NEUTRONS

N. A. Dobrotin, Leningrad

The discovery of particles with charge 0 and with a mass approximately equal to the mass of the hydrogen atom is one of the greatest discoveries made in physics in recent years.

Chadwick’s remarkable work, in which experimental proof of the existence of neutrons was given for the first time, appeared on May 10, 1932.

Interest in this field is so great that there are already more than 150 papers devoted to this question.

Therefore, despite the fact that there are still many uncertainties in the question of neutrons, it seems desirable to give a review, if only of the principal works in this field.

E. Rutherford¹, in his Bakerian Lecture as early as 1920, pointed to the possibility of the existence of an incomparably more intimate combination of the proton and electron than that which we have in the hydrogen atom.

In 1930 G. F. H. Furne² published a theoretical work on the structure of the atomic nucleus, in which neutrons with mass 1 and charge 0 are introduced as a constituent part of the nucleus. However, before 1932 a number of attempts undertaken by various authors with the aim of detecting such particles led to no results.

I. The First Experiments of W. Bothe and H. Becker

In 1930 W. Bothe and H. Becker¹⁷ discovered that some light elements, under the action of Po α-rays, emit rays with great penetrating power.

Bothe and Becker’s apparatus is shown in Fig. 1. Here \(Z\) is a Geiger counter, \(P\) is a polonium preparation of 7–3 millicuries, with its active side facing upward. For convenience, the two substances under investigation, \(SS\), were arranged in the form of sectors of \(120^\circ\) and placed directly above the preparation on a mica slide, \(Sch\). The third sector remained free. By placing it above the preparation, it was possible to determine the number of counter discharges caused by extraneous causes (in particular by the \(\gamma\)-radiation of Po, discovered in these experiments).

The results of these experiments by Bothe and Becker are presented in Table 1 and in Fig. 2, which give the ratio of the number of $\gamma$-quanta of this radiation to the number of $\alpha$-particles for various elements. The black portions of the columns depict the probable errors of the observations.

From these data it is seen that Li, Be, B, F and, probably, Mg and Al, under the action of $\alpha$-rays of Po, emit rays that produce discharges of the counter. An approximate determination of the absorption of this radiation showed that the intensity of the Be rays, on passing through 1 cm of lead, decreases approximately by 3%, while the intensity of the B rays decreases by 53%. For comparison it is indicated that the $\gamma$-rays of a Ra preparation are absorbed under these conditions also by 53%. Hence Bothe and Becker drew the entirely natural conclusion that the radiation they observed is

Fig. 1.

TABLE 1

Substance	Deflection in 5 min per 1 millicurie of Po	$\dfrac{\gamma}{\alpha}\cdot 10^6$ (yield)
$\mathrm{Li_2CO_3}$	$3.7 \pm 1.1$	$1.0 \pm 0.3$
Li	$17.2 \pm 1.4$	$4.7 \pm 0.4$
Be	$125.0 \pm 2.5$	$34.0 \pm 0.7$
B	$15.3 \pm 1.0$	$4.2 \pm 0.3$
C	$0.54 \pm 0.74$	$0.15 \pm 0.20$
$(\mathrm{CN})X$	$0.78 \pm 0.82$	$0.21 \pm 0.22$
Sugar	$-0.12 \pm 0.92$	$-0.03 \pm 0.20$
$\mathrm{CaF_2}$	$7.5 \pm 1.6$	$1.9 \pm 0.4$
Ne	$0.10 \pm 1.6$	$0.03 \pm 0.42$
$\mathrm{Na_2CO_3}$	$1.8 \pm 1.5$	$0.45 \pm 0.4$
Mg	$3.6 \pm 0.7$	$1.0 \pm 0.2$
Al	$4.7 \pm 0.8$	$1.3 \pm 0.2$
Ca	$0.37 \pm 1.7$	$0.10 \pm 0.48$
Ag	$0.11 \pm 1.0$	$0.03 \pm 0.27$

composed of $\gamma$-quanta emitted by the nuclei of atoms of light elements upon their excitation by impacts of $\alpha$-particles. However, a more detailed [[unclear: continuation cut off]]

study of this radiation showed that, besides \(\gamma\)-rays, it contains particles of an entirely special kind—neutrons.

II. Discovery of recoil nuclei

The next major step in the study of this radiation was made by I. Curie and F. Joliot \(^{22}\).

Determining the absorption of Be and B rays by means of an ionization chamber, they found that the ionization current increases greatly if the ionization chamber is covered by a substance containing hydrogen, such as, for example, paraffin.

If, however, a sheet of Al \(0.2\ \mathrm{mm}\) thick is placed between the ionization chamber and the paraffin, no increase in the current occurs. Further study of this effect showed that the increase of the ionization current occurs because the Be and B rays knock protons out of the paraffin, and these increase the ionization in the chamber. The range of these protons in air under normal conditions reaches approximately \(25\ \mathrm{cm}\) in the direction of the rays that knock out these protons. This corresponds to a velocity of approximately \(3.3 \cdot 10^9\ \mathrm{cm/sec}\) and an energy of \(5.7 \cdot 10^6\) V-electrons. Attempts to detect a similar ejection of protons by ThC\({}^{\prime\prime}\) \(\gamma\)-rays were unsuccessful. Thus this effect represents a characteristic feature of the new radiation.

Fig. 2.

Experiments with a Wilson chamber fully confirmed the ability of Be rays to knock protons out of substances containing hydrogen. In Fig. 3 is shown a Wilson photograph obtained by Curie and Joliot.

The source of Be rays (a Po + Be preparation) was placed outside the Wilson chamber. The Be rays passed through the envelope of the preparation and through the chamber wall and knocked protons out of a paraffined plate (the white strip at the bottom) placed inside the chamber.

Subsequently, with the aid of the Wilson chamber, it was found that these rays are capable of setting in motion not only protons, but also the nuclei of atoms of other light elements: He, N, O, Ne.

Fig. 4 shows a Wilson photograph^34 of an ejected He atom.

III. The Neutron Hypothesis

The work of Webster^30 and especially of Chadwick^4 showed that the interpretation of Be and B radiation as streams of quanta of hard $\gamma$-rays encounters a number of contradictions. In this case the process of interaction

Fig. 3.              Fig. 4.

of such a quantum with a proton and an electron has to be regarded as a Compton effect. From the theory of the Compton effect it is known that the maximum energy $E$ imparted to a mass $m$ by a quantum $h\nu$ is given by the formula:

\[ E=\frac{2}{2+\frac{mc^2}{h\nu}}h\nu . \tag{1} \]

Substituting the observed data for protons, we obtain a quantum energy of $55\cdot 10^6$ V-electrons. It is difficult to understand how, as a result of the interaction of a Be nucleus and an $\alpha$-particle with a kinetic energy of $5\cdot 10^6$ V-electrons, a quantum with such a large energy can be obtained. The process capable of giving the greatest amount of energy consists in the capture of the $\alpha$-particle by the Be nucleus and its entry into the composition of this nucleus with the formation of the carbon isotope C$^{13}$. But the maximum energy of the $\gamma$-quantum emitted in this reaction cannot be greater than $14\cdot 10^6$ V-electrons.

Moreover, it is known that the absorption of hard $\gamma$-quanta by electrons is given with great accuracy by the Klein–Nishina formula. The same formula should also be applicable to the scattering of quanta by protons. From this formula it follows that the absorption of $\gamma$-rays by electrons is incomparably greater than absorption by protons. Meanwhile it turns out that the absorption of Be and B rays is due not to electrons, but to atomic nuclei.

A sharp contradiction also arises when calculating the energy of one and the same quantum of Be radiation from the ranges of the recoil nuclei of different-

...of various elements. As has already been indicated, from the ranges of protons^6 on the basis of formula (1), the quantum energy is obtained as \(55\cdot 10^6\) V-electrons. Substituting into this same formula the data for nitrogen, we obtain a quantum energy of \(90\cdot 10^6\) V-electrons; from the data for argon—\(150\cdot 10^6\) V-electrons, etc.

Thus it turns out that for the radiation of Be and B the ordinary theory of the Compton effect is inapplicable. In other words, the adoption of a hypothesis that regards this radiation as a flux of \(\gamma\)-quanta entails abandoning the application of the laws of conservation of energy and momentum to the process of interaction of a quantum with the nucleus of an atom.

However, Chadwick showed that all these difficulties disappear if one assumes that the radiation of Be has a corpuscular character and is a flux of particles with a mass close to the mass of the proton and with charge 0.

The velocity of such neutrons, evidently, must be equal to the maximum velocity of the protons knocked out by them, i.e. \(3.3\cdot 10^9\) cm/sec.

Let us denote the velocity and mass of the neutron by \(V\) and \(M\), and the maximum velocity and mass of the nucleus knocked out by it by \(v\) and \(m\). Then, applying to the collision process the laws of conservation of energy and momentum, we obtain:

\[ v=\frac{2M}{M+m}V. \tag{2} \]

Substituting the data for hydrogen, we obtain:

\[ 3.3\cdot 10^9=\frac{2M}{M+1}V. \]

For nitrogen (the velocity of the nitrogen nucleus is determined from a range of \(3.5\) mm in air on the basis of the range—velocity curve obtained by Blackett and Lees):

\[ 4.7\cdot 10^8=\frac{2M}{M+14}V. \]

Hence

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

and

\[ M=1.15. \]

The error of such a determination of the mass of the neutron may reach 10% owing to errors in determining the velocities of the recoil nuclei. Therefore, for a more precise determination of \(M\), Chadwick turned to the consideration of nuclear reactions occurring when the neutron is knocked out.

IV. Mass and collision radius of the neutron

Chadwick assumes that in the interaction of an \(\alpha\)-particle with a Be nucleus the following process occurs:

\[ \mathrm{Be}^9+\mathrm{He}^4+W_\alpha=\mathrm{C}^{12}+n^1+W_c+W_n, \]

where \(\mathrm{Be}^9\), \(\mathrm{He}^4\), and \(\mathrm{C}^{12}\) denote the masses of the corresponding nuclei, \(n^1\) the mass of the neutron, and \(W_\alpha\), \(W_{\mathrm{C}}\), and \(W_n\) their kinetic energies.

However, an exact measurement of the mass of Be was made only a few months ago. Chadwick therefore turned to the irradiation of boron. From the experiments of Chadwick, Constable, and Pollard \({}^{36}\) it follows that protons are emitted in the disintegration of \(\mathrm{B}^{10}\). Chadwick therefore believes that neutrons are emitted by the isotope of boron \(\mathrm{B}^{11}\), and that upon irradiation with neutrons the following reaction occurs:

\[ \mathrm{B}^{11}+\mathrm{He}^{4}+W_\alpha=\mathrm{N}^{14}+n^1+W_{\mathrm{N}}+W_n . \]

\(W_n\) must be equal to the maximum energy of the protons knocked out by the B neutrons, and is determined from their range (16 cm) in air under normal conditions. \(W_{\mathrm{N}}\) can be determined by applying the law of conservation of momentum to the collision. The values of the masses are taken from Aston’s data. Thus from this equation \(n^1\) can be determined. Substitution of the numbers gives \(n^1=1.0067\) \((\mathrm{O}=16)\).

Subsequently Chadwick \({}^{7}\) calculated the mass of the neutron also on the basis of the reaction for obtaining neutrons from Li:

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

The mass of \(\mathrm{Li}^{7}\) can be determined using Cockcroft and Walton’s data on the energy of the \(\alpha\)-particles obtained in the disintegration of \(\mathrm{Li}^{7}\) by protons. Hence, for the mass of \(\mathrm{Li}^{7}\) the value 7.0133 is obtained. Taking for \(\mathrm{B}^{10}\) the mass 10.01075 (from Aston’s data) and assuming, on the basis of its small penetrating power, that the energy of the neutron from \(\mathrm{Li}^{7}\) is less than \(0.5\cdot 10^6\) V-electrons, Chadwick obtains for the mass of the neutron the value 1.0070.

Thus these data show that the mass of the neutron is somewhat less than the sum of the masses of the proton and the electron, which, as is known, is equal to 1.0078. This confirms the supposition that the neutron is a combination of a proton and an electron. The binding energy of them is found to be about \(1—2\cdot 10^6\) V-electrons.

Chadwick also determined the order of magnitude of the collision radius of the neutron with the nucleus of a lead atom. Let the collision radius of the neutron be \(p\). Then the decrease in the number of neutrons due to absorption and scattering when passing through a layer of substance of thickness \(t\) will be \(\pi p^2nt\), where \(n\) is the number of atoms per unit volume. Chadwick’s experiments showed that the number of counter deflections, when it is shielded from the neutron source by a layer of lead 2.5 cm thick, decreases by 13%. Hence:

\[ \pi p^2nt=0.13 \quad \text{and} \quad p=7\cdot 10^{-13}\,\text{cm}. \]

V. Condition for the Disintegration of an Atomic Nucleus with the Emission of a Neutron

Starting from the conception of neutrons, one can explain why He, N, C, and O do not give neutrons \({}^{7}\). All atomic nuclei known to us satisfy the condition \(A \geqslant 2Z\), where \(A\) is the atomic weight and

\(Z\) is the charge of the nucleus. The splitting of nuclei under the action of α-particles usually occurs with the capture of the α-particle into the composition of the newly formed nucleus. Therefore, as a result of splitting with the emission of a neutron, the atomic weight of the new nucleus increases by 3, and the charge by 2 units. Applying this to the new nucleus, we obtain:

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

or

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

This condition is not fulfilled for \(\mathrm{He}^4\), \(\mathrm{C}^{12}\), \(\mathrm{N}^{14}\), and \(\mathrm{O}^{16}\).

VI. Collisions of neutrons with electrons

Further confirmation of the neutron hypothesis was obtained by Dee \(^{38}\) in a study, using a Wilson chamber, of collisions of neutrons with electrons. In such a collision the maximum velocity of the electron is determined by formula (2)

\[ V_e=\frac{2M}{M+m}V_n, \]

where \(M\) is the mass of the neutron and \(m\) is the mass of the electron. Hence we see that the maximum velocity of the electron is equal to \(2V_n\), i.e. \(6.6\cdot10^9\ \mathrm{cm/sec}\), which corresponds to a range in air of \(3.4\ \mathrm{mm}\). If, however, the Be radiation has the character of \(\gamma\)-quanta, then even for the smallest values of the quantum energies, which may be adopted on the basis of absorption coefficients, the velocities of the electrons obtained as a result of the Compton effect will be such that the ranges of the electrons in air should be of the order of meters. In actuality, Dee, in complete agreement with the neutron hypothesis, found in his photographs 2 electron tracks with a range of several tenths of a millimeter. The probability of a collision of a neutron with an electron proved to be very small—approximately 100 times less than the probability of a collision of a neutron with a nitrogen nucleus. From these same experiments it became clear that the neutron produces fewer than one pair of ions in 3 m of path in air under normal conditions. It should be noted, however, that these experiments are extremely difficult from the experimental point of view. Therefore it should be considered that Dee’s results give only an upper limit for the probability of collision of a neutron with an electron.

VII. γ-rays accompanying neutrons

In addition to short electron tracks, Dee also found in his photographs the paths of fast electrons. In all probability, these electrons are produced by the Compton effect of hard \(\gamma\)-rays accompanying the neutron radiation. Other authors \(^{23,24,34}\) also point to the presence of \(\gamma\)-quanta in the Be radiation. This also follows from the work of Becker and Bothe. In one of their papers \(^{29}\) they investigated the Be radiation with the aid of two Geiger counters by the coincidence method. The probability of collision in both counters of one and the same neutron with a nucleus or electron is negligible,

Therefore all coincidences, except for random ones, could be ascribed to $\gamma$-quanta emitted by Be together with the neutrons. By placing various absorbing layers between the counters, Becker and Bothe found that the energy of this radiation has a value of the order of $5 \cdot 10^6$ V-electrons. However, data of other authors (Auger, Blackett, Occhialini, and Chadwick $^7$) show that at least part of this radiation has a somewhat greater energy: up to $7 \cdot 10^6$ V-electrons. In any case, the question of the energy and spectrum of these $\gamma$-rays still requires further investigation. It may nevertheless be considered that their energy is greater than the energy of the exciting $\alpha$-particles and does not appreciably depend on it. This indicates that these $\gamma$-rays arise in the process of destruction of the Be nucleus and that their emission is probably connected with the emission of neutrons, just as the presence of a fine structure of $\alpha$-rays is connected with the emission of $\gamma$-quanta, and the emission of two groups of protons in the destruction of B is accompanied by the emission of $\gamma$-rays.

The presence of $\gamma$-rays in the radiation of Be is also confirmed by experiments on the investigation of the angular distribution of Be radiation. In complete agreement with Chadwick’s neutron hypothesis $^4$, Webster $^{30}$ found that the ranges of protons knocked out by neutrons flying in the direction of the exciting $\alpha$-rays are greater than the ranges of protons knocked out by neutrons flying in the opposite direction.

I. Curie and F. Joliot $^{29}$ showed that the ratio of ionization “in front” to ionization “behind” (relative to the exciting $\alpha$-particles) in argon is equal to 1.13. If, however, the Be radiation is filtered through a layer of lead 3 cm thick, this ratio increases to 1.40. In helium this ratio is thereby increased from 1.40 to 1.80. This indicates that only the harder part of the radiation is asymmetric. The softer part of the radiation, on the other hand, is symmetric. Finally, Becker and Bothe $^{31}$, in their experiments carried out with counters most sensitive to $\gamma$-rays, found no asymmetry at all. Thus these experiments confirm the presence of $\gamma$-rays in the radiation of Be and show that the neutrons are emitted chiefly in the direction of the exciting $\alpha$-particles. The $\gamma$-rays are symmetric.

Becker and Bothe $^{31}$ also investigated the dependence of the probability of excitation (i.e., the number of $\gamma$-quanta emitted by Be) on the energy of the exciting $\alpha$-particles. For this purpose they varied the mass of the gas layer through which the $\alpha$-particles had to pass on their path from Po to Be. The results of these experiments are given in Fig. 4 (curve $i$). On the abscissa is plotted the energy of the $\alpha$-particles in centimeters of range in air at the moment of their incidence on Be (the residual range after absorption in the gas); on the ordinate, the relative number of $\gamma$-quanta. Curve $d$ was obtained from curve $i$ by differentiation and gives the excitation per 1 cm of path length. At an $\alpha$-particle range of 1.45 cm a distinct maximum is visible on the curve; at a range of 1.9 cm, a minimum.

VIII. Distribution of Neutrons by Velocity

Rasetti^40, I. Curie and F. Joliot^41, and Chadwick^7 obtained similar curves for the probability of neutron excitation. Chadwick’s curve is shown in Fig. 5 (solid curve)*.

It is natural that the curve of γ-ray excitation and the curve of neutron excitation are analogous to one another, since both are essentially determined by the probability of passage of the α-particle through the potential barrier of Be.

I. Curie and F. Joliot point out^12 that the emission of γ-rays generally begins at somewhat smaller values of the energy of the exciting α-rays than for neutrons. This is most sharply observed for Li. In this case the emission of γ-rays begins at an α-particle energy of \(3 \cdot 10^6\) V-electron (range \(1.7\ \mathrm{cm}\)), while the emission of neutrons begins at an energy of \(5 \cdot 10^6\) V-electron. If the range of the α-rays is reduced by only \(5\ \mathrm{mm}\), excitation of neutrons from Li no longer occurs.

Fig. 5

In considering the curve in Fig. 5 one should remember that it in fact represents the dependence of the number of recoil nuclei knocked out by neutrons on the ranges of the exciting α-particles. This may not coincide with the actual curve of neutron excitation, since the probability of collision of a neutron with an atom of the substance may depend on the neutron velocity. In addition, a certain fraction of particles with small ranges, produced by slower neutrons, may remain unregistered.

Practically, penetration of α-particles through the potential barrier of the Be nucleus begins only from ranges of \(0.80\ \mathrm{cm}\) (energy \(1.4 \cdot 10^6\) V-electron). Only a very small fraction of α-particles with lower energy, escaping measurement, is capable of causing the destruction of the Be nucleus and the appearance of a neutron. The energy \(1.4 \cdot 10^6\) V-electron apparently coincides with one of the energy levels of the Be nucleus, and therefore α-particles possessing this energy penetrate especially easily into the nucleus (resonance splitting).

The next resonance maximum corresponds to a range of \(1.46\ \mathrm{cm}\) (energy \(2.5 \cdot 10^6\) V-electron). Beginning with an energy of \(3.5 \cdot 10^6\) V-elec-

* The disagreement with the curve found by Kirsch and Riehlberg^43 is in all probability explained by errors of the latter.

ktron (range \(2.25\) cm), the \(\alpha\)-particles begin to fly over the top of the potential barrier, and therefore, beginning with this value of the energy, the yield of neutrons begins to increase rapidly. The probability of penetration of \(\alpha\)-particles through the potential barrier rapidly decreases with decreasing energy of the \(\alpha\)-particles. Therefore the main part of the neutrons arises in the very surface layers of Be. Nevertheless, the resonance phenomena studied on thick layers of Be are complicated by the fact that, owing to the absorption of \(\alpha\)-particles in the Be itself, the neutrons are produced by \(\alpha\)-particles having a continuous spectrum of energies, beginning with the smallest and ending with the energies of the \(\alpha\)-particles at the surface of the Be. When working with very thin films the resonance maxima should become sharper, since the region of energies of the acting \(\alpha\)-particles is narrowed.

The dotted curve in Fig. 6 was obtained by Chadwick with the aid of a thin Be film deposited by evaporation in vacuum on the surface of a heavy metal. The sharpness of the resonance maxima, especially the second, increased. The slight discrepancy in the positions of the maxima for the film and for the thick Be layer is, in all probability, explained by the changed geometrical conditions of the experiment and by the inhomogeneity of the film.

Fig. 6.
Range of incident \(\alpha\)-particles

For \(\alpha\)-particles which, upon emerging from the film, have a residual range of not less than \(2.25\) cm, one may expect a change in the course of the curve, since now the change in the number of neutrons will be determined only by the dependence of the radius of collision of the \(\alpha\)-particle with the Be nucleus on the velocity of the \(\alpha\)-particle. It is possible that the turn which is suggested on Chadwick’s curve is explained by this phenomenon.

The \(\gamma\)-rays accompanying the emission of neutrons and the presence of resonance maxima indicate that the neutron radiation of Be must consist of separate groups of neutrons with definite values of the energies. This is confirmed by the experiments of Curie, Joliot, and Savely \(^{35}\), who found that the protons knocked out by neutrons are divided into two groups: a principal group with a maximum range of approximately \(28\) cm in air and a considerably weaker one with a maximum range of about \(70\) cm. The first group of protons should correspond to neutrons with a velocity of \(2.9 \cdot 10^9\) cm/sec, the second—to a velocity of \(3.8 \cdot 10^9\) cm/sec.

Chadwick, however, in his experiments with a beryllium film found that

most of the protons knocked out by neutrons belong to the group having a range of 23–24 cm in air. In addition, there was a certain number of particles with a maximum range of about 100 cm, but there were too few of them for a more accurate determination of the range. And, finally, Chadwick believes that his experiments indicate the existence of particles with still greater energy.

Experiments with a thick layer of Be also revealed the main group of protons with a range of 25 cm, a weaker one with a range of 65–75 cm, and again indications of the existence of particles with significantly greater energy.

In the experiments of M. Blau and H. Wambacher\(^{42}\), in which the protons knocked out by neutrons were detected by their tracks in the emulsion layer of a photographic plate, protons of high energy were also found. The path length of these protons in the emulsion reached 560 \(\mu\), which, in the authors’ opinion, corresponds to an energy of at least \(9\cdot 10^6\) V-electrons (range in air about 80 cm).

If the mass of the neutron is known, then its velocity can be calculated on the basis of the nuclear reaction by which the neutrons are produced. Taking the reaction equation

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

and assuming for the mass of Be the value 9.011 found by Bainbridge, and for the neutron 1.0067 (from the reaction of neutron production from B), Chadwick\(^{7}\) finds for the neutron energy the value \(11.9\cdot 10^6\) V-electrons and \(4.77\cdot 10^9\) cm/sec for the velocity. Neutrons with such energy should give protons with a maximum range of 150 cm. Chadwick believes that indications of the existence of such protons are present in his experiments with an ionization chamber. Feather also observed, in a Wilson chamber, recoil atoms of nitrogen, oxygen, and carbon, which must be attributed to neutrons with an energy of about \(10\cdot 10^6\) V-electrons. This was also confirmed in Feather’s latest paper\(^{78,\ II}\). In addition, Harkins, Gans, and Newson\(^{79,\ 80,\ 81,\ 82}\), in their experiments, obtained several cases of disintegrations which should be attributed to neutrons with energies of 13.4, 14.5, and \(16\cdot 10^6\) V-electrons. Although they worked not with Po, but with ThC\(^1\), whose \(\alpha\)-particles have an energy of \(8.8\cdot 10^6\) V-electrons (by \(3.5\cdot 10^6\) V-electrons greater than the \(\alpha\)-particles of Po), nevertheless these neutrons may be assigned to the group of neutrons whose energy, according to Chadwick, should be of the order of \(12\cdot 10^6\) V-electrons. Finally, F. Curie\(^{83}\), working with Po, observed one case of disintegration of nitrogen which should be attributed to a neutron with an energy of \(17\cdot 10^6\) V-electrons*.

* In contrast to Chadwick, G. Walke\(^{84}\) believes that these results can be explained on the basis of the hypothesis of the existence of neutrons with mass 2. Meitner and K. Philipp (Z. Physik, 87, 484, 1934), in their latest work, found, however, that the maximum energy of the neutrons knocked out of Be by Po \(\alpha\)-particles reaches \(13\cdot 10^6\) V-electrons (note added in proof).

Thus Chadwick believes that a Be film, under the action of a homogeneous beam of Po $\alpha$-particles with a velocity of $1.6 \cdot 10^9\ \text{cm/sec}$, should give two groups of neutrons: the main group with a velocity of $2.8 \cdot 10^9\ \text{cm/sec}$ (energy $4.1 \cdot 10^6$ V-electrons) and a weaker group with a velocity of $4.7 \cdot 10^9\ \text{cm/sec}$ (energy $11.9 \cdot 10^6$ V-electrons).

From this point of view of Chadwick, the origin of the $\gamma$-rays accompanying the emission of neutrons can be explained as follows: when an $\alpha$-particle enters the Be nucleus, it splits with the formation of C$^{12}$ and a neutron. A small fraction of the neutrons flies out with the full energy of $12 \cdot 10^6$ V-electrons. But a considerably larger fraction of the neutrons receives an energy of about $4.1 \cdot 10^6$ V-electrons, leaving the C$^{12}$ nucleus in an excited state. In passing to the normal state, C$^{12}$ emits a $\gamma$-quantum with an energy of the order of $7 \cdot 10^6$ V-electrons (part of the energy in the collision process is spent on imparting velocity to the recoil nucleus C$^{12}$). This value for the energy of the $\gamma$-quantum is not in particularly good agreement with the experimental data (see above), but it is not in sharp contradiction with them either. According to this picture, to each resonance maximum of neutron excitation there should correspond two groups of neutrons with an energy difference of about $7 \cdot 10^6$ V-electrons.

Thus, according to Chadwick, a thick layer of Be bombarded by Po $\alpha$-particles should give the following groups of neutrons: for the first resonance level—a more intense group with velocity $1 \cdot 10^9\ \text{cm/sec}$ (energy $0.5 \cdot 10^6$ V-electrons) and a weaker group with velocity $3.92 \cdot 10^9\ \text{cm/sec}$ (energy about $8.0 \cdot 10^6$ V-electrons); for the second resonance level the more intense group has a velocity of about $1.68 \cdot 10^9\ \text{cm/sec}$ (energy $1.4 \cdot 10^6$ V-electrons) and the weaker one—$4.18 \cdot 10^9\ \text{cm/sec}$ (energy $9.1 \cdot 10^6$ V-electrons). Starting from a range of $2.25\ \text{cm}$, the $\alpha$-particles pass over the top of the potential barrier of the Be nucleus. This corresponds to neutrons with velocities from $2.16$ to $2.8 \cdot 10^9\ \text{cm/sec}$ (energy from $2.5$ to $4.1 \cdot 10^6$ V-electrons) and a weaker group with velocities from $4.4$ to $4.77 \cdot 10^9\ \text{cm/sec}$ (energy from $10.1$ to $11.9 \cdot 10^6$ V-electrons). Thus we see that, on theoretical grounds, the velocity spectrum of the neutrons should be rather complex. The question is further complicated by the fact that one must reckon with the possibility of formation, as a result of the interaction of Be$^9$ and the $\alpha$-particle, not of a neutron and C$^{12}$, but of a neutron and three $\alpha$-particles. However, in this case the velocity spectrum of the neutrons should be simpler, which apparently contradicts the experimental results. It is possible that in reality both reactions take place.

Other conclusions about the distribution of neutrons by velocity are reached by Harkins, Gans, and Newson $^{79}$. They calculated the velocities of neutrons knocked out of a thick Be layer from Wilson photographs of the splitting of the nitrogen nucleus by neutrons. As the source of $\alpha$-particles the authors took a mixture of mesothorium, thorium X, and radiothorium. The velocity distribution of 19 neutrons from the work of these authors, 7 neutrons from the work of Feather $^{78}$, and one from the work of Meitner

and Phillips ^58 are shown in Fig. 6. The ordinates of the lower curve give the total number of neutrons whose velocity lies between zero and the given value of the velocity. Neutron velocities are plotted on the abscissa axis. The upper curve was obtained from the lower one by differentiation.

It follows from these data that the neutron velocities are distributed according to a Maxwellian distribution curve about the value \(3.23 \cdot 10^9\ \text{cm/sec}\). According to these data there are no groups of neutrons with a definite velocity.

The shortcoming of this work is that Harkins, Gans, and Newson, in calculating neutron velocities, used the velocities of the nuclei of atoms produced as a result of nitrogen disintegration. But these, in turn, were determined from as yet insufficiently accurately established curves (except for \(\alpha\)-particles) relating the range and the velocity of the atom. Moreover, in general the number of neutrons whose velocities were determined by Harkins, Gans, and Newson is insufficient for statistical conclusions.

Fig. 7.

The excitation curve of neutrons for B is analogous to the curve for Be. The velocity of neutrons knocked out of B by \(\alpha\)-particles possessing a velocity of \(1.6 \cdot 10^9\ \text{cm/sec}\) is approximately equal to \(2.53 \cdot 10^9\ \text{cm/sec}\). The emission of neutrons from B is apparently not accompanied by the emission of \(\gamma\)-quanta*.

* The \(\gamma\)-rays emitted by boron with an energy of \(3 \cdot 10^6\) electron-volts probably must be attributed to the reaction of disintegration of B with the emission of two groups of protons.

Although the velocities of neutrons emitted by a thick layer of B have been studied less well than neutrons from Be, there are nevertheless indications of the existence of discrete groups of neutrons.

The study of the velocity spectrum of neutrons is of especially great importance, since it provides material for constructing a system of nuclear levels of atoms of light elements. But, as is evident from the foregoing, the experimental material available on this question is still quite insufficient.

I. Curie and F. Joliot \(^{12,59}\) attempted to calculate the minimum energy of \(\alpha\)-rays at which the ejection of neutrons from B begins. Let \(I = W_{\mathrm N} + W_n\) be the sum of the kinetic energies of the nitrogen nucleus produced in the disintegration of the B nucleus and of the neutron ejected by an \(\alpha\)-particle with energy \(W_\alpha\). Let us denote by \(I_0\) the sum of the energies of the same particles ejected by an \(\alpha\)-particle with the minimum energy \(W_0\) sufficient for the disintegration of B. Then

\[ I_0=\frac{\alpha}{\mathrm N^{14}+n^1}\,W_0. \]

On the other hand, the reaction equations will be:

\[ \begin{aligned} \mathrm B^{11}+\alpha+W_\alpha&=\mathrm N^{14}+n^1+I,\\ \mathrm B^{11}+\alpha+W_0&=\mathrm N^{14}+n^1+I_0. \end{aligned} \]

Hence:

\[ W_\alpha-W_0=I-I_0=I-\frac{\alpha}{\mathrm N^{14}+n^1}\,W_0. \]

From the greatest energy of the neutrons \(W_n=3.25\cdot10^6\) electron-volts, ejected by the \(\alpha\)-rays of Po, for which \(W_\alpha=5.25\cdot10^6\) electron-volts, one obtains \(W_{\mathrm N}=0.55\cdot10^6\) electron-volts.

Hence \(W_0=2\cdot10^6\) electron-volts, which in general agrees with the experimental data on the excitation threshold of neutrons from B.

IX. Absorption and scattering of neutrons

Extremely important for clarifying the question of the nature and structure of the neutron itself and the character of the forces of interaction between neutrons and atoms of matter is the study of the absorption of neutrons as they pass through matter.

Already from the very first experiments of Bothe and Becker \(^{17,18}\) it became clear that neutrons, like \(\gamma\)-rays, do not have a definite range. However, the absorption of \(\gamma\)-rays differs greatly from the absorption of neutrons. The absorption of \(\gamma\)-rays is explained, chiefly, by Compton scattering on extranuclear electrons. Therefore the absorption coefficient, calculated by the Klein–Nishina formula, is determined chiefly by the number of peripheral electrons and increases with increasing \(Z\). As was already indicated, from the very first work with neutrons it became clear that the Klein–Nishina formula is inappli-

NEUTRONS

to the absorption of neutrons. In one of their papers,^29 Curie and Joliot showed that the absorption of neutrons, in contrast to γ-rays, is determined not by the number of electrons but by the number of nuclei of the atoms of the absorber. This is also confirmed by Dee’s experiments,^38 described above, on collisions of neutrons with electrons.

Further experiments on the passage of neutrons through matter showed that, in addition to absorption of neutrons, there is also scattering. Auger,^46 working with a Wilson chamber, found that the number of recoil atoms knocked out by neutrons increases by a factor of 2–3 if the Wilson chamber is surrounded on all sides by a large amount of copper (about 100 kg). This phenomenon is apparently explained by the fact that, in addition to direct neutrons, neutrons scattered by the copper also enter the chamber; without the scatterer, these would have passed by. Auger also explains by neutron scattering the origin of the group of slow protons observed by him^26,46 in the Wilson chamber, with a range of < 20 mm (30,000–50,000 V-electron). Surrounding the chamber with a paraffin screen 5–10 cm thick, Auger observed a strong decrease in the number of slow protons, which confirms the data of Curie and Joliot on the strong absorption of neutrons by hydrogen. Placing a scatterer near the chamber, Auger again observed an increase in the number of short tracks. Their number then was approximately equal to the number of short tracks that was observed without the paraffin screen and without the scatterer. However, the table he gives, showing the number of protons in 200 photographs in each series of experiments, does not give a sufficiently clear picture, since the number of protons in general is too small.

TABLE 2

	Without scatterer	Without scatterer	With scatterer and paraffin screen	With scatterer and paraffin screen	With scatterer and paraffin screen	With scatterer and paraffin screen
	without paraffin screen	with paraffin screen	Cu	Al	Fe	Pb
Long tracks . .	13	8	10	10	16	23
Short tracks .	6	2	6	7	5	9

Auger believes that the slow protons are knocked out by neutrons that have lost from 90 to 100% of their velocity in inelastic collisions with the nuclei of the atoms of the scatterer. The nuclei excited in this process return to the normal state with the emission of γ-quanta. It may be supposed that the energy level of the excited nucleus is somewhat lower than the mean energy of the incident neutrons. The remainder of the neutron energy after the excitation of such a nucleus is still sufficient to produce a proton with a small range. It may also be supposed that the neutron transfers its energy

not by one nucleus, but by several. If the energy of an already slowed neutron proves to be less than the excitation energy of the nucleus of the scattering atom, then such a neutron can undergo only elastic collisions with the heavy atoms of the scatterer and must be absorbed only weakly in it. Conversely, in collisions with protons such neutrons must be strongly absorbed, which is also confirmed in experiments with a paraffin screen. Feser, however, believes \(^{78,11}\) that these slow protons are knocked out by slow neutrons arising in the resonant disintegration of Be by \(\alpha\)-particles with an energy of \(1.4 \cdot 10^6\) V-electron. It is also possible that they are produced in the disintegration of the \(\mathrm{Be}^9\) nucleus without capture of the incident \(\alpha\)-particle. In his latest work \(^{47a}\), Ože indicates that at least part of these slow neutrons arises as a result of such disintegration of \(\mathrm{Be}^9\)*.

Denning and Pegram \(^{48}\) studied the scattering of neutrons by means of an ionization chamber, using a powerful beam of neutrons of the order of \(10^5\) per sec., obtained from Be bombarded by \(\alpha\)-rays from 1200 millicuries of Ra emanation (in \(\alpha\)-rays equivalent to 3600 millicuries Po). Their results first of all confirm the presence of strong neutron scattering. Thus, for example, they found that paraffin in the form of a cylinder 3 cm in diameter and 4 cm long reduces the number of neutrons registered by the ionization chamber twice as strongly as a large paraffin plate 4 cm thick.

To obtain quantitative data on scattering, Denning and Pegram used a ring-shaped scatterer with a mean radius of 15.5 cm and a cross-sectional area of 25 cm\(^2\). This ring was arranged so that its axis coincided with the axis of the ionization chamber. To absorb the direct neutron beam, a lead cylinder 19 cm long was placed in its path. The distance from the source to the chamber was 31.5 cm.

Table 3 gives the relative scattering in numbers of neutrons registered by the ionization chamber per minute for different angles.

TABLE 3

Material	46° ± 15°	51° ± 20°	82° ± 27°	125° ± 25°	151° ± 15°
Paraffin **	3,68	,65	2,18	1,48	0,21
Water	3,59	3,45	2,50	1,48	0,56
Carbon	2,96	2,17	2,01	1,62	0,79
Lead	2,75	2,52	2,49	1,71	0,58

* L. Meitner and K. Philipp, in their latest work cited above, did not find neutrons with energies less than 195,000 V-electron in the radiation from Be (note added in proof).

** See the scattering by paraffin on p. 356 ff.

This table shows that, with increasing atomic weight of the scatterer, the scattering as a whole becomes more uniform.

It follows from these data that, per unit solid angle and per unit volume of scatterer, at an angle of \(45^\circ\) lead scatters \(2.28\cdot 10^{-2}\), and at an angle of \(125^\circ\), \(1.2\cdot 10^{-2}\) of the incident intensity; carbon scatters \(2.12\cdot 10^{-2}\) at an angle of \(45^\circ\), and \(0.96\cdot 10^{-2}\) at an angle of \(125^\circ\).

Fig. 8.

Fig. 9.

Denning and Pegram believe that these figures are accurate to within 15%.

J. Thibaud and F. Doprè la Tour\(^ {49}\) give absorption curves for a thick (Fig. 8) and a thin (Fig. 9) layer of lead. The curves were obtained with an ionization chamber. The neutron source was an Em Ra + Be preparation. Thus Be was bombarded with \(\alpha\)-particles of very different ranges. A comparison of these curves once again indicates the large role of scattering when neutrons pass through matter. The absorption coefficients of neutrons in lead, calculated from the curve in Fig. 9 for different absorber thicknesses, are given in Table 4 and in Fig. 10.

TABLE 4

\(X\) (cm Pb)	1	3	5	7	9	13	19
\(M\)	0.3	0.2	0.15	0.12	0.10	0.075	0.069

Fig. 10.

Thibaud and Doprè la Tour themselves consider the figures 0.075 and 0.069 less reliable than the others. Analytically, the curve of Fig. 10 can be expressed by the equation \(\mu x^{1/2}=0.3\). This course of the curve can also be explained equally well on the basis of the assumption

about the continuous spectrum of neutrons scattered when passing through an absorber and assuming that in the neutron radiation there are two components with absorption coefficients \(\mu_1 = 0.4\) and \(\mu_2 = 0.065\).

I. Curie and F. Joliot\(^{19}\), on the basis of their measurements for lead, give the value 0.013 for \(\frac{\mu}{\rho}\), without indicating, however, either the dimensions or the thickness of the absorber.

Absorption in other substances has been investigated less well than in Pb. Tibot and Dupre la-Tour indicate that the curve \(\lg I = f(x)\) for Hg is analogous to the curve for Pb. The curves for medium and light elements approach straight lines. \(\mu\), calculated for absorbers containing the same number of atoms, varies only slightly from element to element.

Fig. 11.

The results of measurements of neutron absorption carried out by Dening and Pegram\(^{47}\) are presented in Fig. 11. The absorbers were taken in the form of cylinders 3 cm in diameter; in order to reduce ionization from the \(\gamma\)-rays of Em Ra, the Be radiation was first filtered through 4 cm of Pb. The curves do not give a definite dependence of \(\mu\) on atomic number. Of all the substances investigated, copper has the greatest absorption. The absorption coefficient calculated from these curves is not in complete agreement with the data of Tibot and Dupre la-Tour. For \(\mu\) of Pb for an absorber of 7 cm one obtains the value 0.18, and for an absorber of 20 cm, 0.1.

Tibot and Dupre la-Tour in their work point to one more phenomenon occurring in the absorption of neutrons in lead. It follows from their observations that the absorption of neutrons which produce recoil nuclei of nitrogen in the ionization chamber differs from the general picture of absorption usually determined by measuring the number of protons knocked out by neutrons. When the thickness of the absorber is increased to 7–8 cm, the number of nitrogen recoil nuclei changes almost not at all. For larger thicknesses the number of particles rapidly decreases.

T. W. Bonner\(^{51}\) compared the absorption of neutrons emitted from Be in the direction of the exciting \(\alpha\)-rays (“forward”) with absorption

of somewhat slower neutrons, knocked out opposite to the direction of the α-rays (“backward”). He found that the ionization caused by neutrons emitted “forward” decreases by 43.2% when the neutrons pass through 6 cm of Pb, while the ionization caused by neutrons emitted “backward” decreases by 36.1%. Under the same conditions the ionization caused by neutrons from B (“forward”) decreases by 32%. It follows from these measurements that the faster neutrons are absorbed more strongly than the slower ones. Thus this phenomenon is analogous to the Ramsauer effect in the absorption of slow electrons by gases. These observations have not yet received further confirmation.

The absorption of neutrons knocked out not from Be, but from other elements, has been investigated much less. Besides the preliminary data of Webster ^30, who measured the absorption of the total radiation (neutrons and γ-rays), there are data of I. Curie and F. Joliot ^8, who for neutrons from B found

\[ \frac{\mu}{\rho} = 0.02 \]

for Pb.

On the contrary, as has already been mentioned, T. W. Bonner ^51 found that neutrons from B are absorbed in Pb somewhat less than neutrons from Be. The measurements of de Broglie and Leprince-Ringuet (L. Leprince-Ringuet) ^52 also indicate the same.

Neutrons emitted by Li ^26 are absorbed considerably more strongly. A screen of 5 mm of lead absorbs them almost completely. In paraffin they are absorbed still more strongly than in lead (for the same mass of absorber per unit surface). Likewise, a considerable part of the neutrons emitted by Al is absorbed in 5 mm of Pb ^41. And these neutrons are absorbed in 1 g/cm² of paraffin considerably more strongly than in 1 g/cm² of lead.

In contrast to this, neutrons emitted by F possess very great penetrating power. Even 5 cm of lead do not yet produce a noticeable decrease of ionization ^41. And these neutrons are absorbed in paraffin more strongly than in Pb. According to the measurements of P. Savelyev ^53, a lead screen of 10 g/cm² reduces the intensity of this radiation by only 10%. The same screen made of paraffin produces a reduction of 70%.

The present review of the experimental data on the absorption and scattering of neutrons in matter shows that this question is still far from clarified. There is likewise no clarity in the question of the dependence of the absorption coefficient on the atomic number and density of the absorber. It is possible that the reason for the discrepancies in the experimental data lies in the dependence of the absorption coefficient on the velocity of the neutrons and in the different geometrical conditions of the experiments, which, owing to scattering, can also lead to different results. In addition, in investigations with Em Ra a distorting influence may also be exerted by the ionization caused by secondary electrons.

X. Theory of the Passage of Neutrons Through Matter

The theory of the passage of neutrons through matter has been studied by J. Dethush \(^{61,9}\), Massey \(^{61}\), I. Solomon \(^{65,66}\), I. Rabi \(^{57}\), J. Platt \(^{67}\), E. Wigner \(^{68}\), and G. Wick \(^{69}\).

The process of interaction of a neutron with an atomic nucleus is determined by the potential fields of the nucleus and of the neutron. Therefore, in considering this process it is necessary to make certain assumptions about the field of the neutron, which in turn is connected with assumptions about its structure. All these works regard the neutron as a close combination of a proton with an electron. But under such close interaction the velocities of the electron must be so large that relativistic effects cannot be neglected. Thus the question of the structure of the neutron and of its collisions with atomic nuclei belongs to the still-unconstructed relativistic quantum theory. Therefore all existing theoretical works on this question should be regarded only as preliminary.

Massey attempted to avoid this difficulty by representing the neutron as a hydrogen atom “in a nearly zero quantum state.” Physically this means that the motion of the electron is considered not in the field of the proton, but in the field of a high effective charge \(Z\). To such an atom Massey applies the approximate Born theory of collisions \(^{70}\). The field of the neutron is then given by the formula:

\[ V(r)=e^2\left(\frac{1}{r}+\frac{Z}{a_0}\right)e^{-\frac{2Zr}{a_0}}, \tag{3} \]

where \(a_0\) is the radius of the first Bohr orbit of hydrogen, and \(\frac{Z}{a_0}\) is the “radius” of the neutron. If it is assumed that the electron and proton, down to distances small in comparison with the dimensions of the neutron, behave as point charges, then the collision of any particle with the neutron may be described as the scattering of this particle by the field \(V(r)\).

For the effective collision cross section, Faxén and Holtsmark \(^{71}\) give the expression:

\[ Q=\frac{4\pi}{k^2}\sum_n (2n+1)\sin^2\delta_n, \tag{4} \]

where \(k=\frac{2\pi Mv}{h}\) (\(M\) is the reduced mass of the system; \(v\) is the relative velocity of the particles), and \(\delta_n\) are the phase differences of the waves in scattering. If \(\delta_n\) is small compared with unity, it may be calculated by Mott’s formula \(^{71}\):

\[ \delta_n=\frac{4\pi M}{h^2}\int_0^\infty rV(r)\{I_{n+\frac{1}{2}}(kr)\}^2\,dr. \tag{5} \]

Assuming in (4) \(\sin \delta_n=\delta_n\), with the aid of (5) one can perform the summation. This gives Born’s formula:

\[ Q=\frac{8\pi^{2}M^{2}}{h^{4}}\int \left| \int V(r')e^{2ikr'\cos\theta'\sin\frac12\theta}\,d\omega' \right|^{2}\sin\theta\,d\theta, \tag{6} \]

On the basis of this formula Massey calculates the effective cross section of neutron collision.

Substituting the experimental values for the mass and velocity of the neutron, we obtain:

\[ k=4.76\cdot 10^{12}\ \mathrm{cm}^{-1} \]

and hence:

\[ Q=5.5\cdot 10^{-25}\sum_{n}(2n+1)\sin^{2}\delta_n. \]

Substituting Chadwick’s value found above, \(7\cdot 10^{-13}\ \mathrm{cm}\), for the collision radius of the neutron, we obtain:

\[ Q=1.54\cdot 10^{-24}\ \mathrm{cm}^{2}. \]

Hence:

\[ \sum_{n}(2n+1)\sin^{2}\delta_n=2.8. \]

Thus the upper limit for \(\sin^{2}\delta_n\) will be \(\dfrac{2.8}{2n+1}\). Massey assumes that all phase differences, with the exception of \(\delta_0\), are small in comparison with unity and that they may be expressed with sufficient accuracy by Mott’s formula. Therefore, in order to obtain the exact value of the effective transverse section from \(Q\), as given by Born’s formula (6), one must subtract the correction determined by \(\delta_0\). Massey finds this correction by replacing in (4) \(\sin\delta\) by \(\delta_0\) from (5) and subtracting \(\sin^{2}\delta_0\). Thus we have:

\[ Q=\frac{8\pi^{2}M^{2}}{h^{4}} \int_{0}^{\pi} \left| \int_{0}^{\infty} V(r')e^{2ikr'\cos\theta'\sin\frac12\theta}\,d\omega' \right|^{2} \sin\theta\,d\theta - \frac{4\pi}{k^{2}} \left[ \frac{16\pi^{4}M^{2}}{h^{4}} \left\{ \int_{0}^{\infty} rV(r)\bigl(J_{\frac12}(kr)\bigr)^{2}\,dr \right\}^{2} -\sin^{2}\delta_0 \right]. \tag{7} \]

The field of interaction of the neutron with a nucleus of charge \(Z'\), according to (3), is determined from the formula:

\[ V(r)=Z'e^{2}\left(\frac{1}{r}+\frac{Z}{a_0}\right)e^{-\frac{2Zr}{a_0}}. \tag{8} \]

Substituting (6) into (5) and integrating, we obtain:

\[ Q=\frac{4\pi^{5}M^{2}e^{4}Z^{2}}{k^{4}h^{4}} \left[ \frac{1}{3}\frac{48x^{4}+72x^{2}+28}{x^{2}(x^{2}+1)^{3}} -4\left\{\lg\left(1+\frac{1}{x^{2}}\right)+\frac{1}{1+x^{2}}\right\}^{2} \right] +\frac{4\pi}{k^{2}}\sin^{2}\delta_{0}. \tag{9} \]

Here \(x=\dfrac{Z}{ka_{0}}\).

To determine the lower limit \(Z\) we may drop in the last formula the term \(\dfrac{4\pi}{k^{2}}\sin^{2}\delta_{0}\). Substituting for \(Q\) the value \(1.54\cdot 10^{-24}\ \mathrm{cm}^{2}\) (for the collision of a neutron with lead), we obtain \(x>1.0\), and hence for the effective charge of the neutron nucleus \(Z>25000\).

For light elements \(\delta_{0}=3.5\,\dfrac{Z'}{80}\).

Therefore the correction term in Bohr’s formula in this case drops out, and we find that for light elements \(Q\) should be proportional to \(Z'^{2}\). However, the experiments of I. Curie and F. Joliot \(^{8}\), Dunning and Pegram \(^{48}\), and Chadwick \(^{17}\) show that the absorption of neutrons varies more slowly with \(Z'\). Thus, for example, Chadwick found for the collision radius with carbon the value \(3.5\cdot 10^{-13}\ \mathrm{cm}\), and for Ar—\(5.5\cdot 10^{-13}\ \mathrm{cm}\). Bonner \(^{60}\) also found that for light elements \(Q\) is approximately proportional to \(Z'\).

XI. Scattering of Protons by Neutrons

In connection with the new views on the structure of the atomic nucleus, the question of the interaction of the neutron with the proton becomes especially interesting. For the effective collision cross section of a neutron with a proton, formula (9) gives the following approximate expression:

\[ Q\simeq \frac{16\pi^{5}M^{2}e^{4}a_{0}^{4}}{h^{4}Z^{4}}, \tag{10} \]

where \(M\) is the mass of the proton. Taking \(Z>25000\), we obtain that the radius of the effective collision cross section should be less than \(1.4\cdot 10^{-14}\ \mathrm{cm}\). This is considerably smaller than the observed quantities. Thus, for example, L. Meitner and K. Philipp \(^{58}\), assuming that \(10^{6}\) \(\alpha\)-particles of Po eject 30 neutrons from Be, and observing with a Wilson chamber the number of protons knocked out by neutrons within a certain solid angle in a known mass of hydrogen, calculated that the radius of the effective collision cross section of a neutron with a proton must be greater than \(8\cdot 10^{-13}\ \mathrm{cm}\). Assuming, however, in formula (4) a constant different from 0 and choosing this constant in a suitable manner, Chadwick succeeded \(^{7}\) in obtaining for the effective collision radius the value \(10\cdot 10^{-13}\ \mathrm{cm}\), which is already in significantly better agreement with the experimental data. If we assume that the neutron

represents a certain dipole, and its field is determined by the expression \(\alpha e^2/r^2\), where \(\alpha\) is the dipole moment; then, substituting this expression in formula (5) and assuming that the right-hand side is small in comparison with unity, we obtain:

\[ \frac{2\pi^2 M\alpha e^2}{h^2\left(n+\frac12\right)} \ll 1. \tag{11} \]

If \(\alpha\) is less than \(2.8\cdot 10^{-24}\ \mathrm{cm^3/sec}\), then for \(Q\) one may apply Bohr’s formula (6).

For the distribution of the ejected protons over angles, formula (6) gives the expression:

\[ I(\varphi)\sin 2\varphi\,d\varphi = \frac{4\pi^5\alpha^2 e^4 h^2}{v^2}\,\operatorname{tg}\varphi\,d\varphi. \tag{12} \]

Thus, if the neutron is a dipole, then the maximum number of protons will be emitted at an angle of \(90^\circ\) to the direction of motion of the neutron.

If, however, the field of the neutron is determined by formula (3), then the distribution of protons over angles is given by the expression:

\[ N(\varphi)\sin 2\varphi\,d\varphi = \frac{2\pi^5 M^2 e^4 a_0^4}{h^4} \frac{2Z^2+k^2a_0^2\cos^2\varphi} {\left(Z^2+k^2a_0^2\cos^2\varphi\right)^2} \sin 2\varphi\,d\varphi. \tag{13} \]

In this case the number of ejected protons tends to zero as \(\varphi\) tends to \(0^\circ\) and to \(90^\circ\).

E. Wigner\(^{68}\) applied to the study of the scattering of neutrons by protons the method of Faxén and Holtsmark\(^{71}\). The incident plane monochromatic wave

\[ e^{ipz/h} \]

is expanded into a series of spherical waves:

\[ e^{ipz/h}=a_0\psi_0+a_1\psi_1+a_2\psi_2+\cdots \tag{14} \]

To calculate the scattering, Wigner assumes that the potential energy of the system is equal to \(-v\) when the distance between the particles \(r<a\), and is equal to zero when the distance \(r>a\). For the scattered wave as \(r\to\infty\) he obtains the expression:

\[ r^{-1}e^{ip_a^*(r-a)/h} \left( -\frac{h}{\sqrt{M\varepsilon+ip_a}} -\frac{a}{2} + \frac{0.21\,ip\,a^2}{h}\cos\theta \right). \tag{15} \]

Here \(p_a^*\) is the momentum in the coordinate system referred to the center of gravity of the system, \(\varepsilon\) is the binding energy of the proton with the neutron (\(\varepsilon\) can be determined from the mass defect of \(\mathrm{H}^2\)), and \(M\) is the mass of the proton. Hence, for the intensity of the beam of neutrons scattered in the direction \(\theta\), Wigner finds:

\[ I_\theta= \left( \frac{h\sqrt{M\varepsilon}}{M\varepsilon+p_a^2} +\frac{a}{2} \right)^2 + \left( \frac{p_a h}{M\varepsilon+p_a^2} + \frac{0.21\,p_a a^2}{h}\cos\theta \right)^2. \tag{16} \]

From this formula it follows that, if \(p_a\) is not very small in comparison with \(\sqrt{Me}\) (which in general agrees with the experimental data) and

\[ \frac{0.21a^2(p_a^2+Me)}{h^2} \]

is not very small in comparison with unity, then in collisions with protons the greater part of the neutrons will be scattered at an angle \(\vartheta=0\) with respect to the incident beam.

For the cross section of collision Wigner obtains the expression:

\[ q=\frac{8\pi h^2}{M}\,\frac{1+a\sqrt{Me}/h}{E+2\varepsilon}, \tag{17} \]

where \(E\) is the kinetic energy of the neutron. This formula gives values for \(q\) more or less in agreement with the experimental data only in the case when one puts \(a=0\) (physically this corresponds to an infinitely large value of the potential in an infinitely narrow region).

Experimentally, the question of the angular distribution of the protons knocked out by neutrons was studied by P. Auger and G. Monod-Herzen \({}^{73}\) and by F. Kirchner \({}^{75}\). In addition, as indicated above, Dunning and Pegram \({}^{48}\) determined the scattering of neutrons in paraffin. However, the results of the experiments of Dunning and Pegram were probably affected by the scattering of neutrons by the carbon contained in the paraffin.

Fig. 12.

In the work of Auger and Monod-Herzen the neutron source was placed outside a Wilson chamber filled with hydrogen. From the photographs the angle \(\theta\) between the direction of motion of the neutron and that of the proton knocked out by it was determined. The curve giving the dependence on the angle \(\theta\) of the total number of protons, with large energy, knocked out at the angle \(\theta\), can approximately be expressed by the formula \(N=a\sin\theta\cos\theta\) (Fig. 12), with an excess of protons at an angle of \(85^\circ\).

Passing to the number of protons knocked out per unit solid angle, we obtain a distribution function which corresponds roughly to the fact that, in the coordinate system connected with the center of mass of the neutron–proton system, there is a uniform angular distribution*.

* In their latest work Meitner and Philipp, without dividing the protons into slow and fast, arrived in general at the same results. Monod-Herzen (J. d. Phys. et le Rad. Ser. VII, V, 95, 1934), repeating his earlier experiments, found that the scattering function for the slow protons decreases more slowly than \(\cos\theta\) (note added in proof).

The results for slow protons obtained by Auger and Monod-Herzen proved still less definite.

In F. Curie’s work the neutron source was placed at the center of a Wilson chamber, on its piston. The source was enclosed in a cylindrical brass casing covered with a thin layer of paraffin, from which the protons were knocked out. Although the neutron source was not a point source, this arrangement made it possible to determine the angle \(\vartheta\) between the direction of motion of the neutron and that of the proton more accurately than could be done in the work of Auger and Monod-Herzen. Only those protons whose tracks reached the walls of the chamber were taken into account. Thus Curie considered only the fastest protons.

Fig. 13.

The results of measurements (after introducing corrections for the geometrical conditions of the experiment) on 160 protons are presented in Table 5 and in Fig. 13.

TABLE 5

Scattering angles \(\vartheta\)	Number of protons knocked out in the solid angle \(\Omega\), at angle \(\vartheta\) to the direction of neutron motion
\(0—10^\circ\)	27.5
\(10—20^\circ\)	19.0
\(20—30^\circ\)	15.8
\(30—40^\circ\)	10.9
\(40—50^\circ\)	13.5
\(50—60^\circ\)	11.5
\(60—70^\circ\)	2.2
\(70—80^\circ\)	1.8

Thus these data of F. Curie indicate a more rapid decrease in the number of protons with increasing angle than follows from the data of Auger and Monod-Herzen.

F. Curie believes that the rapid fall of his curve does indeed exist, but that it still cannot be guaranteed that this is truly ...

tially is a property of the interaction of neutrons with protons, and is not caused by the distribution of neutrons over velocities or by any other causes.

It is possible that the discrepancy between Curie and Auger and Monod-Herzen is explained by the fact that Curie’s results refer to faster protons than those of Auger and Monod-Herzen.

The scattering of neutrons in paraffin at large angles was specially investigated by Li[^76]. To separate the effect caused by neutrons from the effect caused by $\gamma$-rays, Li carried out experiments with ionization chambers filled with Ar and H. (In Ar, $\gamma$-rays produce a significantly larger ionization current than in H. For neutrons this ratio is, in order of magnitude, equal to unity.) These experiments confirmed that a significant fraction of the radiation scattered by paraffin at large angles consists of $\gamma$-rays.

Comparing the number of neutrons scattered by paraffin at large angles with the number of neutrons scattered by a corresponding amount of graphite, Li established that hydrogen does not scatter neutrons at angles greater than $90^\circ$.*

Of great interest is the origin of the $\gamma$-rays observed by Li. At present no process is known by which the origin of these rays could be explained as scattering in paraffin of $\gamma$-rays from Po–Be. Therefore Li assumes that they are produced as a result of the reaction $n^1 + H^1 \to H^2$. From Li’s observations it follows that such a reaction must occur in one quarter of all collisions of a neutron and a proton.

The energy of the quanta of these $\gamma$-rays, determined from absorption in lead, proved to be from 2 to $4 \cdot 10^6$ V-electron, which is in general agreement with the reaction $n^1 + H^1 \to H^2$, if for the mass of the neutron $n^1$ one takes the value 1.0067 found by Chadwick.

Thus, if this communication by Li is confirmed, it will constitute a weighty argument in favor of the neutron mass found by Chadwick.

XII. Splitting of Atomic Nuclei by Neutrons

Owing to the absence of an electric charge in the neutron, there is no potential barrier around atomic nuclei for it. Therefore neutrons are an especially convenient means for splitting atomic nuclei. Neutrons were first studied from this point of view by Feather[^78]. He placed a neutron source (Po–Be), enclosed in a brass shell with a lead lining, inside a Wilson chamber filled with a mixture of 96% nitrogen and oxygen. In 2000 photographs Feather found about 100 ato-

* This was to be expected, since from the application of the laws of conservation of energy and momentum to the collision of a neutron and a proton it follows that the angle between the direction of motion of the neutron after the collision and that of the proton knocked out by it is always equal to $90^\circ$.

neutron recoils of nitrogen and 30 forks formed as a result of the splitting of nitrogen nuclei. In Figs. 14 and 15 two examples of such forks are given. As was to be expected, the relative number of inelastic collisions for neutrons is much greater than for $\alpha$-particles. It is known that $\alpha$-particles give 1 nuclear splitting approximately per 1000 collisions; neutrons—one per 4.

The calculation of the momenta and energies of the particles formed as a result of the splitting of the nitrogen nucleus showed that about half of all forks are formed as a result of the reaction:

Fig. 14.

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

the incident neutron enters into the composition of one of the nuclei formed in this process.* For the remaining forks reaction (a) leads to a violation of the law of conservation of momentum.

Fig. 15.

Feather assumes that in these cases no capture of the neutron occurs, i.e. one of the following reactions takes place:

\[ \begin{aligned} \mathrm{N}^{14} + n^1 &\to \mathrm{C}^{13} + \mathrm{H}^1 + n^1, \tag{b}\\ \mathrm{N}^{14} + n^1 &\to \mathrm{C}^{12} + \mathrm{H}^2 + n^1, \tag{c}\\ \mathrm{N}^{14} + n^1 &\to \mathrm{B}^{10} + \mathrm{He}^4 + n^1. \tag{d} \end{aligned} \]

Harkins, Gans and Newson^79, who carried out similar experiments, believe that reactions (b) and (c) should be rejected, since both tracks forming such a fork are too thick and dense for one of them to be attributed to $\mathrm{H}^1$ or $\mathrm{H}^2$. As for reaction (d), as a result of it there must occur an increase of mass by 0.0077 units. And this corresponds to a loss by the neutron of energy of $(7.1 \pm 4.4)10^6$ electron-volts. In addition, part of the neutron energy must be transferred to the recoil nuclei $\mathrm{B}^{11}$ and $\mathrm{He}^4$ (from 1 to $3 \cdot 10^6$ electron-volts).

In Feather’s experiments only a small fraction of the neutrons could have had energy sufficient to produce such a splitting. Therefore Harkins, Gans and Newson suppose that these splittings proceed according to reaction (a), but are caused by neutrons which have changed the direction of their motion during scattering in the surrounding material. Calculations carried out on the basis of this assumption give more correct values for the neutron energies.

One of the possible methods of resolving this question is the study of the change in the number of such splittings when a scatterer of large mass is placed near the Wilson chamber,

* Fig. 15 refers precisely to this case.

The reaction \(N^{14} + n^1 \to B^{11} + He^4\) is especially interesting because it is, as it were, the reverse of the reaction for obtaining neutrons from boron. \(B^{11} + He^4 \to N^{14} + n^1\) occurs with the absorption of an energy of \(1.4 \cdot 10^6\) V-electrons. Therefore one may expect that in the reverse reaction this energy is released. However, Feather’s experiments showed that in 10 out of 12 cases different amounts of energy are absorbed. This indicates that \(B^{11}\) is formed in an excited state. In passing to the normal state it must give off energy in the form of a \(\gamma\)-quantum. The fact that unequal amounts of energy are absorbed indicates several energy levels of \(B^{11}\). Harkins arrived at analogous results in his work.^80

Subsequently Feather investigated, by means of neutrons, the disintegration of oxygen. In 60 simple recoil tracks he obtained 8 forks corresponding to the reaction of disintegration of an oxygen nucleus with neutron capture, \(O^{16} + n^1 \to C^{13} + He^4\). In all 8 cases from 1 to \(9 \cdot 10^6\) V-electrons of energy were absorbed. In Feather’s experiments we have the first example of the disintegration of an oxygen nucleus.

Feather also succeeded in observing one case of disintegration of \(C^{12}\). This reaction is encountered comparatively rarely, since it occurs with the absorption of about \(7.5 \cdot 10^6\) V-electrons, and only a small fraction of the neutrons from Be bombarded by Po \(\alpha\)-rays possess such energy. Harkins, Gans, and Newson^78,79 also obtained several photographs with the disintegration of \(Ne^{20}\) and \(F^{19}\).

The principal difficulties at present encountered in the study of disintegration in the Wilson chamber lie in the insufficiency of the data on the range–velocity curve. It is possible that, with refinement of these data, some of the conclusions made on the basis of these curves will have to be changed.

XIII. Production of Neutrons by Means of Ions Accelerated in an Electric Field

Recently, Crane, Lauritsen, and Soltan^92 applied the technique, developed in recent years, of producing high-velocity positive ions to the production of neutrons from Be. Doubly ionized He atoms were accelerated in a discharge tube by an electric field of \(1\,000\,000\) V, obtained from a cascade transformer. The artificial \(\alpha\)-particles thus obtained struck Be and caused the emission of neutrons, whose presence was detected by the discharge of an electroscope lined inside with paraffin. After the first qualitative experiments at voltages of 600,000 and 975,000 V, the authors intend to proceed to the study of the dependence of the neutron yield on the energy of the exciting \(\alpha\)-particles at such, still comparatively small, voltages. Because of the low yield of neutrons, it is very difficult to study this region with radioactive sources, since too large a number of \(\alpha\)-particles is required to obtain a noticeable effect.

In the following work[^93] these same authors, with the aid of their apparatus, subjected Be and Li to bombardment by ions of the hydrogen isotope H². At an ion velocity of 900,000 V and with an ion-current strength of 30 μA, Be gave approximately 100 times more neutrons than can be obtained with the aid of the strongest Po sources existing at the present time.

In all probability, the neutrons were obtained as the result of the following reactions:

\[ \begin{aligned} \mathrm{Be}^{9} + \mathrm{H}^{2} &\to \mathrm{B}^{10} + n^{1},\\ \mathrm{Li}^{7} + \mathrm{H}^{2} &\to 2\mathrm{He}^{4} + n^{1}. \end{aligned} \]

Calculation of the energy balance of these reactions gives, for the neutrons from Be, an energy of \(9 \cdot 10^{6}\) electron-volts, and for the neutrons from Li—\(16 \cdot 10^{6}\) electron-volts.

The splitting of Be with emission of neutrons under bombardment by H² ions was also confirmed in the work of Livingston, Henderson, and Lawrence[^95]. These authors found that, at an ion velocity H² of \(1.3 \cdot 10^{6}\) V, about 10 neutrons occur per \(10^{6}\) H² ions.

In their latest work[^96], Crane and Lauritsen found that Li, under bombardment by protons with energy from 400 to \(800 \cdot 10^{5}\) electron-volts, gives not only α-particles but also neutrons. They suppose that in this case a double reaction takes place: first, 2 α-particles are obtained:

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

with a total energy of \(17 \cdot 10^{6}\) electron-volts; then these α-particles in turn bombard \(\mathrm{Li}^{7}\) and cause splitting with the emission of a neutron:

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

The probability of this second reaction, according to their observations, proved to be about \(2 \cdot 10^{-4}\).

It is possible, however, that the neutrons are emitted as a result of the following process:

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

However, at the present time there are still no data on \(\mathrm{He}^{3}\).

All these results are only preliminary. Nevertheless, on the basis of these experiments one may think that already in the near future, in investigations with neutrons, the α-particles from radioactive sources will be supplanted by ions accelerated in an electric field.

XIV. Neutrons and Positive Electrons

The experiments of Anderson[^97], Blackett, and Occhialini[^98] showed that cosmic rays, when passing through matter, produce particles with positive charge and with a mass of the order of the mass of ...

electron–positrons. Chadwick, Blackett, and Occhialini found \(^{99}\) that positrons also appear under the action of simultaneous bombardment by neutrons and \(\gamma\)-rays. In their experiments the source of neutrons and \(\gamma\)-rays \((\mathrm{Po} + \mathrm{Be})\) was placed outside the Wilson chamber, close against its wall. From inside, a piece of lead was applied to the wall. Photographs taken with a magnetic field of 800 gauss showed that some of the electrons knocked out of the lead are deflected by the magnetic field in the direction in which a negative charge should be deflected, while some are deflected in the opposite direction. In order to prove that these particles were indeed moving from the lead into the interior of the chamber, a metal plate was placed in the chamber. It was possible to obtain several photographs in which the path of the particle is visible both before and after the plate. The curvature of the particle’s track was always smaller between the lead and the plate. This shows that the velocity of the particle was greater precisely on this side of the plate, which means that this particle was indeed positively charged. Thus these experiments show that Be radiation, as well as cosmic rays, is capable of knocking positrons out of matter.

Further experiments by I. Curie and F. Joliot \(^{12}\) showed that, apparently, positrons are knocked out not by neutrons but by \(\gamma\)-rays. Between the Wilson chamber, in which positrons were observed, and the source of neutrons and \(\gamma\)-rays they placed a plate of \(2\ \mathrm{cm}\) Pb. In this case the neutrons were absorbed only by \(1\%\), while the \(\gamma\)-rays from Be were absorbed by \(50\%\). The experiments showed that the number of positive and negative electrons decreased by \(40\%\). Therefore one must think that at least the greater part of the positrons is knocked out not by neutrons, but by \(\gamma\)-rays. This is also indicated by the experiments of Greenberg \(^{100}\), who obtained positrons with the aid of \(\gamma\)-rays of Th \(6''\).

Fig. 16.

G. Locher \(^{102}\), working with an apparatus similar to the well-known apparatus of Blackett and Occhialini, by means of which positrons were discovered, but with three Geiger–Müller counters arranged not in one line, found that cosmic rays knock out not only positrons but also neutrons. The apparatus was surrounded by a large quantity of lead, copper, and iron. Fig. 16 shows one of the photographs obtained by G. Locher; \(N_1\), \(N_2\), and \(N_3\) are recoil atoms of argon, knocked out by neutrons. Comparison of these tracks with recoil atoms of argon knocked out by neutrons from \((\mathrm{Po} + \mathrm{Be})\) reveals their complete similarity.

In all probability, these neutrons arise in the splitting by cosmic rays of the nuclei of atoms of the substance surrounding the Wilson chamber.

Auger and Monod-Herzen[^104] also pointed to the appearance, in a Wilson chamber surrounded by a large amount of matter, of tracks which by their character cannot be explained by radioactive contaminations.

Similar particles were also observed by other authors. It should be noted that L. V. Mysovsky[^105], soon after the discovery of neutrons, was already pointing to a possible connection between cosmic rays and neutrons.

XV. The Question of the Structure of the Neutron

As we have already seen, Chadwick, from the reaction \(B^{11} + He^4 \to N^{14} + n^1\), found that the mass of the neutron is less than the sum of the masses of the proton and the electron and is equal to 1.0067. This is quite consistent with the view of the neutron as a combination of a proton and an electron. However, this point of view leads to difficulties. First of all, it turns out that the sum of the masses of two \(\alpha\)-particles and 1 neutron is less than the mass of \(Be^9\) (according to Bainbridge[^106], 9.0153, with \(O = 16\)). Therefore \(Be^9\), from this point of view, should be radioactive. R. Langer and R. Wright[^107] believed that they had indeed succeeded in detecting the radioactivity of \(Be\). However, subsequent experiments[^108],[^109],[^110] showed that this is an error.* The next difficulty is that this point of view is unable to explain why the electrons introduced do not attract themselves to the nucleus and do not combine there with protons to form neutrons. In particular, it is not clear why the hydrogen atom does not turn into a neutron with the release of the corresponding amount of energy.

The following difficulty consists in the fact that, in order to explain why, for example, the \(Be^9\) nucleus has spin \(\frac{1}{2}\cdot \frac{h}{2\pi}\),[^111] one has to assume that the neutron too possesses this value of the spin and, consequently, obeys Fermi–Dirac statistics. On the other hand, it is known that the rotational moment of a composite particle consisting of an even number of elementary particles must be an even multiple of the rotational moment of an elementary particle \(\left(\frac{1}{2}\cdot \frac{h}{2\pi}\right)\). Therefore a neutron consisting of a proton and an electron would have to have spin 0 or \(\frac{1}{2\pi}\).

The discovery of positrons made it possible to regard not the neutron, but the proton, as a composite particle. According to this hypothesis, the proton consists of a neutron and a positron. The main argument in favor of this point of view is the value of the neutron mass at which I. Curie and F. Joliot[^112] arrived. They pro—

* This, of course, does not exclude the possibility that \(Be\) is nevertheless radioactive, but with a considerably longer half-life than Langer and Wright supposed. It is possible that this explains the presence of helium in beryllium minerals.

follow from the supposition that, when boron is bombarded by \(\alpha\)-particles, the neutrons emitted are not the boron isotope \(\mathrm{B}^{11}\), as Chadwick assumes, but the isotope \(\mathrm{B}^{10}\):

\[ \mathrm{B}^{10}+\alpha+W_{\alpha}=\mathrm{C}^{13}+n^{1}+\varepsilon^{+}+W_{1}, \]

where \(\varepsilon^{+}\) is the mass of the positron, and \(W_{1}\) is the kinetic energy of all the particles after the reaction. As is known, besides this reaction, \(\mathrm{B}^{10}\) can split with the emission of a proton:

\[ \mathrm{B}^{10}+\alpha+W_{\alpha}=\mathrm{C}^{13}+\pi+W_{2}, \]

where \(\pi\) is the mass of the proton and \(W_{2}\) is again the kinetic energy of the particles after the reaction.

Subtracting one equation from the other, we obtain:

\[ W_{2}-W_{1}=n^{1}-\pi+\varepsilon^{+}. \]

Substituting the observed values for the energies and assuming that the mass of the positron is equal to the mass of the electron, we obtain for the mass of the neutron the value \(1.011\) \((\mathrm{He}=4)\). This at once explains the stability and, at the same time, the relative weakness of the \(\mathrm{Be}^{9}\) nucleus. For the energy of neutrons from \(\mathrm{Po}+\mathrm{Be}\) this gives the value \(8\cdot 10^{6}\) electron-volts, which in general agrees with the experimental data, since part of this energy may be emitted in the form of \(\gamma\)-rays.

The difficulty in explaining the absence of transformations of the proton into a neutron remains here as well. The only difference is that it now becomes incomprehensible why the neutron does not transform into a proton. True, purely hypothetically one may suppose, as F. Perrin does\(^{113}\), that such a transformation occurs, but that it simply escapes observation.

With respect to spin, this hypothesis leads to a difficulty in exactly the same way, since it follows from it that the spin of the positron must be equal to zero or to unity, which contradicts Dirac’s theory of the positron.

D. Ivanenko\(^{114}\) points out that the supposition that the proton is capable of “splitting” into a neutron and a positron leads to the conclusion that, as a result of the interaction of a quantum and a neutron, a proton and an electron may be obtained; i.e., if the proton “consists” of a neutron and a positron, then the neutron also “consists” of a proton and an electron.

Indeed, I. Curie and F. Joliot showed\(^{102}\) that a quantum \(h\nu\) is capable of transforming into a pair of electrons—of positive and negative sign. The energy of the quantum must for this be \(>mc^{2}\), where \(m\) is the mass of the electron. Therefore, by attaching the positron thus formed to a neutron, we obtain a proton and an electron; i.e., we have as it were “split” the neutron into a proton and an electron. By attaching the electron to the proton thus formed, we again obtain a neutron, and so on.

At the present time it is still impossible to say definitively which of the two points of view on the mass of the neutron—Chadwick’s or Curie-Joliot’s—is correct. Both have arguments for and against them. But in any case the fact that Be shows no radioactivity is a weighty argument in favor of Curie-Joliot.

A third value for the mass of the neutron was obtained by Lawrence, Livingston, and Lewis[^115] from their experiments, in which plates of various elements were bombarded by nuclei of the hydrogen isotope H². They found that with such bombardment, at an ion energy of H² of \(1.2 \cdot 10^{6}\) V-electrons, protons with a range of 18 cm are obtained (which corresponds to an energy of \(3.6 \cdot 10^{6}\) V-electrons).

When the energy of the bombarding H² ions was changed, the energy of the protons changed by the same amount.

The simplest explanation of these experiments is that, upon collision with a heavier nucleus, H² splits into a proton and a neutron, the kinetic energy of H² being imparted to the proton, while the energy released in the splitting of H² is distributed equally between the proton and the neutron.

These conclusions were also confirmed in a subsequent note by Livingston, Henderson, and Lawrence[^94], who observed an increase in the proton energy to \(5.2 \cdot 10^{6}\) V-electrons when the energy of the H² ions was increased to \(3.0 \cdot 10^{6}\) V-electrons. In addition, these authors observed (from tracks knocked out in the ionization chamber) neutrons produced by such bombardment with H² ions. The number of these neutrons corresponded approximately to what could be expected on the basis of the assumption of the splitting of H² into a proton and a neutron.

From these experiments it follows that the binding energy of H² is equal to \(4.8 \cdot 10^{6}\) V-electrons, which gives, for the mass of the neutron, the value 1.0006, i.e., still less than the mass of the neutron found by Chadwick.

It is clear that the difficulties connected with Chadwick’s value of the mass of the neutron are in this case increased still further.*

XVI. Neutrons in the Theory of the Structure of the Atomic Nucleus

The discovery of neutrons naturally had a great influence on our views concerning the structure of the atomic nucleus. Before the discovery of neutrons it was believed (see, for example, Gamow’s book Radioactivity and the Structure of the Atomic Nucleus) that the nucleus consists of the maximum possible number of \(\alpha\)-particles, from 0 to 3 protons, and so-called intranuclear electrons, the number of which varies from 1 in the case of Li⁶ to 28 for U²³⁸. As is known, the greatest difficulties (β-decay, nonconservation of spin) in the theory of the structure of the nucleus are connected with the presence of these electrons in the nucleus. Therefore Furrie, as early as 1930, proposed that in the nucleus these electrons combine with protons into hypothetical

* In their most recent work (cited above), Meitner and Philipp also arrive at Chadwick’s value for the mass of the neutron. Nevertheless, even at the present time this question cannot yet be considered definitively settled (note added in proof).

then the particles are neutrons. After the experimental discovery of neutrons, the hypothesis of the absence of free electrons in the nucleus received justification. Thus at the present time it is usually considered that the nucleus consists of \(Z\)-protons and \(A-Z\)-neutrons. 2 protons and 2 neutrons may combine into an \(\alpha\)-particle. Moreover, it is possible that the nucleus of the hydrogen isotope \(H^2\) is also included in the composition of the nucleus.

As was indicated, in order to explain the observed moments of nuclei and the fact that the nitrogen nucleus obeys Bose–Einstein statistics, one must assume that neutrons obey Fermi–Dirac statistics \(^{116,\mathrm{I}}\). From this, among other things, it follows that the neutrons present in the nucleus must be arranged on different levels.

Supplementing this picture of the structure of the nucleus with assumptions about the presence of quantum-mechanical exchange forces between a neutron and a proton and between two neutrons, Heisenberg \(^{106}\) and Majorana \(^{118}\) obtained expressions for the Hamiltonian function describing the nuclei of atoms (for more details on this see Gamow’s article in Usp. Fiz. N. \(^{117}\)).

Assuming that, for decay, the necessary and sufficient condition is the positivity of the energy balance, and introducing the hypothesis that the works of extracting a neutron and a proton from the nucleus are linear functions of the ratio of the number of neutrons in the nucleus to the number of protons, Heisenberg arrives at the following formulas, determining the stability of the nucleus with respect to \(\alpha\)- and \(\beta\)-decay:

\[ \frac{n_1}{n_2} \geq C_1' + C_2' \frac{n_2}{\sqrt[3]{n_1+n_2}} \tag{18} \]

and

\[ \frac{n_1}{n_2} \leq C_1 + C_2 \frac{n_2}{\sqrt[3]{n_1+n_2}} . \tag{19} \]

Here \(n_1\) and \(n_2\) are the numbers of neutrons and protons in the nucleus. \(C_1\) and \(C_2\) are constants. Thus it follows that in a certain region of the ratios \(\frac{n_1}{n_2}\) the nucleus becomes unstable and begins to decay, emitting either an \(\alpha\)-particle or an electron. This picture explains rather well the alternation of two \(\beta\)- and one \(\alpha\)-decay in the region of radioactive elements.

Nevertheless, such essential questions as the spin of the neutron, the interaction of neutrons with protons and with one another, the appearance of an electron in \(\beta\)-decay, the continuity of \(\beta\)-spectra, etc., remain unresolved.

Assuming that the complex particle is the proton and not the neutron, we arrive at a different view of the structure of the atomic nucleus. According to J. Perrin \(^{119}\), all nuclei consist of neutrons and positrons, partially bound into intermediate nuclei: protons, nuclei of the hydrogen isotope, and \(\alpha\)-particles. There are no electrons in the nucleus; \(\beta\)-decay from this point of view is explained as the transformation of the quantum \(h\nu\) into a “pair”

(electron and positron) with subsequent capture of the positron into the composition of the nucleus. Perrin believes that such a pair arises in the nucleus or near it at the expense of intranuclear or extranuclear energy. The positron, combining with one of the neutrons, enters into the composition of the nucleus, while the electron flies off, forming a β-ray. The difficulties with this theory are, apparently, the same as with the preceding one.

BIBLIOGRAPHY

General articles and reviews

1. E. Rutherford, Proc. Roy. Soc. A. 97, 374, 1920; for translation see Uspekhi fizicheskikh nauk, vol. II, issue 2, 1920.
2. G. Sournier, Journ. de Phys. 1, 194, 1930.
3. J. Chadwick, Nature 129, 312, 1932.
4. J. Chadwick, Proc. Roy. Soc. A. 136, 692, 1932; for translation see Uspekhi fizicheskikh nauk, vol. XII, issue 6, 1932.
5. E. V. Shpolsky, Uspekhi fizicheskikh nauk, vol. XII, issue 4, 1932.
6. W. D. Harkins, The neutron, the element neuton and a nuclear exclusion principle.
7. J. Chadwick (Bakerian Lecture), Proc. Roy. Soc. A. 142, 1, 1933.
8. I. Curie et F. Joliot, L’existence du Neutron, Paris 1932.
9. I. L. Destouches, Etat actuel de la théorie du Neutron, Paris 1932.
10. Leprince-Ringuet, Les transmutations artificielles etc., Paris 1933.
11. N. F. Mott, Handbuch der Phys. Bd. XXIV, I.
12. Report by I. Curie et F. Joliot at the Solvay Congress, 1933.
13. R. Kh. Fauler, Uspekhi fizicheskikh nauk, vol. XIII, issue 5, 1933.
14. M. P. Bronshtein, Uspekhi fizicheskikh nauk, vol. XIII, issue 5, 1933.
15. I Curie et F. Joliot, Journ. de Phys. 1, 21, 1931.
16. W. Bothe, Naturwiss. 21, 825, 1933.
17. W. Bothe u. H. Becker, Zs. Physik 66, 289, 1930.
18. H. Becker u. W. Bothe, Naturwiss. 19, 753, 1931.
19. I. Curie, C. R. 193, 1412, 1931.
20. F. Joliot, C. R. 193, 1415, 1931.
21. H. Becker u. W. Bothe, Naturwiss. 20, 349, 1932.
22. I. Curie et F. Joliot, C. R. 194, 273, 1932.
23. I. Curie et F. Joliot, C. R. 194, 876, 1932.
24. de Broglie, F. Dupré la Tour, L. Leprince Ringuet et I. Tibaud, C. R. 194, 1037, 1932.
25. I. Curie et F. Joliot, Nature 130, 57, 1932.
26. P. Auger, C. R. 194, 877, 1932.
27. P. Savel, Journ. de Phys. 10, 609, 1933.
28. R. C. Webster, Nature 129, 402, 1932.
29. I. Curie et F. Joliot, C. R. 194, 1229, 1932.
30. H. C. Webster, Proc. Roy. Soc. A. 136, 428, 1932.
31. H. Becker u. W. Bothe, Zs. Physik. 76, 421, 1932.
32. H Becker u. W. Bothe, Naturwiss. 20, 757, 1932.
33. G. Kirsch u. F. Rieder, Wiener Anz. 141, 1932.
34. E. Rasetti, Naturwiss. 20, 252, 1932.
35. I. Curie et F. Joliot, C. R. 194, 2208, 1932.
36. Chadwick, Constable a. Pollard, Proc. Roy. Soc. A. 130, 463, 1931.
37. Bainbridge, Phys. Rev. 43, 103, 1933.
38. P. L. Dee, Proc. Roy. Soc. A. 136, 727, 1932.

1. L. Meitner u. K. Philipp, Naturwiss. 21, 286, 1933.
2. Rasetti, Zs. Physik. 78, 165, 1932.
3. I. Curie et F. Joliot, C. R. 196, 397, 1933.
4. M. Blau u. H. Wambacher, Wiener Anz. 22, 251, 1932.
5. Kirsch u. Rieder, Wiener Ber. 141 (2a) 501, 1932.
6. G. Kirsch u. W. Slonek, Naturwiss. 21, 62, 1933.
7. G. Kirsch u. F. Rieder, Wiener Anz. 8, 68, 1932.
8. P. Auger, C. R. 195, 234, 1932.
9. P. Auger, C. R. 196, 170, 1933.
   47a. P. Auger, Journ. de Phys. 12, 719, 1933.
10. J. R. Dunning a. G. B. Pegram, Phys. Rev. 43, 397, 1933.
11. J. Thibaud et Dupré la Tour, C. R. 195, 655, 1932.
12. J. Thibaud et F. Dupré la Tour, C. R. 195, 1647, 1932.
13. T. W. Bonner, Phys. Rev. 44, 235, 1933.
14. de Broglie, L. Leprince-Ringuet, Nature 130, 315, 1932.
15. P. Savel, C. R. 196, 1482, 1933.
16. I. Curie et F. Joliot, C. R. 194, 708, 1932.
17. de Broglie et L. Leprince-Ringuet, C. R. 194, 1616, 1932.
18. P. Auger et G. Monod-Herzen, C. R. 196, 543, 1933.
19. J. I. Rabi, Phys. Rev. 43, 838, 1933.
20. L. Meitner u. K Philipp, Naturwiss. 20, 929, 1932.
21. I. Curie et F. Joliot, Journ. de Phys. 6, 278, 1933.
22. T. W. Bonner, Phys. Rev. 43, 871, 1933.
23. J. L. Destouches, C. R. 194, 1909, 1932.
24. H. S. W. Massey, Nature 129, 469, 1932.
25. H. S. W. Massey, Nature 129, 691, 1932.
26. H. S. W. Massey, Proc. Roy. Soc. 178, 460, 1932.
27. I. Solomon, C. R. 196, 607, 1933.
28. I. Solomon, Journ. de Phys. 4, 210, 1933.
29. J. J. Platinceanu, Zs. Physik. 84, 370, 1933.
30. E. Wigner, Zs. Physik. 83, 253, 1933.
31. G. S. Wick, Zs. Physik. 84, 799, 1933.
32. M. Born, Zs. Physik. 38, 803, 1926.
33. Faxén und Holtsmark, Zs. Physik. 45, 308, 1927.
34. Mott, Proc. Camb. Phil. Soc. 25, 304, 1928.
35. P. Auger et G. Monod-Herzen, C. R. 196, 1102, 1933.
36. F. N. D. Kurie, Phys. Rev. 43, 672, 1933.
37. F. N. D. Kurie, Phys. Rev. 44, 463, 1933.
38. D. E. Lea, Nature, 133, 24, 1934.
39. N. Feather, Nature 130, 237, 1932.
40. N. Feather, Proc. Roy. Soc. 136, 709, 1933. P. I; 142, 689, 1933. P. II.
41. W. D. Harkins, D. M. Gans, H. W. Hewson, Phys. Rev. 44, 529, 1933, P. I.
42. W. D. Harkins, Phys. Rev. 43, 362, 1933.
43. W. D. Harkins, D. M. Gans, H. W. Newson, Phys. Rev. 41, 236, 1933.
44. W. D. Harkins, D. M. Gans, H. W. Newson, Phys. Rev. 43, 384, 1933.
45. F. N. D. Kurie, Phys. Rev. 43, 771, 1933.
46. H. Walke, Nature 132, 242, 1933.
47. Feather, Nature 129, 312, 1932.
48. W. D. Harkins, D. M. Gans, H. W. Newson, Phys. Rev. 43, 236, 1933.
49. G. Kirsch. Naturwiss. 21, 332, 1933.
50. G. Kirsch, Naturwiss 21, 640, 1933.
51. Deseyve, Kirsch und Rieder, Wiener Anz., 7, Jul. 1932.
52. Kirsch und Trattner, Wiener Ber. 142, 71, 1932.
53. W. D. Harkins, D. M. Gans, H. W. Hewson, Phys. Rev. 44, 945, 1933.

1. H. R. Crane, C. C. Lauritsen, A. Soltan, Phys. Rev. 44, 16, 1933.

2. H. R. Crane, C. C. Lauritsen, A. Soltan, Phys. Rev. 44, 692, 1933; see also C. R. 197, 913, 1933.

3. M. S. Livingston, M. C. Henderson, E. O. Lawrence, Phys. Rev. 44, 781, 1933.

4. M. S. Livingston, M. C. Henderson, E. O. Lawrence, Phys. Rev. 44, 782, 1933.

5. H. R. Crane, C. O. Lauritsen, Phys. Rev. 44, 783, 1933.

6. Anderson, Science 76, 238, 1932.

7. Blackett and Occhialini, Proc. Roy. Soc. A. 139, 699, 1933; see translation in Uspekhi Fizicheskikh Nauk, vol. XIII, issue 1, 1933.

8. Chadwick, Blackett, Occhialini, Nature 431, 473, 1933.

9. M. Grinberg. C. R. 197, 318, 1933.

10. I. Curie et F. Joliot, C. R. 196, 1581, 1933.

11. I. Curie et F. Joliot, Journ. de Phys. 8, 494, 1933.

12. G L. Locher, Phys. Rev. 44, 779, 1933.

13. P. Auger et G. Monod-Herzen, C. R. 197, 1406, 1933.

14. L. V. Mysovsky, Uspekhi Fizicheskikh Nauk, vol. XII, issue 5–6, 1932.

15. K. T. Bainbridge, Phys. Rev. 43, 367, 1933.

16. R. M. Langer, R. W. Raitt, Phys. Rev. 43, 585, 1933.

17. Gans, Harkins, Newson, Phys. Rev. 44, 310, 1933.

18. R. D. Evans, M. C. Henderson, Phys. Rev. 44, 59, 1933.

19. W. Libby, Phys Rev. 44, 512, 1933.

20. A. E. Parker, Phys. Rev. 43, 1035, 1933.

21. I. Curie et F. Joliot, C. R. 197, 237, 1933.

22. M. P. Bronshtein, Uspekhi Fizicheskikh Nauk, vol. XIII, issue 5, 1933.

23. D. Ivanenko, Doklady Akademii Nauk SSSR No. 2, 50, 1933.

24. E. O. Lawrence, M. S. Livingston and G. V. Lewis, Phys. Rev. 44, 56, 1933.

25. Heisenberg, Zs. Physik. 77, 1, 1932, Th. I; 78, 156, 1932, Th. II; 80, 587, 1933, Th. III.

26. G. Gamow, Uspekhi Fizicheskikh Nauk, vol. XIII, issue 1, 1933.

27. Ettore Majorana, Zs. Physik. 82, 137, 1933.

28. J. Perrin, C. R. 197, 628, 1933.

29. F. Perrin, C. R. 194, 1343, 1932.

30. F. Perrin, Journ. de Phys. 5, 96, 1932; see also Bull. Soc. Franc. de Phys. 324.

31. Wendell M. Latiener, Journ. Am. Chem. Soc. 54, 2125, 1932.

32. R. F. Bacher and E. U. Condon, Phys. Rev. 41, 683, 1932.

33. D. Iwanenko, Nature 129, 798, 1932.

34. D. Iwanenko, Sow. Phys. 1, 820, 1932.

35. Gapon und Iwanenko, Naturwiss. 20, 792, 1932.

36. E. Gwynne Jones, Nature 130, 580, 1932.

37. P. Acholme, C. R. 196, 614, 1933.

38. Grosse, Phys. Rev. 43, 143, 1933.

39. J. J. Placinteanu, C. R. 196, 1474, 1933.

40. I. Curie et F. Joliot, C. R. 196, 1885, 1933.

41. J. J. Placinteanu, C. R. 197, 539, 1933.

42. D. Iwanenko, Nature 130, 892, 1932.

43. H. Rausch von Traubenberg, Naturwiss. 20, 934, 1932.

44. I. F. Carlson and I. R. Oppenheimer, Phys. Rev. 41, 763, 1932.

45. W. Braunbek, Zs. Physik, 77, 534, 1932.

46. E. N. Gapons, Zs. Physik, 79, 679, 1932, Th. I; 81, 419, 1933, Th. II; 82, 404, 1933, Th. III; 84, 509, 1933, Th. IV and V.

47. S. Flügge, Zs. Physik, 81, 491, 1933.

48. W. Wessel, Zs. Physik, 82, 415, 1933.

1. F. Perrin, C. R. 195, 775, 1932.
2. W. Swietoslawski, Nature 130, 964, 1932.
3. Alfred Lange, Phys. Rev. 43, 620, 1933.
4. F. Perrin, C. R. 195, 236, 1932.
5. D. Meksyn, Nature 131, 336, 1933.
6. N. Thon, Nature 131, 878, 1933.
7. W. Elsasser, Nature 131, 764, 1933.
8. G. W. Todd, Nature 132, 65, 1933.
9. J. Estermann, R. Frisch, O. Stern, Nature 132, 169, 1933.
10. Th. Sexl, Nature 132, 174, 1933.
11. B. Wenkatesacher und T. S. Subbaraya, Zs. Physik 85, 264, 1933.
12. H. Schüler, H. Westmeyer, Naturwiss. 21, 674, 1933.
13. J. J. Placintanu, C. R. 197, 549, 1933.
14. B. M. Sen, Nature 132, 518, 1933.
15. Heisenberg, Report at the Solvay Congress, 1933.
16. H. Mandel, Sow. Phys. 4, 646, 1933.

Miscellaneous articles on neutrons

1. Richard Swinne, Zs. techn. Phys. 13, 279, 1932.
2. P. B. Moon, Nature 130, 57, 1932.
3. S. Pienkowski et J. Starkiewicz, Acta physica Polonica II, 105, 1933.
4. H. Herszfinkiel et A. Wronsberg, Acta physica Polonica II, 157, 1933.
5. W. Meissner u. Steiner, Zs. Physik. 80, 1, 1933.
6. G. Bernardini, Z. Physik. 85, 555, 1933.