Discussion on the Structure of the Atomic Nucleus *

(The discussion took place on April 28, 1932, at the Royal Society of London)

Lord Rutherford. In my address today I shall give a brief survey of some of the main lines along which our knowledge of the atomic nucleus has advanced since I had the honor of opening the previous discussion.** In the interval between these discussions there has been considerable progress in many directions, and new and promising methods of attack on this difficult problem have been found. I can only refer to the valuable data obtained by Aston and others concerning the isotopic composition of elements and the relative abundance of the isotopes of many elements. This made possible the determination, with considerable accuracy, of chemical atomic weights by means of the mass spectrograph. New experiments have been carried out on the precise determination of the relative amounts of the isotopes of lead, and in particular of lead obtained from pure uranium and thorium minerals of great geological age. Data of this kind are extremely important and interesting not only from the point of view of radioactivity, but also with regard to establishing an accurate time scale in geology. Apparently, it is certain that the final product of the actinium series—actinium lead—has atomic mass 207, and that actinium arises as a result of the transformation of an isotope of uranium. From the relative abundance of actinium and thorium lead originating from old radioactive minerals, one can derive the average duration

* The report was published in Proc. Roy. Soc., translated by D. Blokhintsev.
** See Uspekhi fizich. nauk, X, 1, p. 149, 1930.

of this uranium isotope. Some time ago I noted in Nature that, from considerations concerning the mean life of the two uranium isotopes, important conclusions may be drawn about the formation of elements in the sun.

Optical methods. One of the most interesting successes of recent years has been the application of optical methods to determining the presence of isotopes and to studying the motion of nuclei. The investigation of the band spectra of molecules of the light elements has revealed the presence of isotopes existing in small quantities in comparison with the principal isotope. It has been shown that oxygen consists of three isotopes with masses 16, 17, 18; carbon—12, 13; beryllium—8, 9; boron—11, 10; and recent observations by Urey, Brickwedde, and Murphy—one may believe—indicate the presence in hydrogen of small quantities of a new isotope with mass 2. At present attempts are being made to concentrate the new isotope by fractional distillation of liquid hydrogen.

Along with the identification of lines belonging to new isotopes, considerable attention has been devoted to the relative intensity of lines in band spectra. Such study gives not only information about the spin of the nucleus, but also prepares a method for mastering one of the most important points of nuclear physics—namely, questions concerning the sameness of the members of a given isotopic system.

In the course of the last few years many investigations have been carried out to determine hyperfine structure in optical spectra. This opens another line of attack on the difficult problem of nuclear spin. I shall leave to Prof. R. H. Fowler the discussion of the data obtained and of the conclusions that may be drawn from them.

Application of wave mechanics. At the last discussion there was considered the application by Gamow, and also by Gurney and Condon, of the then still-new ideas of wave mechanics to certain problems of the atomic nucleus—and in particular to the explanation of the well-known Geiger–Nuttall rule, which relates the velocity of the α-particle emitted from a radioactive-

of matter with its decay constant. In this theory it is assumed that the nucleus is surrounded by a high positive potential barrier and that α-particles or other components of the nucleus are held in a state of equilibrium inside this barrier by considerable attractive forces of an unknown type. According to such a model, there is a finite probability that an α-particle in the nucleus will be able to pass through the barrier without loss of energy—a probability that rapidly increases with increasing energy of the α-particle. This general conception of the nucleus proved very valuable in a number of directions and became a very useful working hypothesis for experimentalists. Unfortunately, it has not yet been possible to give a detailed theoretical picture of the structure of the nucleus. In general it is assumed that the nucleus of a heavy element consists chiefly of α-particles with an admixture of a few free electrons and protons, but the exact subdivision among these constituent parts is unknown. For theory there is a great difficulty in including, within the small nucleus, particles of such different masses as α-particles and electrons. In addition, the nucleus is such a concentrated structure and the particles composing it are so close to one another that the theory of the action of one particle upon another, applicable under ordinary conditions, cannot be applied to such small distances.

The matter appears as though an electron inside the nucleus behaved quite differently from an electron at the periphery of the atom. This difficulty may have been created by ourselves, since it seems to me more probable that an electron cannot exist in a free state in a stable nucleus, but must always be joined with a proton or with another possible massive unit. In this connection, indications of the existence of neutrons in some nuclei are remarkable. Beck’s observation that, in the construction of heavy elements from light ones, electrons are added in pairs is of great interest and suggests that, for the formation of a stable nucleus, it is essential to neutralize the large magnetic moment of the electron by adding another electron.

It is also possible that the uncharged units of mass 2 and the neutrons of mass 1 are secondary units in the structure of the nucleus.

Although at the present time no theory of the nucleus can be regarded as complete, it is nevertheless possible to go far by means of analogies based on the general model of the nucleus outlined above. For example, Gamow derived important conclusions about the mass defect of light atoms formed from \(\alpha\)-particles, i.e. from elements of the type \(4n\), proceeding from the analogy that the forces inside the nucleus are in their general features like the forces acting in a small drop of water. In addition, he analyzed with great clarity the conditions that must be fulfilled for the formation of a stable nucleus of high atomic number. Unfortunately, in order to advance further in this direction, knowledge of the masses of the isotopes of many elements is required with far greater accuracy than is now available.

In another direction as well, the application to the nucleus of many of the general ideas about energy levels that have proved so useful in discussing the electronic structure of the periphery of the atom has also turned out to be fruitful. It has long been assumed that quantum laws retain their significance inside the nucleus also, and the correctness of this assumption has in recent years been sufficiently tested. The conception of energy levels and excitation of the nucleus has proved extremely useful in very recent work on the difficult problem of the origin of \(\gamma\)-rays and in understanding the results of observations on the artificial disintegration of elements.

The origin of \(\gamma\)-rays. It was established long ago that \(\gamma\)-rays arise in the nucleus and represent, in a certain sense, characteristic natural oscillations of the nuclear structure. The interpretation of the complex spectra of \(\gamma\)-rays belonging to radioactive elements was, however, hampered by our ignorance of the origin of this radiation—whether it arises from the constituent parts of the nucleus, the electron, the proton, or the \(\alpha\)-particle, or from the nucleus acting as a single whole. During the last few years this problem has been subjected to vigorous attack and now seems

it clear that nuclear $\gamma$-rays are the result of the transition of an $\alpha$-particle between energy levels in an excited nucleus. Two different lines of attack were developed, based on:

1. The study of the long-range $\alpha$-particles of radium C and thorium C.

2. The fine structure in the emission of $\alpha$-particles from certain radioactive substances.

It may be assumed that the emission of a $\beta$-particle in the process of transformation causes a strong perturbation in the remaining nucleus, so that some of the $\alpha$-particles composing the nucleus are raised to a higher energy level than the normal one. These $\alpha$-particles are unstable and, after a very short interval of time, fall back to the normal level, radiating the excess of their energy in the form of $\gamma$-rays of definite frequency, determined by quantum conditions. In this short interval of time there is a small chance that $\alpha$-particles in high levels may pass through the potential barrier of the nucleus. From this point of view, the $\alpha$-particles escaping from the different levels constitute the observed groups of $\alpha$-particles with large ranges. The energy of the escaping $\alpha$-particles gives the value of the energy level occupied by the $\alpha$-particle in the excited nucleus before its release.

In order to test this hypothesis, the long-range $\alpha$-particles of radium C were carefully analyzed by new counting methods by a group of workers: Wynn Williams, Ward, Lewis, and the author; it was found that they consist of at least ten different groups.

It was found that the energy difference between the various groups is closely connected with the energies of some of the most prominent $\gamma$-rays and, in general, the experiments provide strong evidence that $\gamma$-rays owe their origin to transitions in excited nuclei of one or more $\alpha$-particles. At the same time, the experiments give direct information on the magnitude of a certain number of possible energy levels in this nucleus.

In the overwhelming majority of cases, α-particles are emitted in radioactive transformation with the same velocity. Rosenblum, however, showed that the element thorium C emits not one, but five different groups of α-particles, and since then evidence has been obtained of a fine structure of α-rays also for other radioactive elements. Gamow noted that γ-rays must arise in all cases where such a fine structure of α-rays is present. Owing to certain technical difficulties in the case of thorium C, it was difficult to give clear proof of the correctness of this point of view. Ellis, and also Rosenblum, came to the conclusion that Gamow’s view was correct, but Meitner arrived at the opposite conclusion.

I can only mention in passing some experiments by Mr. Bowden and myself to prove the emission of γ-rays by actinium emanation, for which Lewis and Wynn-Williams found that it emits two different groups of α-rays. The results, as it seems to me, support the general validity of the theory according to which fine structure in the emission of α-rays is always accompanied by the appearance of γ-rays. I shall give one of the following speakers, Dr. Ellis, the opportunity to present a more adequate account of the present state of this important problem.

Once the origin of the rays has been definitely established, there is a reasonable prospect of a successful attack on the problem of interpreting the spectrum of γ-rays—a problem whose solution has only just begun. Obviously, one may expect that the solution of this problem will throw much light on the detailed structure of the nucleus. For this purpose it is very important to investigate the spectrum of γ-rays with the greatest possible accuracy, and this requires many years of work.

Before leaving this part of the subject, I should like to emphasize the remarkable difference in the disturbance of the nucleus upon the emission of α-particles and β-particles. Strangely enough, the liberation of an α-particle either does not excite the nucleus at all, or raises one or more components of α-particles to a comparatively low energy level above the normal one. However, in many cases the liberation of a β-particle creates a strong

excitation of the residual nucleus, as a result of which some α-particles rise to a very high energy level and γ-rays of high energy are emitted. This difference between the actions of the two types of particles is very striking and may be intimately connected with the processes that cause the emission of β-particles in the radioactivity of the element.

Every time we have to deal with the behavior of the electron in the nucleus, we encounter great difficulties in applying our theoretical ideas. The most striking example may be that radioactive nuclei of the β-ray type emit electrons with a continuous energy spectrum, and that, it seems, there are no compensating processes here that would make it possible to establish the definite energy balance expected from quantum dynamics. Undoubtedly, this is one of the most fundamental problems of the present day, but we shall probably not have enough time to discuss it in all its theoretical complexity.

Excitation of the nucleus by γ-rays. Until recently it was generally assumed that the absorption of X-rays and γ-rays is a consequence of the interaction of the radiation only with extranuclear electrons, and that the nucleus itself does not participate in this process. It is now clear that if the quantum energy of γ-rays exceeds 2 million volts, an additional type of absorption by the ordinary nucleus appears, accompanied by the emission of characteristic radiation with frequencies different from the primary one. This effect of absorption by the nucleus was revealed by the work of Chao, Meitner and Hupfeld, Tarrant, and others, who used the penetrating γ-radiation of thorium C with an energy of about \(2.65 \cdot 10^6\) electron-volts.

In a paper now in the stage of publication, Gray and Tarrant* give the results of a detailed study of nuclear excitation of various elements. Not only the γ-rays of thorium C were used, but also the high-frequency components of the radiation of radium C. Gray and Tarrant came to the conclusion that this nuclear excitation is a general—

* Proc. Roy. Soc., A. 186, 662 (see the article by M. Kronstein in the present issue of Uspekhi, p. 649). Ed.

property of the elements, in any case between oxygen and lead. Characteristic radiation of a similar type, it seems, is emitted by all elements, and the intensity of the radiation from the various elements varies approximately as the square of the atomic number. This characteristic radiation of the nucleus, which is emitted uniformly in all directions, can be resolved into two components with quantum energies of about 500,000 and 1,000,000 electron-volts. In their explanation, Gray and Tarrant indicate that γ-radiation excites not the nucleus as a whole, but only certain component parts, similar to α-particles, which are common to all elements. It may be that the observed characteristic radiations represent certain modes of vibration of the very structure of the α-particle. It is of great interest to carry these important investigations further, but success is hindered by the difficulty of obtaining intense sources of high-frequency radiation with a broad spectrum of quantum energies. The excitation of the nucleus by means of high-frequency radiation is undoubtedly closely connected with the process that releases γ-rays from radioactive nuclei, and may help to shed further light on this problem.

Artificial transformation. In the very latest years our knowledge of the artificial transformation of the light elements by bombardment with α-particles has increased. This increase has resulted from the development of new electrical methods for counting α-particles and protons, which replaced the difficult scintillation method. Pose first pointed out that some of the protons ejected from aluminum appear in groups of definite velocities. Our knowledge was extended by the work of Pose, Meitner, Bothe, de Broglie and Ringe, and Chadwick and Constable. For example, Chadwick and Constable resolved the protons released from aluminum by the α-particles of polonium into eight different groups, combined in pairs. In explanation they assumed that protons or α-particles in the bombarded nucleus occupy definite energy levels. It is supposed, following Gamow, that, owing to resonance, there is a much greater chance of passing through the po-

potential barrier of the nucleus, if the bombarding \(\alpha\)-particles have almost the same energy as the proton or \(\alpha\)-particle in the nuclear level. For a given energy of the \(\alpha\)-particles, two groups of protons are emitted, corresponding, as is supposed, to two different processes of capture of the \(\alpha\)-particle by the nucleus. Similar results have been observed in fluorine and other light elements.

It was found that these resonance levels for the selective capture of the \(\alpha\)-particle are rather broad, corresponding to approximately \(5\%\) of the energy level. The results, within the limits of what has been done, provide important information about the values of the energy levels of light nuclei and, by using particles still faster than polonium ones, we may expect a still further extension of our knowledge of these levels.

In the interpretation of these experiments the applicability of the law of conservation of energy and momentum was tacitly assumed. In this way it was possible to calculate, with considerable accuracy, the atomic mass produced as a result of the capture of an \(\alpha\)-particle by the nucleus and the emission of a proton. In those cases where two groups of protons of different velocities are associated with one resonance level, the appearance of \(\gamma\)-rays was found, whose quantum energy approximately corresponds to the difference of the proton energies in the two groups. The study of the \(\gamma\)-radiation emitted in the process of artificial transmutation has in recent months led to new and interesting results. Bothe and Becker, in 1930, found that beryllium bombarded with \(\alpha\)-particles does not emit protons, but gives something that seems to be \(\gamma\)-radiation of greater penetrating power than the \(\gamma\)-rays of radium C.

The absorption of this radiation by matter was studied by I. Curie-Joliot and M. Joliot, and also by Webster. In the current year I. Curie-Joliot and M. Joliot observed, by the ionization method, that this radiation knocks out high-velocity protons from hydrogen-containing substances. At first it was assumed that these fast protons might be the result of interaction between a \(\gamma\)-ray quantum and a proton, but

it turned out that this requires a very high quantum energy of radiation, of the order of 50 million volts. As a result of further experiments by the electrical method, Chadwick found that an analogous recoil effect is observed for all light atoms and came to the conclusion that the effect can be explained by assuming that a stream of fast neutrons is released from the beryllium nucleus. It is not easy to choose between these two assumptions, but enough evidence has accumulated that this new type of radiation possesses remarkable properties and is capable of producing the disintegration of nitrogen, probably by some new route.

I shall leave it to Dr. Chadwick to give you a more complete account of the work on artificial transmutation and of the properties of this new type of radiation. The idea of the possible existence of “neutrons,” i.e. of a close combination of a proton and an electron with a mass of about 1 and with zero charge, is not new. In the Bakerian Lecture before this Society in 1920 I discussed the probable properties of the neutron, at the time when Dr. Glasson and I. Roberts were carrying out experiments in the Cavendish Laboratory with the aim of detecting the formation of neutrons in a strong electric discharge through hydrogen, but without success. If the neutron hypothesis is confirmed by experiment, it will obviously have a great influence on our understanding of the formation of the nucleus and of its composition. Many years ago, in a lecture before the Royal Institute, I discussed the possibility of the formation of heavy nuclei from hydrogen through the mediation of the neutron. It does not seem improbable that neutrons, owing to their interactions, may assemble into massive aggregates which, in the course of processes of disintegration and combination, are rearranged into nuclei of stable elements. I have simply recalled this old idea, which may perhaps be worthy of further reflection in the light of new knowledge.

Scattering of α-particles. In the preceding discussions attention was directed to the anomalous scattering of α-particles by light elements and to the difficulties of interpreting the results obtained. Many of these difficulties were removed by applying the ideas of wave mechanics to this pro-

problem. For example, H. M. Taylor was able to explain, with considerable detail, the anomalous scattering of $\alpha$-particles observed in hydrogen and helium by simple considerations based on wave mechanics. Mott drew attention to the expected anomalies in the scattering of low-velocity $\alpha$-particles by helium atoms, and his conclusions were confirmed by the work of Chadwick and Blackett and of Champion. According to Mott’s theory, similar anomalies should be expected in collisions between two identical nuclei of any kind.

Conclusion. I have tried in this survey to draw your attention to those lines of experimental attack on the problem of the structure of the atomic nucleus which seem to me the most important. I have not entered into speculative questions, such as the question of the possibility of the annihilation of matter and its transformation into radiation; nor have I touched on conjectures about the numerical relation between the unit of charge and Planck’s constant $h$, or the relation between the mass of the proton and that of the electron; I have not gone into the difficult questions of the formation and transformations of the nucleus under the influence of conditions existing in hot stars—questions about which much has been written.

In preparing this survey, I was struck by the comparatively rapid progress that has been made since our last discussion in mastering this central problem of physics. Progress would be greatly accelerated if we could obtain in the laboratory powerful but controllable sources of fast atoms and high-frequency radiation for bombarding matter. In the experiments of Tuve, Hafstad, and Dahl in the Department of Terrestrial Magnetism in Washington, and of Cockcroft and Walton in the Cavendish Laboratory, it proved possible, by means of high potentials, to create an artificial stream of protons with individual energies of about 1 million electron-volts and to study their properties. Some other methods of obtaining fast atoms are being tested by other investigators; I might refer especially to the exceptionally ingenious method developed by Lawrence and Livingston at the University of California, where, by means of repeated accelerations, protons with ener-

whose energy corresponds to approximately 1 million volts. In a recently published article they come to the conclusion that by this method it is possible to obtain a stream of fast atoms of still greater energy. Thus there opens up here a quite promising prospect that in the near future we shall be able to obtain sources of fast atoms and high-frequency radiation and, at the same time, to broaden our knowledge of the structure of the nucleus.

Addendum

While this report was being discussed among the members of the Society, Cockcroft and Walton, in the Cavendish Laboratory, carried out new experiments. An apparatus was assembled that gave a constant voltage of 600—800 thousand volts. By means of an auxiliary discharge tube, protons were produced and then accelerated in a vacuum by a high potential. In this way it was possible to obtain a steady stream of fast protons with energies up to 600 thousand volts and to use them for bombarding certain elements. The material to be bombarded by these fast ions was placed inside the tube at \(45^\circ\) to the direction of the beam. A thin mica window was fixed in the wall of the tube in such a way that the existence of fast particles could be investigated by the scintillation method outside the tube.

The first element subjected to study was lithium; at an accelerating potential of about 125 thousand volts a few bright scintillations were observed. Their number rapidly increased as the voltage was raised to 400 thousand volts, when many hundreds of scintillations per minute were already observed at a proton current of a few microamperes. These particles had a maximum range in air of about 8 cm. The brightness of the particles indicates that they are probably \(\alpha\)-particles, and this was confirmed by observations of the tracks produced by these particles in a Wilson chamber. It seems clear that some of the lithium nuclei are disintegrating. The simplest assumption is that a lithium nucleus of mass 7 captures a proton and that the resulting mass 8 then breaks up into two \(\alpha\)-particles. According to this view, the emitted

the energy corresponds to 16 million electron-volts, a value that is in good agreement with the conservation of energy, if one takes into account the difference between the initial and final mass of the nucleus. If this view is correct, then the disintegration of the lithium nucleus should produce two $\alpha$-particles emitted in opposite directions, and this can be tested experimentally. It may be estimated that at 200 thousand volts the number of disintegrations is 1 per $10^9$ protons.

Experiments have also been carried out with other elements. Boron, fluorine, and aluminum all give particles resembling $\alpha$-particles, with a characteristic range for each element. Scintillations from beryllium and carbon were also observed, some bright, others weak, and there are indications that nitrogen gives a few bright scintillations. Oxygen and copper give no scintillations for protons with energies up to 400 thousand volts.

It is evident that the study by this method of all the elements, and the determination of the nature of the fast particles that may be emitted, requires much further work. In some cases the emitted particles appear to be $\alpha$-particles, but we must always keep in mind the possibility of the emission of particles of various types and masses.

It is not difficult to make conjectures about possible modes of disintegration of some of the elements mentioned, conjectures consistent with the law of conservation of energy. For example, it is possible that a fluorine nucleus of mass 19, after capturing a proton, breaks up into an $\alpha$-particle and an oxygen nucleus. In a similar way, aluminum may be transformed into magnesium. We must, however, await further evidence before any definite decision can be accepted in such questions. It is clear that the successful application of these new methods opens up a new and broad field of research, in which the effect of bombarding matter with fast ions of various kinds can be studied. Dr. Cockcroft and Dr. Walton may be congratulated on their success in these new experiments, which required several years of persistent preparatory work.

J. Chadwick. Experiments in which elements are bombarded by $\alpha$-particles have proved fruitful with respect to information about the structure of the nucleus. The advances made since the last discussion are partly a consequence of the improvement of experimental technique and partly the result of applying the new mechanics to these problems.

To show how this enlargement of knowledge was achieved, I shall take as an example the case of the aluminum nucleus. When a beam of $\alpha$-particles falls on a thin aluminum foil, some of the particles are scattered in collisions with the aluminum nucleus. If the incident $\alpha$-particles are slow, the scattering is fully described by Rutherford’s theory of scattering, and we may conclude that the force between the $\alpha$-particle and the nucleus obeys Coulomb’s law. As the velocity of the incident particles is increased, the scattering begins to deviate from the normal law; for example, the amount of scattering at $135^\circ$ first decreases below the normal value and then rapidly increases with a further increase in the velocity of the $\alpha$-particles.

By the methods of classical mechanics it is difficult to explain this anomalous scattering, but it is readily amenable to interpretation on the basis of wave mechanics.

Let us suppose that the $\alpha$-particle undergoes a very close collision with the nucleus and approaches the point of the potential barrier where the thickness of the barrier is comparable with the wavelength of the $\alpha$-particle. Then there is some probability that the $\alpha$-particle will penetrate through the barrier. The scattered wave representing such a particle will have a certain phase shift and will disturb the classical distribution of the scattered particles. Rietzler’s experiments show that the scattering becomes anomalous when the $\alpha$-particle approaches to a distance of $6 \cdot 10^{-13}\ \mathrm{cm}$ from the aluminum nucleus. On the basis of certain probable assumptions it follows that the radius corresponding to the top of the potential barrier should lie between $3$ and $6 \cdot 10^{-13}\ \mathrm{cm}$. Taking the mean value $4.5 \cdot 10^{-13}\ \mathrm{cm}$, we obtain for the height of the Al barrier (for an $\alpha$-particle) about $8 \cdot 10^6$ electron-volts.

I now turn to observations on artificial

by the disintegration of aluminum. When aluminum is bombarded with $\alpha$-particles, we observe, in addition to scattered $\alpha$-particles, the emission of high-energy protons, which is approximately the same in all directions: an $\alpha$-particle penetrating into the nucleus ${\rm Al}^{27}$ may be captured; one proton is emitted and a ${\rm Si}^{30}$ nucleus is formed. We understand that the $\alpha$-particles and protons in the nucleus are situated at definite energy levels. The captured $\alpha$-particle with kinetic energy $W$ falls, let us say, to the level $E_\alpha$, while the proton is emitted from the level $E_p$ (both below the ground level). The kinetic energy of the ejected proton, neglecting the small energy of the residual nucleus, will be $W + E_\alpha - E_p$. According to this view, a homogeneous beam of $\alpha$-particles incident on a very thin Al foil will give an emission of protons of identical energy (in a definite direction). Observations, however, show that in this case two groups of protons are emitted. This can be explained by assuming that in some (the majority of) cases the final nucleus ${\rm Si}^{30}$ is formed in two stages: the $\alpha$-particle is captured (perhaps at an intermediate level), and a proton is emitted with the formation of an excited ${\rm Si}^{30}$ nucleus, which passes into the ground state with the emission of a quantum of radiation. This explanation is confirmed by the observation that Al bombarded by $\alpha$-particles does indeed emit $\gamma$-rays of the appropriate energy.

Observations of protons emitted from thick Al foil subjected to the action of polonium $\alpha$-rays show that the protons consist of eight groups, joined in pairs. Although collisions between the Al nucleus and $\alpha$-particles occur for all velocities from zero up to the initial velocity of the $\alpha$-particles, nevertheless all the disintegrations appear to be the result of the action of $\alpha$-particles of only some definite velocity. Such a possibility was first noted by Gerney, who pointed out the possibility of a resonance effect between the incident $\alpha$-particles and the atomic nucleus. If an $\alpha$-particle has an energy corresponding to a resonance level of the nucleus, then its chances of penetrating through the potential barrier will be considerably greater than when its energy is greater

or less than this. The first proof of the resonance effect was found by Pose in the disintegration of aluminum. Later observations, only just mentioned, show that there are four resonance levels of the aluminum nucleus between 4 and \(5.3 \cdot 10^6\) electron-volts. The penetration of an \(\alpha\)-particle through each level and its capture gives the emission of two groups of protons.

There is still a large region of the potential barrier of aluminum that has not yet been investigated in this way. Further experiments may reveal certain relations between the levels of one and the same element, and correspondence between the levels of one element and the levels of others.

It has recently been discovered that the disintegration of the elements beryllium and boron is of special interest. Bothe and Becker found that these elements, when bombarded with polonium \(\alpha\)-particles, emit penetrating radiation, apparently of the \(\gamma\)-type. Several months ago I. Curie-Joliot and M. Joliot made striking observations showing that this radiation has the property of ejecting protons at high velocities from substances containing hydrogen. They found that the protons ejected by the radiation from beryllium have velocities up to \(3 \cdot 10^9\) cm/sec. Curie and Joliot suggested that this ejection of a proton occurs through a process analogous to the Compton effect, and concluded that the radiation from beryllium has a quantum with an energy of about 50 million electron-volts. Acceptance of this assumption raises two serious difficulties. First, it is known that the scattering of a quantum by an electron is well described by the Klein–Nishina formula, and there is no reason to suppose that similar relations would not be valid for the scattering of a proton. The observed scattering, however, is too large in comparison with that given by the Klein–Nishina formula. Secondly, it is difficult to understand the emission of a quantum of such high energy in the transformation \(\mathrm{Be}^9 + \mathrm{He}^4 \to \mathrm{C}^{13} +\) quantum. Therefore I studied the properties of this radiation, using a special counter*. It was found that

* See Chadwick’s article “Neutrons,” printed below. — Ed.

radiation ejects particles not only from hydrogen, but from helium, lithium, beryllium, etc., and presumably from all elements. In all cases the particles, apparently, are recoil atoms of the element. It is evidently impossible to ascribe the ejection of these recoil particles to a collision with a quantum of radiation, if energy and momentum are conserved in the impact.

A satisfactory explanation of the experimental results can be obtained if it is assumed that the radiation consists not of quanta, but of particles with mass 1 and charge 0—neutrons. In the case of two elements, hydrogen and nitrogen, the range of the recoil atoms was measured with a high degree of accuracy, and from this their maximum velocities were deduced. They proved to be, respectively, \(3.3 \cdot 10^9\ \text{cm/sec}\) and \(4.7 \cdot 10^8\ \text{cm/sec}\). Let \(M, V\) be the mass and velocity of the particles of which the radiation consists. Then the maximum velocity that can be imparted in a collision to a hydrogen nucleus will be:

\[ U_{\mathrm{H}}=\frac{2M}{M+1}\cdot V, \]

and to a nitrogen nucleus:

\[ U_{\mathrm{N}}=\frac{2M}{M+14}\cdot V, \]

whence:

\[ \frac{M+14}{M+1}=\frac{U_{\mathrm{H}}}{U_{\mathrm{N}}}=\frac{3.3\cdot 10^9}{4.7\cdot 10^8} \]

and

\[ M=1.15. \]

Within the errors of experiment, \(M\) may be taken as 1, and therefore:

\[ V=3.3\cdot 10^9\ \text{cm/sec}. \]

Since the radiation has an extremely great penetrating power, the particles must have a charge very small in comparison with the charge of the electron. It is assumed that this charge is 0, and we may allow that the neutron consists of a proton and an electron in a very close combination.

The available facts strongly support the hypothesis of neutrons. In the case of beryllium, the transformation process that gives neutron emission is \( \mathrm{Be}^9 + \mathrm{He}^4 \rightarrow \mathrm{C}^{12} + \) neutron. It can be shown that the observations are compatible with the energy relations in this process. In the case of boron, the transformation process is probably \( \mathrm{B}^{11} + \mathrm{He}^4 \rightarrow \mathrm{N}^{14} + \mathrm{n}^1 \); in this case the masses of \( \mathrm{B}^{11} \), \( \mathrm{He}^4 \), and \( \mathrm{N}^{14} \) are known from Aston’s measurements, the kinetic energy of the particles can be found experimentally, and it is therefore possible to obtain a closer estimate of the mass of the neutron. The mass derived in this way is 1.0067. Taking into account the error in the mass measurement, it should be thought that the mass of the neutron probably lies between 1.005 and 1.008. These values support the view that the neutron is a combination of a proton and an electron and give for the binding energy of the particles about \(1—2 \cdot 10^6\) electron-volts.

The neutron may be represented as a small dipole, or perhaps better as a proton immersed in an electron. In any case the “radius” of the neutron will be between \(10^{-13}\) cm and \(10^{-12}\) cm. The field of the neutron must be very small, except at very close distances, and neutrons, in passing through matter, will not be affected, except in those cases when they directly enter an atomic nucleus. Measurements made on the passage of neutrons through matter give results that are in general agreement with these views. The collision of neutrons with nitrogen nuclei was studied by Dr. Feather, who used an automatic Wilson chamber. He found that, in addition to the normal tracks of nitrogen recoil atoms, there is also a certain number of branching tracks. This is a consequence of the disintegration of the nitrogen nucleus. In some cases the neutron is captured, an \(\alpha\)-particle is emitted, and a \( \mathrm{B}^{11} \) nucleus is formed. In other cases the mechanism is still not definitely known.

Ch. D. Ellis. It has been known for many years that \(\gamma\)-rays produce a spectrum characteristic of the radioactive nucleus, but only quite recently have facts been obtained giving indications as to the manner of their origin. At first the source

... of γ-rays were considered to be nuclear electrons, but this point of view, so natural in view of our experience with extranuclear structure, began to be called into question as information accumulated indicating that the behavior of nuclear electrons differs strongly from the behavior of electrons outside the nucleus. Rapid progress—both experimental and theoretical—in our knowledge of α-particles has made it possible to avoid this difficulty in a satisfactory way, and it is now generally believed that γ-rays are connected with transitions between stationary states of α-particles inside the nucleus. This conclusion is important in that it stimulates and provides a guiding point of view for further investigation of γ-rays and indicates the possibility of obtaining detailed and precise information about α-particles.

Lord Rutherford has already noted that recent work has revealed a complexity in the emission of α-rays, a complexity not observed in earlier experiments. First, the phenomenon of long-range α-particles was discovered, the most typical example of which is provided by radium C. In the disintegration of this body, out of a million atoms about 99,978 emit α-particles whose energy is \(7.8 \cdot 10^6\ \mathrm{V}\), while the remaining 22 emit particles with greater energy, distributed among at least nine groups. The fastest of these groups has an excess of \(3,000,000\ \mathrm{V}\), just covering the interval of the known γ-rays. Closer study shows that the difference in energy between the fast groups and the principal \((7.8 \cdot 10^6\ \mathrm{V})\) group agrees with \(h\nu\) for the γ-rays. Furthermore, whereas the number of particles in these groups is extremely small, the total number of quanta of the rays reaches one quantum per atom. Both the approximate agreement of the frequencies with the energies and the agreement of the relative intensities of the long-range α-particles with the number of quanta are compatible with the view that the nucleus of radium C is initially formed in an excited state. The nucleus then has two possibilities by which it can release its energy. The first and least probable is immediate disintegration, in this ...

in this case the α-particle carries off all the excitation energy; such α-particles form one of the high-energy groups. Another possibility is that the nucleus will first emit part of its excitation energy in the form of γ-rays, and will then be left with just enough energy to emit normal α-particles with an energy of \(7.8 \cdot 10^6\) V. This explanation was considered in detail by Lord Rutherford and the author* and also subsequently by Gamow and Delbrück**, and, although the available data are still insufficient to test this view in all details, it may nevertheless at least be said that the relations in energy and intensities are compatible with it.

Thorium C also exhibits a series of groups of α-rays which are distributed according to a different scheme. They are usually referred to the fine structure of the groups of α-particles, chiefly because the energy differences in this case amount to only about 300,000 V. There is also another difference: in this case the less intense groups are also the groups with the lowest energy. It is immediately clear that the explanation for radium C cannot be applied here, but Gamow indicated a simple point of view which seems suitable in this case. His view is that the nuclei of thorium C initially are all in one and the same state. Each nucleus has a certain amount of energy capable of being released. The nucleus can release this energy either by emitting an α-particle with this full energy, or it can emit an α-particle in one of a series of groups of lower energy, while the remaining energy is retained in the nucleus as excitation energy. The essential difference in this view of the connection between α-particles and γ-rays, as compared with the first scheme, is that the emission of γ-rays is a process following the emission of the α-particle. This alternative view is unambiguously suggested in this case by the relative intensities of the γ-rays and α-particles in the groups. It should be noted that it is assumed that emission

* Rutherford and Ellis, Proc. Roy. Soc., A. 132, 667 (1931).

** Gamow und Delbrück, Z. Physik 72 492, 1931.

...of \(\gamma\)-rays takes place after the disintegration, whereas, from the point of view of energy relations, it would be just as easy to assume that the \(\alpha\)-particle in the normal state first makes a transition to a state of lower energy with the emission of \(\gamma\)-rays and is then ejected from the nucleus from this level.

Such a view would, however, lead to an extraordinary difficulty: while we have a convincing explanation for the long interval of time during which a radioactive atom can exist, while nevertheless possessing the potential possibility of disintegration, all other evidence shows that any system possessing the possibility of emitting radiation cannot exist as such for more than a small fraction of a second. The period of thorium C for \(\alpha\)-disintegration is approximately 3 hours, and any view different from Gamow’s view would have to proceed from the possibility of radiation with a half-period of 3 hours, which is clearly impossible. I investigated the applicability of Gamow’s theory to the case of thorium C. Details of the fine structure of the \(\alpha\)-particles had been found by Rosenblum from his experiments with the Paris electromagnet, and the first step consisted in showing that thorium C actually emits \(\gamma\)-rays. This had never been thought of before it was predicted by Gamow. Indeed, the \(\gamma\)-rays were investigated by means of the \(\beta\)-ray spectrum, and I measured the \(\beta\)-ray spectra both of the combined emission of thorium C \(+\) C\('\) and of thorium C\('\) alone. The experiments are described in detail in a paper now in press; the results are such that certain groups found in the combined spectrum definitely do not occur in the spectrum of thorium C\('\) alone. The next point in the argument would be the proof that the frequencies of the \(\gamma\)-rays approximately correspond to the differences of the energies of the \(\alpha\)-particle groups found by Rosenblum. This seems indeed to be borne out, within, as a rule, the rather large errors of the data. And finally, the last point in the argument is the consideration of the relative intensities, with the aim of showing that the relative number of \(\alpha\)-particles in the various subgroups corresponds...

relative number of quanta inferred from the spectrum of γ-rays. It is impossible to give a definite answer to this question. All that can be said amounts to the fact that the relative intensities are compatible with this view. Since the writing of the article to which I referred, I have carried out some further experiments. Although I have not obtained any strong evidence, I have nevertheless confirmed the conclusions previously drawn, using a different apparatus. This question deserves further investigation—in particular, in the direction of studying the coincidence of \(h\nu\) for γ-rays with the energy differences of different groups of α-particles, but this requires greater accuracy in both series of measurements. At present, however, it may safely be said that there is strong evidence in favor of a general connection between α-particles and γ-rays, and this seems to be a reasonable hypothesis to follow.

It is appropriate to consider the exact meaning of this hypothesis and to reduce it to the simplest formulation. In this sense it means above all the applicability of the law of conservation of energy to the nucleus, or rather to that part of the nucleus which is associated with the emission of α-particles and γ-rays. It should be noted that in both of these cases the equivalence of the total amount of energy has been established when this energy can be divided in two ways. Either the α-particle carries away all the available energy, or, if it takes only a part, the remainder is emitted in the form of γ-rays. The nucleus is an entire system and contains a large number of particles, and therefore the validity of speaking of one of them separately is doubtful. Therefore it is still unknown whether it makes sense to assert that γ-rays are emitted by α-particles. This would hardly make sense if the law of conservation of energy were applicable to the nucleus as a whole; but in reality, as we know from the phenomenon of the continuous spectrum of β-rays, this is not the case. We have seen that the available evidence shows that the law of conservation of energy is applicable both to the emission of α-particles and to the emission of γ-rays, while it is apparently definitely inapplicable to the emission of β-particles. In such a case it seems legitimate

to distinguish between $\alpha$-particles in the nucleus and electrons, and with that degree of definiteness with which this distinction exists, we may say that $\gamma$-rays are associated with the fractions of $\alpha$-particles of the nucleus. It should not be forgotten that in the nucleus there are other particles on a par with $\alpha$-particles and electrons. Fowler indicated that protons may be responsible for certain features of the spectrum, and recent work shows that, apparently, we must also take account of neutrons of one or many kinds. The study of the detailed connection of $\gamma$-rays with $\alpha$-particles and protons and, possibly, other bodies is a task for the future; but at the present time, as a purely working hypothesis, it is convenient to accept the narrow view according to which $\gamma$-rays are also associated with the states of $\alpha$-particles in the nucleus, just as X-rays and optical spectra are associated with the electronic structure. The investigation of these states of the $\alpha$-particles of a radioactive nucleus requires the joint development—at least of two lines of investigation: on the one hand, the direct investigation of the energies and intensities of the various groups of $\alpha$-particles; on the other hand, measurements of the $\gamma$-ray spectrum. There is no need to speak of the first line of investigation, but an assessment of the importance of the latter naturally leads to the point that I wish especially to emphasize. This is the real need for increasing the accuracy in the region of our knowledge of the $\gamma$-ray spectrum.

There are several methods for investigating the $\gamma$-ray spectrum: the method of interference in crystals, the absorption method, and the method of observing recoil electrons in a Wilson chamber. But in order to establish certain points it is also necessary, as is clear at present, to take care to study the $\beta$-ray spectrum with the aim of obtaining the most exact and detailed information. The first point with which I should like to hasten is a reconnaissance of the type of work needed. We have left behind, as a pioneering stage, the time when the investigation of the $\beta$-rays of a certain body strove to give a general survey of the lines. We now need exact and detailed measurement. Most spectra are so rich in lines that опу-

publication would be undeservedly delayed if any of the investigators tried too anxiously to embrace the entire fullness of the spectrum at once. Therefore I hope that a careful study of small groups of lines, or even of the homogeneity of a single line, will be regarded as a sufficient subject for investigation.

The second point consists in the need to increase accuracy. Determining the ratio \(H\rho\), i.e. the momenta of \(\beta\)-rays in two lines, with an accuracy of at least \(1/3000\), presents no fundamental difficulties, but considerably more attention must be paid to the mechanical construction of the apparatus than was formerly the case. Since the results of measurements must be compared with measurements from another region—with the measurement of \(\alpha\)-rays—relative measurements are of little use; we need absolute measurements. Here the situation is far from satisfactory, and the whole scale of \(\beta\)-ray measurements is unreliable, although it may perhaps have an accuracy of up to half a percent. Determinations by independent observers of the absolute energies of some standard lines throughout the spectrum are urgently needed.

An accuracy of one five-hundredth would be attainable with our present technique, but any further, somewhat significant step forward seems to require a reconsideration of the whole problem and, possibly, the introduction of new methods. It may rightly be thought that deeds are more powerful than words, and that to follow these prescriptions oneself would be the best recommendation of them to others. But only in the last year has the situation with respect to \(\gamma\)-rays become clear, and along with this there has appeared both the necessity and the justification for this type of investigation. Here much remains to be done, and the attainment of results worthy of confidence requires comparison of the results of several independent experimenters.

R. H. Fowler. There are two principal lines of fact which tell us more or less unambiguously what the value of the nuclear spin must be. Both are quite familiar and may be briefly summarized. The first and most-

the best evidence is provided by alternating intensities in the band spectra of diatomic molecules in which the two atoms are identical—for example the molecules H—H, \(N_{14}\)—\(N_{14}\), or \(O_{16}\)—\(O_{16}\) (but not \(O_{16}\)—\(O_{17}\), etc.). Linear molecules, such as acetylene H—\(C_{12}\)\(\equiv\)\(C_{12}\)—H, also give evidence of the same kind, but, of course, here we obtain nothing new, only further evidence for the existence of the proton spin. If the nuclear spin in such molecules is \(n\cdot \frac{h}{2\pi}\), then the intensities of the lines in the bands alternate in the ratio \((n+1):n\). In this way we find with certainty the following spins (the list is not exhaustive):

\[ \mathrm{H}\ \tfrac{1}{2};\quad \mathrm{He}\ 0;\quad \mathrm{N}_{14}\ 1;\quad \mathrm{C}_{12}\ 0;\quad \mathrm{O}_{16}\ 0. \]

Moreover, in this way we obtain the most unambiguous indications of the type of statistics obeyed by nuclei; in particular, \(N_{14}\) obeys Bose–Einstein statistics, which compels us (together with other information) to the profound conclusion, contrary to the usual understanding, that the electrons in the nucleus contribute nothing to the spin or to the statistical type.

The second type of data comes from the details of the hyperfine structure of atomic spectra. Here we are dealing with all the perturbations that the nucleus produces in the optical spectrum, and it is not always easy to separate the effect of spin from others—for example, from the isotope effect. Nevertheless, it has proved possible, especially through the application of the Zeeman effect modified by the Paschen–Back effect for hyperfine structure, to determine with certainty the spin for certain kinds of atoms, in particular for Bi \(^{9}/_{2}\). This determination involves only qualitative data. When quantitative data on the width of the hyperfine structure are used, one can determine the magnitude of the magnetic moment of the nucleus associated with the nuclear spin. In this way it has been shown that nuclear magnetic moments are, in order of magnitude, proton Bohr magnetons, i.e.,

amount to \(1/2000\) of the ordinary Bohr magneton. But a more exact determination still encounters great difficulties.

An auxiliary group of spectroscopic data, which in the future may prove very useful, is connected with the study of the depolarization of resonance radiation by the Ellett method.

For the time being these paths are the principal paths by which the spin of a nucleus can be determined; they have no close relation to radioactive nuclei, and at present we have little hope of a direct determination of the spin of such nuclei by optical methods. Nevertheless, spin may have a very substantial bearing on these nuclei, as was recently shown by Gamow in a letter to Nature.* There he compares the regular sequences of radii for the uranium—radium and thorium series of radioactive elements, calculated theoretically from the observed rate of decay, with the irregular sequences of radii derived for the actinium series. He points out that this may be a consequence of changes in the spin of nuclei of the actinium series. If the spin changes, the \(\alpha\)-particle must carry away the corresponding angular momentum, and the formula for the lifetime of the nucleus will be modified. The observed irregularities will be understandable if, in the actinium series (atomic weights \(4n+3\)), changes in spin by 3 units can occur, whereas they do not occur in the other series (weights \(4n\) and \(4n+2\)). This seems quite possible, but at present is still, of course, pure speculation.

J. McLennan. The data derived from the study of the fine structure of spectral lines are now available for many elements. This gives us the possibility of estimating the mechanical moment and the corresponding multiplier \(g(I)\)—the ratio of the magnetic to the mechanical moment—for some atomic nuclei.

Until now the observed values—\(I\) (the quantum numbers of the spin) of the nucleus—have been explained by the assumption that only protons

* Nature, 129, 470, 1932.

within the atomic nucleus, by their spin, determine the resultant moment of the nucleus. The simple assumption according to which each proton contributes \(1/2\,(h/2\pi)\), until recently, was regarded as sufficient for explaining the known facts. However, some anomalies have recently been discovered. For example, it is known that whereas the relative distances in the hyperfine structure of the components of homologous spectral lines of the spectra Tl II and Pb\(_{(207)}\) III are similar, the actual magnitude of the splittings included in the structure of the spectral lines is considerably smaller than the distances in the corresponding lines of Tl II. The magnitudes of the splittings allow a direct comparison to be made and show that the multiplier \(g(I)\) for the Tl nucleus is approximately four times larger than for the Pb\(_{(207)}\) nucleus. This result has special significance, since according to the simple theory described above the resultant moment of the nuclei of the atoms Tl and Pb\(_{(207)}\), for which \(I = 1/2\), should be the consequence of a single unneutralized rotating proton. The multipliers \(g(I)\) for these two nuclei should then be identical, since there are no data which would indicate that different rotating protons with the very same mechanical moment can have magnetic moments differing over wide limits.

The obvious conclusion is that the moment, at least of one of the nuclei, is complex and is not simply the consequence of a rotating proton. This conclusion devalues the simple rule according to which each proton contributes a share \(\pm 1/2(h/2\pi)\) to the resultant moment. Moreover, it would require us to endow at least one proton with the same property in addition to spin either in one or in both of the nuclei Tl and Pb\(_{(207)}\).

Further evidence in favor of this conclusion is obtained from the ratio of the multipliers \(g(I)\) for thallium and bismuth. Although the value of “\(I\)” for the Bi nucleus is \(9/2\), the value \(g(I)\) should be the same as for Tl, if only the resultant moment of both nuclei is a consequence solely of rotating protons. However, the observed ratio is equal to 4 to 1. This approximate equality

multipliers \(g(I)\) for \(\mathrm{Pb}_{(207)}\) and Bi indicates that the resulting moment of the Tl nucleus is more complex in its origin than has hitherto been thought. Although the available data give no definite indications as to the nature of this additional property, Mac-Lennan, MacLay and Crawford * and also Bartlett ** suggest, as a possibility, orbital motion of protons inside the nucleus. This idea was developed by White *** and Bryden ****, but it seems inadmissible to ascribe orbital motion, as they do, to all protons without distinction inside the atomic nucleus.

Further, I may add that it has recently become known that the mathematical theory of calculating the interaction of electrons of a type other than \(s\)-electrons with nuclear spin was incorrect. This was shown by Wulff’s experiments *****, by the experiments of Fisher and Goudsmit ****** and by Mac-Lennan, MacLay and Crawford (loc. cit). Recently the theory was extended by Breit, who introduced a correction, \(\left(\dfrac{1}{\gamma^3}\right)\), due to the relativistic change in the mass of the interacting electron. This correction, which changes its value in the different states of the doublet arising from the interaction of one non-\(s\)-electron with the nucleus, gives better agreement with experiment. However, even with this improvement the theory is unsatisfactory. For example, the theory predicts for

\[ A_{(1,\,1/2)}^{2} P_{1/2} / A_{(1,\,3/2)}^{2} P_{3/2} = 5/1, \]

where \(A_{(i,j)}\) is the coupling constant in the energy equation:

\[ E_{(i,j)} = A_{(i,j)}\, IJ \cos (IJ). \]

The observed value was \(30/1\). The relativistic correction, which varies from element to element, gives the ratio-

* McLennan, McLay, Proc. Roy. Soc., A, 133, 652, 1931.
** Bartlett, Phys. Rev. 37, 327, 1931.
*** White, Phys. Rev. 38, 2078, 1931.
**** Bryden, Phys. Rev. 38, 1989, 1931.
***** Wulff, Z. Physik, 69, 70, 1931.
****** Fisher and Goudsmit, Phys. Rev. 37, 1057, 1931.

approximately 10/1. This shows that, even with this improvement, the observed values in the theory differ from the theoretical ones by factors of 2 or 3. Racas* gave an interpretation similar to that given by Breit and applied it to observations on the Tl spectrum. His comparisons once again show that the theory is still unsatisfactory.

Recently, a test of the theory of hyperfine structure was made by Becher and Campbell**. By studying the resonance spectral line of indium I, the complete hyperfine structure of the splitting of the two members of a doublet arising from the single \(5p\)-electron was found. The difficulties presented by the study of the spectral lines of thallium, with the complications that arise in the structure of the spectral lines owing to isotopic mixing, are not encountered in the case of indium, since this element is simple and has only one type of nucleus. Becher and Campbell found, for the case of the indium lines, that the spectral splitting \(\Delta^{2}P_{1/2}\) was \(0.390\ \mathrm{cm}^{-1}\), whereas the splitting given by \(\Delta^{2}P_{3/2}\) was \(0.133\ \mathrm{cm}^{-1}\), so that the ratio is \(2.9/2\). It is clear that this is not in agreement with the nonrelativistic theory, which gives the ratio 1.67. It is, however, in better agreement with 2.05, the value corrected according to Racas, and in still better agreement with 2.7—the value corrected by Breit.

N. F. Mott. The application of quantum mechanics to the problem of the anomalous scattering of \(\alpha\)-particles has led to the explanation of experimental results and to the prediction of certain new phenomena.

So long as it is assumed that the law of force between \(\alpha\)-particles and the nucleus is the inverse-square law, classical and quantum mechanics*** lead in general to identical scattering formulae, namely, in the case of an infinitely heavy nucleus to the formula \((2Ze^{2}/2mv^{2})^{2}\operatorname{cosec}^{4}\frac{\theta}{2}\) for

* Racas, Z. Phys., 71, 431, 1931.
* Becher and Campbell, Bull. Amer. Phys. Soc., April 28, 1932.
** Gordon, A. f. Phys. 48, 180, 1928.

number of particles scattered per unit solid angle through the angle \(\theta\). The only case in which classical and quantum mechanics make different predictions is that in which the struck particle belongs to the same kind as the incident particles, for example, the scattering of \(\alpha\)-particles by helium.* The number of scattered particles then depends on the statistics obeyed by the particle and on the number of spin quanta it possesses. Scattering at \(45^\circ\), for example, is greater than that predicted by the classical theory by the factor

\[ 2(s+1)/(2s+1), \quad \text{(Bose-Einstein statistics)} \]

\[ 2s/(2s+1), \quad \text{(Fermi-Dirac statistics),} \]

where \(s+\frac{h}{2\pi}\) is the angular momentum of the particle’s “spin.” Spin and statistics can be determined from the band spectra of diatomic molecules in which the particles under consideration form the nucleus. Scattering thus provides a method for checking the results obtained from band spectra. Data from the band spectrum of He\(_2\) show that \(\alpha\)-particles have no spin and obey Bose-Einstein statistics. It should therefore have been expected that scattering at \(45^\circ\) in helium would be twice the classical value. This was verified experimentally by Chadwick, and other results of the theory were confirmed by Blackett and Champion***. Slow \(\alpha\)-particles were used (velocities \(1—8.5\cdot 10^8\ \text{cm/sec}\)) in order to avoid effects depending on the failure of the inverse-square law at small distances.

To explain the anomalous scattering of fast particles in hydrogen and helium, and also the anomalous scattering in such elements as Al, Mg, B, it is necessary to assume that the inverse-square law loses its validity at distances smaller than some distance \(r\). It is natural to assume that at smaller distances the forces become attractive. Therefore, for the potential energy of \(\alpha\)-particles in the field of a nucleus

\[ \text{* Mott, Proc. Roy. Soc., A. 126, 159, 1930.} \]

\[ \text{** Cf. Kronig, Band Spectra and Molecular Structure, Cambridge, p. 94. 1930.} \]

\[ \text{*** Proc. Roy. Soc., A. 128, 114, 1930.} \]

\[ \text{**** Proc. Roy. Soc., A. 130, 380, 1931.} \]

take the form of the function shown in Fig. 1. We shall now discuss the scattering that should be expected in such a field. If the classical distance of closest approach for a central collision, namely \(2Ze^2/\frac12 mv^2\), is greater than \(r\), then the deviations from classical scattering will in general be very small. It is possible, however, that there will exist energy intervals of width \(0.5\cdot 10^6\) electron-volts or less (resonance levels), and also that an \(\alpha\)-particle with this energy can readily penetrate through the potential barrier. For such energies the scattering will be anomalous and artificial disintegration may occur. The existence and position of the resonance levels depend on the form of the field inside the nucleus; their width depends on the thickness of the potential barrier. The possibility of their existence according to wave mechanics was first noted by Gurney, and they were discussed in several theoretical papers*.

Fig. 1.

If the classical distance of closest approach is less than \(r\), then deviations from the classical formula will occur even for those angles for which the classical particle moves only in the Coulomb field. Therefore there is no longer any need for a nonspherical field of the nucleus in order to explain the fact that anomalous scattering in helium begins at approximately the same energy for both large and small angles.

If the field for \(r_0<r\) is attractive, then the ratio of the observed scattering to the classical scattering would first decrease and then increase with increasing energy. From the observed scattering*** one can estimate the field for

* Gurney, Nature 123, 568, 1929.
* Atkinson, Z. Phys. 64, 507, 1930; Beck, Z. Phys., 64, 32, 1930; Mott, Proc. Roy. Soc. A. 133, 225, 1931.
* Rutherford a. Chadwick, Phil Mag. 4*, 605, 1927.

\(r_0 < r\). This was done by Taylor* for hydrogen and helium. In the case of helium, if one makes the assumption that \(r\) is less than \(4 \cdot 10^{-23}\) cm, the scattering formula derived from the field shown in Fig. 1 is:

\[ R = 2\left|1+\frac{1}{2\alpha}\cdot e^{i\left[4{,}r-\alpha+\lg^2\right]}\left(e^{2ik}-1\right)\right|^2,\qquad \alpha=\frac{2\pi e^2}{hv}, \]

where \(R\) is the ratio of the scattering to that predicted by the inverse-square law. The parameter \(K\) depends on the field and is a function of the energy, but not of the angle. Therefore this is not the case in which the observed scattering can be explained by the choice of a suitable field, since from the observed scattering at a given angle one can derive the value of \(K\) and hence calculate the scattering for all angles at the same energy. Good agreement with experiment was obtained, showing that the problem belongs to the class of problems that can be treated by wave mechanics. Similar results were obtained for hydrogen.

From the observed values of \(K\) and its variation with energy one can estimate the depth \(D\) of the entire potential barrier. However, it was not found possible to use this value to make predictions about any other phenomena; for example, the attractive force between two \(\alpha\)-particles, found from scattering, is greater than that which is required to explain the energy of their binding in the nucleus.

* Proc. Roy. A. 134, 103, 1931, 136, 605, 1932.