NEUTRON*

J. Chadwick, Cambridge

1. Introduction. In one of my earlier papers¹ I showed that certain light elements, when bombarded with α-particles, emit rays containing, among other things, particles with a mass equal to that of the proton and at the same time carrying no electric charge. These particles, called neutrons, possess a number of very interesting properties. Some of these properties—the most striking ones—are described in the paper mentioned above, as well as in the papers of Dr. Feather² and Dee³, published together with my paper¹. The most characteristic property is the ability of neutrons to “ignore” the atoms of the matter through which they pass, and their great penetrating power.

From measurements of the momenta imparted by neutrons to various atoms, their mass was determined and found to be identical with the mass of the proton. At the same time, the great penetrating power of neutrons shows that they cannot carry any appreciable electric charge.

The loss of energy of neutrons passing through matter takes place as a result of collisions with atomic nuclei, and not with electrons. Dee’s experiments showed that the primary ionization along the track of a neutron flying in air is less than 1 ion pair per 3 m of path, in agreement with Massey’s calculations, according to which the ionization should not exceed 1 ion pair per \(10^5\) km. Such behavior, of course, differs very greatly from the behavior of a charged particle, such as a proton, which dissipates its energy almost exclusively as a result of collisions with electrons. The difference between the loss of energy experienced by a proton and by a neutron is especially noticeable if one assumes that these particles are moving with the same initial velocity. A proton moving with a velocity of \(3 \cdot 10^9\) cm/sec has a range in air of about 30 cm, whereas a neutron moving with the same initial velocity will undergo, on average, one collision with a nitrogen nucleus over a distance of 300–400 yards, and may travel several miles before losing all its energy. Collisions of neutrons with atomic nuclei, although they occur much more often than with electrons, are nevertheless very rare events—

* Bakerian Lecture, delivered on May 25, 1933. Published in Proc. Roy. Soc., A, 142, p. 1, October 2, 1933. Translation by V. L. Pulver.

because the electric forces acting between a neutron and a nucleus are weak, provided these particles do not approach to a distance of \(10^{-12}\) cm. In such a close encounter the neutron is deflected from its path, while the recoiling nucleus acquires a velocity sufficient to produce ionization.

Nuclei that have undergone collisions with neutrons can consequently be detected by measurements of ionization in an ionization chamber with a sensitive electrometer or an electric counter, or from the tracks appearing in a Wilson chamber.

Thus neutrons can be detected only by an indirect method, by observing atoms that have undergone collisions with neutrons.

This makes their study difficult and lengthy, especially if one takes into account that not all recoiling atoms can be registered by our instruments.

The nature and properties of the neutron are of interest not merely because it is a new object of study, but also because the neutron is probably a very essential element in the structure of matter.

At present it is assumed that atomic nuclei consist of protons and neutrons; then the fact that the mass of a nucleus is always two or more times greater than its charge means that matter must contain neutrons in greater numbers than protons.

In this article I shall give a brief survey of our knowledge of the neutron and indicate the directions in which the study of this question is at present proceeding.

2. Liberation of neutrons. The appearance of neutrons has so far been observed only in the bombardment of certain elements by \(\alpha\)-particles. This process may be represented as the capture of an \(\alpha\)-particle by an atomic nucleus, accompanied by the formation of a new nucleus and the liberation of a neutron. The new nucleus must then have a charge two units higher and a mass three units higher than the original nucleus. The “yield” of neutrons is very small and comparable with the “yield” of protons in the artificial transmutation of elements occurring under bombardment by \(\alpha\)-particles. Beryllium has the greatest effect; its “yield” apparently reaches 30 neutrons for every million polonium \(\alpha\)-particles bombarding a thick layer of beryllium.

For elements with considerably larger atomic number the “yield” is extremely small—of the order of 1–2 neutrons per million \(\alpha\)-particles. The “yield” can be increased by using \(\alpha\)-rays of greater energy, for example those of radon and its decay products. However, in that case the detection of neutrons may be hindered by the \(\gamma\)-rays of the source, unless appropriate precautions are taken. Neutrons have been obtained from the nuclei of lithium, beryllium, boron, fluorine, neon, sodium, magnesium, and aluminum. Probably neutrons can be obtained from the majority of elements with higher atomic numbers,

up to argon, provided sufficiently fast α-particles are used.

It is remarkable that, with the exception of helium, nitrogen, carbon, and oxygen, the nuclei of all light elements up to aluminum liberate only neutrons, whereas others, for example fluorine, emit protons simultaneously with neutrons. These facts must be connected with the general laws of nuclear structure*. If the nucleus of an element with atomic mass \(A\) and atomic number \(Z\) is changed as a result of the capture of an α-particle and the emission of a neutron, the new nucleus will have mass \(A+3\) and atomic number \(Z+2\). Further, for all known nuclei \(A \geq 2Z\). If the new nucleus also satisfies this condition, then

\[ A+3 \geq 2(Z+2) \]

or

\[ A \geq 2Z+1. \]

This restriction is not fulfilled for** \(\mathrm{He}^{4}_{2}\), \(\mathrm{C}^{12}_{6}\), \(\mathrm{N}^{14}_{7}\), and \(\mathrm{O}^{16}_{8}\), and we should not expect the decay of these nuclei to be accompanied by the emission of neutrons. Application of the above restrictions also forbids the emission of neutrons in \(\mathrm{B}^{10}_{5}\), \(\mathrm{Ne}^{20}_{10}\), and \(\mathrm{Mg}^{24}_{12}\). At the same time, neutrons may be liberated from atoms of other isotopes of these elements.

The cases of fluorine and aluminum are of interest because, when bombarded with α-particles, these elements emit both neutrons alone and neutrons together with protons. One may then conclude that the nuclei \(\mathrm{F}^{19}\) and \(\mathrm{Al}^{27}\) disintegrate in one of two possible ways. For example, capture of an α-particle may cause either the process

\[ \mathrm{F}^{19}_{9}+\mathrm{He}^{4}_{2}\to \mathrm{Ne}^{22}_{10}+\mathrm{H}^{1}_{1} \]

or

\[ \mathrm{F}^{19}_{9}+\mathrm{He}^{4}_{2}\to \mathrm{Na}^{22}_{11}+n^{1}_{0}; \]

as a result of the latter process, an isotope of sodium with mass 22 is formed, which occurs very rarely in nature. If the nucleus of the atom \(\mathrm{Na}^{22}\) is stable, its mass must be less than the mass of \(\mathrm{Ne}^{22}\), since otherwise capture of a K-electron would cause the transformation \(\mathrm{Na}^{22}\to \mathrm{Ne}^{22}\), which would have to be accompanied by the release of energy. Hence it follows that the maximum energy of the neutrons liberated from fluorine must be greater than the maximum energy of the protons.

I have not yet had the opportunity to verify this conclusion, since the “yield” of neutrons from fluorine is small. If it could be shown,

* The following considerations were pointed out to me independently by Dr. Fezer.

** In the symbols that follow, the lower index denotes the charge of the nucleus, and the upper index its mass.

that the energy of the neutrons is less than that of the protons, the natural conclusion would be that the nuclei \(Na^{22}\) are unstable and transform into \(Ne^{22}\) nuclei by capturing electrons, emitting radiant energy in the process. A similar consideration may be applied to explain the double transformation of aluminium, accompanied by the formation of \(Si^{30}\) or—in another case—of the unknown \(P^{30}\).

3. Boron and beryllium. The neutrons liberated from boron and beryllium atoms have been investigated in the greatest detail. These cases are important because in most experiments boron and beryllium have been used as neutron sources.

The element boron consists of two isotopes: \(B^{10}\) and \(B^{11}\). When boron is bombarded with \(\alpha\)-particles, the appearance of both neutrons and protons is observed. The considerations given above\(^4\) lead to the conclusion that the protons are emitted in the decay of \(B^{10}\), and the neutrons in the decay of \(B^{11}\). The distribution of the velocities of neutrons liberated from boron atoms has not been studied in detail, but the experimental results are in agreement with the assumption that the neutrons emitted by a thin film of boron under the action of a monochromatic beam of \(\alpha\)-particles constitute a single group of particles having a definite velocity. \(\alpha\)-particles flying with a velocity of \(1.60 \cdot 10^9\) cm/sec liberate neutrons having velocities of about \(2.53 \cdot 10^9\) cm/sec. There is no indication of the presence of \(\gamma\)-radiation accompanying the emission of neutrons\(^*\).

The dependence of the number of neutrons emitted on the velocity of the bombarding \(\alpha\)-particles was investigated. The source of \(\alpha\)-particles—a silver disk covered with a layer of polonium—was placed in a hermetically sealed vessel at a distance of 2.05 cm from the receiver containing boron.

The neutrons emitted by the boron were recorded by means of an ionization chamber connected through an amplifier to an oscillograph. To increase the effect, the entire front wall of the ionization chamber was coated with a layer of paraffin, so that deflections of the oscillograph were produced both under the action of nitrogen atoms of the air recoiling from neutrons and of protons knocked out of the paraffin. The velocities of the \(\alpha\)-particles bombarding the boron could be reduced by introducing carbon dioxide gas under a pressure of 50 mm into the vessel containing the \(\alpha\)-particle source. After each such operation, the number of oscillograph deflections was counted. In this way the addition of carbon dioxide gas made it possible to find the dependence of the number of emitted neutrons on the velocity of the \(\alpha\)-particles. The results\(^ {**}\) are shown in Fig. 1, in which the ordinates represent the number of oscillograph deflections obtained during 30 min., and the abscissae the range of the \(\alpha\)-particles bombarding the boron, calculated on the assumption that the retarding action of carbon dioxide gas is 1.53 times greater than that of air.

\(^*\) \(\gamma\)-rays with an energy of about \(3 \times 10^6\) electron-volts, emitted by boron when bombarded with \(\alpha\)-particles, accompany the emission of protons by \(B^{10}\) atoms.

\(^ {**}\) Analogous results were obtained by Curie and Joliot\(^5\).

It should be noted that this curve may not quite accurately represent the true dependence of the number of emitted neutrons on the range of the $\alpha$-particles. The number of deflections of the oscillograph depends not only on the number of neutrons, but also on their velocity; the probability of a neutron colliding with a nitrogen atom in the chamber or with a proton in paraffin depends on the neutron’s velocity: the more slowly the neutron moves, the smaller the energy of the recoiling atoms and the greater the chance that some of these atoms will not produce a measurable deflection of the oscillograph.

At present there is no possibility of estimating numerically the influence of these factors and of deriving from the curve in Fig. 1 the true dependence

Fig. 1.

of the number of liberated neutrons on the velocity of the bombarding $\alpha$-particles (the length of their range).

It is seen from Fig. 1 that as long as the velocity of the $\alpha$-particles is such that their range in air does not exceed $1.4\ \text{cm}$, neutrons are not observed. With an increase in the velocity of the $\alpha$-particles, the number of neutrons appearing increases to a stationary value over a small segment of the curve; after that, beginning with the velocity corresponding to a range from $2.4\ \text{cm}$ and up to the maximum range value of $3.86\ \text{cm}$, this number grows rapidly. This suggests that $\alpha$-particles with a range of $1.4\ \text{cm}$ enter the nucleus of the boron atom by means of a resonance level, while those $\alpha$-particles whose range is equal to $2.4\ \text{cm}$ and exceeds this value penetrate the nucleus through the potential barrier or over its top. The corresponding energy values are $2.4 \cdot 10^6$ electron-volts for the resonance level and about $3.7 \cdot 10^6$ electron-volts for the top of the potential barrier (or, more precisely, for that point of it beginning from which $\alpha$-particles penetrate in appreciable numbers). Since the velocity of the neutrons liberated from boron atoms by $\alpha$-particles of the given velocity is known, one can

find the distribution of velocities of neutrons emitted by a thick layer of boron when it is bombarded by polonium α-rays. The resonance level gives a group of neutrons with velocities of about \(1.07 \cdot 10^9\) cm/sec, while the α-particles penetrating “above” the potential barrier cause the appearance of neutrons whose velocities may have all values between \(1.9\) and \(2.53 \cdot 10^9\) cm/sec. The corresponding energy values are \(0.6 \cdot 10^6\) V for the resonance (“monochromatic”) group, and from \(1.9\) to \(3.35 \cdot 10^6\) V for the continuous “band” of velocities. In an analogous way the neutrons appearing when a thick layer of beryllium was bombarded by α-particles of various velocities were investigated.

Fig. 2.

The results are presented in Fig. 2.
The (solid) curve suggests the existence of two resonance levels, the first of which corresponds to α-particles with a range of \(0.80\) cm, and the second to \(1.46\) cm, penetrating into the beryllium atom. A rapid increase in the number of neutrons released occurs when the range of the α-particles begins to exceed \(2.25\) cm. This corresponds to α-particles penetrating through the potential barrier and above it. The energy values of the resonance levels are about \(1.4 \cdot 10^6\) and \(2.5 \cdot 10^6\) electron-volts, and penetration over the top of the barrier begins at energies of about \(3.5 \cdot 10^6\) electron-volts. As was to be expected, the “height” of the potential barrier in beryllium is somewhat less than in boron.

The existence of resonance levels of the beryllium atom was confirmed by measuring the number of neutrons emitted by thin beryllium films. The latter were prepared by evaporating in vacuum a small amount of pure beryllium and condensing it on a cooled copper disk. The thin film thus obtained, although not entirely uniform in thickness, is nevertheless suitable for the present purposes. All measurements were carried out successively

with a preparation of a massive layer of beryllium and with a thin film, placed in one and the same position of the apparatus. The results are represented by the dotted curve in Fig. 2. The first resonance level is only faintly indicated on this curve, whereas the second level is clearly visible. There is a quite definite decrease in the number of neutrons emitted by the thin film when the range of the $\alpha$-particles increases from 1.6 to 2.2 cm, after which there follows a rapid rise corresponding to $\alpha$-particles penetrating over the top of the barrier. The agreement between this curve and the solid curve in Fig. 2, representing the dependence of the number of neutrons on the velocity of the $\alpha$-particles for a thick layer of beryllium, is not complete. The discrepancies should probably be attributed to changes in the geometrical arrangement of the parts of the apparatus occurring when the large mass of beryllium was replaced by the thin film, and also to inhomogeneity in the thickness of the film.

The curve obtained for the thick layer of beryllium does not differ very much from the curves of Rasetti$^{6}$ and Curie and Joliot$^{5}$, which are the result of analogous experiments, or from the excitation function, found by Becker and Bothe$^{7}$, of the $\gamma$-rays of beryllium bombarded by $\alpha$-particles. It should be expected that both these processes—the emission of neutrons and of $\gamma$-rays—must have analogous excitation functions, since both phenomena occur when $\alpha$-particles penetrate into the nucleus of the beryllium atom, and the excitation function expresses the probability of entry into the nucleus of $\alpha$-particles of different velocities. These two processes are more closely connected. Becker and Bothe found that the energy of the $\gamma$-rays does not depend on the energy of the incident $\alpha$-particles and may be greater than the latter. As these authors pointed out, this means that the emission of $\gamma$-rays is not an independent process; probably it accompanies the emission of neutrons, just as the $\gamma$-rays of B$^{10}$ accompany the emission of two groups of protons. From this point of view we might expect to find two groups of neutrons emitted by a thin layer of beryllium bombarded by a homogeneous beam of $\alpha$-particles. Certain facts permit one to think that this is so. Curie, Joliot, and Savels$^{8}$ found that the protons knocked out of paraffin by neutrons liberated in a thick layer of beryllium bombarded by $\alpha$-particles from polonium consist predominantly of particles with a maximum range in air of about 28 cm and, in addition, of a small number of particles with a maximum range of about 70 cm. This indicates that the principal group of neutrons has a maximum velocity of about $2.9 \cdot 10^{9}$ cm/sec and that there is also a small number of neutrons with velocities up to $3.8 \cdot 10^{9}$ cm/sec. Without further experimental data it is impossible to ascertain how these groups arise.

In my experiments I studied the neutrons emitted by a thick layer of beryllium and by a thin film of it. The neutrons passed through a layer of paraffin mass deposited on the front wall of the ionization chamber. The decrease in the number of protons knocked out of the paraffin by the neutrons, occurring when introduced between the paraffin layer

and an ionization chamber of aluminum screens made it possible to determine their range.

Most of the protons knocked out by neutrons from a thin beryllium film had a range in air from 23 to 24 cm (Fig. 3). Considerably faster protons were also present, but their number was very small. There are indications that the maximum range in air reached 100 cm, but the difference between the number of deflections of the oscillograph with paraffin and without it was so small that the range of these fast protons could not be measured accurately.

The results obtained with a thick layer of beryllium likewise showed the presence of a group of protons with a range of 24 cm and, in addition, protons with a range from 65 to 75 cm; there are doubtful indications of the presence of still faster protons.

Fig. 3.

The conclusions that may be drawn on the basis of these experiments are not very definite. It may be asserted, however, that the neutrons liberated in beryllium atoms by the α-particles of polonium, which have a velocity of \(1.6 \cdot 10^{9}\) cm/sec, comprise at least two groups: one, the more numerous, consists of slow neutrons flying with velocities \(2.8 \cdot 10^{9}\) cm/sec (energy \(4.1 \cdot 10^{6}\) electron-volts); the other group of fast particles consists of neutrons having velocities probably exceeding \(4 \cdot 10^{9}\) cm/sec (energy greater than \(8 \cdot 10^{6}\) electron-volts). It remains to consider how these results can be applied to explain the process of disintegration. I assume that the process taking place is:

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

The masses of all the nuclei are known to us with sufficient accuracy; Bainbridge’s measurements give for \({}^{9}\mathrm{Be}\) the value 9.0132; from Aston’s measurements \({}^{4}\mathrm{He} = 4.00106\) and \({}^{12}\mathrm{C} = 12.0003\); finally, the mass of the neutron is 1.0067 (see § 4). Assuming that the laws of conservation of energy and momentum hold, one can calculate the velocity and energy of the neutron liberated by a polonium α-particle (velocity \(1.60 \cdot 10^{9}\) cm/sec, energy \(5.3 \cdot 10^{6}\) electron-volts). Its velocity is \(4.77 \cdot 10^{9}\) cm/sec and its energy \(11.9 \cdot 10^{6}\) electron-volts. These values are considerably greater than those found in all the experiments described above. Such fast neutrons can knock out protons with a range in air of about 150 cm, whereas the fastest protons found experimentally possess a range of 70 cm; there are, however, indications of the presence of protons having

the range is greater than 100 cm. Similar indications of the presence of fast neutrons are given by the study of oscillograms on which deflections are recorded that result from the appearance, in the ionization chamber, of atoms knocked on by neutrons. The magnitude of the oscillograph deflection is proportional, at least approximately, to the energy of the recoil atom and, at the same time, for a given atom, proportional to the energy of the neutron colliding with it.

Neutrons emitted by a thin layer of beryllium bombarded with polonium α-particles (not slowed down by any gas) were admitted into an airtight ionization chamber, which was filled with nitrogen, oxygen, and argon. For each gas a large number of oscillograph deflections was recorded. Study of the oscillograms obtained with all three gases showed very clearly the presence of an intense and sharply defined group of recoil atoms, whose origin was attributed to a group of neutrons with an energy of about \(4 \cdot 10^6\) electron-volts and, in addition, a less numerous group containing recoil atoms with greater energy. The greatest energy corresponding to this group is approximately three times the energy of the neutrons of the first group, which amounts to about \(12 \cdot 10^6\) electron-volts. The separation of the atoms into these two groups was carried out by counting the number of ions corresponding to the oscillograph deflection, which makes it possible to find the energy of the atoms knocked on as a result of the collision. Such a measurement, however, is indirect and somewhat inaccurate. With these reservations the experiments make almost evident the absence of neutrons with energy exceeding \(12 \cdot 10^6\) electron-volts. Some data were also obtained by Feather, who measured the range of recoil atoms of nitrogen, oxygen, and carbon in a Wilson chamber. He observed tracks corresponding to a neutron energy of about \(10 \cdot 10^6\) electron-volts. Feather’s data are more direct and reliable than those mentioned above, but further experiments are necessary for a definitive determination of the maximum energy of the neutrons.

I shall now assume that the energy of the group of fast neutrons emitted by beryllium coincides with the energy calculated for the hypothetical disintegration process
\[ \mathrm{Be}^9 + \mathrm{He}^4 \to \mathrm{C}^{12} + n^1, \]
and that the laws of conservation of energy and momentum hold. From this point of view, a thin beryllium film bombarded by α-particles flying with a velocity of \(1.60 \cdot 10^9\) cm/sec should emit an intense group of neutrons having a velocity of \(2.8 \cdot 10^9\) cm/sec, and a small number of neutrons having a velocity of \(4.7 \cdot 10^9\) cm/sec, accompanied by hard γ-radiation.

These facts can be explained if one imagines the disintegration process in the following way. Suppose that the beryllium nucleus consists of an α-particle, two protons, and three neutrons. For some reasons the formation of another α-particle from two protons and two neutrons cannot take place (or, more precisely, the chances for such condensation are very small). If this occurs, the beryllium nucleus ...

beryllium breaks up into two α-particles and a neutron. Capture of an α-particle by the beryllium nucleus causes such a “condensation,” and the nuclear process is then accompanied by the emission of γ-rays and a neutron. The latter will belong to the group of slow neutrons observed in the experiments. Sometimes, however, the neutron receives all the energy, and such a process corresponds to the emission of fast neutrons. From this point of view we should obtain residual C\(^{12}\) nuclei, consisting of three α-particles, and two groups of neutrons, which should differ in energy by the magnitude of the γ-ray energy (with a correction for the kinetic energy of the recoiling C\(^{12}\) nucleus). If one adopts for the velocities of the two groups of neutrons the values given above, the γ-ray energy comes out equal to \(7 \cdot 10^{6}\) electron-volts. This is considerably higher than the value \(5 \cdot 10^{6}\) electron-volts found by Becker and Bothe from measurements of the ranges in aluminum of the secondary electrons produced by these γ-rays. On the other hand, measurements of the absorption coefficient of the radiation indicate that the energy must be somewhat higher than 5 million electron-volts, and from observations in the Wilson chamber it follows that the radiation causes the appearance of secondary electrons with energies in any case greater than 5 million V. Thus, Auger observed the track of one β-particle produced by this radiation, which had an energy of \(6.5 \cdot 10^{6}\) electron-volts, and of 150 electron tracks measured by Blackett, Occhialini, and me, 10 had energies between 5 and \(7 \cdot 10^{6}\) V. If they had appeared under the action of cosmic rays, a certain number of γ-rays emitted by beryllium, with energies close to the required one, should have been observed. On the other hand, analysis of the tracks leads to the idea that the greater part of the γ-rays has an energy of about \(5 \cdot 10^{6}\) V. There is no complete certainty in the determination of the energy of the γ-rays emitted by beryllium, but there are also no definite facts speaking against the proposed scheme of atomic disintegration.

The spectrum of velocities of the neutrons emitted by a thick layer of beryllium under the action of polonium α-particles can now be described as follows. Each resonant level gives an increase in the number of neutrons liberated in the form of two monochromatic groups, of which the slower is the more intense. The groups of the first level have velocities of about \(1 \cdot 10^{9}\) cm/sec and \(3.92 \cdot 10^{9}\) cm/sec, or energies of about \(0.5 \cdot 10^{6}\) electron-volts and about \(8.0 \cdot 10^{6}\) electron-volts*. The groups of the second level have velocities of about \(1.68 \cdot 10^{9}\) cm/sec and \(4.18 \cdot 10^{9}\) cm/sec, corresponding to energies of about \(1.47 \cdot 10^{6}\) and \(9.1 \cdot 10^{6}\) electron-volts. Owing to the fact that penetration through the top of the potential barrier begins with α-particles having a range of 2.25 cm, a group of neutrons is observed with velocities between \(2.16 \cdot 10^{9}\) and \(2.8 \cdot 10^{9}\) cm/sec and, consequently—

* The group of neutrons with velocities of about \(3.8 \cdot 10^{9}\) cm/sec, emitted by a thick layer of beryllium, may belong to this small resonant group.

respectively, with energies between \(2.5\) and \(4.1\cdot 10^6\) electron-volts, and a small group with velocities from \(4.4\) to \(4.77\cdot 10^9\) cm/sec and with corresponding energy from \(10.1\) to \(11.9\cdot 10^9\) electron-volts. Thus the emission of neutrons by a thick layer of beryllium is comparatively complex. The majority of neutrons belong to the slow group, and the velocities indicated for them have been determined with great accuracy. It should be remembered that there are some direct data on the velocities of neutrons of the fast group. The values obtained have been found on the assumption that, in the decay process proceeding in a definite way, conservation of energy takes place. The conception of the decay process may be tested in two ways: by detecting very fast neutrons and by measuring the energy of \(\gamma\)-rays.

These two points cannot yet be regarded as fully clarified.

It is possible that either one of the assumptions made above, or both, are incorrect. It may turn out that the capture of an \(\alpha\)-particle by the beryllium nucleus causes complete destruction of the nucleus, in which there occurs the emission of three \(\alpha\)-particles, a neutron, and \(\gamma\)-rays. There is, however, then no reason to expect the emission of neutrons in two definite groups, as apparently occurs. It may be that both processes take place, with a \(C^{12}\) nucleus sometimes being formed, and sometimes three \(\alpha\)-particles; then it would be necessary to take into account the presence of \(\gamma\)-rays not only with energy of about \(7\cdot 10^6\) V, but also \(5\cdot 10^6\) V, as follows from the measurements of Becker and Bothe.

In none of the experiments carried out on the artificial transmutation of elements was there any reason to doubt the conservation of energy; in some cases, moreover, it may be asserted that this law is fulfilled with great accuracy. If it were violated in our particular case, one might rather suppose that part of the energy goes into the motion of some as yet undetected particle. Assumptions concerning the possible existence of neutral particles of very small mass have been made repeatedly, and these assumptions have recently been revived in order to explain the continuous spectrum of velocities of \(\beta\)-particles emitted by radioactive bodies. It would be very difficult to detect the emission of such particles in all cases of artificial transmutation of elements, owing to their very rare occurrence, and the most favorable case for this, apparently, is radioactive \(\beta\)-decay.

About two years ago Mr. Tarrant, at my request, made some measurements with the object of detecting these neutral rays in the radiation of radium E, but we could find no proof of their existence. Recently Mr. Lee and I made a more careful investigation, with the very same result. On the basis of the experiments we concluded that, if radium E emits neutral rays compensating for the distribution of the energy of the \(\beta\)-rays, these neutral rays must consist of particles with small

mass and such a small magnetic moment that they cannot produce in air more than one pair of ions per 100 miles of path.

1. The mass of the neutron. Whereas the determination of the momenta imparted by neutrons in collisions with atomic nuclei makes it possible to show that the mass of the neutron is close to the mass of the proton, this measurement cannot be made with great accuracy. For an accurate determination of the mass of the neutron we must make use of the energy relations of the disintegration process in which the neutron is liberated from the atomic nucleus. Assuming that conservation of energy and momentum holds in the disintegration, it is sufficient to know the kinetic energy of the neutron liberated by an $\alpha$-particle of known velocity in order to determine its mass, if only the masses of the atomic nuclei are known. I represented the disintegration process as

\[ \mathrm{B}^{11} + \mathrm{He}^{4} \longrightarrow \mathrm{N}^{14} + n^{1}. \]

The kinetic energy of the neutrons liberated by $\alpha$-particles of polonium from boron was found from measurements of the maximum range of the particles knocked out of paraffin. Using Aston’s data for the masses of atomic nuclei, I obtained for the mass of the neutron the value 1.0067.

Another value may be obtained from the process:

\[ \mathrm{Li}^{7} + \mathrm{He}^{4} \longrightarrow \mathrm{B}^{10} + n^{1}. \]

The mass of $\mathrm{Li}^{7}$ is best determined in Cockcroft and Walton’s experiments on the disintegration of lithium by fast protons. The lithium nucleus captures a proton and disintegrates into 2 $\alpha$-particles:

\[ \mathrm{Li}^{7} + \mathrm{H}^{1} \longrightarrow 2\,\mathrm{He}^{4}. \]

When Cockcroft and Walton used protons with an energy of 300,000 V, the range of the $\alpha$-particles in air was found by them to be 8.4 cm, which corresponds to an energy of 8.7 million electron-volts. This leads to the value 7.0133 for the mass of the $\mathrm{Li}$ nucleus. Aston’s measurements give the value 4.00106 for the mass of $\mathrm{He}^{4}$ and 10.01075 for $\mathrm{B}^{10}$. The kinetic energy of the neutrons liberated from $\mathrm{Li}^{7}$ by the $\alpha$-particles of polonium (having an energy of 0.00565 mass units) was not determined. It is small, probably less than 0.5 million V, since the neutrons are readily absorbed by several millimeters of lead. If we assume that the emitted neutrons have energy equal to zero, we obtain a maximum value for the mass of the neutron; it will have the value $1.0070 \pm 0.0005$. The error of this method of determining the mass depends chiefly on the error of Aston’s measurements of the mass of $\mathrm{B}^{10}$.

If we assume that the hydrogen isotope with mass 2 consists of a proton and a neutron, we can find a minimum value for the mass of the neutron, since the sum of the masses of the two particles must exceed the mass of their physical combination by an amount corresponding to the binding energy of their “packing.” The mass of the nucleus of the isotope $\mathrm{H}^{2}$

is equal to 2.0130. Consequently, the mass of the neutron must be greater than \(2.0130 - 1.0072 = 1.0058\). Thus the mass of the neutron lies between the values 1.0058 and 1.0070. We may provisionally adopt the value 1.0067, which I obtained from a calculation of the process of boron disintegration.

Undoubtedly the mass of the neutron is appreciably less than the mass of the hydrogen atom. This agrees with the view that the neutron consists of a proton and an electron. Then the residual mass 0.0011 should represent the “binding” energy of two such particles, corresponding to 1 million electron-volts. It may perhaps be noted that this “mass defect” corresponds to a change of the electron energy from \(+mc^2\) to \(-mc^2\).

Such considerations, expressed on the basis of knowledge of the neutron mass, may indeed speak in favor of a composite structure of the neutron, but they are by no means conclusive. The most direct proof would be the splitting of the neutron into a proton and an electron in collision with some nucleus, but both calculations and experiment show that this event must be very rare. Certain considerations concerning the composite structure either of the neutron or of the proton, as I shall show below, can be derived from observations of collisions of neutrons with protons.

On the other hand, some arguments may be advanced in favor of the neutron being an elementary particle. According to the modern conception of quantum mechanics, the hydrogen atom is the only possible combination of a proton and an electron. However, the “binding” energy of the particles turns out to be greater than the electron’s own mass, and relativistic mechanics would be required to describe their interaction.

The next argument comes from the moment (spin) of the neutron. This argument is based on consideration of the spins of light elements under the assumption: 1) that the nucleus consists of the corresponding number of \(\alpha\)-particles and, in addition, of protons and neutrons (and not of free electrons); 2) that the nuclear spin is expressed by the vector sum of the spins of its constituent parts. Apparently, the neutron must then have a spin equal to \(\frac{1}{2}\frac{h}{2\pi}\) and obey Fermi statistics. The proton has spin \(\frac{1}{2}\frac{h}{2\pi}\) and obeys Fermi statistics. If the neutron is regarded as a combination of a proton with an electron, the latter would have to have spin equal to zero and obey Bose statistics. This contradicts the behavior of the free electron. The spin of the nuclei of light elements proves compatible with the statistics to which they are subject only if it is assumed that the neutron is an elementary particle.

One may also use a more general argument. If the neutron is a combination of a proton and an electron, then why cannot the hydrogen atom transform into a neutron with the emission of energy?

It can be shown exhaustively that such a process must be extremely rare. This proof seems to me a strong argument in favor of the elementary nature of the neutron. These difficulties still have to be clarified and, while for certain purposes still accepting the hypothesis of a complex structure of the neutron, it should be regarded in other cases as an elementary unit of the structure of the atomic nucleus.

It is probably possible to try to suppose that the proton is a complex particle consisting of a neutron and a positive electron. The mass of the proton, apparently, can then be regarded as less than the sum of the masses of the neutron and the positron, if for the mass of the neutron one takes a value close to the upper limit indicated above. But this does not remove the difficulties with the spins. We would have to suppose that the spin of the positron is equal to zero, and then it would be difficult to imagine the fusion of a positron with an electron, in which these particles annihilate each other.

5. Collisions of neutrons with atomic nuclei.

The elastic collision of a neutron with an atomic nucleus can be described in general terms. Independently of the point of view adopted concerning the nature of the neutron, its interaction with an atomic nucleus must be very weak if the distance between the nucleus and the neutron considerably exceeds \(10^{-12}\) cm. In passing through matter the neutron will not change its trajectory until it finds itself in the immediate vicinity of some nucleus. One may say that the scattering of neutrons is caused chiefly by the internal fields of nuclei; the effective cross section of an atom will then be of the same order as the dimensions of the potential barrier of the nucleus, and the distribution of the scattered neutrons should not have a noticeable anisotropy. As I have shown in my papers, this picture gives a plausible interpretation of the scattering of neutrons by heavy nuclei.

Of course, this is only a rough description of the collision process; however, Massey’s calculations \(^{10}\) lead to a considerable extent to the same conclusions. Massey represented the neutron as a hydrogen atom in the zero quantum state. The field of such a particle must be quite analogous to the field of a hydrogen atom outside the Bohr orbit, but the scale of distances must be considerably reduced. This field may be represented by the function:

\[ V(r)=e^2\left(\frac{1}{r}+\frac{Z}{a_0}\right)e^{-2Zr/a_0}, \]

where \(Z\) is the effective charge of the nucleus, which must be very large, and \(a_0\) is the radius of the first Bohr orbit of the hydrogen atom.

The “radius” of the neutron will then be equal to \(\frac{a_0}{Z}\).

The field of the forces acting between the neutron and a nucleus with charge \(Z'\), at distances exceeding the radius of the nucleus, will be equal to \(Z'\cdot V(r)\).

Experiments on the scattering of neutrons by lead show that in collisions the effective radius has the same order of magnitude,

that both the radius of the nucleus and, from this, Massey obtained, as the smallest value for \(Z\), the quantity 25,000. (This gives for the radius of the neutron the maximum value \(2\cdot 10^{-13}\,\mathrm{cm}\).)

The application of the found value of \(Z\) to the investigation of collisions of neutrons with light nuclei enabled Massey to show that in collisions the effective radius of atoms should be proportional to the charge of the nucleus. This result does not agree with experiment, which shows that the effective radius changes little for considerable changes in the nuclear charge, from carbon (effective radius \(3.5\cdot 10^{-13}\,\mathrm{cm}\)) to argon (\(5.5\cdot 10^{-13}\,\mathrm{cm}\)). From this Massey concluded that the effective cross section is determined by the internal field of the nucleus and that the external interaction takes place in an extremely limited region of space, playing a role only when the colliding systems penetrate into one another.

Of greatest interest are collisions of neutrons with protons. The latter should behave, even at very small distances, as elementary charges. If there were no interaction between the neutron and the proton other than that expressed by the function \(V(r)\), the effective radius for such collisions should not exceed \(1.4\cdot 10^{-14}\,\mathrm{cm}\). The discrepancy with experiment in this case is very large, since the experimentally found radius reaches values from \(4\) to \(5\cdot 10^{-13}\,\mathrm{cm}\) for neutrons flying with a velocity of \(2.7\cdot 10^{9}\,\mathrm{cm/sec}\), and is still larger for slower neutrons. Before discussing the causes of such a discrepancy, I shall briefly describe the experimental data on collisions of neutrons with protons.

These collisions have not yet been studied in detail because of great experimental difficulties. The most direct method of study consists in introducing a known number of neutrons of definite velocity into a Wilson chamber filled with hydrogen and photographing the tracks of the recoiling hydrogen atoms. This makes it possible to find both the frequency of collisions and the angular distribution of the recoiling protons. Unfortunately, we have only very indirect methods for determining the number of neutrons in the beam, and collisions occur so rarely that the experiment becomes extremely prolonged.

Some data concerning the angular distribution of protons were obtained by this method by Auger and Monod-Herzen\(^{11}\), and also by the American physicist Kurie\(^{12}\), who used a somewhat different technique. In both experiments the source of neutrons was beryllium, a massive layer of which was bombarded with \(\alpha\)-particles of polonium. The emitted neutrons had various velocities, in the majority not exceeding \(2.8\cdot 10^{9}\,\mathrm{cm/sec}\). In Auger’s experiments, the overwhelming majority of recoiling protons appeared in collisions with slow neutrons. The distribution of protons that had undergone collision with neutrons was approximately uni-

nonuniform. Cory especially carefully investigated protons knocked out by faster neutrons, and also found that their angular distribution is quite uniform relative to the center of mass of the moving system.

Meitner and Philipp \(^{12}\) used a Wilson chamber to determine the effective radius. These authors assumed that a thick layer of beryllium emits 30 neutrons for every million polonium \(\alpha\)-particles bombarding it, and in each separate experiment measured the interval of time during which tracks produced as a result of the action of a source of \(\alpha\)-particles of known intensity were registered in the chamber. From the frequency of appearance of proton tracks Meitner and Philipp found that the effective collision radius exceeds \(8\cdot 10^{-13}\) cm. From the information given by the authors one may conclude that, apparently, most of the collisions which they observed occurred with slow neutrons having velocities close to \(10^9\) cm/sec.

My own experiments, in which the method of electrical counting was used, are in general agreement with the results of Meitner and Philipp. The angular distribution of protons was measured by counting the number of protons knocked out of paraffin diaphragms of different diameter. The results, although very inaccurate, showed that the angular distribution of protons is approximately uniform. Attempts to observe the distribution obtained under the action of a monochromatized beam of neutrons were unsuccessful because of the small intensity of the effect.

The effective radius was determined by the above-mentioned method. The neutron source was a thin beryllium film with an absorption equivalent to a 5-millimeter layer of air, bombarded by polonium \(\alpha\)-particles. The neutron beam was thereby sufficiently monochromatic; most of the particles had a velocity of about \(2.7\cdot 10^9\) cm/sec, with a small number of faster neutrons. The neutron source was adjusted in a definite position relative to an ionization chamber connected in the usual way through an amplifier to an oscillograph. The chamber could be evacuated and filled with various gases. The number of deflections of the oscillograph was observed with the chamber filled alternately with hydrogen and with heavier gases, namely nitrogen, oxygen, or argon. Each deflection of the oscillograph corresponded to the appearance in the chamber of an atom recoiling in the collision of neutrons with a nucleus. Since the number of neutrons entering the chamber remained in all cases the same, the number of deflections of the oscillograph should have been proportional to the effective cross section of the nuclei. It was found that the number of deflections with the chamber filled with hydrogen was somewhat smaller than when it was filled with nitrogen or oxygen. Corresponding to this, the effective radius in collisions with hydrogen nuclei must be somewhat smaller than with nitrogen and oxygen nuclei. A count of the number of deflections of the oscillograph with a thick plate placed in the path of the neutrons

in a graphite wall made it possible to determine the effective radius of the carbon nucleus. The value found proved to be approximately \(3.5\cdot 10^{-13}\) cm. The effective radii of the nuclei of nitrogen and oxygen are probably somewhat larger, and for them one may adopt the value \(4\cdot 10^{-13}\) cm. The above-mentioned comparison of the effective radii of hydrogen and nitrogen may contain a small error, difficult to estimate, arising from the fact that those recoil atoms which produce only a small number of ions are not registered by the oscillograph. This affects the count both with a chamber filled with hydrogen and with one filled with nitrogen. In the first case the number of recoils is in general smaller than in the second, owing to the lower ionizing power of protons and the low density of the gas. On the other hand, the energy imparted in collisions to nitrogen atoms is smaller, and collisions occurring at large distances between the encountering particles may remain unregistered.

To determine the fraction of unregistered collisions occurring in hydrogen, experiments were carried out in which the ionization chamber was filled with a mixture of hydrogen and nitrogen. It proved impossible, however, to find a correction for unregistered collisions in nitrogen. Keeping this source of error in mind, we may take the effective radius of the hydrogen nucleus for neutrons traveling with a velocity of \(2.7\cdot 10^{9}\) cm/sec to be from \(4\) to \(5\cdot 10^{-13}\) cm.

Analogous experiments were performed with a neutron source—a thick layer of boron bombarded by \(\alpha\)-particles of polonium. These neutrons have velocities not exceeding \(2.5\cdot 10^{9}\) cm/sec, and on the average somewhat less than \(2\cdot 10^{9}\) cm/sec. The number of oscillograph deflections when the chamber was filled with hydrogen in this case exceeded almost twice the number of deflections obtained with nitrogen; this leads one to suppose that the effective radius of the nucleus of either hydrogen or nitrogen depends strongly on the velocity of the neutrons. Measurement of the scattering of these slow neutrons in graphite and paraffin showed that the strong dependence must be attributed chiefly to hydrogen. Comparison with nitrogen gives for the effective radius of the hydrogen nucleus the value \(6\cdot 10^{-13}\) cm; at the same time, comparison of the experiments with graphite and paraffin leads to a value close to \(7\cdot 10^{-13}\) cm. Some experiments with still slower neutrons suggest that the effective radius of protons undergoing collisions with neutrons continues to increase as the velocity of the neutrons decreases.

In considering collisions of neutrons with protons* we had in view explaining the experimental facts according to which the angular distribution of protons that have undergone collision is approximately uniform, while their effective radius is very large and increases as the velocity of the neutrons decreases. If we suppose—

* In the argument presented here I am much indebted to Mr. Massey.

expect that the hydrogen isotope of mass 2 consists of a proton and a neutron, we obtain the new experimental fact that the binding energy of this isotope is about \(10^6\) V.

The wave theory of the collision of two independent particles gives, for the effective cross section, the expression:

\[ Q=\frac{h^2}{\pi M^2 v^2}\sum_n (2n+1)\sin^2 \delta_n, \]

where \(M\) is the reduced mass of the system, \(v\) is the initial relative velocity of the particles, and the quantities \(\delta_n\) are phase constants depending on \(M\), \(v\), and \(V(r)\), the energy of interaction of the particles. The number of scattered particles falling per unit angle in a coordinate system whose origin is at the center of mass is expressed by the function:

\[ I(\theta)\sin\theta= \frac{h^2}{8\pi^2 M^2 v^2} \left|\sum_n (e^{2i\delta_n}+1)(2n+1)P_n(\cos\theta)\right|^2 \sin\theta, \]

where

\[ P_0(\cos\theta)=1,\qquad P_1(\cos\theta)=\cos\theta,\qquad P_2(\cos\theta)=\frac12(3\cos^2\theta-1) \]

and so on.

Fig. 4.

The fact that the angular distribution is uniform shows that only the spherical function of zero order is significant, i.e. that the scattering depends mainly on “head-on” collisions of the particles. This means that the distance at which the interaction of the neutron with the proton begins is small in comparison with the quantity:

\[ \frac{\text{wavelength}}{2\pi} \left(=\frac{h}{2\pi Mv}\right), \]

i.e. the region of interaction is \(\ll 10^{-12}\,\mathrm{cm}\). (This result is in agreement with earlier calculations of neutron collisions, in which the neutron was likened to an atom with an effective nuclear charge equal to at least 25,000.)

Let us consider the isotope \(\mathrm{H}^2\), assuming it to consist of a proton and a neutron. We shall take the potential field between the neutron and the proton to be as shown in Fig. 4. The values of the function \(V(r)\) may be neglected at distances \(r>r_0\). From the fact that there exists an energy level with energy \(-E_0\) (equal to the “binding” energy), we can conclude that the values of \(V(r)\) must be very large in the region \(r<r_0\), since the field must be so large that half a wavelength can fit into this region. We found that the wavelength of the incident protons is significantly

greater than \(r_0\), and their energy is of the same order as the “packing” energy \(E_0\). Thus \(V(r)\) must be \(\gg E_0\), or \(E\), the energy of the incident protons.

The potential field of protons and neutrons may be roughly likened to a very deep hole of small radius. It can be shown that the influence of this hole is manifested in the fact that the wave function describing the collision of a neutron and a proton, at \(r=r_0\), assumes a value close to a maximum, instead of being close to zero. This corresponds to a phase shift of almost \({}^{1}/_{2}\pi\). Thus \(\delta_0\) is approximately equal to \({}^{1}/_{4}\pi\), and

\[ Q \simeq \frac{h^2}{\pi M^2v^2}, \]

which amounts to about \(2\cdot 10^{-27}\cdot v^{-2}\,\mathrm{cm}^2\), when \(v\) is measured in milliards \((10^9)\,\mathrm{cm/sec}\). The effective radius is approximately \(2.5\cdot 10^{-12}\cdot v^{-1}\,\mathrm{cm}\). Since for \(\delta_0\) we have taken the maximum value, this value of the effective radius is also the largest. It is quite improbable that \(\delta_0\) should be less than \({}^{1}/_{4}\pi\). Putting \(\delta_0={}^{1}/_{4}\pi\), we obtain the smallest possible value for the effective radius, equal to \(1.8\cdot 10^{-12}\cdot v^{-1}\,\mathrm{cm}\).

This value agrees with experiment better than the first. The effective cross section for the collision of protons is large and depends on the velocity in the required manner. On the other hand, the effective cross section has now turned out to be too large. Putting \(v=2.7\cdot 10^9\,\mathrm{cm/sec}\), we obtain a value of the effective radius close to \(10\cdot 10^{-13}\,\mathrm{cm}\) and, of course, not less than \(7\cdot 10^{-13}\,\mathrm{cm}\), whereas observations give a value somewhat smaller than \(5\cdot 10^{-13}\,\mathrm{cm}\). I do not think that such a discrepancy could be caused by errors of measurement, and the explanation should be sought in something else.

It is possible that this explanation can be given by introducing a certain mutual exchange occurring between the proton and the neutron. For example, if the neutron consists of a proton and an electron, one may suppose that between the colliding particles there occurs a special interaction—the transition of the electron from the neutron to the proton and an exchange of protons. This interaction is analogous to that experienced by a hydrogen atom and a proton. As a result, there appear strong repulsive and attractive fields, decreasing very rapidly with distance. To obtain the final value of the effective cross section, our result must be multiplied by a coefficient depending on the spin of the proton. If the latter is equal to \({}^{1}/_{2}\,\dfrac{h}{2\pi}\), the new value of the effective cross section should be not less than \({}^{1}/_{4}\) of the former, i.e.

\[ Q \simeq \frac{1}{4}\frac{h^2}{\pi M^2v^2} \simeq 5\cdot 10^{-24}\cdot v^{-2}\,\mathrm{cm}^2, \]

where \(v\) is expressed in milliards \((10^9)\,\mathrm{cm/sec}\). This gives, for neutrons flying with velocity \(2.7\cdot 10^9\,\mathrm{cm/sec}\), an effective radius of about

\(5 \cdot 10^{-13}\) cm, in good agreement with the experimental value *.

It would be premature to draw a final conclusion about the complex structure of the neutron, since the theory of collisions is still insufficiently developed, and the measurements are inaccurate. The experimental facts, apparently, can be interpreted only with the aid of the notion of a certain “exchange” interaction existing between the neutron and the proton. The mechanism of this interaction may turn out to be different from that which we assumed above, and perhaps there is no need to regard one of the particles as complex. We have not considered the spins of the particles and the possible influence of any magnetic forces.

It may turn out that, in the interactions under consideration, these magnetic forces play an essential role.

The study of the interaction between the neutron and the proton plays a great role in the theory of the structure of the nucleus. If one assumes that the latter is built of protons and neutrons, the forces “binding” it will be the forces of interaction of proton with proton, neutron with neutron, and proton with neutron. The interaction between two protons must be ascribed to Coulomb forces (if magnetic forces are neglected), and knowledge of the nature of the fields in the nucleus makes it quite clear that these forces play only a small role inside the nucleus, certainly in the case of light elements. The forces of interaction between two neutrons are probably small in comparison with the others. Thus the most essential forces for the structure of the nucleus are those acting between neutrons and protons, and it is on them that its stability depends.

6. Disintegration of nuclei by neutrons. Most collisions of neutrons with atomic nuclei are elastic, but in individual cases they are also inelastic. Inelastic collisions were first discovered by Feather in the study of collisions of neutrons with nitrogen nuclei by means of a Wilson chamber. Collisions in general occur, of course, very rarely, and, only after making 2000 photographs, Feather obtained about 100 tracks of recoiling nitrogen atoms, which appeared, evidently, as the result of elastic collisions, and about 30 forked tracks of an entirely different type.

* The dependence of the effective cross-section on the velocity of the neutrons is, apparently, stronger than is given by the expression cited above. This may be explained by a theory developed in more detail. It is important to note that the strong dependence of the effective cross-section on velocity in collisions with hydrogen atoms constitutes one of the difficulties encountered in the observations of fast neutrons emitted by protons (§ 3). Whereas the effective cross-section of other nuclei also depends on the velocity of the neutrons, its decrease with increasing velocity is not as rapid as in hydrogen. The strong dependence of the effective cross-section also explains the noticeable predominance of short proton tracks in photographs obtained with the Wilson chamber, as occurred in the experiments of Auger and Meitner and Philipp.

The latter were attributed to the disintegration of nitrogen nuclei subjected to collisions with neutrons. In almost half the cases one gets the impression that the nucleus captures the neutron and emits an $\alpha$-particle, thereby forming a boron isotope of mass 11:

\[ \mathrm{N}^{14}+n^{1}\to \mathrm{B}^{11}+\mathrm{He}^{4}. \]

Obviously, this represents the reverse of the process that occurs when neutrons are emitted under the influence of the bombardment of boron by $\alpha$-particles. The mechanism of the disintegration of the nucleus in other cases is still unclear. It seems possible that the neutron is not captured by the nucleus and that the particle emitted is a proton. If it could be proved that this point of view is correct, we would have the first case of transmutation of elements in which the bombarding particle remains uncaptured.

The disintegration of nitrogen by neutrons was also discovered by Meitner and Philipp$^{13,20}$, Harkins, Gans, and Newson$^{14}$, and Curie$^{15}$.

Feather$^{16}$ also observed forked tracks appearing in oxygen. Their number was found to be approximately in the same ratio to the normal tracks of elastically recoiling oxygen atoms as in nitrogen. In all such collisions the neutron appeared to be captured, while the $\alpha$-particle was emitted, forming a $\mathrm{C}^{13}$ nucleus:

\[ \mathrm{O}^{16}+n^{1}\to \mathrm{C}^{13}+\mathrm{He}^{4}. \]

This transmutation of elements is especially interesting, since oxygen nuclei apparently withstand bombardment well both by $\alpha$-particles and by protons.

Feather also found several cases of disintegration when neutrons were passed through a Wilson chamber filled with acetylene.

In this case, some of the tracks apparently appeared owing to the presence of a small amount of air, and only in two cases could it be stated definitely that disintegration of a carbon nucleus had taken place. From the available results one may apparently conclude that inelastic collisions occur in carbon considerably more rarely than in nitrogen or oxygen. This could have been expected, since the process

\[ \mathrm{C}^{12}+n^{1}\to \mathrm{Be}^{9}+\mathrm{He}^{4} \]

requires such a large amount of energy (about 7.5 million electron-volts), possessed by only a small fraction of the neutrons used in Feather’s experiments (the neutron source was beryllium bombarded by polonium $\alpha$-particles). Furthermore, if the idea of the structure of the nuclei $\mathrm{B}^{9}$ and $\mathrm{C}^{12}$ expressed above is correct, the transmutation of $\mathrm{C}^{12}$ into $\mathrm{B}^{9}$ must be extremely improbable, since the $\alpha$-particle must considerably “loosen” the dense structure of the $\mathrm{C}^{12}$ nucleus.

At the present time there are examples of the disintegration by neutrons of the nuclei of only a few elements, but it is possible that many other elements too can be transformed in the same way.

The energy relations characterizing the disintegration of nuclei by neutrons possess certain interesting features. The disintegration

\[ \mathrm{B}^{11} + \mathrm{He}^{4} \to \mathrm{N}^{14} + n^{1} \]

is connected with the absorption of 1.4 million electron-volts of kinetic energy. We may then expect that the reverse process is accompanied by the release of the same amount of energy. Feather indicates that, of 12 measurements made by him for this process, in 10 there was an absorption of energy, and that the change of energy was not always one and the same. This leads to the idea that the disintegration is usually accompanied by the formation of an excited nucleus \(\mathrm{B}^{11}\), and the remaining energy is emitted in the form of \(\gamma\)-rays. Taking into account the different changes of energy, one may suppose that there probably exists more than one excited state of the nucleus \(\mathrm{B}^{11}\). In a similar way, study of the phenomenon of the disintegration of oxygen leads to the conclusion that \(\mathrm{C}^{13}\) nuclei may also be formed in various excited states.

In many cases of disintegration accompanied by the emission of protons, the process is usually connected with the formation of an excited nucleus, but there is no certainty about the existence of more than one excited state.* It should be pointed out that the changes of energy calculated for cases of the disintegration of nuclei by neutrons may be erroneous partly owing to inaccuracy in the measurements of tracks, and partly because of their incorrect interpretation; the fact that the resulting nucleus is in an excited state is beyond doubt, whereas the existence of several excited states requires confirmation.

7. Liberation of Positive Electrons

As I mentioned in § 3, beryllium bombarded with \(\alpha\)-particles emits, besides neutrons, also very hard \(\gamma\)-rays, and it is sometimes difficult to distinguish whether the phenomena observed in experiments with beryllium occur under the action of neutrons or of \(\gamma\)-rays. The most interesting example of this kind is the liberation of positive electrons—particles with the mass of an electron but positively charged. The first proof of the existence of positive electrons was obtained in the experiments of Anderson\(^{17}\) and of Blackett and Occhialini\(^{18}\), who studied, with the aid of Wilson’s chamber, phenomena occurring in the atmosphere under the influence of cosmic rays. It was highly desirable to find some more ordinary method for the liberation of positive electrons, which—

* Author’s note in proof. Recent experiments on the disintegration of aluminium by \(\alpha\)-particles make quite evident the existence of two excited states of the nucleus obtained as a result of the disintegration.

which would confirm their existence and make it possible to investigate the properties of these particles. Certain experimental facts led Blackett, Occhialini, and me \(^{19}\) to the conclusion that positive electrons can be liberated in the interaction of beryllium rays with matter.

Near a Wilson chamber, close against its wall, an ampoule containing polonium and a certain amount of beryllium was placed. On the inner side of the wall of the chamber a lead “target” was installed, having a thickness of \(2\) mm and an area of \(2 \frac{1}{2}\) cm\(^2\). This target was subjected to the action of \(\gamma\)-rays and neutrons emitted by the beryllium. Exposures were made with two cameras, which made it possible to obtain stereoscopic photographs. At the moments when expansion was produced in the chamber, a magnetic field was applied, usually having a strength of about 800 gauss; the electrons emitted from the target were acted upon by the magnetic field; the direction of the radii of curvature of their tracks made it possible to determine the sign of the charge, and the value of the radius of curvature gave the quantity \(H\rho\). Of all the tracks of particles issuing from the target, 200 undoubtedly belonged to negative electrons, while 70 were curved in the opposite direction. It was possible to give a rather improbable explanation, according to which these tracks belong to negative electrons knocked out from distant parts of the chamber and flying, under the influence of the magnetic field, in such a way that their trajectories all converge in the lead target. A statistical study of all the photographed tracks compelled preference for the point of view according to which these tracks belong to positive electrons. Final proof was obtained in the following way. Across the Wilson chamber a metallic plate was placed so that it intersected the trajectories of the particles. Several photographs were obtained in which the tracks corresponding to positive particles crossed the plate and remained sharp throughout their entire length. The curvature of the tracks proved to be smaller on that side of the metallic plate on which the lead target was located; this serves as reliable indication that such particles move away from the target and, consequently, that they carry a positive charge. For example, in one case the track had, on the side of the copper plate (of thickness \(0.25\) mm) facing the target, a curvature corresponding to the value \(H\rho = 12\,700\), whereas on the other side of the plate the curvature corresponded to \(H\rho = 10\,000\); in another case, with an aluminum plate of thickness \(0.33\) mm placed across the chamber, the corresponding values of \(H\rho\) were found to be 5000 and 4000.

Measurements of the magnitude of the ionization in gases and of the loss of energy in passing through metallic plates show that the mass and the magnitude of the charge of the positive particle are the same as those of the negative electron.

Analogous experiments were carried out by Meitner and Philipp \(^{20}\) and by Curie and Joliot \(^{21}\). Some results of the latter investiga-

suggest that the liberation of positive electrons should be attributed, at least chiefly, to the γ-rays emitted by beryllium, and not to neutrons.

In our subsequent experiments* it was shown that γ-rays can liberate positive electrons. In these experiments beryllium was replaced by a very weak source consisting of the active decay products of thorium, enclosed in a lead chamber with walls one centimeter thick. The target was then bombarded only by γ-rays, the hardest of which had an energy \(h\nu = 2.62 \cdot 10^6\) electron-volts. Photography was carried out, as before, with a metal plate placed across the Wilson chamber, making it possible to determine the direction of motion of the particles.

Along with 1200 tracks of negative electrons, about 50 tracks belonging to positive electrons were observed. The origin of the latter should, of course, be attributed to the action of γ-rays, in all probability hard ones, with energy \(h\nu = 2.62 \cdot 10^6\) electron-volts. The ratio of the number of positive electrons to the number of negative ones was in this case considerably smaller than under the action of beryllium rays. According to the hypothesis first expressed by Blackett and Occhialini, according to which negative and positive electrons are liberated simultaneously in some interaction of γ-rays and the electric field with the atomic nucleus, it is possible that the effect will increase rapidly with increasing γ-ray energy, as, apparently, occurs in the experiments described above. The liberation of two electrons requires \(1.02 \cdot 10^6\) electron-volts, so that the energy of a positive electron liberated by γ-rays with energy \(h\nu = 2.62 \cdot 10^6\) electron-volts should never exceed \(1.60 \cdot 10^6\) electron-volts.

Measurement of the energy distribution of the positive electrons is in agreement with this hypothesis of their origin. Moreover, in some experiments carried out with the active decay products of thorium and with a beryllium source, tracks of negative particles apparently appeared together with tracks of positive particles. The available data, however, are still insufficient for a final decision on the question of the liberation of positive electrons from the nucleus.

Some experiments were carried out in which boron, bombarded by polonium α-particles, was used as the radiation source. In this case a lead target was subjected to the action of neutrons liberated in the decay of \(B^{11}\), and of the γ-radiation accompanying the emission of protons by boron \(B^{10}\). The energy of these γ-rays is somewhat less than 3,000,000 electron-volts, so that the ratio of the number of positive electrons to the number of negative ones should have been of the same order as that found in experiments with produc-

* And also in Anderson’s experiments \(^{22}\).

of thorium decay, i.e. \(1:25\). In reality, the fraction of positive electrons proved to be considerably greater, but the total number of electrons observed in the experiments was small.

It seems possible that positive electrons may be released not only under the action of \(\gamma\)-rays, but also of neutrons, although there are still insufficient data to decide this question.

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