Nuclear Physics

by W Heisenberg

  Before proceeding to the discussion of other decay processes, let us write down the formulae of a few more processes involving both alpha and beta radiation. When the uranium atom 92U238 decays under emission of an alpha particle, 2He4, the product of the process is an atom of mass number 234 and atomic number 90—uranium X1, 90UX1234. We write this process as follows:

  92U238 → 90UX1234 + 2He4

  Figure 23.—Life and energy of natural and artificially produced beta radiators (Sargent diagram).

  As always, the mass numbers and atomic numbers (superscripts and subscripts) must balance on both sides of the arrow.

  The boron atom 5B12, for instance, emits an electron and changes into the carbon atom 6C12. Simultaneously with the emission of the electron, a neutrino is emitted, of which both the rest mass and the charge are 0; its symbol, therefore, is 0ν0. We write, consequently:

  5B12 → 6C12 + -1e0 + 0ν0

  An example of a positron emitter is the nitrogen atom 7N13, which changes into the carbon atom 6C13 by the emission of a positron, 1e0 and a neutrino, i.e.:

  7N13 → 6C13 + 1e0 + 0ν0

  III. OTHER TYPES OF SPONTANEOUS NUCLEAR TRANSMUTATION

  Alpha and beta radiation are by far the most frequent types of radioactive transmutation. However, there is also a third process, already mentioned in a cursory manner, which is more or less the converse process of electron emission. In cases where it is advantageous, from the point of view of energetics, for a proton in the nucleus to change into a neutron, this transformation can be accomplished in two different ways. We have already discussed one of them—the emission of a positron. However, the same result is attained when the nucleus absorbs one of its own planetary electrons, in which case the electron, naturally, vanishes (as an absorbed photon vanishes) since its charge offsets the charge of the proton and changes the latter into a neutron. This process is called electron capture. As in this process no charged particle is emitted, the process can only be observed, from outside, by the consequent x-ray emission, K-radiation, since the absorbed electron usually comes from the innermost electron shell, the K-shell. As this process reduces the nuclear charge (atomic number) by one unit, the number of remaining electrons (the original number of planetary electrons minus one) is sufficient for the newly formed atom. But the remaining planetary electrons must now re-group themselves; an electron originally occupying a position in shell farther from the nucleus falls into and occupies the place vacated by the captured electron. This produces the x-ray emission, which is the K-radiation characteristic of the element in question. At the same time, in order to conserve the angular momentum or spin value of the atom—since the captured electron had a spin value of 1/2 h—a neutrino is emitted.

  Such a process occurs, for instance, in the beryllium nucleus 4Be7, an artificially produced radioactive isotope of beryllium. Capturing a planetary electron, it changes into the lithium nucleus 3Li7. The formula expressing this process is:

  4Be7 + -1e0 → 3Li7 + 0ν0

  Such processes are not so very rare. They are frequently associated with fairly long half-lives. The half-life of 4Be7 is approximately fifty-three days. In our Table IV, the atomic nuclei which change by K-capture are indicated by circles.

  And finally, there is still another process, discovered by Hahn and Strassmann in 1938. This is the reaction already mentioned in which nuclei split into two parts of approximately equal size. Occasionally it may occur spontaneously, too. But this process will be discussed under the heading of artificially induced nuclear transmutations.

  IV. ARTIFICIALLY INDUCED NUCLEAR TRANSMUTATIONS

  As was first demonstrated by Rutherford, a nuclear transmutation can be produced artificially by shooting some particle into the nucleus. In the majority of the cases, this particle will remain in the nucleus without producing any reaction. But the result may be that a particle of some kind is emitted in turn by the nucleus. If this emitted particle is not of the same kind as the first particle, this reaction means a nuclear transmutation.

  Bohr formulated the following theory about such a reaction: When a particle is hurled at the nucleus and actually strikes it, it usually remains in it, for the simple reason that it is held fast there by the exceedingly powerful nuclear forces. As a result, the energy of this particle becomes distributed very rapidly among the other particles in the nucleus, and eventually throughout the entire nucleus. Figure 24 shows a schematic picture of a nucleus. A neutron is approaching it from the outside. The white and black circles represent the nuclear neutrons and protons. As shown by the arrows, these nuclear particles receive an impact from the foreign neutron and, in turn, collide with other particles. When the neutron has penetrated into the interior of the nucleus and its energy has become distributed among all the particles within it, the situation can be expressed in the simplest form as follows: The atomic nucleus is being heated. A pile of sand becomes heated in exactly the same manner when a bullet is fired into it. This reaction is analogous to the heating of a microscopic structure, if we bear in mind that an increase in the kinetic energy of the molecules in the sand pile corresponds to an increase in its temperature. In a nucleus, instead of molecules we deal with neutrons and protons, and the kinetic energy is associated with a certain temperature of the nucleus.

  Figure 24.—Neutron penetrating a nucleus.

  The temperature attained by a nucleus in this way—for instance, when a particle with an energy of approximately 8 Mev. is shot into it—has, in conformity with the laws of the kinetic theory of gases, the order of magnitude of ten thousand million degrees. It is roughly a thousand times higher than the highest temperatures that otherwise occur in the universe, the temperature in the interiors of the fixed stars. However, in this case, these high temperatures only affect the infinitesimally minute territory of that one nucleus.

  If we imagine the nucleus in this state as a highly heated drop of liquid, the logically inevitable conclusion is that the nucleus will evaporate in consequence of the high temperature. This means that after a short while, some particle or another will emerge from the nucleus—generally that particle, the emergence of which is most advantageous from the point of view of energetics, in other words, the one the emergence of which requires the least energy. The energy necessary here corresponds to the heat of evaporation in an actual liquid. The nucleus cools off as a result of having yielded up this energy. Occasionally, a second particle will emerge, too. Or else, the residue of the energy, which is not sufficient for the emission of another particle, departs in the form of a gamma ray, as a photon. In a certain respect, this process is like the case of an incandescent drop of liquid which, due to its high temperature, emits visible light, too.

  The process just described can continue unimpeded only if the particle used to bombard the nucleus is uncharged, i.e. if it is a neutron or a photon. But if the bombarding particle is a proton or an alpha particle, it must come up in the vicinity of the nucleus, against the potential barrier, the height of which is in proportion to the magnitude of the charge of the bombarded nucleus. The ‘projectile’ would be slowed up in its flight against the nucleus, and in many cases—especially those involving heavy nuclei—it would either come to rest at some distance from the nucleus or would be deflected so far from its path that it would never strike the nucleus. Therefore, in order actually to hit a heavier nucleus, the charged particle would have to be accelerated by means of exceedingly high voltages, which can be produced only in apparatus especially designed for this purpose. For this reason, nuclear transmutation by means of charged particles is possible, as a rule, in relatively light atoms only.

  On the other hand, there is no potential barrier for uncharged particles, and therefore they can be used to transmute atoms of any mass number. Transmutations of heavier atomic nuclei by photons, i.e. gamma rays, have been observed by Bothe and his collaborators, while the transmutation by neutrons was first demonstrated by Fermi. The neutron will become incorporated in the nucleus, in many cases at any ra
te, and the surplus energy then will be carried off by one or more gamma-ray photons.

  While this reaction signifies a change in the nucleus, it does not involve any change in the chemical properties of the atom. The chemical properties change only when the resulting nucleus is unstable because it has too many neutrons within it. In that case, a subsequent process takes place, in which a neutron changes into a proton, by the emission of an electron, with the result that the nucleus becomes a nucleus of the element whose atomic number is one higher.

  Since a neutron can approach a nucleus unimpeded, the velocity plays no essential role in the process, unlike the case of charged particles. On the contrary, slow neutrons are frequently more effective than fast ones, for they remain longer in the vicinity of the nucleus, and so the probability of their eventual capture by the nuclear forces is greater than for fast neutrons.

  Experiments have shown that this probability can be extraordinarily great for neutrons having a certain, but not too high, energy. According to Bethe, this becomes quite logical when we consider the neutron under the wave aspect, i.e. as a wave incident on the nucleus. The nucleus is a structure capable of vibration, and as such, it can enter into resonance with any wave it encounters, if the frequency of that wave coincides with one of its own fundamental frequencies. In this case, an exceedingly strong selective absorption of the wave occurs, a process quite familiar to us in connection with the absorption of light. Now the frequency of the wave is a function of the velocity of the neutron, and therefore there exists a very definite velocity where the requirements for resonance are fulfilled and the wave is especially strongly absorbed by the nucleus. But translated back again into terms of the particle aspect, this means that the probability of the capture of the neutron by the nucleus is a very high one. This dependence on the velocity is often described in terms of a nuclear cross-section. Let us assume that nuclei are spheres, neutrons are points, and no force of any kind is acting between them at all. In that case, the larger are the cross-sections of the spheres, the greater would be the probability of striking a nucleus with neutrons shot at it at random. In this model, the nuclei would apparently have cross-sections of different sizes for neutrons of different velocities. Under particularly favourable conditions, this nuclear cross-section may be about 10,000 times larger than the actual geometrical cross-sectional area of the nucleus. This means an exceedingly high probability of capture. This is why Fermi, who discovered this circumstance, first applied the device already mentioned of slowing down the neutrons (which are always rather fast when they are first produced) to thermal velocity. He made them pass through a hydrogen-containing substances, such as water or paraffin. Hydrogen is the best substance for this purpose, because the mass of a proton is approximately the same as that of a neutron, and also because the conditions for a rapid exchange of energy are most favourable here, in conformity with the laws of elastic impacts. When such slow neutrons are captured by a nucleus, they are accelerated within the range of attraction of the nuclear forces sufficiently to produce that heating of the nucleus which has already been discussed.

  Conversely, too, it is naturally easier for a neutron to emerge out of such a heated nucleus than it would be for a charged particle. In fact, the charged particle has to ‘climb over’ the potential barrier in order to get out, whereas for the neutron the potential barrier is non-existent. This is the reason why nuclear transmutations involving the emission of a proton or an alpha particle are relatively rare in heavy nuclei where the potential barrier is high.

  Of course, when a nucleus is heated to a very high degree, a larger number of charged and uncharged particles can come out of it, analogously to the evaporation of a liquid drop. With laboratory apparatus it is very difficult to impart such high energies to the nucleus. But particles possessing the vast energy of 1,000 Mev., or even more, are present in cosmic radiation. If such a particle happens to hit a nucleus, the result of the encounter is that the nucleus is heated to such a high degree and emits numerous protons and neutrons, at times even heavier fragments, such as helium or lithium nuclei. When a nuclear disintegration of this kind actually takes place in the emulsion on a photographic plate, the nuclear particles leave tracks which become visible when the plate is developed. This technique was developed by Blau, Wambacher and Schopper, and has recently been improved considerably by Powell and his collaborators. Figure 25A shows such a photograph. It is a much enlarged reproduction; the range of the protons in the emulsion is actually less than 1 mm. We are thus looking here at an actual record of the disintegration of an atom, in which at least forty particles or so have ‘evaporated’ out of the nucleus. For, in addition to the charged particles, many neutrons, too, are sure to have been liberated. Figure 25B shows a similar, still more complicated process. In the disintegration of one nucleus a particle has been liberated, which subsequently induces a transmutation reaction in a second nucleus. The difference in the density of the silver grains in the individual tracks is due to the difference in the velocities of the nuclear particles. The faster they are, the more thinly they are spread, and the longer is the track which they leave. Of course, actually, the particles are dispersed in all directions, and therefore, the majority of their paths appear more or less foreshortened.

  Figure 25A.—Disintegration of a nucleus by cosmic ray particle of very big energy (after Powell and Occhialini).

  Figure 25B.—Primary and secondary nuclear disintegration.

  A last, quite especially important case of the disintegration of nuclei is nuclear fission (the splitting of nuclei), discovered by Hahn and Strassmann in Berlin in 1938. This is what occurs in this case: It may happen that a heated nucleus ejects no individual particles at first, but begins to vibrate as a whole, utilizing all or part of the introduced energy for the excitation of these vibrations. This is often the case when a uranium nucleus is bombarded by a neutron. A reaction ensues then, which is shown diagrammatically in Figure 26. The nucleus, orginally spherical in shape, will vibrate first so as to assume alternately an elongated and a flattened elliptical form. The longitudinal deformation may reach a degree where the nucleus—like an iron rod which is about to break in two—becomes very thin approximately in its middle, and finally breaks into two more or less equal parts. Splinters fly off, as a rule, since several neutrons are ejected.

  The fact that such fission is possible at all and is most likely to occur in the heaviest nuclei, is easy to understand. The nuclear forces which guarantee the stability of a nucleus are opposed by the electric force of repulsion which increases with the nuclear mass, since, considered on the whole, the charge also increases with the mass. The repulsion produces a decrease of the binding energy per particle, and thus a decrease of the stability with the increase in the mass. If in addition to this factor, the stability of the nucleus is imperilled by its vibration, the electric force of repulsion is able to make its effect felt more freely. Above a certain amplitude of vibration, it is able to increase still further the vibration initiated, and eventually to tear the nucleus apart.

  Figure 26.—Nuclear fission.

  This fission of the nucleus may take place in various ways. As a rule, the two fragments are not of equal size. For instance, when the rare uranium isotope 92U235 has absorbed a neutron, it may split into a strontium atom, 38Sr90, and a xenon atom, 54Xe144, and two neutrons, i.e.:

  92U235 + 0n1→ 38Sr90 + 54Xe144 + 0n1 + 0n1

  In this case, too, naturally, the totals of the mass numbers must be equal on both sides of the arrow, and the charge numbers must balance likewise.

  However, instead of producing the results thus indicated, the nuclear fission of this uranium atom may produce from the latter, for instance, the strontium atom 38Sr88 and the xenon atom 54Xe146, plus two neutrons, or atoms of two different elements and a different number of neutrons. In fact, in such fissions the formation of a very considerable number of different elements has been observed. The precise way in which the uranium nucleus splits (in which fission oc
curs) is a matter of chance to a certain extent.

  We have thus obtained a general bird’s eye view of the different possibilities of nuclear transmutation. Neutrons can be used to transmute all nuclei; charged particles are most suitable for producing a transmutation of the lighter nuclear species. Among the charged particles which primarily enter into consideration are protons and deuterons, which are capable of being sufficiently accelerated in electric fields, as well as the alpha particles, both natural and artificially produced by an intensive acceleration of helium nuclei in electric fields. Finally, there are several nuclei which can be heated to such a high degree by a sufficiently energy-rich gamma-ray photon that they emit a neutron; this emission changes their mass only, but not the chemical properties of that particular atom.