Recent Advances in the Study of Atomic Nuclei*

R. H. Fowler, Cambridge

The current year 1932 has proved for nuclear physics an annus mirabilis (“year of miracles”). It seems of interest to recount briefly, in historical order, the harvest of new discoveries gathered in this year, and to try to clarify their significance for the knowledge of the atomic nucleus and their influence on the formulation of the problems of nuclear physics.

The first discovery was the discovery of the neutron and the study of some of its properties. The highly significant observations made by Joliot (F. Joliot) and his wife Curie-Joliot (J. Curie-Joliot) in the study of the penetrating radiation emitted by beryllium when bombarded by its $\alpha$-rays were continued by Chadwick (J. Chadwick), and he succeeded in proving with a certainty admitting no reasonable doubt that at least part of this highly penetrating radiation consists of particles of mass 1 and charge 0, whose kinetic energy is approximately $4 \cdot 10^6$ electron-volts; these particles were named neutrons by Chadwick. Chadwick studied the recoil particles (recoil-atoms) knocked out by the radiation of beryllium from the atomic layers of various elements. The range and ionizing power of these recoil particles can be measured by sensitive ionization methods; on this basis the mass of these particles and their maximum energy can be determined with sufficient certainty. If the mass and energy of at least two different kinds of particles knocked out by the radiation are known, then, with the aid of the laws of conservation of energy and momentum, one can calculate the mass and energy of the particles of which this radiation consists. The values of mass and energy obtained in this way could also be explained by the assumption that the beryllium radiation under consideration consists of protons. It has been established, however, that this radiation cannot consist of protons, but must consist of uncharged particles whose mass is approximately equal to unity. The assertion that their mass is very close

* Lecture delivered on September 24, 1932, at the Research Institute of Physics of Moscow University. Translated from the author’s manuscript.

to the mass of the proton, is at present only a quite natural assumption.

Upon further study of this radiation it was discovered that, under bombardment by $\alpha$-rays, neutrons are emitted both by beryllium and by boron, and that not all neutrons are emitted with the same initial energy. The question of groups of neutrons of different energies and of their dependence on the energies of the incident $\alpha$-particles has not yet been clarified. It is known, however, that at least beryllium emits, together with neutrons, also $\gamma$-rays, as was assumed by Bothe, who first discovered the very fact of the radiation.

The properties of neutrons have not yet been studied in all details, but a number of characteristic facts have already been established. In passing through various substances, neutrons almost do not interact at all with electrons. It has been experimentally established that, in passing through air under normal conditions, they form fewer than one pair of ions along a path of 3 m. Theoretically it is highly probable to suppose, in complete agreement with the experimental facts, that in reality neutrons form in air, on average, one pair of ions along a path of 1 km or even more. The calculation by means of which one can show that the interaction of neutrons with electrons is much weaker than their interaction with protons and other nuclei is one of the most remarkable examples of the application of elementary wave mechanics.*

Thus, when passing through matter, neutrons are slowed only by, in essence, elastic collisions with nuclei, to which they thereby impart a definite momentum. It is extremely difficult to devise a method by which neutrons could be detected after they have lost their initial velocity.

By passing neutrons through Wilson’s chamber and studying the corresponding photographs, it has been possible to show that, in addition to elastic collisions, there also occur inelastic collisions of neutrons with nitrogen nuclei, in which—

* The point is the following argument, due to Bohr. Let a flux of particles of mass $m$ and velocity $v$ be incident upon a neutron. To these particles there corresponds a wave whose length is

\[ \lambda_n=\frac{h}{mv}. \]

If $\lambda_n$ is large in comparison with the dimensions of the neutron, then one may apply Rayleigh’s formula, derived by him for the scattering of waves by small particles, according to which the scattering is proportional to the quantity

\[ \sigma=\frac{(n^2-1)^2 V^2}{\lambda_0^4}, \]

where $V$ is the volume of the scattering particle, in the present case the neutron, and $n$ is the mean refractive index inside it. According to the elementary propositions of wave mechanics, this refractive index for waves,

in which these nuclei disintegrate with the emission of $\alpha$-particles. This new type of disintegration process is all the more interesting because the well-known disintegration of nuclei by bombarding them with $\alpha$-particles is accompanied by the emission of protons. Energy considerations make it probable that, in an inelastic collision, a neutron is captured by the nucleus. Here, it may be appropriate to note the extraordinary importance of studying the exact energy relations in all these nuclear processes, including the numerous processes discovered earlier in which a proton is emitted by a nucleus bombarded with $\alpha$-rays. For this it is necessary to know accurately the masses both of the reacting nuclei and of the nuclei obtained as a result of the reaction. The masses of nuclei may be determined either by Aston’s method or from the study of band spectra, although as yet the accuracy of these measurements is hardly sufficient for the purposes indicated. Further, it is necessary to know, with the same accuracy, the kinetic energy of all the particles participating in the reaction, which can be determined—though with considerable difficulty—only by measuring their ranges. All the excess energy will be emitted in the form of $\alpha$-rays, which, if possible, must also be measured in order to check the calculations. Much patient experimentation will be required before all these details can be clarified.

The second remarkable discovery of this year is the discovery of the disintegration of lithium by protons of very small kinetic energy. An accelerating potential of approximately $100\,000\ \mathrm{V}$ is sufficient for this process already to begin, although at higher voltages it proceeds much more rapidly. During the last two years Cockcroft and Walton have been engaged in designing and assembling a small apparatus making it possible to experiment

corresponding to particles of mass $m$ and velocity $v$, is determined by the formula:

\[ n^2 = 1 + \frac{U}{\frac{1}{2}mv^2}, \]

where $U$ is the mean value of the potential energy of the incident particles inside the scattering particle. Substituting the values of $\lambda_0$ and $n^2$ into the expression for $\sigma$, we obtain:

\[ \sigma = \frac{U^2 \lambda^2}{\frac{1}{4}m^2 v^4} \left(\frac{mv}{h}\right)^4 = \frac{4U^2 V^2 m^2}{h^4}. \]

Thus, the scattering of particles by neutrons, characterizing the strength of their interaction, first, does not depend on the velocities of the incident particles and, second, is proportional to the square of their mass; that is, in the case of protons it should be millions of times stronger than in the case of electrons.

Editor’s note.

at voltages up to 800,000 V, which at the same time was an installation of laboratory type, saving space and electrical energy. Their very first experiments on the bombardment of light substances with protons were at once crowned with success and showed that lithium can be split and that in doing so it emits an $\alpha$-particle with an energy of 8,000,000 V (range 8 cm). In order to satisfy the laws of conservation of energy and momentum, it is necessary to assume that the proton is captured by the nucleus $\mathrm{Li}_{7}^{3}$*, which thus becomes the nucleus $\mathrm{Be}_{8}^{4}$. This nucleus, being in an unstable state, immediately explodes, with the formation of two $\alpha$-particles flying apart in opposite directions, each of which has a range of 8 cm. The circumstance that the disintegration occurs precisely in this way was verified and confirmed by simultaneous observation and counting of the $\alpha$-particles in two directly opposite directions from the bombarded lithium specimen.

In addition to Li, the splitting of many other elements was also discovered when they were bombarded with protons of energies of 250,000 V and higher. As yet not all the observed effects are completely understood, and it has not yet been proved that all the particles emitted during the splitting are undoubtedly $\alpha$-particles. It is possible that other types of splitting also occur. But there is no doubt that boron splits according to the same type as lithium; moreover, from energy considerations it follows that $\mathrm{B}_{11}^{5}$ undergoes splitting, forming the nucleus $\mathrm{C}_{12}^{6}$ in an excited state, which immediately ejects an $\alpha$-particle with an energy of 5,000,000 V. It is more probable, although it has not yet been verified experimentally, that in this explosion of $\mathrm{C}_{12}^{6}$ three $\alpha$-particles of equal energy are formed at once, flying apart in one plane at an angle of 120° to one another. Further, it is highly probable that when bombarded with protons, very heavy elements, even uranium, are also split. The corresponding effects have been established beyond doubt, but precisely the circumstance that they have been established for so many different substances raises the suspicion that they may be due to the presence in the heavy elements of some impurities, which produce these effects. With respect to the heavy elements, the observations are not yet entirely convincing, but if the present results are confirmed, they will have exceedingly important significance, for they will require the most radical change in all our present views of the nucleus. The presently existing

* The upper index at the symbol of a chemical element denotes its ordinal number, equal to the charge of the nucleus, and the lower index denotes the atomic weight of the corresponding isotope. Editor’s note.

the theory apparently excludes any possibility of acting on heavy nuclei by bombarding them with protons of such insignificant energy.

Both these discoveries have very greatly widened the range of the varied processes now known to us that occur when nuclei are bombarded. Let us dwell somewhat on this question and consider a number of typical representatives of these processes, including also those which were discovered by earlier observations of the ejection of protons by nuclei when they are bombarded with \(\alpha\)-rays. The processes listed in the table have all been well studied, and we may be confident both as regards the structure of the reaction products and as regards the approximate energy balance, although the data on the energies are not given in the table*.

\[ \alpha \to \mathrm{N},\quad \mathrm{N}^{7}_{14}+\alpha^{2}_{4} = \mathrm{O}^{8}_{17}+p^{1}_{1}; \tag{I} \]

\[ \alpha \to \mathrm{B}\left\{ \begin{aligned} \mathrm{B}^{5}_{10}+\alpha^{2}_{4} &= \mathrm{C}^{6}_{13}+p^{1}_{1}\;(\gamma\text{-rays})\\ \mathrm{B}^{5}_{10}+\alpha^{2}_{4} &= \mathrm{Be}^{4}_{9}+\alpha^{2}_{4}+p^{1}_{1}; \end{aligned} \right. \tag{II} \]

\[ p \to \mathrm{B};\quad \mathrm{B}^{5}_{11}+p^{1}_{1} \left(=\mathrm{C}^{6}_{12}\ \text{excited}\right) = 3\alpha^{2}_{4}; \tag{III} \]

\[ p \to \mathrm{Li},\quad \mathrm{Li}^{3}_{7}+p^{1}_{1} \left(=\mathrm{Be}^{4}_{8}\ \text{excited}\right) = 2\alpha^{2}_{4}; \tag{IV} \]

\[ \alpha \to \mathrm{Be},\quad \mathrm{Be}^{4}_{9}+\alpha^{2}_{4} = \mathrm{C}^{6}_{12}+n^{0}_{1}\;(\gamma\text{-rays}); \tag{V} \]

\[ \alpha \to \mathrm{B},\quad \mathrm{B}^{5}_{11}+\alpha^{2}_{4} = \mathrm{N}^{7}_{14}+n^{0}_{1}\;(\gamma\text{-rays?}); \tag{VI} \]

\[ n \to \mathrm{N},\quad \mathrm{N}^{7}_{14}+n^{0}_{1} = \mathrm{B}^{5}_{11}+\alpha^{2}_{4}. \tag{VII} \]

Processes (VI) and (VII) are the reverse of one another. It may be expected that, in the future, other pairs of mutually reverse processes will also be discovered experimentally.

After these striking novelties, all the remaining events about which I still have to speak may seem commonplace and dull, but nevertheless they are connected with very real successes in our work on elucidating the nature of the nucleus.

Thus, the third question concerns a substantial increase in the accuracy of measurements of the energy of \(\alpha\)- and \(\gamma\)-rays emitted by radioactive nuclei. Of course, it has long been considered quite beyond doubt that \(\gamma\)-rays are emitted by an \(\alpha\)-particle, or by \(\alpha\)-particles, in the nucleus when the nucleus passes from one quantum state to another state of lower energy, in exactly the same way as ordinary light is emitted in an analogous change of state of the outer electrons of an atom. The energy of the quantum \(h\nu\) of various \(\gamma\)-rays can be measured by measuring the energy of those \(\beta\)-electrons which are ejected by the \(\gamma\)-rays from the outer electron shell of the atom that produces them. For this purpose one may measure the deflection of the \(\beta\)-rays in a transverse magnetic field, using, for example, the method of semicircular focusing. The energy of the \(\gamma\)-rays must correspond to the difference

* \(p\) denotes a proton, \(n\)—a neutron.

energies of the two states of the nucleus. On the other hand, although the decay of the majority of radioactive nuclei with the emission of $\alpha$-particles takes place in the state of least energy of these nuclei, some nuclei, in particular RaC′ and ThC′, also emit a measurable number of $\alpha$-particles whose range and energy are greater than normal. In all probability, these fast $\alpha$-particles are emitted not in the direct decay of those same nuclei when they are in an excited state, as would correspond to the general principles of Gamow’s theory of $\alpha$-decay. The energy of these fast $\alpha$-particles was determined from measurements of the length of their range in air, by extrapolating the empirical relation between range and velocity.

In order to determine the system of energy levels of the nucleus, it is evidently necessary first to establish the correspondence between the energies of $\gamma$-rays and the energies of $\alpha$-rays. For this, in turn, it is essential that the energies of the $\gamma$-rays be known, if possible, with an accuracy of one thousandth, and that the differences between the energies of the various kinds of $\alpha$-rays be known with the same accuracy. Until recently it was believed that the data of Meitner and Ellis for the energies of $\gamma$-rays possessed approximately this degree of accuracy. However, recently Ellis, using improved apparatus and a very constant and homogeneous magnetic field excited by a permanent magnet, established that all these values of $\gamma$-ray energies, which had been considered correct, are higher than the true values by $0.7\%$. Almost simultaneously with this, Rosenblum in Paris succeeded in significantly refining our knowledge of ray energies. In his new measurements Rosenblum used the method of semicircular focusing, and in doing so took those necessary precautions which he had not taken in his previous measurements two years earlier. Independently of this, Rutherford and Lewis in Cambridge developed the same method of measurement in a somewhat different form; moreover, the energy values obtained by them, within the limits of the very high present degree of accuracy, coincide with Rosenblum’s data.

As a result of all this, it is now possible with a certain confidence to compare the measured energies of the $\gamma$-rays of RaC′ with the observed differences in the energies of $\alpha$-rays. The work being carried out in this direction has not yet been completed, and I shall confine myself here to reporting only one result. The two most important $\gamma$-lines of RaC′, whose corrected energies are equal to $h\nu = 6.12 \cdot 10^{5}\ \mathrm{V}$ and $h\nu = 14.18 \cdot 10^{5}\ \mathrm{V}$, undoubtedly correspond to transitions of the nucleus to the normal state from two states in which the nucleus emits two най-

more important groups of $\alpha$-particles of long range. The validity of these relations had long been assumed hypothetically, but it is highly significant that now we have complete certainty in this matter.

The fourth and last achievement of this year, about which I must report, is of a theoretical nature, and its explanation will require somewhat more time.

The process of emission of a line spectrum of $\beta$-rays, which is a secondary result of the emission by the nucleus of $\gamma$-rays, may be considered from two different points of view. We may suppose that the nucleus emits $\gamma$-rays in approximately the same way as a Hertz oscillator emits ordinary electromagnetic waves, and that then part of the $\gamma$-rays is absorbed by the electrons (in particular the $K$-electrons) of the very atom that produced them; moreover, the electrons that have absorbed the energy fly out of the atom in the form of $\beta$-rays (the so-called “internal photoeffect” or “internal conversion of $\gamma$-rays”). On the other hand, following Rosseland and Auger, we may also suppose that there exists a direct (although complex) interaction between the excited nucleus and the extranuclear (outer) electrons of the atom, as a result of which the nucleus passes into an unexcited state, while an electron is ejected from the atom with a high velocity corresponding to the energy balance. The first of these methods of description is more appropriate in those cases where, in the nuclear quantum transition under consideration, $\gamma$-rays are actually emitted as such, for in these cases the most essential part of the interaction reduces to the action of the field of a classical electromagnetic oscillator on an electron situated in that region of space outside the nucleus where the electron is most likely to be. The second method of description, however, corresponds to those cases where $\gamma$-rays are not emitted outward at all, or are emitted only to a small extent, and where, in the interaction of the electron with the nucleus, the region of space inside the nucleus plays the most important role. In what follows I shall have in mind those quantum transitions to which the first method of description is more applicable.

Several years have already passed since Miss Surrles first theoretically calculated, by order of magnitude, the probability of internal conversion of $\gamma$-rays in the $K$-shell of the atom. These calculations were based on the Schrödinger equation for the electron and led to a result that proved to be approximately ten times smaller than the observed one. Subsequently these calculations were refined by Casimir, who started from the Dirac equation for the electron and used retarded potentials to determine the interaction of the electron with the nearby

in the nucleus by an oscillator. However, Casimir did not calculate exactly the integral by which this interaction is determined, but obtained for it only an asymptotic expression for large values of the ratio \(\frac{h\nu}{m_0c^2}\), where \(m_0\) denotes the mass of the electron. Casimir’s formula was applied to the \(\gamma\)-rays of RaC′, for which the ratio \(\frac{h\nu}{m_0c^2}\) approaches unity, and again led to values of the probabilities of internal conversion ten times smaller than those observed.

However, quite recently Holme, in Cambridge, who checked Casimir’s calculations at Casimir’s request, succeeded in finding an exact, and not merely asymptotic, solution of the Casimir problem, for which, it is true, he had to carry out one complicated numerical summation. The exact value of the probability of internal conversion, calculated as a function of \(\nu\), proves, for values of the ratio \(\frac{h\nu}{m_0c^2}\) of practical interest, to be much larger than could be supposed from the asymptotic expression. Holme’s curve passes so close to a number of values experimentally found by Ellis for RaC′ that the discrepancies turn out to lie within the limits of the experimental errors.

However, the coefficients of internal conversion for certain other \(\gamma\)-lines of RaC′ and for softer \(\gamma\)-lines of RaB still considerably exceed the values calculated for these frequencies from the Holme–Casimir curve. In connection with this, Mott suggested that these observed values may correspond to internal absorption of quadrupole radiation of the nucleus, whereas Holme’s calculations refer to dipole radiation. Quadrupole radiation should correspond to such quantum transitions of the nucleus in which its azimuthal quantum number changes by \(0\) or \(\pm 2\) \((\Delta l=0,\pm 2)\), whereas dipole radiation corresponds to \(\Delta l=\pm 1\). It is well known that in ordinary optical atomic spectra both dipole and quadrupole lines occur, but that quadrupole lines, generally speaking, have extremely small intensity. Only under exceptional conditions do they become bright. The green line in the spectrum of the northern lights and in the spectrum of the corona, belonging to neutral oxygen, as well as the well-known lines in the spectra of nebulae belonging to ionized oxygen and nitrogen, are quadrupole lines. However, there are serious grounds for supposing that in nuclear radiation the intensities of lines of both types should be of the same order, and that bright lines may be either dipole or quadrupole. For nuclei,

consist almost exclusively of $\alpha$-particles, i.e., particles characterized by one definite value of the ratio of charge to mass. If only such particles entered into the composition of nuclei, then the dipole moment of nuclei would always be exactly equal to zero. The circumstance that, in reality, the structure of nuclei approaches this limiting case must reduce the dipole moment of nuclei without affecting their quadrupole moment, so that lines of different types may be of the same order of brightness.

On the basis of these considerations, Mott and Taylor calculated the coefficient of internal conversion of quadrupole radiation and found that it is greater than the conversion coefficient calculated by Hulme. It turned out that the theoretical curve agrees surprisingly well with the values of this coefficient determined by Ellis for those RaC′ lines which did not fit Hulme’s curve, and for all the measured RaB lines.

This result is in itself very satisfactory; in addition, it is necessary to emphasize its significance for the general problem of the study of the nucleus. We now have all the $\gamma$-lines for which the coefficient of internal conversion has been measured. This circumstance may play an essential role in the problem of constructing a correct systematics of the quantum states of the nucleus, and will correspond to the first steps in the classification of atomic spectra—the division of spectral lines into principal and diffuse series.

It can hardly be expected that in the future equally significant advances will continue to follow one another with the same rapidity, continuously enriching our science. But in any case it is difficult to overestimate those substantial changes in our views which the last six months have brought.