Essay on the Development of the Doctrine of the Structure of the Atomic Nucleus

III. Artificial Transmutation of Elements*

G. Gamov, Leningrad

§ 1. In 1921 Rutherford succeeded for the first time, by bombarding nitrogen atoms with fast α-particles (from RaC′), in detecting protons knocked out of nitrogen nuclei; this marked the beginning of research on the artificial transmutation of elements. After nitrogen, Rutherford, together with Chadwick, succeeded in demonstrating the possibility of a similar artificial transmutation for a whole series of other light elements. It turned out that, as the atomic number \(Z\) of the element being bombarded increases, the number of protons knocked out falls sharply on average, so that for elements with atomic number greater than twenty the effect could practically not be observed.

Among the light elements, no effect was observed for elements having only one isotope with an atomic weight divisible by four (helium \(\mathrm{He}_4\), carbon \(\mathrm{C}_{12}\), oxygen \(\mathrm{O}_{16}\)),** nor also for lithium (\(\mathrm{Li}_6, \mathrm{Li}_7\)) and beryllium (\(\mathrm{Be}_9\)). Fairly fast protons are observed in the bombardment of boron (\(\mathrm{B}_{10}, \mathrm{B}_{11}\)), nitrogen (\(\mathrm{N}_{14}\)), fluorine (\(\mathrm{F}_{19}\)), sodium (\(\mathrm{Na}_{23}\)), magnesium (\(\mathrm{Mg}_{24}, \mathrm{Mg}_{25}, \mathrm{Mg}_{26}\)), aluminum (\(\mathrm{Al}_{27}\)) and phosphorus (\(\mathrm{P}_{31}\)). For the remaining light elements: neon (\(\mathrm{Ne}_{20}, \mathrm{Ne}_{22}\)), silicon (\(\mathrm{Si}_{28}, \mathrm{Si}_{29},\)

* See Uspekhi fizicheskikh nauk, 10, 531, 1930 and 12, 31, 1932.
** The recently found isotopes of carbon (\(\mathrm{C}_{13}\)) and oxygen (\(\mathrm{O}_{17}, \mathrm{O}_{18}\)) are present in such small quantities (\(< 0.1\%\)) that there can be no question of observing their disintegration.

Si_{30}), sulfur (S_{32}, S_{33}, S_{34}), chlorine (Cl_{35}, Cl_{37}), argon (A_{36}, A_{40}) and potassium (K_{39}, K_{41}), the ejected protons lie almost at the limit of measurement.

§ 2. In considering the process of knocking out a nuclear proton, one must decide what happens to the α-particle that has knocked it out: it may either be captured by the nucleus and remain in it, or rebound with a smaller energy.

The process of proton ejection in the first case is represented schematically in Fig. 1. From the figure it is seen that, in the case of capture of the α-particle onto some quantum level in the nucleus, the energy of the ejected proton will be greater or less than the energy of the incident α-particle, depending on the relative position of the levels of the proton and of the captured α-particle in the nucleus. Therefore, for a given energy of the incident α-particle, the energy of the ejected proton is fully determined, and we should observe a sharp line in the energy spectrum of the protons. More precisely, we should observe several sharp lines, since, first, the ejected proton may be torn off from various energy levels in the nucleus, and, second, the α-particle that has ejected the proton may itself be captured on one of the higher-lying levels of the nucleus and only later pass to the ground level, emitting the excess of the still remaining energy in the form of hard electromagnetic radiation (such “artificial γ-rays” do indeed often accompany the artificial disintegration of light elements). We shall return to this process somewhat later when considering the experimental data; for now we shall indicate only the following.

Fig. 1.

In light elements there may be up to three free protons (in the presence of a fourth proton a new α-particle is formed), and according to the Pauli principle only in nuclei with atomic weight \(4n+3\) should there be protons located on two different energy levels.

As for α-particles, to which the Pauli principle does not

if we apply it, then in the normal state of the nucleus all $\alpha$-particles must be on the fundamental orbit; in view of this, the ejection of a proton with capture of an $\alpha$-particle onto one of the higher levels must always be accompanied by radiation of the entire energy difference between this level and the fundamental one.

The situation is quite different if the $\alpha$-particle is not captured by the nucleus, but rebounds after knocking out a proton with some loss of energy (Fig. 2). In this process the energy of the proton is always less than the energy of the incident $\alpha$-particle. Depending on the energy given up by the $\alpha$-particle in the collision, the ejected proton may have all energy values from some maximum (the energy of the $\alpha$-particle minus the work of tearing the proton out) down to zero; in other words, we must observe a continuous spectrum. This process is possible in general only in those cases in which the energy of the incident $\alpha$-particle is greater than the binding energy of the proton in the nucleus, which, as we shall see below, apparently usually is not the case.

Fig. 2.

Fig. 3.

The first experimental proof of the capture of an $\alpha$-particle by a nucleus was the work of Blackett, in which Wilson cloud-chamber photographs were obtained of the elementary act of knocking a proton out of a nitrogen nucleus.

One of these photographs is shown in Fig. 3, where a “fork” is clearly visible at the end of the path of one of the $\alpha$-particles. The left branch of the fork represents the path of the proton knocked out of the nucleus, while the right branch is the path of the recoiling product nucleus; the path of the recoiling $\alpha$-particle was not observed. From the length

of these two branches we can determine the velocities of the two particles produced in the collision and verify that the law of conservation of momentum will be satisfied only if we assign to the first particle the mass of a proton, and to the second a mass three units greater than that of the bombarded nitrogen nucleus (i.e., a nitrogen nucleus minus a proton plus an \(\alpha\)-particle). This proves that in this case the \(\alpha\)-particle which knocked out the proton remains captured by the bombarded nucleus. Calculating the kinetic energies of the particles participating in the collision process, Blackett was able to show that, in the transformation of the nitrogen nucleus, there is an energy loss of \(1.7 \times 10^{-5}\) erg; from what has been said above it follows that, in the nitrogen nucleus, the proton level lies lower than the level onto which the captured \(\alpha\)-particle settles.

For other elements (which cannot be investigated in the Wilson chamber), the question of the capture of an \(\alpha\)-particle by the nucleus is resolved by studying the distribution of the velocities of protons in various directions relative to the initial beam of \(\alpha\)-particles; these velocities will differ because the recoil nucleus, in different cases, will receive different amounts of kinetic energy. In the case of capture of an \(\alpha\)-particle, it is easy to see from the law of conservation of momentum that in the direction of the beam of \(\alpha\)-particles the proton velocity will be maximal, and in the opposite direction minimal; if, however, we refer the proton velocities to a moving coordinate system associated with the center of mass of the system, then these relative velocities will be identical in all directions. In Fig. 4, according to Bothe, are plotted the velocities of protons ejected in different directions from boron (boron consists of two isotopes \(B_{10}\) and \(B_{11}\) in the ratio \(1:4\)). Here, as we see, there are three groups of protons, of which one, the slowest, is observed only in the forward direction. The points corresponding to the two fastest groups lie, with great accuracy, on circles with somewhat displaced centers, which indicates that in these two cases we are dealing with capture of an \(\alpha\)-particle by the nucleus. From the displacements

the displacement of the centers of the circles, it should be possible to determine to which of the boron isotopes the observed groups belong. The experiments were carried out with polonium $\alpha$-particles having a velocity of $1.59 \cdot 10^9\ \text{cm/sec}$, so that the velocity of the center of mass in the case of a collision of an $\alpha$-particle with a boron nucleus at rest, $B_{10}$, should be

\[ \frac{4}{4+10}\cdot 1.59\cdot 10^9 = 0.45\cdot 10^9\ \text{cm/sec}; \]

and in the case of $B_{11}$:

\[ \frac{4}{4+11}\cdot 1.59\cdot 10^9 = 0.42\cdot 10^9\ \text{cm/sec}. \]

The observed displacements for the first and second groups of protons prove to be equal to $0.52\cdot 10^9\ \text{cm/sec}$ and $0.38\cdot 10^9\ \text{cm/sec}$; the accuracy of these values, however, is very low, since the proton velocities are calculated from the range by means of the usual Geiger formula, whose accuracy in this case may be called into question.

Fig. 4.

In view of this, the solution of the question of whether the two fast groups of protons belong to different boron isotopes or to one and the same isotope (and to which one) must be postponed until the dependence between the range of the fast protons and their velocity has been clarified more precisely.

In the bombardment of boron, Bothe succeeded in detecting the presence of fairly hard $\gamma$-rays, evidently emitted by the boron nuclei in the process of transformation. The energy of the emitted $\gamma$-quanta, according to a preliminary estimate (from the absorption coefficient), is of the same order as the energy difference between the two fast groups of protons, and their number approximately coincides with the number of ejected protons of the second group. This makes probable the supposition that both fast groups belong to one and the same boron isotope (more probably $B_{11}$, since there is four times as much of it,

weeks \(B_{10}\)), and the emission of a proton of the second group leaves the nucleus in an excited state.

Calculating the energy balance in the transformation of boron nuclei, we obtain for the two fast groups an energy gain of \(+7.4\cdot 10^{-6}\) erg and \(+0.9\cdot 10^{-6}\) erg; this proves once again the fact of capture of the \(\alpha\)-particle, for in a transformation without capture the energy balance must always be negative. The slower group behaves somewhat strangely. Having a negative energy balance of \(-1.8\cdot 10^{-6}\) erg (which in itself proves nothing), it disappears very rapidly with increasing angle and can practically be observed only in the forward direction; this arouses the suspicion that we may here be dealing with a process of knocking out a proton without capture of the \(\alpha\)-particle (though this is still only a suspicion). It is possible, however, that this group corresponds simply to a transformation with capture of the \(\alpha\)-particle by the isotope \(B_{10}\), which in atomic weight is analogous to nitrogen.

When fluorine and aluminum were bombarded with \(\alpha\)-particles, in each case two groups of protons were observed (here too the phenomenon of “resonance splitting” was observed, on which we shall dwell somewhat further on). Since both of these elements each consist of only one isotope (\(F_{19}\) and \(Al_{27}\)), it is clear that we are dealing with excitation of the nucleus when the proton is knocked out. In these cases there were also observed hard \(\gamma\)-rays accompanying the transformation of the nuclei, whose energy and intensity agree satisfactorily with the energy and number of protons of the slower groups. The energy balance in the case of aluminum is \(+4.8\cdot 10^{-6}\) erg and \(+0.4\cdot 10^{-6}\) erg.

In the case of sodium (\(Na_{23}\)) there are also indications of the existence of several groups of protons, although up to the present time it has not been possible to separate them—the protons of maximum velocity give an energy balance of \(+1.6\cdot 10^{-6}\) erg.

For the other light elements that undergo disintegration, a detailed investigation of the velocity spectrum of the protons has not yet been carried out.

In conclusion, a few words must be said about the “first elements”—lithium and beryllium, which, as was indicated

higher, unlike other light elements not of type \(4n\), could not be disintegrated. This is explained, as can be seen from the mass-defect curve at the beginning, by the fact that in them the protons are bound considerably more strongly than in other light elements and require, for knocking out \(\alpha\)-particles, particles of considerably higher velocity than those usually used.

Fig. 5.

Summarizing the experimental results, we must note the following regularities: 1) from nuclei of the type \(4n\) it was not possible to knock out protons; b) from nuclei of the type \(4n+2\) the protons knocked out constitute one group and have a very low energy balance; 3) from nuclei of the type \(4n+3\) the protons knocked out usually split into two groups, of which the first has a comparatively high energy balance.

Fig. 6.

According to the Pauli principle, two protons can be situated on one level, while the third must already occupy the next one. Thus we can arrive at the following scheme for the arrangement of protons on quantum levels in nuclei of various types (Fig. 5).

If we recall what was said above concerning the two possibilities for the formation of different groups of protons, it is easy to conclude that here the principal role is evidently played by the first process, which in the case of nuclei of the type \(4n+2\) (and also \(4n+1\)) leads to the formation of one group of protons, and in the case of nuclei of the type \(4n+3\) to the formation of two groups, of which one has a comparatively high energy balance (the proton is torn from the level \(p^{(1)}\)).

§ 3. We shall now turn to a theoretical consideration of the question of the probability that a bombarding $\alpha$-particle penetrates into the nucleus through the potential barrier surrounding it, restricting ourselves to the simplest case of a “rectangular barrier” (Fig. 6) in order to clarify the general properties of such a process. The distribution of the potential energy as a function of the distance from the center of the nucleus is given as follows:

\[ \left. \begin{aligned} U(r)&=0 &&\text{for } r<r_1\\ U(r)&=U_0 &&\text{for } r_1<r<r_2\\ U(r)&=0 &&\text{for } r_2<r \end{aligned} \right\}. \tag{1} \]

In view of the spherical symmetry of the potential distribution and its independence of time, the solution of the Schrödinger equation:

\[ \nabla^2 \psi-\frac{4\pi i}{h}\frac{\partial \psi}{\partial t} +\frac{8\pi^2 m}{h}U(r)\psi=0 \tag{2} \]

can be represented, introducing spherical coordinates $(V,\varphi,\theta)$, in the form:

\[ \psi(r,\varphi,\theta,t)=\frac{1}{r}X_j(r)\Upsilon_j(\varphi,\theta)e^{\frac{2\pi i}{h}Et}, \tag{3} \]

where $\Upsilon_j(\varphi,\theta)$ is the spherical function of order $j$, $E$ is the energy of the incident particle, and $X_j(r)$ satisfies the equation:

\[ \frac{d^2X}{dr^2} +\frac{8\pi^2m}{h}\left[E-U(r)\right]X +\frac{j(j+1)}{r^2}X=0. \tag{4} \]

Considering only particles incident “straight” upon the nucleus, i.e. putting $j=0$, we reduce (4) to the form:

\[ \frac{d^2X}{dr^2} +\frac{8\pi^2m}{h}\left[E-U(r)\right]X=0. \tag{4'} \]

In order that $\psi$ should not become infinite at $r=0$, it is necessary, according to (3), to subject the solution of equation (4′) to the condition

\[ X(0)=0. \tag{5} \]

The solution of the equation in region I is represented by an ordinary sinusoid. Taking into account condition (5), we must write:

\[ X_I(r)=A\sin kr, \tag{6} \]

where

\[ k=\frac{2\pi}{h}\sqrt{2mE}. \tag{6'} \]

In region II the general solution has the form:

\[ X_I(r)=B_+ e^{+k'(r-r_1)}+B_- e^{-k'(r-r_1)}, \tag{7} \]

where

\[ k'=\frac{2\pi}{h}\sqrt{2m(U_0-E)} \]

and the coefficients \(B_+\) and \(B_-\) must be determined from the condition of continuity of the function \(X\) and its first derivative at the boundary \(r=r_1\). The continuity conditions give:

\[ \begin{aligned} A\sin kr_1&=B_+ + B_-,\\ AK\cos kr_1&=K'(B_+-B_-), \end{aligned} \tag{8} \]

whence

\[ \begin{aligned} B_+&=\frac12 A\left(\sin kr_1+\frac{k}{k'}\cos kr_1\right)\\ B_-&=\frac12 A\left(\sin kr-\frac{K}{K'}\cos kr\right). \end{aligned} \tag{8'} \]

In region III the solution is written in the form:

\[ X_{III}(r)=C_+ e^{+ik(r-r_2)}+C_- e^{-ik(r-r_2)}. \tag{9} \]

The continuity condition at \(r=r_2\) gives:

\[ \begin{aligned} B_+ e^{k'(r_1-r_2)}+B_- e^{-k(r_2-r_1)}&=C_+ + C_-,\\ K'\left(B_+ e^{k(r_2-r_1)}-B_- e^{-k'(r_2-r_1)}\right)&=ik'(C_+-C_-), \end{aligned} \tag{10} \]

whence

\[ \left. \begin{aligned} C_{+} &= \frac{1}{2}\left[ B_{+}e^{k'(r_2-r_1)}\left(1-i\frac{k'}{k}\right) +B_{-}e^{-k'(r_2-r_1)}\left(1+i\frac{k'}{k}\right) \right],\\ C_{-} &= \frac{1}{2}\left[ B_{+}e^{k'(r_2-r_1)}\left(1-i\frac{k'}{k}\right) + B_{-}e^{-k'(r-r_1)}\left(1-i\frac{k'}{k}\right) \right]. \end{aligned} \right\} \tag{10'} \]

Introducing the notation:

\[ \vartheta=e^{k'(r_2-r_1)} \tag{11} \]

we finally obtain for the coefficients \(C_{+}\) and \(C_{1}\) two complex-conjugate expressions:

\[ \left. \begin{aligned} C_{+} &= \frac{A}{4}\sin kr_1\left[ \vartheta\left(1+\frac{k}{k'}\operatorname{ctg}kr_1\right) \left(1-i\frac{k'}{k}\right) + \vartheta^{-1}\left(1-\frac{k}{k'}\operatorname{ctg}kr_1\right) \left(1+i\frac{k'}{k}\right) \right],\\ C_{-} &= \frac{A}{4}\sin kr_1\left[ \vartheta\left(1+\frac{k}{k'}\operatorname{ctg}kr_1\right) \left(1+i\frac{k'}{k}\right) + \vartheta^{-1}\left(1-\frac{k}{k'}\operatorname{ctg}kr_1\right) \left(1-i\frac{k'}{k}\right) \right]. \end{aligned} \right\} \tag{12} \]

Substituting expression (12) into (9), outside the nucleus we obtain two waves of equal amplitude (in the case of real \(E\)), representing the incident and reflected beams of \(\alpha\)-particles.

For the ratio of the amplitude of the incident wave to the amplitude of the oscillations inside the nucleus, we thus obtain:

\[ \frac{C}{A}=\frac{1}{4}\sin kr_1\left[ \vartheta\left(1+\frac{k}{k'}\operatorname{ctg}kr_1\right) \left(1-i\frac{k'}{k}\right) + \vartheta^{-1}\left(1-\frac{k}{k'}\operatorname{ctg}kr_1\right) \left(1+i\frac{k'}{k}\right) \right]. \tag{13} \]

Generally speaking, for arbitrary values of the energy \(E\) of the incident particles this ratio will be a quantity of order \(\vartheta\). This corresponds to the fact that the amplitude of the oscillations inside the nucleus is considerably smaller than the amplitude of the incident

waves; in other words, only a small number of the $\alpha$-particles incident on the nucleus can penetrate into the nucleus.

However, for certain particular values of $E$ the coefficient of $\vartheta$ may vanish, and in this case the ratio of amplitudes will be of order $\vartheta^{-1}$; the amplitude of the oscillations inside the nucleus will be considerably greater than that of the incident wave. Thus the “resonance” values of $E$ can be determined from the equation:

\[ 1+\frac{k}{k'}\operatorname{ctg} kr_1=0. \tag{14} \]

Using (6′) and (7′), we reduce (14) to the form:

\[ \operatorname{tg}\frac{2\pi\sqrt{2m}}{h}\sqrt{Er_1} = -\sqrt{\frac{E}{U_0-E}}, \tag{14′} \]

whence approximately:

\[ E=\frac{n^2h^2}{8r_1^2m}, \tag{14″} \]

where $n$ is an integer.

Expression (14), as is known from the theory of radioactive decay, defines the virtual quantum levels of the $\alpha$-particle inside the nucleus. Therefore we may formulate our result as follows: the probability of penetration of the incident $\alpha$-particle into the nucleus (given by the square of the amplitude) is significantly increased (from $\vartheta^{-2}$ to $\vartheta^2$) if its energy coincides with one of the virtual levels of the nucleus itself. This is the ordinary phenomenon of resonance, which was to be expected in our case on the basis of the wave character of modern quantum mechanics.

The width of the resonance maximum in our problem, as in any other case of resonance, will be determined by the damping coefficient, i.e. will have the order of magnitude $\vartheta^{-2}$. We see, therefore, that for light elements, for which the potential barrier is not very high and, consequently, the value $\vartheta^{-2}$ is not too small,

\[ * \]

the resonance maxima will be comparatively broad and low, whereas for heavy elements they will be very narrow and high. The area of the resonance curve, giving the total number of penetrations into the nucleus, will in both cases be approximately the same.

Up to the present we have spoken only of the process of penetration of an $\alpha$-particle into the nucleus; when considering the process of artificial transformation, two further factors must be taken into account: the interaction of the $\alpha$-particle that has entered the nucleus with the nuclear proton, necessary for transferring to it an excess of energy, and the probability of the emission of the proton itself through the barrier surrounding the nucleus. As regards the interaction of the $\alpha$-particle and the proton inside the nucleus, we have every reason to expect that it is sufficiently large. The probability of emission of the proton through the barrier will be given by a formula entirely analogous to the formula for the emission of an $\alpha$-particle; here, too, cases of resonance may occur if the energy received by the proton from the $\alpha$-particle happens to correspond exactly to one of the virtual quantum levels of the proton in the nucleus under consideration.

The investigation of resonance phenomena with these factors taken into account becomes considerably more complicated and lies outside the scope of the present article.

§ 4. The phenomenon of resonance splitting, soon after its prediction on the basis of the quantum theory of the structure of the nucleus, was found experimentally.

In his experiments on the splitting of aluminum nuclei by polonium $\alpha$-particles, Pose noticed in the velocity spectrum of the protons obtained from a comparatively rather thick aluminum plate two rather sharp lines. The presence of these lines might have seemed quite unexpected, since the $\alpha$-particles, passing through the aluminum plate, had at different depths different energies (from the initial value down to zero) and therefore should have knocked out protons of all possible velocities. The presence of discrete lines indicated, however, that in certain layers the production of protons increased considerably; this was evidently in those places where the $\alpha$-particles had precisely the energy suitable for resonance.

The scheme of Pose’s experiments is shown in Fig. 7, where in the velocity spectrum of the protons knocked out of the plate two maxima are clearly visible, arising from a resonance increase in the production of protons in two internal layers of the plate. To confirm this view, Pose tried to make the plate thinner (so to speak, cutting it down from the right side); in this case both maxima remained unchanged until the layer corresponding to the energy \(E_2\) of the \(\alpha\)-particles had been “cut out,”—then the slower group of protons suddenly disappeared. With further thinning of the plate, the second maximum likewise suddenly disappeared. This made it possible to determine both resonance energies of the \(\alpha\)-particles in aluminum and to calculate the energy balance of the transformation, which, as was to be expected, turned out to be the same for both groups and in fairly good agreement with the balance of the process of capture of the \(\alpha\)-particle into the ground level of the aluminum nucleus.

Fig. 7.

Fig. 8.

Pose’s experiments have recently been confirmed by Chadwick, who for aluminum found eight resonance groups, arranged in four pairs, with the distance

between the lines of each pair is the same for all four pairs.

For fluorine, Chadwick found six lines, likewise splitting into three pairs (Fig. 8). As the thickness of the plate is decreased, the lines disappear pairwise, which indicates that each pair owes its origin to one definite resonance velocity of the incident $\alpha$-particles.

Evidently, there are here several resonance levels (four for aluminum and three for fluorine), and an $\alpha$-particle, penetrating by the “resonance channel” into the interior of the nucleus, can knock out a proton from one or another proton level, thereby giving rise to two groups. The distance between the two groups of one pair obviously represents the difference in energy between the first and the ground levels of the proton in the nucleus.

The study of resonance splitting, so far only begun, should give us much valuable information about the arrangement of quantum levels in the nuclei of light elements and bring us closer to the solution of the fundamental problem of the energy levels of the atomic nucleus.

§ 5. Let us now turn to another process that is possible in principle, when an $\alpha$-particle, flying into the interior of a nucleus, remains in it, giving up the excess energy in the form of a very hard $\gamma$-quantum. The probability of such a process, as can be calculated by estimating the probability of $\gamma$-radiation, is, generally speaking, not very large and is much smaller than the probability of knocking out a proton. However, in the case where the energy of the $\alpha$-particle is close to one of the resonance levels of the nucleus, this probability may increase considerably.

The process indicated has so far been observed with certainty only in the case of beryllium, which, as Bothe showed, under $\alpha$-bombardment gives fairly intense $\gamma$-radiation despite the complete absence of ejected protons. According to Bothe, the absorption coefficient of this radiation in lead is equal to $0.3\ \mathrm{cm}^{-1}$, which corresponds to a light quantum energy $h\nu$ of about $17 \times 10^{-6}$ erg. The energy of the $\alpha$-particles bombarding beryllium nuclei is $8.5 \times 10^{-6}$ erg, which (for se-

taking into account the kinetic energy acquired by the beryllium nucleus in the collision) gives, for that acquired by the nucleus upon capture of the $\alpha$-particle, $6.5 \times 10^{-6}$ erg.

Assuming that the $\alpha$-particle is captured into the ground level, which for light elements lies at a depth of $1.5 \times 10^{-6}$ erg, we obtain for the released energy $17 \times 10^{-6}$ erg, in good agreement with observation. Bothe also investigated the change in the intensity of the radiation with the change in the energy of the bombarding $\alpha$-particles; his results are presented in Fig. 9. We see that the intensity of the $\gamma$-radiation, as the energy of the $\alpha$-particles increases, at first increases rapidly, reaches a maximum, and thereafter tends to decrease again. This indicates that here we are probably dealing with a resonance region. It is very likely that a similar effect also occurs in other elements, where, however, it is greatly weakened and masked by $\gamma$-rays emitted in connection with the ejection of a proton.*

Fig. 9.

* Proof correction note. This article was written and submitted for publication before the appearance of the works of Curie, Joliot, and Chadwick on neutrons.