The conception of the nucleus atom had its origin in 1911 in order to explain the scattering of an α particle through a large angle as the result of a single collision. The observation that the α particle is in some cases deflected through more than a right angle as the result of an encounter with a single atom first brought to light the intense forces that exist close to the nucleus. Geiger and Marsden showed that the number of particles scattered through different angles was in close accord with the simple theory which supposed that, for the distance involved, the α particle and nucleus behaved like charged points, repelling each other according to the law of the inverse square. The accuracy of this law has been independently verified by Chadwick, so that we are now certain that in a region close to the nucleus the ordinary laws of force are valid.
These scattering experiments also gave us the first idea as to the probable dimensions of the nuclei of heavy atoms, for it is to be anticipated that the law of the inverse square must break down if the α particle approaches closely to or actually enters the nuclear structure. This variation in the law of force would show itself by a difference between the observed and calculated numbers of α particles scattered through large angles. Geiger and Marsden, however, observed no certain variation even when the α particles of range about 4 cms. were scattered through 100° by a gold nucleus. In such an encounter, the closest distance of approach of the α particle to the center of the nucleus is about 5 x 10-12 cm., so that it would appear that the radius of the gold nucleus, assumed spherical, could not be much greater than this value.
There is another argument, based on radioactive data, which gives a similar value for the dimensions of the radius of a heavy atom. The α particle escaping from the nucleus increases in energy as it passes through the repulsive field of the nucleus. To fix a minimum limit, suppose the α particle from uranium, which is the slowest of all α particles expelled from a nucleus, gains all its energy from the electrostatic field. It can be calculated on these data that the radius of the uranium nucleus cannot be less than 6 x 10-12 cm. This is based on the assumption that the forces outside the nucleus are repulsive and purely electrostatic. If, as seems not unlikely, there also exist close to the nucleus strong attractive forces, varying more rapidly than an inverse square law, the actual dimensions may be less than the value calculated above.
At this stage of our knowledge it is of great importance to test whether the law of force breaks down for the distance of closest approach of an α particle to a nucleus. This can be done by comparing the observed with the calculated number of α particles scattered through angles of nearly 180°. It seems almost certain that the inverse square law must break down when swift α particles are used. This can be seen from the following argument. If an α particle, of the same speed as that ejected during the transformation of uranium, is fired directly at the uranium nucleus, it must penetrate into the nuclear structure. If a still swifter α particle is used, e. g. that from radium C, which has about twice the energy of the uranium α particle, it is clear that it must penetrate still more deeply into the nuclear structure. This is based on the assumption that the field due to a nucleus is approximately symmetrical in all directions. If this is not true, it may happen that only a fraction of the head-on collisions may be effective in penetrating the nucleus. It is hoped soon to attack this difficult problem experimentally.
We have so far dealt with collisions of an α particle with a heavy atom. We know, however, from the results of Rutherford, Chadwick and Bieler that in a collision of an α particle with the lightest atom, hydrogen, the law of the inverse square breaks down entirely when swift particles are used. Not only are the numbers of H nuclei set in swift motion much greater than is to be expected in the simple-point nucleus theory, but the change of number with the velocity of the α particle varies in the opposite way from the simple theory. Such wide departures between theory and experiment are only explicable if we assume either that the nuclei have sensible dimensions or that the inverse square law of repulsion entirely breaks down in such close collisions. If we suppose the complexity in structure and in laws of force is to be ascribed to the α particle rather than to the hydrogen nucleus, Chadwick and Bieler, as the result of a careful series of experiments, concluded that the α particle behaved as if it were a perfectly elastic body, spheroidal in shape with its minor axis 4 x 10-13 cm. in the direction of motion and major axis 8 x 10-13 cm. Outside this spheroidal region the forces fell off according to the ordinary inverse square law, but inside this region the forces increased so rapidly that a particle was reflected from it as from a perfectly elastic body. No doubt such a conception is somewhat artificial, but it does serve to bring out the essential points involved in the collision, viz., that when the nuclei approach within a certain critical distance of each other, forces come into play which vary more rapidly than the inverse square. It is difficult to ascribe this break-down of the law of force merely to the finite size or complexity of the nuclear structure or to its distortion, but the results rather point to the presence of new and unexpected forces which come into play at such small distances. This view has been confirmed by some recent experiments of Bieler in the Cavendish Laboratory in which he has made, by scattering methods, a detailed examination of the law of force in the neighborhood of a light nucleus like that of aluminum. For this purpose he compared the relative number of α particles scattered within the same angular limit from aluminum and from gold. For the range of angles employed, viz., up to 100°, it is assumed that the scattering of gold follows the inverse square law. He found that the ratio of the scattering in aluminum compared with that in gold depended on the velocity of the α particle. For example, for an α particle of 3.4 cms. range, the theoretical ratio was obtained for angles of deflection below 40° but was about 7 per cent lower for an average angle of deflection of 80°. On the other hand, for swifter particles of range 6.6 cms. a departure from the theoretical ratio was much more marked and amounted to 29 per cent for an angle of 80°. In order to account for these results he supposes that close to the aluminum nucleus an attractive force is superimposed on the ordinary repulsive forces. The results agreed best with the assumption that the attractive force varies according to the inverse fourth power of the distance and that the forces of attraction and repulsion balanced at about 3.4 x 10-13 cm. from the nuclear center. Inside this critical radius the forces are entirely attractive; outside they are repulsive.
While we need not lay too much stress on the accuracy of the actual value obtained or of the law of attractive force, we shall probably not be far in error in supposing the radius of the aluminum nucleus is not greater than 4 x 10-13 cm. It is of interest to note that the forces between an α particle and a hydrogen nucleus were found to vary rapidly at about the same distance.
It thus seems clear that the dimensions of the nuclei of light atoms are small, and almost unexpectedly small in the case of aluminum when we remember that 27 protons and 14 electrons are concentrated in such a minute region. The view that the forces between nuclei change from repulsion to attraction when they are very close together seems very probable, for otherwise it is exceedingly difficult to understand why a heavy nucleus with a large excess of positive charge can hold together in such a confined region. We shall see that the evidence from various other directions supports such a conception, but it is very unlikely that the attractive forces close to a complex nucleus can be expressed by any simple power law.
RADIOACTIVE EVIDENCE
A study of the long series of transformations which occur in uranium and thorium provides us with a wealth of information on the modes of disintegration of atoms, but unfortunately our theories of nuclear structure are not sufficiently advanced to interpret these data with any detail. The expulsion of high speed α and β particles from the radioactive nucleus gives us some idea of the powerful forces resident in the nucleus, for it can be estimated that the energy of emission of the α particle is in some cases greater than the energy that would be acquired if the α particle fell freely between two points differing in potential by about 4 million volts. The energies of the β and γ rays are on a similar scale of magnitude.
Notwithstanding our detailed knowledge of the successive transformation of the radio-elements, we have not so far been able to obtain any definite idea of their nuclear structure, while the cause of the disintegration is still a complete enigma. In comparing the uranium, thorium, and actinium series of transformations, one cannot fail to be struck by the many points of similarity in their modes of disintegration. Not only are the radiations similar in type and in energy, but, in all cases, the end product is believed to be an isotope of lead. This remarkable similarity in the modes of transformation is especially exemplified in the case of the "C" bodies, each of which is known to break up in at least two distinct ways, giving rise to branch products. For example, thorium C emits two types of α rays, 65 percent of range 8.6 cms. and 35 per cent of range 4.8 cms., and in addition some β rays.