Neutron Capture and Nuclear Structure*

Niels Bohr, Copenhagen

Of all the properties of atomic nuclei discovered by the fundamental investigations of Rutherford and his followers in the phenomena of artificial nuclear transformations, one of the most striking is the exceptional tendency of such nuclei to enter into reaction with one another as soon as direct contact is established between them. Indeed, almost all types of nuclear reactions consistent with the conservation of energy apparently occur in close collisions of nuclei. Of course, in collisions between charged particles and nuclei, contact is often hindered or made less probable by their mutual electrical repulsion; as a result, the typical features of nuclear reactions may perhaps appear especially vividly in collisions with neutrons. Already in his first works on the study of the properties of fast neutrons, Chadwick discovered the high effectiveness of the latter with respect to the nuclear transformations they produce.¹ In particular, after the discovery by Curie and Joliot of artificial radioactivity, the most interesting data were obtained as a result of investigations by Fermi and his collaborators on artificial radioactivity under bombardment both by fast neutrons and by neutrons of thermal velocities.²

A typical result of experiments with high-speed neutrons is the considerable probability of the emission of an α-particle or a proton when a neutron collides with a nucleus of not too large an atomic number—an emission accompanied by the capture of the neutron and the formation of a nucleus of a new, for the most part β-radioactive, element. The effective cross section of the nucleus in such collisions is, in fact, of the same order of magnitude as the cross section corresponding to the simple scattering of fast neutrons by nuclei, which in turn corresponds to the usual dimensions of the nucleus. Another typical result of these experiments may be regarded as the unexpectedly strong tendency, even in the case of a collision of a fast neutron with a heavy atom, to attach itself to the nucleus with the emission of a γ-quantum and to form a new isotope, stable or radioactive according to circumstances. In fact, for processes of this kind

* Nature, Febr. 29, 1936. Translated by A. A. Il’ina.

NIELS BOHR

effective cross section, although it becomes several times larger, still has the same order of magnitude as the dimensions of the nucleus.

The processes of capture of fast neutrons of the type just mentioned are especially significant for elucidating the mechanism of collisions between a neutron and a nucleus. Indeed, the remarkable sharpness of the lines of the characteristic spectra of the γ-rays of radioactive elements indicates that the lifetime, in the excited state, of the nuclei associated with the emission of these lines is greater than the period (about \(10^{-20}\) sec.) of the lines themselves. In order that the probability of emission of such radiation during the collision time of a fast neutron with a nucleus should be sufficient to explain the experimentally found effective cross section of this capture process, the duration of the collision would have to be much longer than the time interval (about \(10^{-21}\) sec.) required for the simple passage of the neutron through the nucleus.

The phenomena of neutron capture thus compel us to suppose that the collision between a fast neutron and a heavy nucleus must lead, first of all, to the formation of a complex system characterized by remarkable stability. The possible subsequent decay of this intermediate system, with the ejection of a material particle, or the transition to the final stable state with the emission of a quantum of radiant energy, should be regarded as independent processes having no direct connection with the first phase of the collision. Here we encounter an essential distinction, not previously clearly recognized, between true nuclear reactions and ordinary collisions of fast particles and atomic systems—collisions which up to now have been for us the chief source of information concerning the structure of the atom. Indeed, the possibility of accounting, by means of such collisions, for individual atomic particles and of studying their properties is due above all to the “openness” of the systems considered, which makes an exchange of energy between the individual constituent particles during the collision very unlikely. However, owing to the close packing of particles in the nucleus, we must be prepared for precisely this exchange of energy to play the principal role in typical nuclear reactions.

If, for example, we consider a collision between a fast neutron and a nucleus, then it is evident that this process cannot be compared with a simple deflection of the neutron’s path in the internal field of the nucleus, perhaps associated with a collision with a separate nuclear particle leading to the ejection of the latter. On the contrary, we must clearly understand that the excess energy of the incident neutron must rapidly be distributed among all the particles of the nucleus in such a way that, for some interval of time, no single particle will possess kinetic energy sufficient to leave the nucleus. The possible subsequent liberation of a proton, an \(\alpha\)-particle, or even a neutron from the intermediate complex ...

The capture of a neutron and the structure of the nucleus

...system, we must therefore speak of a complex process in which the energy can again become concentrated on some particle at the surface of the nucleus.

At the present time it is hardly possible to form a detailed picture of these processes. Indeed, we must admit that we have no justification even for assumptions about the existence, inside the nucleus, of particles released when the nucleus is destroyed. In particular, the well-known difficulties connected with the individual existence, in a region of nuclear dimensions, of charged particles with so small a rest mass as electrons and positrons have compel us to regard $\beta$-decay as a process leading to the creation of the electron as a mechanical individuality.$^{3}$ In this respect the situation here, of course, differs essentially from the case of nuclear disintegration with the emission of heavy particles—neutrons, protons, and $\alpha$-particles. The fact that the masses of all nuclei, to a first approximation, are integral multiples of units close to the mass of the neutron, makes it possible to regard these particles as mechanical individuals inside the nucleus. Because of the small difference between the masses of the neutron and the proton in comparison with the binding energies in the nucleus, measured by the so-called mass defects, the assumption of the existence in the nucleus of particles with the same electrical and magnetic properties as free neutrons must appear more hypothetical. Owing to the insufficiency of our information about that exceptionally dense state of matter with which we deal in nuclei, we may rather regard the integer values of the units of electric charge of nuclei and of the products of their splitting as a fundamental aspect of the atomistics of electricity, which, however, is not explained by contemporary theories of atomic structure.

If, however, we leave aside the problem of the nature of the nuclear components, which is not the aim of the present discussion, then in any case it is clear that the models of the nucleus that have been considered in detail up to now do not make it possible to explain the typical properties of nuclei, for which, as we have already seen, the exchange of energy between individual particles is the decisive factor. Indeed, in these models, for the sake of simplicity, it was assumed that the state of motion of each particle in the nucleus can, in a first approximation, be considered as motion in a conservative field of forces and can therefore be characterized by quantum numbers, just as the motion of the electron in an ordinary atom. Meanwhile, in the atom and in the nucleus we have two limiting cases of problems in the mechanics of many bodies; moreover, the approximation procedure based on combining one-body problems, so effective in the first case, loses all its value in the latter, where from the very beginning we are dealing with essentially collective aspects of the interaction between the constituent particles.

In this connection it is important also to recall that the successful quantum-mechanical explanation of the simple law relating

the lifetime of the products of $\alpha$-radiation with the energy of the emitted particles is entirely independent of special assumptions concerning the behavior of individual particles in the nucleus. Owing to the extremely long lifetime of these products in comparison with all proper periods of the nucleus, the probability of such a disintegration depends, in the first approximation, only on the electric field outside the nucleus, which forms the so-called potential barrier obstructing the escape of $\alpha$-particles. It seems exceedingly doubtful that $\alpha$-particles exist in the nucleus in the form assumed by the existing theories of $\alpha$-decay. The frequent appearance of $\alpha$-rays as the result of natural and artificial disintegration of the nucleus can rather be explained by the fact that energy is released in the very formation of $\alpha$-particles, and that the release of these particles may thus be associated with a lesser degree of concentration of excess energy than the release of protons or neutrons. For the time being, therefore, the study of $\alpha$-decay and of its close connection with $\gamma$-spectra—clarified by Gamow—gives us information only about possible energy values and, to some extent, about spin moments for the stationary states of the nuclear systems with which we are dealing.

The circumstance that the states of the nucleus associated with the phenomena just mentioned constitute a discrete distribution of extremely sharp energy levels may at first appear to contradict our assumptions about the existence of semistable intermediate states of the complex system formed upon neutron capture, with apparently continuous values of the kinetic energy of the incident neutron. One may imagine, however, that in the capture of fast neutrons we are dealing with a much higher excitation of the complex system than the usual $\gamma$-excitation. Whereas the latter has its greatest significance at several million volts, the excitation in our case may considerably exceed the energy required for the complete removal of a neutron from the normal state of the nucleus. Aston’s measured mass defects of isotopes show that this energy is about 10 million V.

It is precisely such a striking difference in the level schemes of low and high excitation of heavy nuclei that we may expect from the point of view discussed here. In contrast to the usual point of view, in which excitation is ascribed to an excited quantum state of an individual particle in the nucleus, we must assume that excitation will correspond to some quantized collective type of motion of all nuclear particles. Owing to the rapid increase in the possibilities of combining the proper frequencies of such motions as the total energy of the nucleus increases, we should expect the spacing between neighboring levels to become much smaller for high excitations caused by neutron collisions than for ordinary $\gamma$-levels, where we are probably dealing with states of collective motion of the simplest types.

With this point of view, however, even for excitations whose levels are very close to one another, the probability of a transition with radiation does not differ very strongly from the probability of the same transition in the lower \(\gamma\)-states, and no substantial increase in the width of the levels occurs until the probability of emission of a material particle becomes comparable with the probability of radiation.

In experiments on the collision of fast neutrons with heavy nuclei, the effective cross section for scattering is usually several times greater than the effective cross section for capture. Correspondingly, we may conclude that in this case the probability of emission of a neutron from the compound system is greater than the probability of a transition with radiation, and that the energy levels of the metastable states are therefore, to some extent, broader than ordinary \(\gamma\)-levels. This circumstance, together with the rapidly decreasing spacing between neighboring levels in this energy region, makes it very plausible to conclude that such levels here are not separated at all—a conclusion necessary for explaining the apparently nonselective character of the capture phenomena. However, as the velocities of the incident neutrons decrease, the emission of a neutron from the compound system rapidly becomes improbable, in accordance with the decrease in the probability of the necessary concentration of the system’s excess energy on a single neutron. One may therefore expect that the sharpness of the levels of the intermediate states will approach the sharpness of \(\gamma\)-levels as soon as the kinetic energy of the free neutrons becomes less than the total excitation energy in this state.

The most interesting confirmation of these considerations is provided by the remarkable phenomena of selective capture of neutrons of very low velocities. Working with neutrons of thermal velocities, obtained by passing a neutron beam through thick layers of substances containing hydrogen, Fermi and his collaborators found, as is well known, a value of the effective cross section for neutron capture that varies in an extremely capricious way from element to element. Whereas for most elements these values are of one and the same order of magnitude, or only slightly larger than the ordinary nuclear cross section, for certain elements or isotopes, irregularly distributed in the periodic system, cross sections were found that exceed the normal value by several thousand times. This effect, surprising at first glance, may evidently be connected with the circumstance that for such slow neutrons the de Broglie wavelengths are very large in comparison with the dimensions of the nucleus, and therefore the simple notions of trajectory and impact, which approximately justify themselves in the case of the capture of fast neutrons, here prove to be completely inapplicable.

Instructive attempts were also made to explain the phenomenon of selective capture as a phenomenon of quantum-mechanical resonance arising when the energy of certain almost stable stationary states of the neutron in the nucleus is close to the sum of the energies of the initial state of the nucleus and of the free neutron.\(^{4}\) These

theories, in which the state of motion of the neutron in the nucleus is treated as the motion of a particle in a field of conservative forces, cannot, however, explain the fact that the effective cross section for scattering of neutrons by all the selectively absorbing elements investigated is much smaller than the effective capture cross section. In fact, the high probability of reflection of the waves describing the behavior of the neutron in the nucleus, which follows from the fact that the wavelength of this wave is very short in comparison with the wavelength of the free motion of the neutron, means that the average interval of time during which the neutron can, so to speak, remain in the nucleus is much longer than the interval of time during which a fast neutron passes through the nucleus.

Nevertheless, even in the case of complete resonance, the probability of emission of a neutron found in this way must be greater than the probability of emission of a quantum. As a consequence of the much closer interaction between the nucleus and the neutron, which follows from the phenomena of capture of fast neutrons, we should indeed have expected the absence of selective scattering of very slow neutrons possessing a small excess of energy, since in this case the probability of emission of the neutron is negligibly small in comparison with the transition accompanied by radiation.

However, in the recent experiments of Fermi and others^5 an extreme sensitivity of the phenomena of selective capture of neutrons to small changes in the velocity of the latter was discovered, leading to a degree of resonance wholly incompatible with the above-described model of the nucleus. Indeed, when a beam of slow neutrons was filtered through thin plates of various selectively absorbing elements, very diverse effective cross sections of selective capture were obtained, showing that the resonance is confined to a narrow range of neutron-energy values, different for different selective absorbers. Using, for comparison, the capture of neutrons by light elements leading to the emission of $\alpha$-particles, where the selectivity is expressed much less sharply and where, therefore, from basic quantum-mechanical considerations one can find that the probability of capture within the energy region will in general be inversely proportional to the velocity of the neutron, one may even conclude that the energy region of resonance for some selectively absorbing elements is limited to an interval measured in fractions of a volt^6.

On the basis of this small width of the energy levels of the complex system produced by the capture of a slow neutron, we arrive, with the aid of simple statistical considerations, for the case of selective capture by heavy elements, at a value of about ten volts for the distance between neighboring energy levels of excitation with which one has to deal in these phenomena. This is not only in complete agreement with the conclusions concerning the close spacing of the energy levels of a nucleus in a state of high excitation, which we reached in discussing the non-selective absorption of fast

NEUTRON CAPTURE AND THE STRUCTURE OF THE NUCLEUS

neutrons, but also the exceptional sharpness of the levels with which we are dealing in the phenomena of selective neutron capture, provides a most interesting confirmation of our initial assumptions concerning the long lifetime of intermediate states in neutron collisions. Indeed, the close arrangement of levels in a complex system strikingly confirms the extremely small value of the probability of nuclear transitions with emission, and leads to a value for the duration of the collision between a fast neutron and a nucleus that exceeds by a million times the time interval of the simple passage of a neutron through the nucleus.

The absence of selectivity in the capture of fast neutrons, strictly speaking, refers only to the probability of capture of a neutron by a nucleus and the emission from it of a material particle. The detailed course of these phenomena must, however, depend essentially on the system of levels of the nucleus that is formed. In fact, after the collision this system must be in some stable state, and if the kinetic energy of the incident neutron is not too large, all the states among which a choice can be made must lie in the region of ordinary discrete γ-levels. If, therefore, the kinetic energy of neutrons entering a heavy nucleus is less than the lowest level of this nucleus, the energy of the neutron emitted from the complex system must necessarily be equal to the energy of the incident one. However, in the case of a collision of a neutron with higher energy, there is evidently a certain probability that the nucleus may remain in an excited state after the emission of a neutron with correspondingly lower energy.

In fact, the probability of a process occurring in this way, which presupposes a smaller concentration of the excess energy of the complex system on the emitted neutron, may often considerably exceed the probability of neutron emission without excitation. Apparently, there is also experimental evidence of nuclear excitation in collisions with neutrons—namely, in observations of energy losses of fast neutrons penetrating substances of large atomic weight⁷, where the direct exchange of energy between neutrons and nuclei must be extremely small.

As was already mentioned earlier, collisions between fast neutrons and nuclei of elements of small atomic number must in most cases lead to the emission of an α-particle or a proton. From this, and also from the considerable effective cross section for these impacts, we may conclude that the collision first leads to the formation of a semi-stable complex system with a continuous distribution of energy levels. In spite of the fact that the lifetime of such a system may be much shorter than the lifetime of γ-states in heavy nuclei, we must nevertheless consider that the subsequent emission of α-rays or protons requires a separate process of concentration of the excess energy, and that we cannot arrive at definite conclusions from these phenomena regarding the existence of such particles in nuclei under normal conditions. For example

the greater probability of emission of an \(\alpha\)-particle as compared with the ejection of a neutron from a compound system must, as has already been pointed out, be explained rather by the comparatively small degree of concentration of energy in the first process. As for the emission of charged particles, we must, of course, also take into account their repulsion by the nuclear residue and, in particular, the considerable difficulty for a charged particle (as compared with an uncharged one, with the same final kinetic energy) of penetrating through the potential barrier surrounding the nucleus.

As has already been pointed out more than once, the latter circumstance leads to a simple explanation not only of the rapid decrease in the yield of \(\alpha\)-particles and protons, as a result of the capture of fast neutrons, with increasing nuclear charge, but also of the decrease, with increasing neutron energy, in the ratio of the probabilities of emission of these two kinds of charged particles. The probability that the nucleus, after the emission of these particles, may be in a normal or in an excited state depends in both cases on the distribution of energy levels of the final system—more widely spaced for light nuclei—and also on the balance between the greater ease, for fast particles, of penetrating through the potential barrier of the nucleus, on the one hand, and the necessity of a greater concentration of energy in the former case as compared with the latter, on the other. Similar considerations may be applied to the details of ordinary \(\alpha\)-decay, such as, for example, to weak groups of long-range \(\alpha\)-particles and to the fine structure of the strongest lines of \(\alpha\)-rays.

In the case of a nuclear transformation caused by the capture of charged particles, just as for the disintegration of nuclei by \(\gamma\)-quanta, the formation of an intermediate semi-stable compound system apparently has decisive importance for explaining the great variety of phenomena. In addition to typical non-selective effects, such as the ejection of a neutron or a proton by fast \(\alpha\)-particles, we encounter, as is well known, an effect of a clearly expressed resonance for the capture of slow \(\alpha\)-particles, as well as in the phenomena of capture, by light nuclei, of artificially accelerated protons. Owing to the very short lifetime of the intermediate state, the degree of resonance in this case is, however, considerably smaller than in the case of selective capture of neutrons by heavy nuclei. In this connection it should perhaps be noted that such expressions as “\(\alpha\)-particle levels” or “proton levels”—expressions usually used in considering these effects and based on attributing the excitation to individual nuclear particles—lose all meaning from the point of view of nuclear excitation adopted by us. Indeed, an essential feature of nuclear reactions excited by collisions or by absorption of radiation may be regarded as the free competition among all the various possible processes of release of material particles or transitions with radiation, which can occur in a compound system in a semi-stable state.

A detailed discussion from this point of view of the existing empirical data concerning spontaneous and induced transformations of the nucleus will soon be published by me jointly with F. Kalckar,^8 who has given me great assistance in deriving the consequences of the general conception developed here. We shall then also discuss the limitation of these ideas in the case of very light nuclei, such as deuterium, where the distinction between the mechanism of accumulation of energy in the nucleus and the mechanism of release of particles—so sharply expressed for reactions with heavy nuclei—gradually loses its significance. Here, however, I must briefly point out that, in the arguments set forth above, one may expect modifications even for heavy nuclei if the energy of the intermediate system greatly exceeds the energy of the normal state.

If we could carry out experiments with neutrons and protons having energies exceeding 100 MeV, we should have to expect that the excess energy of these particles, when they penetrate into a nucleus of not very small mass, must first of all be distributed among the particles of the nucleus, with the result that the release of any one of them would inevitably cause a subsequent concentration of energy. Instead of the usual course of a nuclear reaction, we may in this case expect that not one but several charged or uncharged particles will leave the nucleus as a result of the collision. For an even stronger impact with capture of a particle possessing an energy of 100 MeV, we should be prepared for the possibility that the collision may lead to an explosion of the whole nucleus. Such energies at present, of course, lie far beyond the limits of experimental possibilities, and there is no need to emphasize that such effects can hardly bring us closer to solving the much-discussed problems of the use of nuclear energy for practical purposes. Unfortunately, the more extensive our knowledge of nuclear reactions becomes, the more remote the attainment of this goal appears.

In conclusion to this report, I should like to say that even though hypotheses on the structure of the nucleus still lack the mechanical simplicity which is so characteristic of the theory of the structure of the atom, and which so greatly helped in disentangling the interrelations of the elements in terms of their ordinary physical and chemical properties, nevertheless, as I have tried to show, the problem of the structure of the nucleus possesses distinctive features that facilitate the interpretation of the characteristic properties of nuclei—for example, with respect to the division of nuclear reactions into separate stages with a clarity that has no analogue in the mechanical behavior of atoms.

Addendum

In the lecture delivered by Prof. N. Bohr at the Physical and Chemical Society of the University of London on February 11, the ideas set forth above were illustrated by two diagrams, which are reproduced here. The model of Fig. 1 is an attempt to represe-

to understand the case that occurs when a neutron collides with a nucleus. Let us imagine a shallow cup with a certain number of billiard balls lying in it, as shown in Fig. 1. If the cup were empty, then a ball moving from outside would roll down one side of the cup and pass to the opposite side, retaining its initial speed. However, owing to the presence of other balls at the bottom of the cup, this free passage will not take place. The striking ball will share its energy with the first ball of the cup that it encounters; these two balls will in the same way share their energy with others, and so on, until the initial kinetic energy of the incident ball is distributed

Fig. 1.

among all the balls in the cup. If the cup and the balls were perfectly smooth and elastic, the collisions would continue until, by chance, the kinetic energy were concentrated in some ball near the rim. This ball would then have to fly out of the cup, while the energy of the remaining balls would already be insufficient for yet another ball to rise to the rim and fly out. The figure therefore shows that the “excess energy” of the incident neutron is rapidly distributed among all the nuclear particles, as a result of which, after some time, not a single particle will still have enough energy to escape from the nucleus.

Fig. 2.

ENERGY LEVELS IN THE NUCLEUS

Fig. 2 gives an idea of the character of the distribution of energy levels in a nucleus of not too small atomic weight. The lowest lines represent excitation levels of the same order of magnitude,

as well as the usually excited \(\gamma\)-states. According to the views developed in the preceding communication, as the degree of excitation increases the levels should become closer and closer to one another and, at an excitation of 15 MeV, corresponding to a collision between the nucleus and a fast neutron, they merge, whereas in the region of small energy excesses, at about 10 MeV of excitation, they should still be sharply separated from one another. This situation is illustrated by means of two lenses with high magnification, placed in two regions of our level scheme. The dotted line in the middle of the image of the lower lens represents zero excess energy, and the fact that one of the levels, very close to this line (at a distance of about \(1/2\) V), corresponds to the possibility of selective capture of very slow neutrons. The mean distance between neighboring levels in this region is about \(10\) V, according to calculations based on the statistics of cases of selective capture. The upper limit of the levels is not visible in the scheme, and in reality it can be extended to very large values of the energy. If it were possible to carry out experiments with neutrons or protons having energies above 100 MeV, then, as a result of their collisions with the nucleus, several charged or uncharged particles would have to fly out of the latter, and, Prof. Bohr adds, “with particles of about a thousand MeV we could expect collisions leading to the explosion of the entire nucleus.”

LITERATURE

1. J. Chadwick, Proc. Roy. Soc., A 142, 1, 1933.
2. E. Fermi et al., Proc. Roy. Soc., A 147, 483, 1934; 149, 522, 1935.
3. See N. Bohr, Faraday Lecture, J. Chem. Soc., 349, 1932. W. Heisenberg, Zeeman Verhandlingen, p. 108.
4. E. Fermi et al., Proc. Roy. Soc., A 149, 522, 1935; Perrin and Elsasser, J. Phys., 6, 195, 1935; Bethe, Phys. Rev., 47, 747, 1935.
5. Fermi and Amaldi, La Ricercio Sci. A 6, 544, 1935; Szilard, Nature, 136, 849, 1935; Frich, Hevesy and McKay, Nature, 137, 149, 1936.
6. R. Frisch and G. Placzek, Nature, 137, 357, 1936.
7. W. Ehrenberg, Nature, 135, 870, 1935.
8. N. Bohr and F. Kalckar, Kgl. Dan. Vid. Selsk. Math-fys. Medd.