by W Heisenberg
Short-range forces are known to exist in nature elsewhere, too; the most important example is exhibited by the chemical forces, the so-called valencies (unless we are dealing with what is called a polar combination), in other words, the forces, which, for instance, bind two hydrogen atoms to one oxygen atom in a water molecule. These, too, are short-range forces which are operative actually only when the atoms are in direct contact, but become infinitesimally small as soon as the distance between the atoms increases.
It is due to this extremely short range that in heavier, macroscopic structures we can perceive neither the chemical nor the nuclear forces, whereas electric or magnetic forces are perceptible without any difficulty. The force between two magnetic poles is felt directly by the hand in which a magnet is held, and your hair stands on end as you approach an electrical high-tension apparatus. But chemical forces can never be perceived in this direct fashion, for they are operative over molecular distances only. The same applies to nuclear forces; they cannot be perceived anywhere except in the nuclear phenomena themselves.
Figure 15.—Potential of the force between neutron and proton.
Figure 16.—Potential of the force between proton and proton.
This has already supplied us with a certain general view of the nature of the force operative between a proton and a neutron. But what about the force between two protons?
One might surmise, to start with, that electric repulsion only is operative between them, since the force between protons and neutrons would be sufficient in itself to explain both nuclear cohesion and the fact that nuclear matter in a stable state consists of an approximately equal number of protons and neutrons. For if some force were operative between protons and neutrons only, the symmetry would already be guaranteed, to begin with. But experience concerning the deflection of protons by protons proves that forces of attraction are acting between particles of the same kind—in other words, not only between protons but between neutrons, too—which forces of attraction are approximately equal to those acting between protons and neutrons. In the case of two protons the situation is more complicated, because the electric force of repulsion is superimposed on the nuclear force of attraction. But when dealing with very short distances, the force of repulsion is much weaker than the nuclear force, so that in this case, practically, only the latter is operative. However, due to its long range, the electric force continues to be perceptible long after the nuclear force has ceased to be operative. If we draw a diagram of the potential energy of a proton at various distances from another proton, it will look more or less like the one reproduced in Figure 16. In fact, up to a distance of the order of 5 × 10−13 cm., the picture is practically identical with the one shown in Figure 15. From that point on, however, the potential energy does not approach 0 asymptotically, but passes through 0, rises to positive magnitudes, and only then does it drop asymptotically toward 0. Between two protons there exists what we call a potential barrier, a specimen of which will be discussed repeatedly later on.
According to all this, one might surmise that there exists a state in which two individual protons are bound to each other, namely, when their distances from each other are so small that the nuclear force of attraction overcomes the electric force of repulsion. But this is probably never the case. As pointed out before, two particles bound to each other vibrate constantly in relation to each other, even in their normal or ground state, the state of least energy. This ‘zero-point vibration’ is probably so powerful that it makes it impossible for any permanent bond to exist between two individual protons. But the attraction between protons is certain to play an important part in the more complex nuclei.
So now we have obtained our first overall view of nuclear forces. The most important of these is the force of attraction between neutron and proton. There is, furthermore, a force of a similar order of magnitude acting between two protons or two neutrons. The operative range of these nuclear forces diminishes rapidly with the distance, and in this respect they resemble the chemical valency forces, which likewise possess a very short range only.
II. THE NUCLEAR FORCES AS EXCHANGE FORCES
Let us now continue to formulate our queries in the same way as we did when dealing with the electric forces. Thus our first question will be: Does there exist any analogy permitting us to link nuclear forces with particles in a way similar to that in which we link electric forces with photons? With this object in view, we must once again study the chart appearing on page 60. The building blocks of the extranuclear structure of the atom are the electrons which are bound to the nucleus by the electric field. The electric field, in turn, is linked with the photons emitted by the atom when certain changes occur in this extranuclear structure. The building blocks of the nucleus are the neutrons and protons, which are held together by the nuclear field, while in this case the electric field is not a binding but a disruptive factor. Here, too, there are particles emitted by the nucleus as a result of changes in state, and in this case, we must distinguish between different kinds of particles. First, there are the gamma rays or photons. Analogously to the photons originating in the extranuclear atomic structure, these photons are linked to the electric field in the nucleus. In addition to these, there are the electrons and positrons, emitted in nuclear transmutations, and the neutrinos which always accompany them. The latter are similar to photons in many respects. The only difference is that neutrinos have a spin or angular momentum of /2, whereas that of a photon is either 0 or h.
It seems logical here to assume that the emission of these particles is linked up with the nuclear force field, somewhat in the same way as is the emission of photons with the electric field in the extranuclear atomic structure. But such an analogy would mean that the force between neutron and proton is transmitted because of the electrons, positrons and neutrinos. A similar linking of certain particles to a field must not be misinterpreted as meaning that the field is composed of such particles. The expression ‘composed of’ always suggests that the field might be conceived, to be, as it were, replaced by such particles. Actually, however, field and particles are, so to speak, merely different aspects of the very same concept, as was discussed earlier, in connection with the extranuclear structure of the atom.
The most correct way of expressing the situation is: There is a nuclear field, and in stationary states this nuclear field takes on the aspect of a short-range field, continually diminishing in intensity away from its centre, while in non-stationary processes it takes on the aspect of a wave radiation. The latter can be observed either as a wave radiation or as particles, according to the method of observation employed. We shall attempt to explain this by comparison with the more familiar electric field, by describing the force exerted by one electron upon another in two languages—first, in the language of waves, and then in the language of particles.
We can say, first, that an electron produces an electric field around itself, and that this electric field spreads in conformity with Maxwell’s equations. It may act on another electron and create a force on the latter. The corresponding description in terms of the other aspect is: One electron produces a particle, a photon, and this photon is subsequently absorbed by another electron. Thus in the first phrasing we speak of a ‘production of a field,’ and in the other of a ‘production of a particle’; in the first statement, we refer to an ‘ action of a field’, in the second one to an ‘absorption of a photon by a particle’. This state of affairs can be expressed schematically as follows:
Wave Aspect: Electron creates field; field acts on another electron.
Particle Aspect: Electron emits photon; photon is absorbed by another electron.
Both statements describe the same event. The first version is familiar to everybody who has ever had any dealings with electric fields. The second one is unfamiliar to most people, because in technical science as well as in macroscopic physics it is always unnecessary to conceive of an electric field as linked to photons. Under atomic conditions, however, this very
frequently proves to be a useful expedient. With reference to atomic radiation, it is often more convenient to speak of photons than of spherical waves.
Now let us apply exactly the same type of phraseology to the forces operative between protons and neutrons. First, we can say: The neutron produces a nuclear field, and this field acts on the proton. This is the description in terms of the wave aspect. In the terminology of the particle aspect, our description will be: The neutron produces particles, and these particles are absorbed by the proton. Let us again express this schematically, as follows:
Wave Aspect: Neutron creates field; field acts on proton.
Particle Aspect: Neutron emits electron plus neutrino; electron and neutrino are absorbed by proton.
Interpreting in this manner the force operative between neutron and proton, we see that an exchange of charge is linked with the action of the force. Namely, if in order to exert this force, the neutron must emit an electron and a neutrino, its charge is altered; it changes into a proton. And conversely, a proton changes into a neutron, due to the absorption of an electron and a neutrino. An exactly analogous conversion may occur also when a proton emits a positron and a neutrino, which are then absorbed by the neutron.
Thus, the nuclear forces are associated with an exchange of charged particles, and for this reason, forces of this kind are called exchange forces. They are of a very peculiar character, and it is their characteristic feature that their action is linked with an exchange of roles between the two partners. In this respect, therefore, they are totally different from the electric forces. But a close relationship with chemical forces is again evident. Quantum theory has already shown that chemical forces may also be regarded in general as exchange forces. For a similar exchange of charges occurs in the case of chemical forces, too. The simplest example of this is the hydrogen molecule ion, which consists of a hydrogen atom and a hydrogen nucleus (Figure 17). It is therefore actually a structure composed of two protons with an electron circling around them. This ion is a truly stable structure, and the force which holds it together owes its existence to the circumstance that the one electron revolves at times around one proton, at times around the other one. This means that in this case, too, we find that the force is linked with an exchange of charge—the shift of the electron from one proton to the other.
The concept of ‘exchange force’ can be comprehended most easily on the ground of the following experiment, carried out with the big Lawrence cyclotron in California in 1948 (cf. page 155). Neutrons of great energy are hurled against protons in a cloud chamber. The paths of the protons after collision become visible in the cloud chamber. In the case of an ordinary force, one would expect the great majority of the neutrons to be deflected to a very slight extent only (since they would not hit the proton exactly in the centre), while the protons would be hurled aside, with a relatively low velocity, at an angle of 90 deg. to the path of the neutrons. But in the case of an exchange force, the neutrons and protons must exchange roles after the collision; in the majority of collisions, the protons must continue along the paths of the oncoming neutrons (since the neutrons have actually been changed into protons) while the neutron is hurled aside at an angle of approximately 90 deg. This is exactly what we actually see in the cloud chamber. Figure 17A shows the tracks of the protons, most of which fly on along an almost straight path in the direction in which the oncoming neutrons were travelling. A magnetic field causes their paths to become more or less strongly curved, according to their energy. (The straight lines slanted at less than 45 deg. are produced by a thin wire mesh in the cloud chamber.)
Figure 17.—Ion of hydrogen molecule.
Figure 17A.—Scattering of neutrons in hydrogen.
The situation is, however, not quite so simple as we have made it appear. If the analogy of nuclear and electric forces were as we have been supposing, we would be in a position to determine the frequency of the occurrence of beta decay in a manner similar to that employed to determine the frequency of the occurrence of the emission of a photon in the extranuclear structure of the atom. When an extranuclear atomic structure is in an excited state, there exists in it at any given moment a certain probability of the emission of a light ray. By ‘certain probability’ we mean the following: In the wave aspect, the continuous movement of electrons causes a wave radiation to issue forth. In the particle aspect, there exists at any given moment a certain probability of the emission of a photon. These two views of the situation are linked to each other by the fact that the probability of radiation is given by the intensity of the emitted wave. The stronger is the wave, the greater is the probability of radiation, and the shorter-lived is the excited state. The duration of the excited state depends, therefore, on the amplitude of the vibration of the electrons.
The lifetime of a beta-unstable nucleus thus depends on the intensity of the wave radiation issuing forth from it. But if we carry out this computation on the ground of the considerations outlined above, we arrive at lifetimes much shorter than those actually observed. There still exists a discrepancy at this point, and this realization led the Japanese scientist Yukawa to a somewhat modified theory.
Yukawa assumes that between the nuclear field and the electrons, positrons and neutrinos there is still another species of particle, which may be called Yukawa particle for the time being. These Yukawa particles are assumed to have a mass several hundred times that of an electron, and to be capable of disintegrating into electrons, positrons and neutrinos, directly or eventually through other decay processes. So, according to Yukawa’s theory in nuclear transmutations, such a Yukawa particle should actually be emitted. However, this does not happen, because the Yukawa particle has such a great rest mass that the energy, mc2, necessary for its formation is not available. But the Yukawa particle can break up (directly, or indirectly through other processes) into electrons and neutrinos, and this happens, in a certain sense, in the moment of its formation, so that on the whole, it is sufficient to provide the energy required for the formation of the light particles, the electron and neutrino. This theory thus regards the process of nuclear transmutation as occurring in several steps. First, the Yukawa particle is formed from the nuclear field—or more correctly, the nuclear field itself is identical with the Yukawa particle, which for lack of sufficient energy for its formation cannot manifest itself as a real particle. Instead, no sooner is it formed than it breaks up into electrons and neutrinos, which then actually leave the nucleus.
If we accept this theory as a working hypothesis—and there is much in it to make it plausible—there arises the question whether the Yukawa particles are perhaps identical with a certain species of particle already observed in cosmic radiation. Actually, the most recent experiments make it extremely probable that the role of the Yukawa particles is played—in part, at any rate—by the heavy mesons (or ‘π particles’) observed by Powell; for in cases of nuclear fission of very high energy, these π particles have been observed to be hurled forth from the nuclei. The π particles (already mentioned on page 55) are about 275 times as heavy as an electron. According to Powell’s observations, they first break up into a light meson and a neutral particle (the latter is probably simply a neutrino). This light meson (its mass is about 213 times the mass of an electron) then breaks up further into an electron and probably two neutral particles. It is recognized here that the emission of electrons and neutrinos can occur by very roundabout ways only, possibly due somehow to the fact that the probability of the occurrence of a beta decay is extraordinarily small compared with the probability of other nuclear changes.
These considerations show also that the problem of the relationship between nuclear forces and the elementary particles regarded as being linked with them is a very complex one, which cannot be solved for many more years to come. At this moment, the only thing we know for certain is that the nuclear forces are, to a considerable extent at any rate, exchange forces, and that there exist unstable elementary particles, the mass of which is between the m
ass of an electron and the mass of a proton, and which are associated somehow with these nuclear forces. Any further clarification will become possible only when the very high energy nuclear disintegration processes have been investigated much more thoroughly than they have been up to now.