess extremely low absorbability. The introduction of a second particle, emitted simultaneously with the electron, makes it possible to remove the contradiction with the law of conservation of energy. In each decay the nucleus must emit a quite definite energy, equal to the difference between the mass defects of the product nucleus and the original nucleus. The sum of the energies of the two emitted particles, the $\beta$-particle and the neutrino, must be equal (in the absence of $\gamma$-radiation) to the energy emitted by the nucleus, but it may be distributed between the two particles in any manner.

From this point of view, the boundary of the continuous spectrum (in the absence of $\gamma$-radiation) corresponds to the case when all the energy emitted by the nucleus has fallen to the electron’s share; thus, the boundary of the continuous spectrum of $\beta$-particles acquires the same meaning as, in $\alpha$-decay, the completely definite energy of the emitted $\alpha$-particle.

Since neutrinos must be absorbed only very weakly, in measurements of the total energy released in $\beta$-decay, the part of the energy carried away by the neutrino will not be absorbed and, correspondingly, will not be taken into account by the instrument measuring the released energy (for example, by a calorimeter).

The best proof of this theory would be the experimental discovery of this hypothetical particle—the neutrino,

However, so far all the experiments undertaken in this direction have not yielded a positive result.

On the other hand, Ellis and Mott[^21] found an extremely convincing argument in favor of the supposition that the boundary of the continuous spectrum of β-particles represents the energy emitted by the nucleus in β-decay.

Let us consider, in general form, a series of successive decays in which a substance \(A\) is transformed into \(B\), \(B\)—into \(C\). Let the substances \(A\) and \(B\), and the particle emitted in the decay, have mass numbers (atomic weights in whole numbers) \(M_1\), \(M_2\), and \(m\), respectively, so that

\[ M_1 = M_2 + m. \]

If now the masses of these nuclei and of the emitted particle are \(M_1 + \Delta_1\), \(M_2 + \Delta_2\), \(m + \delta\) \((\Delta_1,\ \Delta_2\) and \(\delta\) are the mass defects of the nuclei and of the emitted particle), and \(W\) and \(w\) are the kinetic energies of the emitted particle and the recoil atom, then the energy balance may be written as follows:

\[ M_1 + \Delta_1 = M_2 + \Delta_2 + m + \delta + \left(\frac{W}{c^2} + \frac{w}{c^2}\right)K, \]

where \(K\) is the coefficient for converting from units of energy to units of mass.

Hence we obtain that the energy emitted in the transition from the ground level \(A\) to the ground level \(B\) is equal to

\[ W + w = \frac{c^2}{K}(\Delta_1 - \Delta_2 - \delta). \]

If, however, the product nucleus \(B\) is obtained in an excited state, i.e. the transition occurs from the ground level \(A\) to one of the levels \(b_1\), \(b_2\), or \(b_3\) of the nucleus \(B\), then the mass of the nucleus \(B\) will now be greater and equal to

\[ M_2 + \Delta_2'(\Delta_2' > \Delta_2); \]

the emitted energy is smaller and equal to

\[ W' + w' = \frac{c^2}{K}(\Delta_1 - \Delta_2' - \delta). \]

In Fig. 12, the horizontal lines show the energy levels of the nuclei \(A\), \(B\), and \(C\).

The kinetic energy of the emitted particle and of the recoil nucleus is represented in the diagram by the difference in the heights of the levels \(a_0b_0\) in the transition from the ground level \(A\) to the ground level \(B\), or \(a_0b_1\), \(a_0b_2,\ldots\) in the transition from the ground level \(A\) to one of the excited levels of the nucleus \(B\).

Subsequently the excited nucleus \(B\) passes into the normal state, emitting a γ-quantum, and the total energy emitted as a result of the transition \(A \to B\) will again be equal to

\[ W + w = W' + w' + \gamma. \]

It is also possible that the nucleus \(B\), formed in an excited state, will immediately emit a particle and pass into one of the states \(C\).

In those cases where an \(\alpha\)-particle is emitted during decay, all the phenomena described above have been observed experimentally. Corresponding to the various possible transitions from \(a_0\) to \(b_0, b_1, b_2\), and \(b_3\), sharply defined groups of \(\alpha\)-particles and \(\gamma\)-rays corresponding to the differences \(b_3 - b_0\), \(b_2 - b_0\), etc., were found. These groups of \(\alpha\)-particles were called the fine structure. In exactly the same way, corresponding to transitions from \(b_3, b_2 \ldots\) to \(c_0, c_1 \ldots\), groups of \(\alpha\)-particles were found—the so-called “long-range” \(\alpha\)-particles.

All the considerations given above may also be applied to the case of \(\beta\)-decay, with the only difference that, instead of sharply defined energies of the emitted \(\alpha\)-particles, here we have a continuous spectrum of \(\beta\)-particle energies with a sharply defined spectral limit \(W\). This spectral limit may play in our reasoning the same role as the energy of the groups of \(\alpha\)-particles; however, it is obvious that, because of the presence of the remaining continuous spectrum, in the case of \(\beta\)-decay we are deprived of the possibility of experimentally finding the fine structure and the “long-range groups.” Indeed, when smooth curves are superposed on one another, even if they have a well-defined limit, in practice we obtain a resultant smooth curve and cannot notice on it any signs of different limits.

Fig. 12. Energy levels of nuclei

Meanwhile, we have no grounds for assuming that in \(\beta\)-decay there is always a transition to the ground level. On the contrary, the presence of intense \(\gamma\)-radiation in \(\beta\)-decay indicates that in most cases transitions occur to excited levels. For example, in the transition \(\mathrm{ThC''} \to \mathrm{Pb}\), 90% of the decays proceed with a transition to the excited level \(+\,3.2 \cdot 10^6\ \mathrm{V}\). This excitation energy is emitted in the form of \(\gamma\)-quanta \(0.53 \cdot 10^6\ \mathrm{V}\) and

$2.62 \cdot 10^{6}$ V. The limit of the spectrum of ThC$''$ is $1.79 \cdot 10^{6}$ V. Thus the total energy emitted in the transition from ThC$''$ to the ground level of Pb is $4.99 \cdot 10^{6}$ V, if one assumes that the limit of the continuous $\beta$-spectrum gives the true value of the energy emitted in the transition from ThC$''$ to the excited level of Pb. An extremely convincing confirmation of these considerations was first pointed out by Ellis and Mott. In all three radioactive families there are cases where, from one substance (product $C$), the subsequent decay proceeds along two different paths, arriving, however, at one and the same final product. The authors applied these considerations to branching in the thorium family. The branching scheme is shown in Fig. 13. The initial product is ThC, the final one—Pb. Along one branch there first occurs $\beta$-decay (spectrum limit $2.25 \cdot 10^{6}$ V), and then $\alpha$-decay (energy of the $\alpha$-particles $8.95 \cdot 10^{6}$ V); along the other branch there is first $\alpha$-decay (energy of the $\alpha$-particles $6.20 \cdot 10^{6}$ V), and then $\beta$-decay (spectrum limit $1.79 \cdot 10^{6}$ V), accompanied by hard and intense $\gamma$-radiation ($5.80 \cdot 10^{5}$ V and $2.62 \cdot 10^{6}$ V).

Fig. 13. Branching in the thorium family

If one sums all the energies released along each branch separately, using the value of the $\beta$-spectrum limit in the sense described, then one should expect that the total energies released along one and the other branch will be equal to each other, since the initial and final substances are the same. Indeed, the sum of the energies emitted along one branch is $11.20 \cdot 10^{6}$ V, and along the other $11.19 \cdot 10^{6}$. This brilliant agreement proves with great conviction that, indeed, the spectrum limit may be assigned the meaning of the energy emitted by the nucleus in $\beta$-decay.

Therefore the measurement of the limits of $\beta$-spectra is one of the very important tasks in the investigation of artificially produced radioactive substances.

The ordinary methods of investigating spectra, used in the case of strong radioactive sources, are of little use for artificially produced radioactive sources, since at present these sources can be obtained only in the form of very weak preparations.

The most convenient methods for studying the $\beta$-spectra of artificially produced radioactive elements have proved to be the Wilson chamber and the method of magnetic focusing, which will be described below. However, the Wilson-chamber method has the substantial disadvantage that, in order to obtain a reliable distribution curve, it is necessary—

...it is necessary to make a very large number of photographs. A more convenient method is the method of magnetic focusing in combination with two Geiger–Müller counters operating in coincidence, first applied by Alikhanov and Kozodaev. This apparatus is shown in Fig. 14. The electrons coming from the source \(S\) are deflected by a magnetic field perpendicular to the plane of the drawing and are focused in the slit \(S'\), located between two Geiger–Müller counters. The electrons, passing through the first and second counters, produce simultaneous discharges in them. With the aid of a special valve circuit the pulses in the counters are amplified, and then, by means of a special selector, only those pulses that occur simultaneously in the two counters are selected and recorded.

Fig. 14. Apparatus with two Geiger–Müller counters.

The coincidence method proves convenient for the following reasons. It is known that in an ordinary Geiger–Müller counter about 30–40 spontaneous discharges occur each minute (spontaneous discharges, cosmic rays, radioactive contaminations). We have already said that the sources of artificially produced radioactive elements are very weak, and therefore one should expect that the number of additional pulses caused by electrons will be very small, of the order of several units per minute. If, however, the coincidence method is used, then the number of spontaneous coincidences, in view of the high resolving power of the valve circuit, will be small—only 2–3 per minute. These spontaneous coincidences are caused by cosmic particles passing simultaneously through both counters. As a result of the study of the \(\beta\)-spectra of new radioactive elements by the Wilson chamber method (Curie and Joliot, Anderson and Neddermeyer, Nahmias\(^{25}\)) and by the method described above (Alikhanov, Alikhanian, and Dzelepov\(^{24}\)), it was shown that the \(\beta\)-spectra of these radioactive elements represent a continuous spectrum with a sharply expressed limit, characteristic for each radioactive element. Moreover, Alikhanov, Alikhanian, and Dzelepov showed that the distribution of electrons by velocities, and also the limits of the spectrum, do not depend on the energy of the \(\alpha\)-particles by whose bombardment the given radioactive element is formed. In Fig. 15 are shown the distribution curves of the positive electrons emitted by radioactive phosphorus. The upper curve refers to the case when the radioactive phosphorus was obtained by bombardment with \(\alpha\)-particles having a range of 6 cm. The lower curve was obtained with \(\alpha\)-particles...

TABLE 2

Limits of the β-spectra of certain artificially produced radioactive elements

\(^{1}\) According to Alikhanov, Alikhanian, and Dzhelepov.
\(^{2}\) “ ” Curie and Joliot.
\(^{3}\) “ ” Cockcroft, Walton, and Gilbert.
\(^{4}\) “ ” Ellis and Henderson.
\(^{5}\) “ ” Meitner.
\(^{6}\) “ ” Nishina et al.
\(^{7}\) “ ” Ambrosen.

Fig. 15. Energy distribution of positrons emitted by radioactive phosphorus.

with a range of 5 cm. As can be seen from the figure, the form of the curve, the position of the maximum, and the limit of the spectrum did not change. Fig. 16 gives the energy-distribution curve of the positive electrons emitted by radioactive nitrogen.

Of the new radioactive elements obtained by neutron bombardment, the β-spectra have so far been studied

Fig. 16. Energy distribution of positrons emitted by radioactive nitrogen

for \(P_{15}^{32}\) (Ambrosen\(^{23}\)) and for the radioactive haloids—chlorine, bromine, and iodine (Alikhanov, Alikhanyan, and Dzhelepov\(^{24}\)).

Table 2 gives the limits of the spectra of all artificially produced radioactive elements investigated up to the present time.

Table 3 (p. 308) gives a list of artificially produced radioactive substances obtained up to the present time.

TABLE 3

Continuation 1

Continuation 2

Continuation 3

Continuation 4

Continuation of Table 5

References

1. Curie and F. Joliot, Report at the Leningrad Nuclear Conference (Atomic Nucleus, GTTI, 1934).

2. J. Curie and F. Joliot, Report at the London Conference, 1934, Jour. d. Physique, 5, 153, 1934.

3. A. I. Alikhanov, A. I. Alikhanyan, V. S. Dzhelepov, Nature, 133, 871, 1934.

4. Wertenstein, Nature, 133, 565, 1934.

5. Frisch, Nature, 133, 721, 1934.

6. L. Meitner, Naturwiss., 423, 1934,

7. Cokroft, Report at the London Conference, 1934.