Abstract
The twelfth Guthrie Lecture, delivered on February 25, 1927.
Full Text
ATOMIC NUCLEI AND THEIR TRANSFORMATIONS¹
Sir E. Rutherford, Cambridge.
In 1911, when I proposed the nuclear theory of the structure of the atom, based on the explanation of the simple scattering of α-particles by matter, there was little hope of rapid progress in our knowledge of the details of the structure of the nucleus. The situation was such that, during a discussion on the structure of the atom held at the Royal Society in 1913, when asked about the structure of the nucleus I had to reply that consideration of this question would best be left to the next generation. True, in the interval that has elapsed since then we have succeeded in making far greater progress than could have been expected; but at the same time it must be admitted that only a beginning has been made in the solution of this fundamental and most difficult problem of physics. It seems, however, of interest to give a brief survey of our successes in recent years and then to consider in more or less detail some of the most promising paths toward the solution of this problem.
From the first experiments on the scattering of α-particles it became clear that the space occupied by the atomic nucleus is small in comparison with the space occupied by the whole atom. Consequently, the constituent parts of the charged nucleus must be bound within this small volume by such enormous forces that we could not hope to exert any serious influence on the nucleus by
¹ Twelfth Guthrie Lecture, delivered February 25, 1927, published in Proceedings of the Physical Society of London 39 (Part 4), June 15, 1927, p. 359. Translated by N. A. Shishakov.
with the aid of physical forces that we use in the laboratory. The enormous magnitude of the forces acting in the nucleus of a heavy atom may be judged from the high kinetic energy of the $\alpha$- and $\beta$-particles that are liberated in radioactive transformations. Later, through the work of Ellis, Meitner, and others, it was definitely proved that the greater part of $\gamma$-radiation originates from the nucleus. The wavelengths of some of these $\gamma$-rays were measured, and in this way definite indications were obtained concerning certain modes of vibration of the constituent parts of the nucleus. The quantum energy of these $\gamma$-rays proves to be very high: in some cases it corresponds to at least 3 million volts.
The remarkable series of transformations occurring in the elements uranium, thorium, and actinium provides us, in abundance, with data concerning the course of transformations in these heavy elements; but, unfortunately, our theories of the structure of the nucleus are at present in so rudimentary a state that we can make only slight use of the multitude of accumulated facts. I shall return to this question later; for the time being it will suffice to note that the study of these transformations has given us certain general, extremely important indications concerning the nucleus.
Since helium nuclei ($\alpha$-particles) and fast electrons ($\beta$-particles) are emitted by the nucleus, one might conclude that the nuclei of heavy atoms must contain electrons and helium nuclei as their constituent parts, unless one excludes the supposition that the helium nucleus is formed in some way from simpler constituent parts at the moment of its ejection from the main nucleus.
The study of radioactive transformations has given us the most convincing arguments in favor of the nuclear theory and has led to the discovery of an extremely simple relation between the change in the atomic number of the disintegrating element and the nature of the transformation. The emission of an $\alpha$-particle, whose charge is equal to $2e$, decreases the charge of the nucleus by two units, while the emission of an electron increases the charge of the nucleus by one unit. This generalization, known as the displacement rule,
proposed in general form by Russell, Fajans, and Soddy, gives us at one and the same time the charge of the nucleus and the mass of each element in the radioactive series and, thus, determines the ordinary physical and chemical properties of each of the radioactive elements, as well as their atomic weights. This relation is remarkable both for its simplicity and for its generality and, in my opinion, represents the most important and interesting achievement in our knowledge of the nucleus.
I can only mention in passing the enormous step forward that was made by Moseley, who showed that the charge of the nucleus of an element, expressed in fundamental units, is its ordinal, or atomic, number. This conclusion was directly confirmed for a whole series of cases by Chadwick, by means of an exact measurement of the scattering of α-particles.
The discovery, in the radioactive series, of elements that are now known under the name of isotopes and that prove to be identical in their chemical properties, but have different masses and different radioactive properties, was a substantial advance in our knowledge. It could be seen that similarity in chemical behavior is definite proof that isotopes have the same nuclear charge, and that the difference in mass and in radioactivity shows that the nuclei of isotopes differ in structure and stability. The difference in mass of certain radioactive isotopes is very remarkable. In these radioactive series there are, for example, 7 isotopes of lead, whose masses vary within the limits from 214 to 206, while the half-life for the radioactive isotopes ranges from 27 minutes to 16 years. The final products—uranium lead (206) and thorium lead (208)—are stable.
I can only mention in passing the proof, given by Aston, that many ordinary elements consist of a mixture of isotopes. One of the most important conclusions from his work is the “whole-number rule”: it turned out that in many cases the mass of each isotope is an integer, if one starts from the mass of oxygen, taken as
equal to 16. This shows that the limiting constituent unit of the structure of the nucleus has a mass equal to unity. This unit, called the proton, has a somewhat smaller mass than the hydrogen nucleus, whose mass is equal to 1.0072; the difference is ascribed to the “packing effect,” i.e., to the interaction of electromagnetic fields in a strongly compressed nucleus. However, subsequent experiments have shown that, while the rule of whole numbers is in many cases justified with a high degree of accuracy, in others considerable deviations are observed. The validity of the “rule of whole numbers” is now again being investigated by Aston, who is using a spectrograph of much greater resolving power, so that we may soon expect more precise information about the relative masses of isotopes. If it proves possible to obtain these constants with sufficient accuracy, then they will probably be of great importance for elucidating many questions of nuclear structure. The reasons for this will be clear from the subsequent discussion in this article.
We have seen that radioactive phenomena indicate that helium nuclei and electrons are constituent parts of the nuclei of heavy atoms; however, despite the fundamental character of radioactive transformations, the proton is not in any case released from the nucleus. The whole body of facts known to us very strongly supports the idea that electrons and protons are the fundamental units in the structure of the nucleus; direct proof of the correctness of this view was provided by the experiments of Rutherford and Chadwick, Peterson and Kirsch on the artificial disintegration of light elements by \(\alpha\)-particles. For twelve elements definite evidence was obtained that protons are ejected with great velocity when the substance is subjected to bombardment by fast \(\alpha\)-particles. With the exception of carbon and oxygen, for which the experimental results are disputed, all elements from boron to potassium inclusive release protons when bombarded.
In most of these experiments the scintillation method was used where the known observations could be made
only with the emission of particles having a greater range than the α-particles, for the number of the latter usually considerably exceeds the number of protons emitted. Generally speaking, protons are emitted almost uniformly in all directions relative to the bombarding beam of α-particles, but the velocity of the protons proves to be greater in the direction of the beam than in the opposite direction, which is probably due to the motion of the bombarded nucleus.
Unfortunately, the disintegration caused even by the fastest α-particles proves to be very small,—one proton is liberated approximately per 100,000 bombarding α-particles. The experimental study of this artificial disintegration of the elements, although in principle very simple, is in practice associated with many difficulties, so that obtaining quantitative results requires great skill in these observations.
Dimensions of the Nucleus and the Law of Force.
We have seen that the study of the scattering of α-particles first led to the discovery of the nuclear theory of the atom, and that even now this scattering is the only reliable method by means of which the laws of force around the nucleus can be investigated and some ideas about its dimensions obtained. In the classical experiments of Geiger and Marsden, the scattering of α-particles through various angles was found to agree with the Coulomb law of forces for silver and gold. This question was recently investigated again by Rutherford and Chadwick with the aid of a somewhat modified method and led to similar results. Even for the fastest α-particles used, their scattering through angles up to 135° for the elements copper, silver, and gold showed no noticeable departure from the scattering calculated according to the law of inverse proportionality to the square of the distance. For these elements the closest approach of the α-particle to the nucleus, when using radium C α-particles with a velocity of \(1.922 \cdot 10^9\) cm/sec, proved to be: \(1.23\) (Cu), \(1.94\) (Ag), and \(3.15 \cdot 10^{-12}\) cm. (Au). Since it may be assumed that, in the case of penetra-
of the $\alpha$-particle into the nuclear system itself is not to be justified, we may conclude from this that the radii of charged nuclei (if they are taken to be spherical) must be smaller than the numbers given above for copper, silver, and gold. If it proves impossible to use $\alpha$-particles with still greater velocities, then by this method it will in no way be possible to establish a minimum limit for the dimensions of the nucleus. Analogous experiments made with a thin layer of sprayed metallic uranium showed no definite change in the law of forces at a distance of $3\cdot10^{-12}\,\text{cm}$ from the center of the nucleus. This observation leads to considerable complications, for, as will be seen below, certain data from the field of radioactivity indicate that the uranium nucleus, or at any rate some of its constituent parts, may exceed this distance by more than a factor of two.
In the case of light atoms with a small nuclear charge, the $\alpha$-particle, in a close collision, can approach the nucleus much more closely, and thus we are in a position to study the law of forces at much smaller distances. Rutherford’s experiments and the detailed investigations of Chadwick and Bieler had already shown from the very beginning that the Coulomb law of forces becomes inapplicable when fast $\alpha$-particles collide with hydrogen nuclei. The variation of the scattering with the change of angle, as well as with the change of velocity of the $\alpha$-particles, proves to be almost the opposite of what one would expect on the basis of the inverse-square law. For the fastest $\alpha$-particles, the number of H-particles knocked out forward within a small angle with the direction of the $\alpha$-particles is a hundred times greater than the calculated value.
The character of the results obtained may be illustrated by the following example. The number of H-particles flying, after collision, in directions making an angle from $20^\circ$ to $30^\circ$ with the direction of flight of the $\alpha$-particles was counted. When the velocity of the $\alpha$-particles was small, corresponding for example to a range in air of about $2\,\text{cm}$, the number of $\alpha$-particles scattered in the indicated direction proved to be close to that which can
was to be expected on the basis of Coulomb’s law of forces. With increasing velocity of the α-particles, the number of H-particles observed proved to be greater than the theoretical value, and the discrepancy increased very rapidly with increasing velocity of the α-particles. For example, for α-particles having a range of about \(2.9\ \mathrm{cm}\), the observed number is three times greater than the calculated one, while for α-particles with a range of \(6.6\ \mathrm{cm}\) this ratio rises almost to thirty.
This deviation from the inverse-square law was interpreted by Chadwick and Bieler in the following way. If the H-nucleus is regarded as a point charge, then for the helium nucleus (the α-particle) one can find such a model as will give a general explanation of all the experimental results. From Darwin’s calculations it appeared that, under such conditions, α-particles behave as bodies possessing properties intermediate between those of a charged electric sphere and a charged electric plate, and, in a first approximation, may be regarded as elastically flattened spheroids with semiaxes of about \(8\cdot10^{-13}\ \mathrm{cm}\) and \(4\cdot10^{-13}\ \mathrm{cm}\), moving in the direction of their minor axes. An H-nucleus ejected by such an α-particle will be in the field of ordinary electrostatic forces until it reaches the surface of the spheroid with the above-mentioned dimensions. There it encounters a very strong field and undergoes reflection, as from a solid elastic body. However, owing to the difficulties that arise in calculating collisions with such a spheroid, it proved impossible to obtain closer comparisons with this model.
Considering this model from the physical point of view, we may say that the scattering will be normal for all those particles which do not reach the spheroidal surface, and that, conversely, particles crossing this surface encounter a deflecting field in which the forces on the particles will increase far more rapidly than follows from the inverse-square law, so that the scattering will be anomalous.
Before examining this model in greater detail, let us first consider certain experiments which were
recently carried out by Chadwick and myself for the purpose of studying the scattering of $\alpha$-particles in helium by means of the same method. In this case the particles taking part in the collisions are identical both in charge and mass, and also in structure. These experiments, however, are connected with one difficulty which does not arise in the study of collisions between $\alpha$-particles and H-nuclei, when the ejected H-particles, owing to their greater range, can in many cases be observed independently of the $\alpha$-particles. In the case of a collision between two particles of equal mass, the angle between the scattered $\alpha$-particle and the recoiling nucleus is always equal to $90^\circ$, so that in this case it is in no way possible to distinguish the two types of particles. Suppose, for example, that we observe particles which are deflected through an angle $\varphi$ from the direction of the incident particles. They will include $\alpha$-particles scattered through the angle $\varphi$, and recoiling nuclei which arise under the action of $\alpha$-particles scattered through the angle $90^\circ-\varphi$, so that in many cases, where the inverse-square law becomes less applicable, we can only roughly estimate the relative significance of the two groups.
Taken as a whole, the distribution of the particles scattered in collisions between $\alpha$-particles and helium nuclei is, in type, very similar to the distribution observed in the case of $\alpha$-particles and H-nuclei. In both cases there will be the same concentration of scattered $\alpha$-particles in the forward direction, and this becomes the more marked the faster the $\alpha$-particles are. In one respect these experiments gave us information which could not easily have been obtained from the results of the study of H-nuclei. When the scattered particles are observed at angles of $40^\circ$ and $50^\circ$ to the direction of the incident rays, the number of scattered $\alpha$-particles and helium nuclei set in motion by the collisions proves to be the same in number and velocity. The curve of the variation of the number of $\alpha$-particles with energy is shown in Fig. 1, where the ordinates represent the ratio of the observed number to the calculated one, and the abscissae are the values of $\dfrac{1}{E}$, where $E$ is the energy of the colliding $\alpha$-particles. The dashed line
for the ordinate 1 represents the ratio that would be observed for the inverse-square law. Obviously, this ratio is large for fast $\alpha$-particles, then rapidly falls below unity and again rises to the calculated value. A much more noticeable fall below the calculated value is observed for $\alpha$-particles with a range of about 3 cm, when the scattering is observed between $10^\circ$ and $20^\circ$.
Thus it is clear that, for a certain series of velocities of $\alpha$-particles, the scattering between certain angles will be greater than the “normal” value, i.e. the value calculated for point charges, or, in other words, obeying the inverse-square law. For another series of velocities, the scattering becomes lower than normal and, as the velocity of the $\alpha$-particles decreases, finally reaches the normal value.
Fig. 1.
Fig. 2.
This insufficiency of scattering between known angles for $\alpha$-particles of a given velocity may be expected for collisions of such a type where the scattering is abnormally large for other scattering angles. Since this conclusion is of the most general character and is entirely independent of our knowledge of the forces that play a role in the collision, it would be desirable to consider it in greater detail.
In Fig. 2 a central section is shown of an imaginary surface which represents the boundary between
regions where the forces emanating from the nucleus are normal and anomalous. Every particle which does not enter this region undergoes normal scattering, but a particle sufficiently fast to penetrate inside the surface is deflected from its path by some unknown combination of forces. Suppose, for simplicity, that an α-particle flies normally to the section of Fig. 2. This section, therefore, represents a target exposed to the impacts of α-particles. Let us assume, for definiteness, that all particles falling on the area \(A\) undergo scattering through a certain range of angles and that the number of α-particles thus scattered is above normal. Since the number of α-particles striking the surface is determined by the area of the target, and since each particle is deflected in one or another direction, the excess of scattered particles, depending on the area \(A\), must exactly balance the deficiency in the number of particles scattered through another range of angles in the region \(B\). This must always be true for a given velocity of the α-particles, provided only that the latter are not absorbed by the nucleus.
In certain respects this conclusion—i.e. that an excess of α-particles in one direction must be equal to the deficiency in another direction—is an obvious consequence; but, so far as I know, the usefulness of this concept for interpreting scattering phenomena has not been fully recognized. It can be applied when the angular distribution of the scattered α-particles has been determined for a given velocity of the α-particles, and it has the great advantage that it does not require the development of any theory concerning the nature of the collision or the structure of the nucleus.
Chadwick and Bieler considered, for example, the scattering of H-particles for α-particles with a range of \(6.3\ \mathrm{cm}\) in air between angles \(0^\circ\) and \(60^\circ\). The curve obtained by them is shown in Fig. 3, where the ordinates represent the ratio of the number of H-particles to the number of α-particles. Above a certain angle of deflection, the scattering must, in the end, become normal. The values calculated according to the inverse-square law are shown on curve \(B\). After extrapolation of the observed
curve; both curves intersect at the point \(P\), corresponding to an angle of about \(80^\circ\) and representing the boundary between the two regions of angles in which the scattering is normal and anomalous. Since between the angles \(0^\circ\) and \(60^\circ\) there is a large excess of scattered \(\alpha\)-particles, between \(60^\circ\) and \(80^\circ\) there must be a corresponding deficiency. This is illustrated in Fig. 4, where the number of particles scattered per degree from \(0^\circ\) to \(80^\circ\) is compared with the theoretical number.
Fig. 3.
The area \(AA\) above the theoretical curve must be equal to the area between this curve and \(BB\). If the data presented here are considered correct, then it is obvious that at about \(70^\circ\) there should be a noticeable deficiency in the scattering, and that at about \(80^\circ\), where the scattering becomes normal, the curve should rise rapidly.
Fig. 4.
Owing to the small range of the \(H\)-particles at such large angles, this conclusion is difficult to confirm experimentally; however, one can hardly doubt that in essence it is correct.
In this connection, the scattering of \(\alpha\)-particles by aluminum is of particular interest—a question which has been carefully studied during the last several years. Bieler compared
scattering by thin sheets of aluminum and gold; assuming that in the case of gold normal scattering takes place, he concludes that the number of \(\alpha\)-particles scattered by aluminum is less than normal. This deficiency, in comparison with the calculated value, increases with increasing velocity of the \(\alpha\)-particles and with the angle of scattering of the \(\alpha\)-particles. Rutherford and Chadwick observed scattering at large angles \((135^\circ)\) and obtained the unexpected result shown in Fig. 5, where the dotted line denotes the normal calculated scattering, and the solid line the experimental results. The abscissae represent the reciprocal values of the energy of the \(\alpha\)-particles, so that the left-hand side of the curve corresponds to large velocities of the \(\alpha\)-particles.
Fig. 5.
For small energies the ratio of the observed scattering to the calculated is less than unity and decreases with increasing energy of the \(\alpha\)-particles, passing through a minimum corresponding to \(\alpha\)-particles with a range of \(5\ \mathrm{cm}\); for particles with a higher range \((6.6\ \mathrm{cm})\) the scattering curve rises steeply. Results similar to these were also observed for magnesium. For \(90^\circ\) the scattering curves show a noticeable deviation from normal scattering, but no minimum is observed. However, there can hardly be any doubt that, if \(\alpha\)-particles of still greater range were used, the curve would have a minimum corresponding to the curve of Fig. 5.
Using the data published by Bieler, Rutherford and Chadwick, it proves possible to estimate the deficiency of scattering for \(\alpha\)-particles with a range of \(5\ \mathrm{cm}\) at all angles between \(30^\circ\) and \(135^\circ\). The results are presented in Fig. 6. It is evident that there is a noticeable deficiency of scattering throughout this wide range of angles. From what was said earlier, it is clear that this deficiency is compensated by an excess of scattering in another region of angles. It seems improbable that scattering at \(180^\circ\) can be sufficiently large for such compensation, since this
would correspond to an increase in the calculated value in this region by roughly a factor of one hundred. The investigation of this question is not an easy matter, but nevertheless the experiments now being carried out are capable of answering whether a noticeable excess will be observed. If there is not sufficient compensation in this region, then the excess of scattering should lie in the region between \(0^\circ\) and \(30^\circ\). This question is now being studied, but obtaining results of the accuracy required to settle the question may encounter difficulties, since a small percentage excess of scattering at small angles can easily be compensated by a deficiency in the region above \(100^\circ\), shown in the figure.
All the examples cited above are an interesting illustration of the advantages of this principle of compensation, whose application promises to develop research in useful directions.
Fig. 6.
The principle of compensation proves valid only when the disappearance of \(\alpha\)-particles in the nucleus does not occur. It is now known that aluminum and magnesium emit protons when bombarded by \(\alpha\)-particles; it seems entirely probable that the collision which leads to the emission of a proton is connected with the capture of an \(\alpha\)-particle.
Blackett, by observing Wilson tracks in collisions accompanied by the disintegration of nuclei, gave convincing evidence of such capture of \(\alpha\)-particles in nitrogen. Unfortunately, the data which are at present useful in deciding the question of the number of protons emitted by aluminum and magnesium at various angles with the direction of the \(\alpha\)-particles prove unreliable for giving a definite answer as to whether the deficiency of scattering shown in Fig. 6 can be ...
explain by the capture of α-particles. Some data rather indicate that the number of ejected protons represents only a part of this deficiency of scattered α-particles. If this is indeed the case, then we must consider it probable that, for the deficiency of scattering, there is an excess at other angles.
Nuclear Forces and the Structure of the Nucleus
Until now we have compared the observed scattering of α-particles by nuclei with the scattering calculated according to classical mechanics. If one assumes that nuclei behave as point charges, then any discrepancy with the calculation must be ascribed to a deviation of the forces from Coulomb’s law, or to the structure of the nucleus, whose dimensions are comparable with the distances obtained in close collisions.
In recent years, however, the applicability of classical mechanics to the solution of the problem of intra-atomic physics has been called into question, and a new mechanics has arisen, founded on the works of Heisenberg, Schrödinger, Born, Dirac, and others. The new mechanics has already demonstrated its power by providing the correct solution to various atomic problems, and one may suppose that the anomalous scattering of α-particles by light elements is quite natural and depends rather on the inadequacy of classical mechanics when it is applied to α-particle collisions than on any deficiency of the Coulomb law of force.
Recently, however, Wentzel, Born, and Oppenheimer have shown that, under certain assumptions, the laws of scattering by a central field of forces obeying the inverse-square law have one and the same form both in wave mechanics and in classical mechanics. A general study of this collision problem is now under way, but I believe that, with the exception of small perturbations, it seems improbable that wave mechanics can give any explanation of the anomalous scattering of high-velocity α-particles by light elements—hydrogen, helium, and aluminum.
Schrödinger and de Broglie indicated certain criteria under which one may expect the appearance of a diffraction pattern1. In an article prepared for publication and kindly shown to me by Blackett2, these criteria are interpreted in application to the conditions that occur in collisions, according to classical mechanics. Unfortunately these criteria are not sufficiently precise, and until some scattering phenomena are completely explained by wave mechanics, so that we obtain the data necessary for comparison, it is difficult to be certain exactly when one may expect that, in collisions like those studied by us—i.e. in collisions of massive particles with heavy nuclei—a definite diffraction pattern will appear.
In general, if we try to determine these conditions, assuming, say, that the anomalous scattering of $\alpha$-particles by aluminium is explained by wave mechanics, then the criteria prove to be completely unsuitable for collisions of $\alpha$-particles with hydrogen and helium nuclei.
Thus it appears probable that, in order to explain the anomalous scattering of $\alpha$-particles, we must turn to the study of the detailed structure of the nucleus and of the forces emanating from its constituent particles. We must also take into account the enormous distorting forces in nuclei which must arise in these extremely violent collisions, when the nuclei approach one another closely. In my original article3 on the scattering of $\alpha$-particles by—
with native nuclei, I drew attention to the significance of these distorting forces when the normal structure of nuclei is altered, i.e., forces acting near the nucleus, and pointed out that at very small distances the forces may change from repulsive forces into attractive forces.
In order to give an explanation for the deficiency of scattering in aluminium, Bieler investigated mathematically the question of the change in the expected scattering on the assumption that the action of the $\alpha$-particle reduces to a combination of forces, namely the ordinary repulsive electrostatic forces acting between nuclei, and an attractive force varying inversely as the fourth power of the distance. In this way he was able to give an approximate explanation of his experimental results with aluminium. More recently this question was considered in greater detail by Debye and Hardmeier on somewhat different grounds. They assume that when an $\alpha$-particle approaches the nucleus closely, polarization of the nucleus takes place, just as a neutral atom is polarized when a charged particle approaches it. Owing to this polarization, attractive forces act on the $\alpha$-particle, varying proportionally to $r^{-5}$, where $r$ is the distance from the center of the nucleus. It was further assumed that the forces are proportional to the volume occupied by the nucleus. With suitable assumptions concerning the constants entering into the formulae, these authors succeeded in calculating the scattering of $\alpha$-particles with different velocities for a scattering angle of $135^\circ$. In this way they obtained a theoretical scattering curve for aluminium which, in its general features, resembles the curve of Fig. 5. The deficiency of scattering proves to be similar to that given by experiment, and the minimum in the theoretical scattering curve is expressed just as distinctly. Thus it seems that there is nothing improbable in the fact that the principal features of the scattering of $\alpha$-particles by aluminium and magnesium may be due to polarization of the nucleus by the charged $\alpha$-particle. It seems improbable, however, that the attractive forces arising in this way can be expressed by a simple power law, since the distances obtained here ...
states have the same order of magnitude as the dimensions of the nucleus, which cannot have a symmetrical structure. Nevertheless, it would be of great interest to develop this simple theory in detail, in order to determine the scattering of $\alpha$-particles of a given velocity for all angles. Such a calculation could give valuable indications concerning the range of angles in which the number of scattered $\alpha$-particles is in excess of the normal number, so as to explain the already discovered insufficiency of scattering at large angles.
In connection with this, another interesting circumstance should be pointed out. Since, in close collisions of the types considered, considerable motions of the constituent parts of the nucleus would have to occur, and these may move also not along quantum orbits, then, as a result of the collision, energy must in one form or another be dissipated. If this actually occurred, then the ordinary laws of conservation of energy and momentum would not be applicable to such collisions. Up to now no convincing proof of such an effect has been obtained, apart from those cases in which the nucleus undergoes disintegration. The velocity of the scattered $\alpha$-particles, so far as our experiments allow us to judge, agrees with the velocity calculated on the basis of the laws of elastic collision. The most exact method for studying this question consists in the careful photographic observation of branching tracks caused by collisions in a Wilson chamber. Blackett studied a large number of such photographs and, within the limits of the small experimental errors, found no evidence of any loss of energy even in the closest collisions of $\alpha$-particles with light elements. This question is very important, but in order to give a definite answer to it still more precise data are required. It seems, however, quite certain that the loss of energy in such collisions cannot exceed one or two percent of the total energy of the $\alpha$-particle. Thus it appears probable that, if not all, then the greater part of the energy lost by the $\alpha$-particle during the distortion of the nucleus in the first stage of the collision,
returns to this $\alpha$-particle when it leaves the nucleus. It would be natural to hold to the view that the $\alpha$-particles, upon impact, just like the nucleus upon reflection, both undergo some distortion and that, in the case of the collision of an $\alpha$-particle with light atoms, this distortion may be of the same order of magnitude for both nuclei.
We have already considered some striking features in the scattering of $\alpha$-particles by the nuclei of hydrogen and helium and have indicated a path toward explaining the principal features of these phenomena. There are, however, a whole series of other interesting circumstances on which one ought to dwell. In explaining collisions between $\alpha$-particles and H-nuclei it was assumed that the latter can be regarded as point charges, whence the conclusion was drawn concerning the “shape” of the $\alpha$-particle, or, more precisely, of that region where the forces are anomalous. It is of interest to compare the results obtained for hydrogen and helium. As we saw, in the case of very close collisions, the scattering in both cases proves to be anomalous, but becomes normal for sufficiently slow $\alpha$-particles, when the closest approach to the nucleus is of the order of $4\cdot 10^{-13}\ \text{cm}$. However, a whole series of data shows that the scattering for helium nuclei is normal even at a closer approach to the nucleus than for H-nuclei. If the complexity in the forces is to be ascribed wholly to the $\alpha$-particle and one considers that the H-nucleus acts as a point charge, then we must expect that the scattering will be anomalous at twice as great a distance of the $\alpha$-particles in collision with helium nuclei as in collision with hydrogen nuclei. However, be that as it may, this shortest distance from the nucleus is, for helium, even smaller than for hydrogen. Of course, it is very difficult to estimate the effect of the distortion, but it turns out in this way that hydrogen nuclei, or protons, must have dimensions comparable with the dimensions of $\alpha$-particles. This is an unexpected result, since it has usually been believed that the proton, in its dimensions, should be much smaller than the electron. Since, however, we had in mind rather the region in which the manifestation of anomalous forces takes place than the space occupied by the structure of the nucleus itself, a more precise ...
one may say that the region around the proton where the forces are anomalous is comparable with the dimensions of the corresponding region for an $\alpha$-particle.
Of course, it is very difficult to give an exact explanation of the origin of the forces that are observed in collisions, since it must be remembered that both nuclei during the collision are in motion and that both are in an anomalous state, which is caused by the distorting forces arising when the nuclei come very close to one another.
It is, however, quite possible that the anomalous scattering is caused not only by a modification of the electrostatic forces under distortion, but that in such close collisions the magnetic forces become very considerable; these, of course, may play a predominant role in the scattering of light elements. In the course of the last few years it has been pointed out that the negative electron has a definite magnetic moment belonging to it; if this is so, then it will be quite a reasonable assumption that the proton also has a corresponding magnetic moment. Frenkel, who has dealt with the question of the influence of magnetic forces on the structure of the $\alpha$-particle, supposes that the proton has a magnetic moment equal to only $1/1840$ of the magnetic moment of the electron.
However we may look at this question, it is clear that we may expect the manifestation of large magnetic forces near the nucleus, caused by the intrinsic magnetic moment of its constituent parts or by their motion. There is no doubt that, while the particles composing the nucleus may tend toward such an arrangement as entails a reduction of the magnetic moment to a minimum, there must always be large local magnetic forces in the vicinity of the constituent parts of the nucleus.
In the case of the helium nucleus, which may be imagined as consisting of four protons and two electrons, it is not difficult to calculate from the available data that the influence of these magnetic forces becomes significant for distances of the order of $4 \cdot 10^{-13}\ \mathrm{cm}$, i.e. for such a distance at which, as we know, the scattering of $\alpha$-particles by hydrogen and helium nuclei becomes noticeably anomalous. It is also very important
It should be noted that, since the force deflecting a charged particle, caused by a magnetic field, is proportional to the velocity of the particle, we are able to understand in general terms why the anomaly in scattering in hydrogen and helium increases so strongly with increasing velocity of the $\alpha$-particle.
It seems very probable that the magnetic forces in the vicinity of helium nuclei have just such a magnitude that they can account for the anomalous scattering observed in close collisions with $\alpha$-particles. To give an explanation for the scattering of $\alpha$-particles by hydrogen nuclei, it was concluded that the region in which the forces produced by the $\alpha$-particle are anomalous has a spheroidal form, and that this spheroid must move with its short axis in the direction of motion of the $\alpha$-particle. This indicates a certain orientation of the $\alpha$-particle, which may occur during the collision owing to a couple of forces caused by the interaction of the magnetic fields of both nuclei. While such arguments are undoubtedly of a highly speculative character, general considerations support the view that the region surrounding the nucleus must be the seat of intense magnetic forces, which exert a broad influence on anomalous scattering.
Radioactive Nuclei.
We shall first have to dwell on the discrepancy between the dimensions of the uranium nucleus calculated from scattering and radioactivity data. Rutherford and Chadwick found that scattering by a uranium film proceeds normally, i.e. in accordance with the Coulomb law of forces, down to distances of $3.2 \cdot 10^{-12}$ cm. It should be noted, however, that while, with a change in the velocity of the $\alpha$-particles, the scattering remains normal within the errors of experiment, the actual number of scattered $\alpha$-particles, because of the difficulties in determining with sufficient accuracy the weight of the uranium film, could not be confidently compared with the calculated number.
The $\alpha$-particle emitted by uranium I has the smallest of the known initial energies, namely $6.77 \cdot 10^{-6}$ erg, or $4.25 \cdot 10^6$ volts. Since an $\alpha$-particle must acquire at least part of its energy during its flight in the repulsive field, it is easy to calculate from Coulomb’s laws of force that even in the case where the $\alpha$-particle has no initial velocity whatever upon leaving the inner parts of the nucleus, it cannot originate from points lying closer than $7 \cdot 10^{-12}$ cm to the center of a nucleus with charge 90.
Whereas it appears quite impossible that positively charged particles, such as the proton or the $\alpha$-particle, could remain in equilibrium under the action of Coulomb’s law of repulsive forces, the situation is entirely different when the particles are electrically neutral. A neutral particle may be held in equilibrium by attractive forces either owing to its polarization, caused by the electric field of the charged central nucleus, or owing to magnetic forces arising around the nucleus, or owing to a combination of both types of forces. Preliminary calculations, based on cautious assumptions, show that the attractive forces caused by such reasons are just of the magnitude required to hold the particles in equilibrium as they move around the central nucleus.
Thus we arrive at a general conception of such a structure of the nucleus in which the latter, in turn, has a central charged nucleus surrounded by a known number of uncharged particles. In a paper delivered at the Franklin Institute in 19241, I expressed the supposition that the central nucleus is a closely arranged grouping of $\alpha$-particles and electrons, like a crystalline formation, and showed thereby that the known simple groupings are in good agreement with the charge and mass of certain atoms. However we may look at this question, I am inclined to think that the central
the nucleus of heavy elements has a very dense structure, occupying a very small volume of radius of the order of \(1\cdot 10^{-12}\) cm. Neutral satellites revolving around this nucleus may be situated at distances comparatively large in comparison with the linear dimensions of the main nucleus.
If, as a neutral satellite, we imagine an uncharged \(\alpha\)-particle, then it must consist of a helium nucleus which has acquired two electrons. These electrons cannot occupy the same position as they do in an ordinary helium atom in its free state, for in that case they would at once be swept away by the strong electric field of the nucleus. They are probably much more tightly bound to the nucleus and revolve in such orbits as prove possible only owing to the distortion of the structure of the \(\alpha\)-particle nucleus by the intense electric or magnetic fields proceeding from the central nucleus. Such a view does not seem unconvincing, since there is no doubt that all complex nuclei must undergo considerable deformations under the influence of the enormous fields present in nuclear systems. In fields below this critical magnitude these electronic orbits cannot exist and, consequently, the neutral \(\alpha\)-particle, flying out of the complex nucleus, must lose its two electrons when this critical field is reached.
We may thus picture the following scheme of the emission of \(\alpha\)-particles by radioactive elements. It may happen that a neutral \(\alpha\)-particle, which, in all probability, revolves in a quantum orbit, for some reason is displaced from its position of equilibrium and has sufficient kinetic energy to escape from the field of attractive forces of the central nucleus. When the field strength falls below the critical value, the neutralizing electrons leave the particle and fall back onto the nucleus. After this the \(\alpha\)-particle, which now has a double positive charge, acquires additional energy, passes through the field of the repulsive forces of the nucleus, and flies out in the form of an \(\alpha\)-particle with great velocity. In connection with this it is interesting to note that L. Meitner, from consider-
that a sequence of transformations of radioactive atoms implies that some of the $\alpha$-particles in the nucleus must exist in a neutral state.
According to the views presented here, all $\alpha$-particles that are emitted by radioactive nuclei must originate from neutral satellites.
We must now briefly trace the fate of the electrons that are liberated from the neutral $\alpha$-particle. From the known change of charge in radioactive transformations it is clear that the electrons must move away toward the main nucleus, where they will probably describe orbits under the influence of the complex system of forces that exist near the nucleus and that, owing to distortions of the nucleus, may be of enormous magnitude. It may happen that one of these electrons will have sufficient energy to tear itself completely away from the nucleus and thereby make possible the appearance of a $\beta$-ray.
In our description of the nucleus, we thus have a concentrated internal nucleus bearing a positive charge and surrounded at short distances by many electrons, and then, at certain distances, having many neutral satellites revolving around the system. I hope in a subsequent article to give a fuller treatment of a nuclear structure of this type, which may place at our disposal certain possibilities for explaining the wealth of radioactive data.
This picture of the structure of the nucleus is not restricted only to radioactive atoms, but may be applied to ordinary atoms to the same extent. Up to now we have spoken of the possibility of the existence of neutral satellites only in the form of an $\alpha$-particle, i.e. with mass 4. It appears, however, quite possible that other types of neutral satellites may have mass 2 or 3. Many authors have drawn attention to the possibility of the existence of such nuclei in the form of secondary units, which play the role of a superstructure upon nuclear formations—but they have usually thought that these units exist rather in the form of charged than of neutral masses. Such secondary neutral-
... units can be capable of existing only in the presence of powerful nuclear fields and, consequently, cannot be observed in the free state.
This view of the structure of the nucleus at the same time also gives a plausible explanation for the existence of a multitude of isotopes in an element with a given atomic number. As soon as a central nucleus has formed, a multitude of neutral satellites may be added to it, held in equilibrium by forces of attraction. Aston showed that in some cases a large number of isotopes can exist, which apparently indicates that many satellites can be added to a nuclear formation without disturbing its equilibrium. He drew attention to the fact that in all cases heavy elements with an odd ordinal number either have no isotopes at all, or have two isotopes whose masses differ by two units, whereas elements with an even number may have a whole series of isotopes. This striking difference between the elements is analogous to the observed fact that elements with an odd atomic number which undergo disintegration when bombarded by α-particles emit protons with a much higher average velocity than even elements. Harkins also showed that elements with even numbers are far more abundant in nature than elements with odd numbers.
This difference in isotopic properties between even and odd elements appears to be fundamental in character. A possible explanation may be obtained with the aid of the general view of the structure of the nucleus which we have sketched. It was assumed, as usual, that the central nucleus is built up of helium nuclei, bearing two charges arranged in a definite way, and that even elements must have an even number of electrons.
These latter tend to come into equilibrium so that the resultant magnetic moment of the system is minimal. If now, by adding a proton or removing...
if an element with an odd atomic number is formed by the addition of an electron, then subsequently this equilibrium between the magnetic moments may already prove impossible, as in the case of an element with an even number. The action of the resultant magnetic field of the nuclear system may lead to the impossibility, for neutral satellites, of rotating in stable orbits around the nucleus. If this view is correct, then we must acknowledge that the nuclear magnetic moment of odd elements should differ noticeably from the magnetic moments of even elements. So far as I know, at the present time there is no definite evidence on this point.
In this examination of atomic structure we have dealt for the most part with heavy elements, where the nuclei are represented as consisting chiefly of $\alpha$-particles and satellites, and where it must be admitted that the rule of integral numbers of atomic masses should be justified within narrow limits. If the presence of neutral satellites in the nuclear system depends mainly on the electric charge of the nucleus, the addition of such satellites should be possible only when the nuclear charge exceeds a certain value. For this reason the structure of the light elements in its general features may differ considerably from the structure of the heavy elements, and deviations from the rule of integral numbers of atomic masses may be more strongly expressed than for heavy elements. The exact determination of the atomic masses of the light elements, such as was undertaken by Aston, is therefore of enormous theoretical as well as practical interest, for it can give us valuable information as to how closely the components of the nucleus—protons and electrons—are bound together.
Since the structure of the light elements is unknown, it appears very difficult to combine the decomposition of such elements by $\alpha$-particles with the study of any special features of their structure. The views presented here are, by their nature, it must be admitted, highly speculative, but they may render useful service by indicating possible paths toward the study of this fundamental pro-
problems. Although the nuclei of heavy elements are undoubtedly very complex in their structure, they may possess certain simple general features that may be absent, or may escape observation, in the light elements. For this reason I have great hope that, in studying radioactive data, we may nevertheless be able to shed light on some outstanding features of the structure of the nuclei of heavy elements.