THE PROBLEM OF THE ATOMIC NUCLEUS

I. E. Tamm, Moscow

As recently as five years ago, very pessimistic attitudes prevailed among the majority of physicists as to whether substantial progress in the physics of the atomic nucleus could be expected in the near future. It seemed to many that, in order to make any significant advance in this difficult problem, a development of the technique of physical experiment would be necessary of a kind that could be achieved only over a long series of years. The brilliant discoveries of recent years have shown, however, that within the reach of modern physical experiment there lies an enormous unexplored domain of phenomena, which is only now beginning to open up before us and whose significance is difficult to overestimate.

As with every penetration into a new domain, as with every truly fundamental step forward, one may expect from the development of nuclear physics not only new information about new regions of phenomena, but it is quite beyond doubt that this new knowledge will also make it possible to see in a new light that range of facts which pertains to what had seemed to be well-studied areas of physics, and will lead to a revision and substantial broadening of physical concepts and ideas in general.

At the same time, as with every major and fundamentally important success of science, the development of nuclear physics will undoubtedly be associated with practical applications; moreover, there is reason to think that precisely in the field of nuclear physics the future promises very great technical and practical prospects.

I shall first of all allow myself briefly to characterize the basic features of this field of physical research. Among its principal characteristics is, on the one hand, the extraordinarily small geometrical size of the object of investigation: in its linear dimensions the nucleus amounts to approximately only one hundred-thousandth part of the atom. The study of such small objects presents enormous difficulties, but these difficulties, fortunately, are partly compensated by another characteristic feature of this range of phenomena, namely: by the enormous magnitude of the energy with which the phenomena of nuclear physics are associated. The energy of elementary nuclear processes exceeds by approximately a million times the energy of ordinary physical and chemical processes. This circumstance, on the one hand,

facilitates the investigation of nuclear processes; on the other hand, it entails important practical prospects, of which I shall speak somewhat later.

For the moment I would like only to note that this combination of small dimensions and enormous energy is by no means accidental, and finds its explanation in modern quantum mechanics. The point is that, according to quantum mechanics, in particular according to the uncertainty principle, if some particle—for example under the influence of certain forces—is compelled to be in a small region of space, then it cannot fail to possess a large kinetic energy. One may say that if you in some way narrow down, restrict, the volume within which a particle may be located, then by that very fact you inevitably increase its kinetic energy. On the basis of quantum mechanics one can calculate that the kinetic energy of a particle situated in a volume as small as the volume of a nucleus cannot be less than tens and even hundreds of millions of electron-volts. But since the kinetic energy of the motion of particles in the nucleus is so great, and since at the same time they nevertheless do not fly out of the nucleus, this means that they are held inside the nucleus by certain very large forces. Thus we arrive at an estimate of the energy of nuclear processes that agrees with experimental data and reveals to us the inner reasons for this remarkable combination of the smallness of geometrical dimensions with the enormity of energy.

Allow me to turn to the question of the structure of the nucleus. It must be said that on this question, even before 1932—a year which in many respects constitutes a boundary in the development of nuclear physics—entirely incorrect conceptions prevailed. It was thought that the nucleus consisted of protons and electrons, and although the notion that these two sorts of particles were present in the nucleus encountered a whole series of insurmountable contradictions, nevertheless no way out of these difficulties was apparent. Quite unexpectedly, in 1932 the existence of the neutron was discovered—a particle whose mass is approximately equal to the mass of the proton and which, from the point of view of atomic and nuclear scales, thus belongs to the class of heavy particles, since both the proton and the neutron are approximately 2 thousand times heavier than the electron. However, unlike the proton and the electron, the neutron has no electric charge. The discovery of this new, uncharged particle was completely unexpected, entirely contradicting the electrical picture of the structure of matter which had become so firmly established over the preceding decades.

As soon as the neutron was discovered, D. D. Ivanenko expressed the idea that nuclei consist only of protons and neutrons. This hypothesis formed the basis of extremely important work by a number of physicists, especially Heisenberg, and at the present time it is very well substantiated, so that there can hardly be any doubt that nuclei consist only of protons and neutrons. The neutron is a quite peculiar particle. Being devoid of electric charge, it, so far as we know, practically does not interact with the electron. On the other hand, there exist

extremely large forces of interaction between the proton and the neutron, and it is precisely these forces that determine the stability and structure of atomic nuclei. The point is that between the protons entering into the composition of the nucleus there is electric repulsion of like charges. But there is no doubt that at small distances of nuclear scale these repulsive forces, which predominate at large distances, play an entirely secondary role in comparison with the forces of attraction between protons and neutrons. The nature of these forces of attraction between protons and neutrons is quite peculiar. These forces belong neither to the class of electric or electromagnetic forces, nor to the class of gravitational forces, i.e. they do not belong to any of the classes of forces previously known to us. Our information about the attraction between neutrons and protons is still very scanty. I shall note here only the peculiar dependence of these forces on distance. If along the horizontal we lay off the distance \(R\) between two particles, and downward we lay off that energy of attraction between the particles which corresponds to the forces of interaction between them, then the solid curve in Fig. 1 will correspond to the ordinary Coulomb attraction of oppositely charged particles—\(-\dfrac{e^2}{R}\), while the dotted curve, in the roughest approximation, gives a representation of the dependence of the specific forces of attraction between a proton and a neutron on distance. It is seen that at large distances these forces play no role in comparison with the electric forces, whereas at small distances, inside the nucleus, the forces of attraction between neutrons and protons, on the contrary, substantially exceed the forces of Coulomb repulsion of protons from one another. I note that it is impossible to maintain the correct scale in the drawing, so that the drawing presented gives only a very rough qualitative representation of the relation between these two classes of forces.

Fig. 1.

The circumstance that the specific forces of interaction of neutrons and protons were unknown to us until very recently is partly due precisely to the fact that they act only at very short distances, upon the immediate approach of a proton and a neutron.

It must be said that between the particles entering into the composition of the nucleus there probably also exist other forces besides the attraction between protons and neutrons and besides the electric repulsion between protons. Thus, between protons there exist, apparently, also forces of nonelectric origin, probably

of the same origin as the forces acting between protons and neutrons. This is indicated by recent experiments on the anomalous scattering of fast protons in hydrogen. It is possible, further, that there exist forces of interaction between neutrons. In any case, however, it may be said that the fundamental role in all processes taking place in the nucleus is played by the forces of attraction between protons and neutrons, which are schematically shown in Fig. 1, and that it is precisely they that determine the stability of nuclei.

From a fundamental point of view, the discovery of the neutron is of extraordinarily great significance. It demonstrated the inadequacy of the electrical picture of the structure of matter, which until quite recently had held undivided sway in physics; or, more precisely, it established the boundaries of the range of applicability of the corresponding concepts. Of course, in that domain on the basis of whose study the electrical picture of the structure of matter was created—in the domain of atomic and electronic phenomena—in this domain it continues to retain its significance, for the interaction of electrons with the nucleus, as well as of electrons with one another, is wholly determined by electrical forces. Moreover, because of the small dimensions of the nucleus in comparison with the dimensions of atoms, when considering the majority of physical and chemical processes the nucleus may be treated simply as an electric charge, since the structure of the nucleus in most cases does not make itself felt in these processes.

The sharp contradiction between the existence of the uncharged neutron and the established views on the electrical structure of matter led, at first after the discovery of the neutron, to the suggestion that the neutron represents a close combination of a proton with an electron. At the present time one may be convinced that this supposition is incorrect and that the neutron is just as elementary a particle as the proton. At the end of the report I shall return to this and dwell on certain facts proving this proposition.

One of the most important methods of studying the structure of the nucleus is undoubtedly the study of nuclear reactions, i.e. such reactions in which not rearrangements of atoms occur, but transformations of atomic nuclei, transformations of chemical elements. Although the artificial splitting of the nucleus was first carried out as long as 15 years ago by Rutherford, only in the very recent years has an abundant accumulation of new factual material begun. At present the number of nuclear reactions known to us exceeds 200.

A characteristic feature of these reactions for the time being is their extraordinarily negligible efficiency. To bring about most reactions, one has to bombard some substance with a stream of rapidly moving charged particles—protons, alpha particles, deuterons, etc.; and only a very small fraction of the particles with which the given substance is bombarded enter into reaction with the nuclei of the substance. This fraction ranges from one hundredth to one billionth. This low efficiency is due-

is explained above all by the smallness of the dimensions of the nucleus, by the small probability that the given fast-flying particle will happen to hit one of the nuclei of the bombarded substance, which occupy such a small fraction of the volume of the entire substance. In addition, an essential role is also played by the fact that all heavy charged particles whose bombardment causes nuclear reactions possess, like all atomic nuclei, a positive electric charge and therefore at comparatively large distances are very strongly repelled by nuclei. And only when the particles come into direct contact with one another do the specific forces of attraction between the proton and the neutron come into play, overcoming the forces of electrical repulsion.

It is true that, if a substance is bombarded not with charged particles but with neutrons, the efficiency of the reactions may become comparatively very great. However, the very production of neutrons is connected with reactions of the first type, with low-efficiency reactions carried out either by bombarding nuclei with charged particles or by illuminating them with $\gamma$-rays. Therefore nuclear reactions and transformations of chemical elements cannot yet have practical significance, although in certain special cases they may acquire practical significance in the very near future. Thus, for example, the possibility is not excluded that in the near future the production of artificial radioactive substances by means of the corresponding nuclear reactions will prove possible on a sufficiently large scale and that these substances will be widely used in medicine.

The reactions that occur when various substances are bombarded with neutrons are distinguished by a number of interesting and peculiar features. Thus, for example, it turns out that in the case of bombardment by slow neutrons the yield of the reaction is extremely large, many times—sometimes a thousand times—exceeding that useful yield of the reaction which could have been predicted on the basis of a simple calculation of the probability of a neutron hitting one of the atomic nuclei of the bombarded substance. In other words, the number of neutrons entering into reaction substantially exceeds the number of neutron hits on nuclei that can be calculated on the basis of simple geometrical considerations. This fact, wholly incomprehensible from the point of view of classical physics, becomes intelligible if one takes into account the wave properties of the neutron and considers that, according to quantum mechanics, in certain cases the measure of the effective dimensions of a particle is the wavelength corresponding to this particle, and that at small particle velocities this wavelength may be very large.

But if the facts of the extraordinarily large yield of reaction products in bombardment by slow neutrons do find a fundamental explanation in wave mechanics, then up to the very last time the explanation of certain features of these reactions presented extraordinary difficulty. In particular, one cannot fail to mention the remarkable phenomenon of so-called selective absorption

of neutrons, consisting in the fact that, when various substances are bombarded by slow neutrons, very small changes in the velocity of the neutrons in some cases lead to a colossal change in the probability of neutron capture by the nuclei of the substance being bombarded, to a colossal change in the amount of substance produced as a result of the bombardment. The intervals of velocities within which the neutrons are exceptionally active in the sense of exciting a reaction turn out to be very narrow, and the position of these narrow velocity intervals depends in the most capricious way on the nature of the substance being bombarded.

These phenomena appeared extremely mysterious, and only about \(2 \frac{1}{2}\) weeks ago there appeared a remarkable paper by Bohr, which opened the possibility of explaining them. In this paper Bohr succeeded for the first time in elucidating a whole series of characteristic features of the structure of atomic nuclei and of the nuclear reactions connected with these features. In order to explain the peculiarities of the structure of nuclei, Bohr compares it with the well-known structure of the atom or, more precisely, with the structure of the outer electron shell of the atom, which surrounds the central nucleus of the atom and in which the majority of physicochemical processes take place. The theory of the structure of the atom—the structure of the electron shell of the atom—presents extraordinary difficulty if only because, like the theory of the nucleus, it is connected with the problem of the motion of a large number of interacting bodies—tens of electrons, which are not only attracted by the nucleus but also repel one another. It is known that in classical mechanics even the problem of the motion of three bodies mutually attracting one another already presents very serious difficulties. It is clear how much more complicated this problem becomes when not three, but ten, sometimes hundreds of bodies interact. In order to understand the motion of such a complex system, it is absolutely necessary to resort to approximate methods.

In questions of the structure of the atom, the following proved to be a suitable first approximation: in known cases one may regard as given the motion of all the electrons in the atom except one, and then investigate the motion of this one electron, which interests us at the given moment, as a function of the given motion of the other electrons. In other words, the many-body problem may approximately be replaced by the one-body problem, neglecting in the first approximation the back action of the electron we have singled out on the motion of the remaining electrons. This approximate method enabled us to understand the structure of the atom. Bohr emphasizes in his paper that an approximation of this sort, familiar to us, is completely inapplicable in the case of the nucleus, in view of the fact that the mutual coupling—the interaction of the particles composing the nucleus—is extraordinarily large. In the nucleus it is impossible to single out the motion of one particle from the complex motion of the whole system, for the motion of each particle substantially affects the motions of all the remaining particles, i.e. it is impossible to replace the many-body problem by the problem of one body moving in a prescribed field of forces. This, on the one hand, extraordinarily complicates

theory of the nucleus; on the other hand, taking this circumstance into account makes it possible to understand a number of characteristic features of nuclear reactions. In order to clarify his idea, Bohr resorts to the following illustration.

Let us imagine (Fig. 2) a board with a cup-shaped depression and a ball which rolls along the board and falls into the cup. If this cup were empty, the ball would run along the bottom of the cup and then fly out again onto the surface of the board. But if there are a large number of other balls in the cup, then the first ball, having fallen into the cup, will collide with one of the balls in it and will transfer its energy to it. In turn, this ball too, colliding with others, will transfer part of its energy to its neighbors, and so on. As a result, the energy of motion of the first ball will very quickly be distributed among the balls in the cup, and the balls will come into a state of disordered motion.

Fig. 2.

At the same time, none of the balls in the cup will have enough energy to jump out of the cup and rise up onto the surface of the board until, under the influence of random collisions, the excess energy brought in by the first ball happens again to be concentrated in one of them, so that this ball will be able to fly out. Thus there exists such a semistable state of this system, when the excess energy of the first ball, sufficient in magnitude for it or another ball to fly out, is distributed in small portions among all the balls, as a consequence of which none of the balls, for a certain time, can fly out of the cup, and the whole system continues to be in a state of semistationary motion.

Something analogous occurs in the case of nuclear reactions. If, instead of the ball, we imagine a neutron, then this neutron, entering the nucleus, gets stuck in it and transfers its energy to it. At the same time, the excess energy brought in by the neutron that has flown into the nucleus is transferred not to one particular neutron or proton of the nucleus, but, owing to the extremely strong coupling and interaction of the particles in the nucleus, is distributed in small portions among all the particles of the nucleus. Therefore a fairly considerable time must pass before this excess energy is again concentrated on some one particle or group of particles, which thereby acquires enough energy to fly out of the nucleus.

Thus the existence of intermediate semistable states of the nucleus becomes understandable, separating the moment of penetration of the neutron into the nucleus from the moment of emission from the nucleus of this same or some other particle. This latent period analogi-

furnishes a kind of radioactivity, because the energy of the semi-stable—fairly long-lived—state of the nucleus is sufficiently large for the decay of the nucleus to be able to occur. The emission from the nucleus, at the end of the latent period, of one or several particles is thus a decay of the nucleus analogous to radioactive decay. This type of semi-stable state is quite unknown in the electron shell of the atom. If an electron entering the atom transfers its energy by impact to one of the atom’s electrons, then this second electron, generally speaking, will fly out of the atom with all this energy, for the interaction between the electrons in the atom is comparatively so weak that an exchange of energy between them has no time to take place.

Although in the theory of complex molecules one does encounter semi-stable states analogous to those just described, nevertheless in the majority of cases such states are based on an entirely different mechanism. We have known such semi-stable states of nuclei, when the system (the nucleus) has sufficient energy for its decay to occur, accompanied by the emission outward of parts or fragments of this system ($\alpha$-radioactivity); however, the existence of these states is explained by the presence of repulsive forces between the parts making up the system. These forces create around the nucleus the so-called potential barrier, which prevents the emission of $\alpha$-particles from the nucleus outward. Thus the presence of the potential barrier also creates the possibility of the existence of semi-stable states of nuclei with excess energy, but the nature of these states in this case is entirely different.

Bohr’s theory, the fundamental idea of which I have set forth, made it possible for him for the first time to explain both the selective absorption of neutrons and a whole series of other peculiarities of nuclear reactions. There can be no doubt that this theory will be of very great importance for all nuclear physics. To Bohr we owed the clarification of the structure of the atom and the theory of the structure of the periodic system of the elements. Apparently, now the same Bohr has succeeded in elucidating the fundamental features of the structure of the nucleus.

I should now like, after the question of the structure of the nucleus, to dwell on another remarkable discovery, also belonging to 1932: the discovery of the positron. Although the positron is not a constituent of the nucleus, nevertheless the discovery of its existence was of enormous importance for all nuclear physics. The history of the discovery of the positron is entirely different from the history of the discovery of the neutron. Whereas the neutron was discovered quite unexpectedly, the existence of the positron had been predicted theoretically.

In 1930 Dirac, proceeding from an analysis of the fundamental principles of quantum mechanics in combination with the fundamental principles of the theory of relativity, proceeding in particular from his own works, in which for the first time a well-known synthesis of these two theories, which had developed independently of one another, was given, arrived at the paradoxical conclusion that if the foundations of these theories—quantum mechanics,

...on the one hand, and the theory of relativity, on the other, are correct, then particles of positive electric charge must exist in nature, differing from the electron only in the sign of their charge and having the same mass as the electron. In contrast to protons, which also possess a positive charge but have a mass 2,000 times greater than that of the electron, these particles were called positrons.

In Dirac’s first works on this question there were certain erroneous propositions; it was not clear that the mass of the positive particles had to be equal to the mass of the electron, but this misunderstanding was soon clarified.

According to Dirac’s theory, this hypothetical particle—the positron—had to possess, to the highest degree, astonishing properties. In a collision of a positron with an electron, both of these oppositely charged particles can mutually neutralize one another and disappear, with the energy of this “pair” of particles—the electron and the positron—passing into another form of energy, for example into the energy of light. The reverse process is also possible, when, under certain conditions, light of very high frequency ($\gamma$-rays or very hard X-rays) can disappear with the simultaneous appearance, at the expense of its energy, of a “pair” of oppositely charged particles—an electron and a positron. These processes received the quite unfortunate names of annihilation of matter and materialization of energy, which in no way correspond to the meaning of the philosophical understanding of the term “matter.” Owing to the processes of disappearance (neutralization) of the “pair,” with the transition of its energy into the energy of light, the lifetime of positrons under terrestrial conditions is extremely small, because in a very short time every positron will probably collide with some electron—which are present everywhere on Earth in abundance—and in this collision it will be neutralized and disappear.

This theory of Dirac seemed so paradoxical that it occurred to no one to verify it experimentally. Moreover, the author himself considered it too paradoxical to trust its conclusions, although in the initial assumptions of the theory no vulnerable points could be found. Quite independently of this theory, in 1932 the positron was unexpectedly discovered by the American Anderson in the study of cosmic rays. Soon after this discovery it was established that, with the aid of $\gamma$-rays, positrons can easily be obtained under laboratory conditions. At the present time the production of positrons presents no difficulty. It is remarkable that not only the very existence of the positron, but also its various properties—the probability of neutralization of a positron when it collides with an electron, the probability of the appearance of a “pair” at the expense of the energy of light—all these phenomena and facts, as it turned out, are in complete agreement with Dirac’s theory. There is no doubt that in the history of physics one can scarcely point to another such brilliant example of a scientific prediction, fully confirmed by experiment, as the triumph of Dirac’s theory.

It must be said, however, that, despite the unquestionable value and remarkable success of Dirac’s theory, this theory nevertheless has its vulnerable points. On the one hand, it contains difficulties of a rather formal character, connected with the separation of negative- and positive-energy levels in the presence of force fields; but there are also certain shortcomings of a deeper, more fundamental character.

The point is that Dirac’s theory operates with the idea of the existence of an infinite number of electrons filling all space and existing in the so-called states of negative energy, but, owing to the uniformity with which they fill all space, inaccessible to our observation. Only when the uniformity of the filling of space by electrons of negative energy is disturbed does this departure from uniformity (the so-called “hole”) manifest itself in the form of the appearance of a positive electric charge—the positron. The introduction into consideration of such a background of negative-energy electrons, inaccessible to observation, appears, from the general point of view, little satisfactory, and I do not think that it can long remain in science. At present we do not know how Dirac’s theory, which has enormous merits and undoubtedly reflects an essential share of truth, could be modified. But it nevertheless seems to me that its present form will undergo substantial changes in the future.

To explain my thought I recall, for example, that the so-called Lorentz transformations were first obtained by Lorentz on the basis of the idea of the existence of an immobile ether inaccessible to observation. Subsequently the theory of relativity rejected this wholly unsatisfactory idea, but fully preserved the Lorentz transformations themselves, which have for it an entirely fundamental significance.

The discovery of the positron has disturbed the deep conviction, established over the last 50 years, in the eternity and indestructibility of the electron. When the law of conservation of electricity was discovered, which even now appears entirely unshakable, this law was at first understood in the sense that the algebraic sum of electric charges could not change in any processes. The emergence and disappearance in equal quantities of positive and negative electricity (for example, in electrification by friction) was considered quite possible. However, from the end of the last century the successes of electron theory led to the fact that this general formulation of the law of conservation of electricity was gradually displaced by the narrower assertion according to which not only is the algebraic sum of charges conserved unchanged, but each individual element of charge—the electron or the proton—is an unchanging and eternal particle. The discovery of the positron and of the phenomena of neutralization of the positron and electron, on the one hand, and of the creation of “pairs,” on the other, leads to the fact that we are compelled to abandon this conception of the eternity of the electron.

and we must return to the original form of the law of conservation of electricity, referring only to the algebraic sum of charges. It is true that the modern Dirac theory of the positron is formally based on the idea of conservation of the number of electrons, but this is achieved only by introducing into consideration an unobservable background of electrons of negative energy—an idea of a formal character, which is unlikely to remain in science for long.

When the existence of the positron and the phenomena of formation and disappearance of “pairs” were discovered, it immediately became possible to answer one important puzzling question that had arisen in connection with the phenomena of radioactive $\beta$-decay. In $\beta$-decay an electron flies out of the nucleus (in contrast to $\alpha$-decay, when a heavy positive $\alpha$-particle flies out of the nucleus). The fact that electrons fly out of the nucleus had until recently been considered undoubted proof that electrons are always present in the nucleus, although this conception also led to insoluble contradictions. We may now be convinced that nuclei consist only of protons and neutrons and that no electrons exist in the nucleus; moreover, in $\beta$-decay the electrons arise at the very moment of their emission from the nucleus, at the expense of the existing decrease in the energy of the nucleus and the corresponding change in its charge, just as, in the emission of light by an atom, a photon, or light quantum, arises at the moment of emission from the atom, in the very act of radiation. The charge carried away by the electron is compensated by the corresponding change in the charge of the nucleus, so that the total sum of charges does not change in $\beta$-decay.

At the present time we know not only the phenomena of radioactive $\beta$-decay, in which electrons fly out of nuclei, but also the phenomena of positron decay, in which positrons fly out of nuclei. By means of various nuclear reactions it is possible to produce unstable, so-called artificially radioactive nuclei, which then decay according to the laws of radioactive decay and eject from themselves, in some cases, electrons, and in other cases positrons. These phenomena of positron and electron decay are of extraordinarily great interest. In view of the fact that the laws of both phenomena are very similar to each other, both these phenomena are often called $\beta$-decay. Let us give two examples of artificial radioactivity, chosen at random. For example, besides the stable nitrogen known to everyone, ${}^{14}_{7}\mathrm{N}$, with atomic weight 14 and atomic number 7, there are two unstable isotopes of nitrogen, i.e. two sorts of nuclei with the same charge 7 but with different mass: in one case 16 (${}^{16}_{7}\mathrm{N}$), in the other case 13 (${}^{13}_{7}\mathrm{N}$), which are obtained artificially as the result of certain nuclear reactions. Nitrogen ${}^{16}_{7}\mathrm{N}$, decaying, gives oxygen ${}^{16}_{8}\mathrm{O}$, and an electron flies out of it. The sum of charges—since the charge of the oxygen nucleus is equal to 8—is conserved in this decay ($7=8-1$).

On the other hand, nitrogen ${}^{13}_{7}\mathrm{N}$, decaying, gives a positron and a carbon nucleus ${}^{13}_{6}\mathrm{C}$ with charge 6, though not ordinary carbon

with mass 12, and the carbon isotope with mass 13, but this is not essential.

Such processes may be interpreted as the transformation of one of the intranuclear protons into a neutron, or conversely. For example, nitrogen \({}^{16}_{7}\mathrm{N}\) has 7 protons with positive charge and 9 neutrons without charge (the total mass is 16). In the decay of this nucleus an electron is emitted from it, and one of its neutrons is transformed into a proton. Thus an oxygen nucleus is obtained, in which there are 8 protons instead of 7 and 8 neutrons instead of 9.

Conversely, in the decay of nitrogen \({}^{13}_{7}\mathrm{N}\) there occurs, accompanied by the emission of a positron, the transformation of one of the protons into a neutron. Thus it may be said that in the first example of radioactive decay \(\left({}^{16}_{7}\mathrm{N}\right)\) we have a case of the transformation of a neutron into a proton and an electron, while in the second example \(\left({}^{13}_{7}\mathrm{N}\right)\)—the transformation of a proton into a neutron and a positron.

The possibility of such transformations of heavy particles—neutrons and protons—into one another, with the simultaneous emission of the corresponding light particles—electrons and positrons—is an extremely important fact. In particular, this fact is one of the confirmations that the neutron and the proton are equivalent particles. If only transformations of one type took place, for example only transformations of a neutron into a proton and an electron, then one could assert that the proton is an elementary particle, whereas the neutron consists of a proton and an electron. But since the proton can likewise be transformed into a neutron and a positron, these transformations must be regarded as the transition of a heavy particle from a charged state (proton) to an uncharged one (neutron) and back, these transitions being accompanied by the radiation of the corresponding energy and charge.

It must be said that when one speaks of the presence of a definite number of protons and neutrons in a nucleus, this must be understood with some caution. The point is that the interaction of protons and neutrons inside the nucleus is so strong, the forces acting on these particles so great, that one cannot consider the electrical and magnetic properties of protons and neutrons in the nucleus to be the same as the properties of free neutrons and protons outside the nucleus.

Undoubtedly the matter is not so simple. In particular, it is beyond doubt that it is impossible to specify whether a given intranuclear heavy particle is a proton or a neutron, because inside the nucleus there is a continual transformation of neutrons into protons and back.

The study of radioactive \(\beta\)-decay has had extremely great significance for the entire field of nuclear phenomena.

In speaking here of \(\beta\)-decay, I have used the quite natural idea that if electrons fly out of the nucleus, then the energy carried away by them is taken from the store of intranuclear energy.

However, when tested experimentally, this seemingly natural assumption was not confirmed. The point is that it is possible to measure the energy balance in radioactive β-decay. To do this experimentally is not so simple, but it is nevertheless possible. And it turned out that this energy balance does not close.

When, 6–8 years ago, this circumstance became known, two currents of opinion formed among physicists from the very beginning. One group of physicists regarded this violation of the law of conservation of energy as entirely real and treated it as an established fact. Another group of physicists—above all Pauli—put forward the suggestion that this non-conservation of energy could be explained simply by the fact that, in β-decay, part of the energy of the nucleus is carried away in a form that cannot yet be detected by our measuring instruments. The supposition was expressed that, simultaneously with the electron, some other, hypothetical particle flies out of the nucleus, which was called the neutrino. This particle, like the neutron, has no charge, but unlike the neutron it possesses a very small mass; it may even be that its mass, like the mass of a light quantum, is wholly reducible to the mass of motion. It was assumed that, in β-decay, part of the energy is carried away by this particle—the neutrino—which flies out of the nucleus simultaneously with the electron, but for the time being escapes direct observation.

A substantial success of this hypothesis dates to 1934, when Fermi succeeded in constructing a genuine theory of β-decay, based on the law of conservation of energy and on the supposition that a neutrino is emitted from the nucleus simultaneously with the emission of an electron. On the basis of this theory it proved possible to explain a number of features of β-decay. For example, in radioactive decay electrons fly out of the nucleus with very diverse energies. Fermi was able to explain, at least in general outline, the quantitative distribution of these electrons by energy. It also became possible to explain the experimental fact of a definite dependence between the rapidity of decay of radioactive elements—that is, what is called the decay period—and the maximum energy with which electrons can fly out in the decay of a given element.

It is not surprising that Fermi’s theory received very broad recognition. It must be said that the persuasiveness of this theory is to a considerable extent connected with the fact that, as Fermi showed, the hypothesis of the emission from the nucleus, simultaneously with the electron, of still another particle—the neutrino—is not simply a hypothesis specially invented only to save the law of conservation of energy. Why, in fact, cannot an electron fly out of the nucleus without a partner, without this hypothetical neutrino particle? An analysis of the law of conservation of the moments of quantity of motion showed that the emission of a single electron in the decay of a nucleus is impossible. From the law of conservation of the moments of quantity of motion in its quantum-mechanically refined form it follows that the transformation of a neutron into a proton and an electron is impossible if, simultaneously with this, one more particle—the neutrino—is not also born. Similarly, the transformation of a proton into a neutron and a positron

must necessarily be accompanied by the emission of a neutrino. This circumstance substantially increases the persuasiveness of Fermi’s theory.

At the same time, Fermi’s theory made it possible to advance substantially in the question of the nature of the forces of interaction between protons and neutrons, a question that plays such an important role for all nuclear physics.

As soon as the neutron was discovered, Heisenberg immediately put forward a definite hypothesis concerning the nature of the peculiar non-electric forces of interaction between the proton and the neutron, which at that time necessarily reduced to a rather vague indication of the connection of these forces with the possibility of exchange of charges between the neutron and the proton, i.e. with the possibility of the transformation of a proton into a neutron simultaneously with the transformation of another neutron into a proton.

Since such a possibility of exchange of charges between the proton and the neutron is directly contained in Fermi’s theory, there naturally arises the idea of constructing, on the basis of the theory of \(\beta\)-decay, a theory of nuclear forces of interaction.

In 1934, about two years ago, I put forward the hypothesis that in this way it is possible to connect two completely heterogeneous domains of phenomena: \(\beta\)-decay, on the one hand, and the binding forces of nuclear particles, on the other; and I subjected this hypothesis to quantitative treatment. Simultaneously with me, this idea was also expressed by D. D. Ivanenko.

The idea of the calculations that I carried out is as follows. We are well acquainted with electromagnetic phenomena connected with the existence of electric charges, i.e. electrons and protons. In electromagnetic phenomena we first of all encounter the radiation of energy by charges in the form of light and other electromagnetic waves, or, from the point of view of the hypothesis of light quanta, in the form of photons or light quanta. Thus electric charges, on the one hand, are characterized by the ability to radiate energy in the form of light. On the other hand, they are characterized by the fact that between them there are definite electric forces of interaction, the so-called Coulomb forces. These two circles of phenomena—the radiation of light and the interaction of charges—are not independent of one another, but are organically connected. The Coulomb forces depend on the magnitude of the charge by which the given particle is characterized, and the radiation of light by the given particle depends on the same magnitude of its charge. And if one knows the laws of interaction of charged particles, then on this basis one can theoretically determine the laws of radiation of light. Conversely, if one knows the laws of radiation of light by electric charges, then from this one can theoretically derive the forces of interaction of these charges. Thus, I repeat, these two circles of phenomena are closely connected with one another.

Let us now turn to neutrons and protons. They are likewise characterized by the ability to radiate energy, but not in the form of light, but in the form of a pair of particles consisting either of an electron and a neutrino, or of a positron and a neutrino, i.e. in the form of that very radiation which manifests itself in the phenomena of \(\beta\)-decay. And so

there also exist certain forces of interaction between neutrons and protons. These two circles of phenomena must be linked by an internal connection, just as is the case in electromagnetic phenomena.

This idea can be cast in quantitative form. Starting from Fermi’s theory of β-decay and from experimental data on the rate at which radioactive β-decay proceeds, one can theoretically calculate the force of interaction between a proton and an electron. When I first carried out these calculations about two years ago, the results proved to be highly unsatisfactory. The magnitude of the forces of interaction between protons and neutrons, calculated on the basis of the data on β-decay, turned out to be almost 10–12 times smaller than the magnitude directly determined from experimental data. This failure led me to reject this hypothesis as not agreeing with experiment, and to come to the idea of some other possible nature of the forces of interaction between the neutron and the proton. I spent about a year and a half developing this second hypothesis, and only at the end of last year became convinced of its untenability.

Meanwhile, during this time my first hypothesis underwent substantial development. First, Bethe and Peierls showed that it is possible in principle, without violating the physical content of Fermi’s theory, to alter the mathematical form of the laws of emission of light particles (electrons, positrons, neutrinos) accompanying the transformation of a neutron into a proton and conversely, so that these laws of emission would correspond to our information about β-decay and at the same time would yield, according to the scheme indicated by me, forces of interaction of heavy particles of the correct magnitude. In other words, they showed that the difficulties encountered by my hypothesis, and which personally frightened me off, can be eliminated by a certain mathematical modification of the theory that does not violate its physical essence.

Second, Wick in Rome pointed out that, on the basis of my hypothesis, it is possible, at least qualitatively and in order of magnitude, to explain certain anomalous properties of heavy particles which until recently had seemed very puzzling. Namely, the proton, like the electron, in addition to charge also possesses a magnetic moment, i.e. in a certain respect is equivalent to a magnetic needle. Experiment has shown that this magnetic moment of the proton has an anomalous value, i.e. not the value that one would have expected according to Dirac’s theory, whereas the magnetic moment of the electron agrees with this theory. Still more striking is the fact that, as follows from the totality of our information about the neutron, the neutron, while possessing no electric charge, apparently nevertheless has some magnetic moment, whereas from the point of view of modern theory all magnetic properties and phenomena are connected with the motion of electric charges. From the point of view of the concept developed above, this paradoxical fact also finds its explanation, at least from the qualitative side.

Finally, Heisenberg pointed out that, within the framework of these ideas, it proves possible to understand qualitatively the magnitude of the masses of the proton and the neutron. Just as the mass of the electron is a mass of electromagnetic origin, so the mass of the proton and the neutron is chiefly connected with the specific interaction forces of heavy particles of non-electrical origin, just as the mass of the electron is connected with Coulomb forces.

It must be said that at present the theory set forth can by no means be regarded as having already reached a satisfactory state. Although it proves possible to encompass qualitatively a varied range of phenomena, great difficulties are encountered in the quantitative development of the theory. If there is not so large a discrepancy between the calculated and observed magnitudes of the interaction forces of heavy particles as seemed at first, nevertheless any satisfactory quantitative explanation of the entire range of phenomena that interests us is still impossible, so that the theory undoubtedly requires further development. The difficulties connected with the quantitative formulation of the theory may have various causes. First, these difficulties may be connected with the basic hypothesis of the existence of the neutrino, which to this day remains a hypothetical particle, in contrast to the neutron and the positron, whose existence is beyond doubt. Secondly, if the neutrino does exist, there may be doubts as to whether the equations of motion of the neutrino that we use in constructing the theory correspond to reality.

And, finally, a third reason may lie in the fact that, for the development of the quantitative side of our theory, knowledge is needed of the properties of electrons which, on the one hand, are an intermediate link in the mechanism of the interaction forces and, on the other, arise as a result of β-radiation. In this connection, electrons of extremely high energies play an essential role—energies at which the modern theory of the electron clearly ceases to be applicable.

It is quite possible that a more accurate theory of high-energy electrons will introduce changes into the quantitative results of the modern theory of the interaction of heavy particles. I repeat that, quantitatively, the modern theory is very far from perfection. However, it makes it possible to encompass in a unified way a very diverse range of phenomena: β-decay, the interaction forces that determine the structure of atomic nuclei, the magnitude of magnetic moments, and the magnitude of the masses of heavy particles; it has now gained wide recognition, and at present there exists no other theory that would make it possible to explain in any other way the facts known to us.

I would now like to touch very briefly on the question that has already been debated in the discussions of the preceding reports, in connection with Shankland’s recently published work. The results of this work, which concerns the scattering of γ-rays, a domain very closely connected with the range of phenomena of nuclear physics, contradict the law of conservation of energy. These results cannot yet be regarded as final.

careful; they require thorough checking and repetition, and it is difficult to say what this checking will lead to. On the other hand, these experiments can in no way be dismissed. If verification confirms Shankland’s experimental results, then it is very difficult to foresee what changes will have to be introduced, in connection with this, into contemporary physical theory*.

In this connection I should like to dwell on those misunderstandings which often arise when the question is raised of the nonconservation of energy. And it must be said that the experimental investigations of the range of phenomena that interests us are not for the first time confronting us with this question: let us recall what was said above about the energy balance in β-decay.

First of all, there can be no doubt as to the validity of the law of conservation of energy with respect to the enormous range of the majority of ordinary physical and chemical phenomena, and even with respect to the majority of nuclear reactions.

Although I by no means think that at the present moment, while Shankland’s experiments have not been checked and refined, there is any ground for a fruitful discussion of the possibility of the nonconservation of energy, nevertheless, since this question has arisen before us more than once in recent times, I wish to clarify the very formulation of the question. It is necessary strictly to distinguish the question of the validity of the given concrete physical law of conservation of energy from the question of the validity of much more general and profound philosophical propositions. There is no doubt that scientific knowledge cannot fail to be based on the proposition of the eternity and indestructibility of matter and motion in the general, philosophical sense of these terms. This necessary general premise of all scientific knowledge in a particular field of science—in physics—has found its expression in the fact that physics has always been based, and will continue to be based, on some conservation laws or other. But the question of whether this particular form of conservation law—the law of conservation of energy—has universal significance, or whether the applicability of this conservation law is limited to a certain range of phenomena, while it itself is, for that limited range of phenomena, a consequence of some more general conservation law whose content we cannot yet foresee—this question can be decided only by experiment.

I have already pointed out that there can be no doubt about the applicability of the law of conservation of energy to a large range of nuclear processes, not to mention ordinary chemical and physical processes. In any case, this law is applicable to all those processes in which the velocities of the particles are not too great, i.e. to the majority of nuclear reactions. In recent times the study of nuclear reactions has led to a brilliant confirmation of the law of conservation of energy and of the law of proportionality of energy and mass,

* Verification of Shankland’s experiments, carried out very recently simultaneously in several laboratories, has shown the untenability of these experiments. Note added in proof.

which is one of the most important conclusions of Einstein’s theory of relativity. According to this Einstein law, every change in mass is accompanied by a corresponding change in energy and, conversely, every change in energy is associated with a corresponding change in mass. Until recently this proposition could not be subjected to direct experimental verification, because the transformations of energy in ordinary physico-chemical processes are too small for it to be possible to detect the corresponding exceedingly small changes in mass. Therefore one had to appeal mainly to considerations of an astrophysical order. Only in the field of nuclear processes, where we are dealing with enormous energies, does the change in mass corresponding to a given change in energy become accessible to measurement and, as it turns out, fully agrees with the predictions of the theory.

Allow me to give a concrete example. One of the best-studied nuclear reactions occurs when lithium is bombarded by fast nuclei of hydrogen. Of course, the hydrogen must first be ionized, which can be accomplished, for example, by placing a heated metal filament in hydrogen. Bare hydrogen nuclei are obtained, which are accelerated by an electric field to high velocities and then fall upon a plate containing lithium. As a result of the collision of the nuclei of hydrogen and lithium, two helium nuclei ($\alpha$-particles) are produced, which fly apart in opposite directions with very large kinetic energy, substantially exceeding the kinetic energy of the initial particles of hydrogen and lithium. These flying $\alpha$-particles can be observed by the most varied methods; for example, one can observe the flashes produced when $\alpha$-particles strike a phosphorescent screen.

This reaction makes it possible to test the law of conservation of mass. One can measure the masses of all the atoms entering into the reaction and write the mass values as follows:

\[ {}^{1}_{1}\mathrm{H}+{}^{7}_{3}\mathrm{Li}\to{}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He}. \]

\[ 1{,}0081+7{,}0169\to4{,}0034+4{,}0034. \]

The sum of the masses on the left is $8{,}0250$; the sum of the masses on the right is $8{,}0068$; thus in this reaction the mass of the product is smaller than the initial mass by $0{,}0182$ units. This apparent violation of the law of conservation of mass is explained by the fact that in this reaction a very large energy is released. Indeed, the energy of the helium nuclei flying apart as a result of the reaction, as direct measurement of their velocity shows, exceeds the initial energy of motion of the hydrogen nucleus by $2{,}72\cdot10^{-5}$ erg (the lithium nucleus has no appreciable velocity before the reaction). According to the theory of relativity, this amount of energy corresponds to a definite mass, numerically equal to the energy divided by the square of the velocity of light. Expressing this mass in atomic units, we obtain $0{,}0182$, i.e. just the difference between the initial mass and the mass of the reaction products,

Thus, direct measurements fully confirm the law of conservation of energy and the law of conservation of mass in that generalized form which follows from the theory of relativity. The data given on the masses and energy of the reaction under consideration may be interpreted to mean that, in checking the law of conservation of mass, one must take into account the dependence of a particle’s mass on its velocity. When the velocity of the departing helium nuclei gradually decreases owing to collisions with the atoms encountered in their path, their mass correspondingly decreases, and the excess of mass, together with the energy, is transferred to the surrounding bodies (for example, in the form of thermal energy).

The experimental verification of the law of conservation of energy and of Einstein’s relation in the domain of nuclear physics played a very positive role in improving experimental technique. The point is that the masses of nuclei are measured directly by special instruments, in particular by Aston’s mass spectrograph. When the first nuclear reactions were studied, Einstein’s relation was checked, on the one hand, on the basis of data on nuclear masses obtained by Aston, and on the other hand on the basis of direct measurements of the kinetic energy of nuclei before and after the reaction. The results of the measurements confirmed the conservation laws. Later, however, as the accuracy with which nuclear reactions were studied increased, discrepancies appeared between the experimental data and the conservation laws. It was soon suggested that the trouble lay not in the fundamental principles of the theory being wrong, but in the fact that an experimental error had crept into Aston’s measurements.

Indeed, the discrepancies that had emerged prompted Aston to check his measurements, as a result of which he found in his apparatus a definite source of experimental errors. The elimination of these shortcomings led to a complete experimental confirmation both of the law of conservation of energy and of the law of equivalence of mass and energy.

Within nuclei there is stored an entirely inexhaustible reserve of energy. If humanity masters this reserve—and sooner or later this must happen—then it will be of decisive importance for all our technology and economy. At the present time, however, any predictions as to the date when the practical mastery of nuclear energy will become possible would be utterly groundless. From the history of physics it is well known that, in estimating the interval separating a fundamental scientific discovery—the discovery of a new domain of physical phenomena—from the practical use of that discovery, the best minds of humanity have often fallen into the grossest errors, and could hardly have avoided doing so. When Hertz discovered electromagnetic waves, a special inquiry was sent to him: could this discovery be applied to wireless telegraphy? He replied that it could not. Yet after a very short time, some 8 years later, wireless telegraphy was realized by Popov and Marconi. On the other hand, errors of the opposite character have also occurred. After the invention of radiotelegraphy,

To Popov and Marconi at the end of the last century it seemed to very many that the further application of electromagnetic waves for transmitting energy wirelessly over a distance would present no special difficulties. However, to this day this problem remains in the same discouraging state as 30–35 years ago, and its solution appears to us hopeless.

At the present time we are only beginning to penetrate an entirely new domain of phenomena. Our knowledge of the nucleus is in so rudimentary a state that we cannot even sensibly pose the very question of practical paths toward mastering the reserves of nuclear energy. This question has no practical significance at present. In order for the question of mastering nuclear phenomena to acquire practical significance, it is first of all necessary to understand these phenomena. In this respect enormous prospects are opening before physics, and one may hope that purely scientific investigations will sooner or later reveal the possibility of practical mastery of nuclear energy.

I have finished the survey part of my report and would like to say a few more words on two questions.

First, as concerns the development of work on nuclear physics here in the Union, in connection with the report by A. F. Ioffe mention has already been made of the successes we have achieved in this respect. Indeed, as our strongest nuclear laboratory it is necessary first of all to note the laboratory of the Leningrad Physico-Technical Institute, whose work is of very great value and which in recent years has been developing very successfully. Among the work of this laboratory one must first of all mention the investigations of D. V. Skobeltsyn. In the first group of studies D. V. Skobeltsyn developed a method for measuring the energy of charged particles by placing a Wilson chamber in a magnetic field. This is one of the most valuable methods in this entire field of physics, and at present it has become universally widespread. This method, in particular, enabled Skobeltsyn to be the first to detect the tracks of cosmic rays in a Wilson chamber and laid the foundation for a whole series of his investigations. In the very last years Skobeltsyn has obtained extremely interesting results in studying the scattering and absorption of fast electrons as they pass through matter. The results obtained were entirely unexpected, contradicting the expectations of the modern theory of the electron. It should be noted that contradictions between experiment and modern theory have recently arisen in various fields of nuclear physics, and it is possible that there exists an internal connection between the repeatedly mentioned data of Shankland’s experiments and the new results of D. V. Skobeltsyn. I think that D. V. Skobeltsyn, in his contribution to the discussion, will touch on these investigations in greater detail and will also dwell on the problem of cosmic rays. The study of cosmic rays is of extraordinarily great importance for all nuclear physics, but for lack of time I was compelled to omit this question from my report.

At the same Leningrad Physico-Technical Institute, extremely valuable work of great scientific significance is being carried out by the Alikhanov brothers, who have developed a new, very precise method for studying $\beta$-radioactivity and determining the energies of electrons and positrons. The experimental data of the Alikhanov brothers are the principal material presently available on this question. In particular, the data they have recently obtained on the $\beta$-spectrum of RaE are of very great importance for the whole theory of the question.

The work of I. V. Kurchatov at the same institute on the properties of the neutron and on the study of a number of nuclear reactions is also extremely interesting and valuable.

At the Kharkov Physico-Technical Institute, the construction and commissioning of a special high-voltage laboratory are nearing completion; this will open very broad prospects for experimental nuclear physicists. It is also necessary to note the very promising work of A. I. Leipunsky, who proposes to use in Kharkov a new, very ingenious and subtle method, recently developed by him, which opens up entirely new possibilities in the study of $\beta$-radioactivity. It may be expected that the results of these investigations will be of great importance for the question of the existence of the neutrino.

Here in Moscow we have the Physical Institute of the Academy of Sciences, which contains a nuclear laboratory. This laboratory is perhaps one of the youngest nuclear laboratories in the Union, but it has a number of workers who are working very successfully in the field of the study of positrons and neutrons. One may hope that this nuclear laboratory of the Physical Institute of the Academy of Sciences will develop successfully, become stronger, and grow.

I have by no means covered all the places in our Union where work on the nucleus is being conducted; for example, I have not touched upon the work of the Radium Institute and of the Physical Institute of Leningrad University. It would be wrong if all work on the nucleus were concentrated entirely in only a few laboratories, but it seems to me that the main work on the physics of the atomic nucleus in our Union should be concentrated in three institutes: the Leningrad Physico-Technical Institute, the Kharkov Physico-Technical Institute, and the Moscow Physical Institute of the Academy of Sciences.