A VISUAL MODEL OF THE ATOMIC NUCLEUS

There has long been a need for a simple and visual model of the atomic nucleus, illustrating the principal features of its structure. The model described below satisfies these requirements to a sufficient degree and can undoubtedly be used successfully in lecture demonstrations, in schools, at exhibitions, and so on.

The model1 consists of bar magnets (“protons”) floating vertically (with the aid of special floats) in a vessel of water and similar bars of soft iron (“neutrons”).

The idea of using magnets for such purposes is not new. A model of the atom is widely known in which electrons are represented by vertically floating magnets with similarly directed moments (see, for example,2); these “electrons” mutually repel one another and float to the edges of the vessel. If an electromagnet is then placed beneath the latter, then, when a current of suitable sign is switched on, all the “electrons” group themselves into a series of concentric rings (“orbits”), the number of which is determined by the number of “electrons.”

In the proposed model of the nucleus, the repulsion of similarly directed magnets (“protons”) is balanced by their attraction to iron rods (“neutrons”).

The model makes it possible to reproduce the following features of the structure of the nucleus:

1. Nuclei consist of protons and neutrons.
2. Protons are positively charged and repel one another with a force \(\sim r^{-2}\).
3. Neutrons are uncharged and do not interact electrically.
4. Between a proton and a neutron there acts an attractive force of small radius.
5. This force has the property of saturation, i.e., any third nucleon is attracted to a pair of nucleons (for example, proton—neutron) with a force smaller than the force of attraction between these last two nucleons.

In the model under consideration, the electrostatic repulsion of protons is represented by the repulsion of magnets. The repulsive force, it is true, is \(\sim r^{-2}\) only at distances small in comparison with the length of the magnet; at large distances the repulsion falls off more rapidly. The decrease in the rate of growth of the repulsive force at small distances can, however, be qualitatively interpreted as the influence of the short-range “nuclear force” of attraction between protons.

Rods of soft iron (“neutrons”) do not possess magnetic charges and therefore do not interact with one another. This corresponds to the absence of electrostatic interaction between neutrons. Under the action of a constant magnet, however, a magnetic moment is induced ...

of opposite sign. This moment causes attraction between the iron rod and the magnet, i.e., a “proton-neutron” force. Because of the dependence of the magnetic moment of the iron rod on the magnitude of the inducing field, this attractive force falls off with distance faster than the repulsive force of the magnets. This corresponds to the small radius of action of the nuclear force between a proton and a neutron.

“Saturation” of the attractive force between the magnet and the rod would be practically complete if, in the case of their contact, all the lines of force of the magnet passed through the iron. In order that the saturation be incomplete, as it must be in the nucleus (otherwise nuclei more complex than deuterons could not exist), the diameter of the floats is chosen sufficiently large.

The essential shortcomings of this model are obvious: it does not contain any reflection of the nuclear interaction force between two protons and between two neutrons. If the first shortcoming is somewhat “softened” by the slowing of the increase in the repulsive force of the magnets at small distances (the “nuclear force” of attraction of “protons” comes into action), then between “neutrons,” on the contrary, only the repulsive force acts, which in idea is not of “electrical” origin. In other words, in the model the “neutron-neutron nuclear force” appears rather in the form of repulsion.

On the other hand, the model makes it possible to demonstrate a number of nuclear phenomena.

Thus, owing to friction between the rods, various stable configurations of “protons” and “neutrons” are possible.

Some of these “isomeric” states for “lithium” are shown in the figure. The most stable configurations turn out to be those with a circular arrangement of the “nucleons.”

It is easy to carry out “nuclear disintegrations” by bombardment with fast “particles.”

Thus, if a “proton” is quickly pushed into the “nucleus” \({}_{3}\mathrm{Li}^{7}\), or a “deuteron” into the “nucleus” \({}_{3}\mathrm{Li}^{6}\), a “compound nucleus” \({}_{4}\mathrm{Be}^{8}\) is formed, which in approximately 10% of cases decays into two “\(\alpha\)-particles.” This fully corresponds to the classical experiments of Cockcroft and Walton:

\[ {}_{3}\mathrm{Li}^{7}+{}_{1}\mathrm{H}^{1}\to{}_{4}\mathrm{Be}^{8}\to{}_{2}\mathrm{He}^{4}+{}_{2}\mathrm{He}^{4}; \qquad {}_{3}\mathrm{Li}^{6}+{}_{1}\mathrm{H}^{2}\to{}_{4}\mathrm{Be}^{8}\to{}_{2}\mathrm{He}^{4}+{}_{2}\mathrm{He}^{4}. \]

The lithium nuclei that have a circular distribution of nucleons are the most difficult of all to split.

As the number of nucleons increases, the stability of the nucleus under bombardment decreases. For nuclei with mass numbers \(A=40\text{--}50\), it was possible to obtain “fission” cases into several nuclei containing 10 or more nucleons, and into several single nucleons.

Since processes analogous to \(\beta\)-decay or \(K\)-capture are not carried out in the model, for a given \(A\) the number of stable combinations of neutrons and protons in the model is considerably greater than the actual observed number. For this reason, apparently, it is not possible to carry out fission of a nucleus by bombardment with slow “neutrons,” although any nucleus can be split by fast “neutrons” (or by any other objects of sufficient energy).

L. Bell

CITED LITERATURE

1. C. Milner, Nucleonics 4, 56 (1949).
2. S. Bragg, On the Nature of Things, p. 26. State Technical-Theoretical Publishing House, 1932.