by W Heisenberg
II. THE PROCEDURES FOR PRODUCING NUCLEAR TRANSMUTATION
As a general rule, particles very rich in energy are required to produce a nuclear transmutation. It is only when the transmutation is induced by neutrons that the energy content of the bombarding particle is frequently reduced deliberately as much as possible. But neutrons, to start with, must be produced by a nuclear reaction induced by fast particles, such, for instance, as the bombardment of beryllium by alpha particles.
Nature itself provides us with the most convenient source of energy-rich particles: The natural alpha emitters. To be sure, the radiation of even the most powerful radioactive preparations is always relatively weak, and sufficient for the transmutation of only a small number of atoms. On the other hand, in addition to the alpha particles, still other types of particles, namely, fast protons and deuterons, are needed in order to produce all possible sorts of nuclear transformation.
The most logical method of producing particles of high energy consists in a very strong acceleration of charged particles by a very high voltage, possibly 1,000,000 volts or more. Of course, direct-current voltage must be used. It is of course much more difficult to produce such a high direct-current voltage than it would be to generate an alternating-current voltage of the same magnitude.
The system known as the Greinacher circuit (Figure 33) is one very frequently employed today in high-voltage generators. Two columns, with condensers, C, are connected by a system of valves, V, each of which permits a beam of electrons to pass through in one direction only, for instance, in the direction indicated by arrows in our diagram. The entire system is designed so that the point d, for instance, can be charged positively (but not negatively) relative to the earthed point a, without being discharged. Similarly, c can be charged positively relative to d, likewise f relative to c, e relative to f, etc. Now, if an alternating-current voltage (usually between 200 and 300 kv or so) is applied, by means of a transformer, T, between the two columns, the points d, c, f, etc., become positively charged through the valves until the alternating-current voltage of, for instance, the point d never falls, throughout an entire period, below that of a, which may be taken as equal to 0; for otherwise a current would still flow through the valve V1. Thus, if the peak voltage of the transformer is +E, the potential of the point d, in a stationary state, fluctuates between 0 and 2E, and the point c has the constant potential 2E. No current flows then through the valves. Similarly, we find that in a stationary state the points e, g, i have the constant potentials 4E, 6E and 8E, while the potential of the points f, h, k fluctuates between 2E and 4E, between 4E and 6E, and between 6E and 8E, respectively. When, for instance, a current enters at the point i, the potential there decreases slightly, and the valves let through a beam of electrons in the direction of the arrow; these electrons carry the charge along, so that the potential at the point i cannot drop very far below 8E. Thus, proceeding by n steps, we obtain a 2n-fold of the peak voltage of the transformer—for instance, when the initial voltage E is 200 kv and three steps are used, the direct-current voltage ultimately obtained is 1,200,000 volts.
Figure 34 shows an exterior view of the high-voltage generator of the Kaiser Wilhelm Institut für Physik in Berlin-Dahlem. The slanting parts are the valves, and the globes correspond to the points c, e, f in Figure 33.
Figure 33.—Greinacher’s form.
The high voltage thus produced must now be used to accelerate charged particles. These latter originate as canal rays in an ordinary discharge tube. They then enter the highly evacuated accelerator tube, with the high voltage drop between its terminals. At the end of the accelerator tube they hit the substance which is meant to be transmuted.
The disadvantage of this apparatus is that it is extremely expensive. Therefore efforts have been made to achieve the same results by simpler means. In this connection the Van de Graaff high-voltage generator deserves attention. It is based on the old, and now hardly ever used principle of the influence machine. This generator consists of a large hollow metal sphere (Figure 35), or cylinder, serving as conductor, with a pulley within it and another pulley underneath it. A wide closed belt of some insulating material, for instance, silk, travels on these two pulleys. Outside of the conductor, electric charge is sprayed on the belt by means of a rectifier and a corona comb, and the belt, carrying this charge, enters the conductor, in which the charge is removed by a second corona comb and is transferred to the conductor. The conductor can thus be charged up to any desired voltage. Certain limitations are imposed by the dimensions of the space in which the generator is installed, since when a certain voltage is reached (the magnitude of which depends on the dimensions of this space and of the conductor itself) a spark jumps across to the walls and discharges the conductor. In 1939, there existed as yet no operating generator capable of attaining more than 2,000,000 volts. Figure 36 shows the largest installation of this nature, which was under construction in the United States several years ago. It is designed to produce 5,000,000 volts, and therefore built in a very large space, an old airship hangar. It has two conductors, supposed to be charged with opposite charges, in order to produce the double voltage for the discharge tube.
Figure 34.—High tension generator of the Kaiser Wilhelm Institute (Max Planck Institute) in Berlin-Dahlem.
Figure 35.—Van de Graaff’s high tension generator.
By far the most efficient apparatus for the production of fast particles is the cyclotron, invented by the American Lawrence. It is based on a very interesting principle, that of very frequently repeated acceleration by the same, not very high, voltage; thus it has, among other advantages, the good feature that it dispenses with the high voltages which are so difficult both to obtain and to control. The essential part of the cyclotron is a very large electromagnet which creates a powerful, very homogeneous and wide magnetic field of 10,000–15,000 oersteds between its pole pieces. The pole pieces are placed quite near to each other and the space between them is well evacuated. When a moving particle enters such a field, it describes a circular path, the radius of which is proportional to the velocity of the particle (Figure 37). Therefore, the velocity of the particles is proportional also to the circumference of the circle, and as a result, particles of the same kind, even though having different velocities, require exactly the same time to complete a full revolution. The space between the pole pieces houses two semicylindrical boxes, called dees, insulated from each other; between these dees, a potential difference of 30–100 kv is produced by a high-frequency generator. The result is a high-frequency alternating field in the small space between the dees. The frequency of this alternating field is regulated so as to correspond exactly to the period of the revolution of the particles in the magnetic field. The charged particles are made to enter the space between the pole pieces, near the centre (Z). There they come under the influence of the electric field; they attain a certain velocity and move in a semicircle in the space inside a dee where there is a magnetic field only. Proceeding in this manner, they reach the channel between the dees at the exact moment when the electric potential drop there is exactly equal, but opposite in direction, to what it was at the moment of their initial acceleration. They are now of course moving from one dee to the other in the opposite sense, which is that of the electric field, and in consequence are further accelerated. So the same process is repeated over and over again, and the velocity of the particles continues to mount. They move in an approximately spiral orbit, composed of semicircles, always further and further outward, until they are hurled through a window (T), designed so as to be penetrable by them, to perform their appointed task, the production of nuclear reactions.
Figure 36.—Van de Graaff’s high tension apparatus.
Figure 37.—Cyclotron.
The adjustment of such an apparatus calls for a great deal of technical skill. Moreover, the cyclotron is a machine of such dimensions as are seldom encountered in any other appliance used in physical research. Let us illustrate this by mentioning a few f
igures. The pole pieces of a cyclotron in use in the United States for some time are 95 cm. in diameter. The magnet of this cyclotron produces a magnetic field of 14,000 oersteds, and 60 tons of iron and 10 tons of copper went into its construction. The production of the magnetic field of 14,000 oersteds requires an input of 30 kilowatts. If this cyclotron is used to accelerate deuterons, these will emerge from it with an energy of 9 Mev.—in other words, as if they had passed through a potential drop of 9,000,000 volts. A current of only 0·1 milliampere flowing through this drop of potential would represent a power of nearly 1 kilowatt (900 watts to be precise). As each particle carries an elementary quantum of electricity, 1·6 × 10−19 coulombs, it is easy to compute that this current is the equivalent of roughly 6 × 1014 particles per second.
Figure 38 shows an exterior view of such a cyclotron. The windings of the magnet are visible; between the pole pieces of the magnet are the dees, in which the particles begin their acceleration. The beam emerging from the cyclotron is also visible in the photograph.
Numerous cyclotrons are already in use in the United States. Several have been built in Europe, too. Germany has had one since 1944, in the Kaiser Wilhelm Institut in Heidelberg, destined primarily for medical use. The universal recognition of the importance of the cyclotron is demonstrated by the amount of money spent on it in the United States, where the rough structure of a giant cyclotron was completed in 1940; its size makes it look more like a battleship than a scientific instrument. Its pole pieces are 4·7 metres in diameter, and its magnet is 17·8 metres in length (Figure 39). Its foundation contains 1,200 tons of concrete; the magnet contains 3,700 tons of iron and 300 tons of copper, wound in a strip of 10·2 cm. in width and 6 mm. in thickness. The frame of the magnet is made of 36 steel plates, each 5·5 mm. in thickness. The magnetic field intensity is 10,000 oersteds, and the frequency of the alternating electric field corresponds to a wavelength of 39 metres. Lawrence completed this cyclotron after the war, and it has enabled him to accelerate deuterons up to 100 Mev. and alpha particles up to 200 Mev.
In other words, the cyclotron is an extremely costly and also extremely complex apparatus. However, it is still by far the most useful nuclear-physical research instrument designed for the same purpose. In the United States it has made it possible to accomplish many nuclear reactions which would not have been feasible by any other means.
Figure 38.—Cyclotron.
Figure 39.—Magnet of the giant cyclotron.
8. THE PRACTICAL APPLICATIONS OF NUCLEAR PHYSICS
I. THE EXPLOITATION OF ATOMIC ENERGY FOR USEFUL PURPOSES
In studying the practical applications of nuclear physics, it is helpful to start out with analogies with chemistry. Chemistry deals with the combination of different elements in more complex substances, the chemical compounds, or conversely, with the separation of elements from such compounds, whereas nuclear physics deals with the transmutation of one element into another. Chemical processes serve two fundamentally different purposes: First, they can be used to convert less valuable materials into others of greater value, as, for instance, the combination of carbon and hydrogen to form benzol; secondly, a chemical conversion can be utilized in order to obtain energy, as, for instance, the combustion of coal to form carbon dioxide, in order to produce heat. It is obvious that these two applications are not independent of each other. It is often the case that a material is produced solely in order to be used as a source of energy—as, for instance, benzol.
The same is true, we may say, of nuclear processes. They can be applied, first, to produce a more valuable material out of one of lesser value, and secondly, they can be instrumental in producing energy.
In order to gain an idea of the order of magnitude of the energy which can be obtained through nuclear reactions, let us make use of another analogy with chemistry. The combustion of carbon with oxygen resulting in the formation of carbon dioxide can be written in the form of an equation which also shows the energy yielded by this process:
C + O2 → CO2 + 96 kilocalories
This formula relates to units of 1 mole and 1 gramme-atom, and states that the combustion of 1 gramme-atom = 12 grammes of carbon with 1 mole = 32 grammes of gaseous oxygen produces 1 mole = 44 grammes of carbon dioxide and liberates 96 kilocalories of heat.
Another example is the combustion of oxygen with hydrogen, resulting in water. The formula describing this process, likewise relating to units of 1 mole, is:
This means that the quantity of heat liberated is 68·4 kilocalories for every mole of water formed.
It may be said, quite generally, that these heat emissions of chemical processes are, throughout, of the order of magnitude of approximately 100 kilocalories per mole.
Now let us write the formula of a nuclear reaction, which happens to be one frequently applied in nuclear physics today, and which according to Döpel, can be released by ordinary canal rays having an energy corresponding to 5–10 kilovolts, viz.: the reciprocal reaction of two deuterons, which results in the formation of a hydrogen nucleus of mass number 1 and a hydrogen nucleus of mass number 3. The formula of the reaction, again relating to 1 mole, is:
1D2 + 1D2 → 1H1 + 1H3 + 100,000,000 kilocalories
In other words, the two deuterons do combine at first, but the compound nucleus thus formed splits up immediately into the two nuclei indicated above, since this is more favourable from the point of view of energetics, as is demonstrated by the tremendous heat emission of 100,000,000 kilocalories per mole. The heat emissions in the majority of the other nuclear reactions are of a similar order of magnitude. We see, therefore, how important nuclear reactions become as soon as they can be produced on a really large scale. The energy yield of nuclear reactions is about one million times greater than that obtainable by chemical processes. In other words, the nuclear ‘combustion’ of matter yields a millionfold of the energy released by a chemical combustion of the same quantity of the substance.
In nature, such nuclear reactions occur, as a rule, on a small scale only—due to the effect of cosmic radiation and of the radiation of radioactive substances. The fact that the energy released by these natural phenomena is not observed, is due to the fact that the quantities of energy produced are far too small, and also far too scattered.
Nevertheless, it is not quite right to claim that the energy liberated by nuclear reactions has never before played any part in nature. On the contrary, it may be claimed with full justification that in the long run, we owe our entire existence on earth to such processes. For, firstly radioactivity plays an extremely important part in determining the temperature and climate of the earth’s surface, and secondly, it is owing to such reactions in the sun that it shines on the earth and sustains life on our planet.
Nuclear reactions on a large scale are in fact taking place in the interiors of the stars. We know today that the energy which the stars—including our own sun—radiate into space is the product of such nuclear reactions. The source of this radiated energy was a puzzle for a long time, the solution of which called for a great deal of mental skill. We know that our sun has shone upon the earth with approximately the same intensity for at least two thousand million years, and in former years nobody could comprehend why it had not expended its total energy a long time ago. The solution of this problem had to wait for nuclear physics, and today we are in the position to specify exactly the only process that can possibly account for it. This solution was established as a result of three studies carried out by Atkinson and Houtermans, v. Weizsäcker, and Bethe. We cannot describe here the way that led to this solution; we can merely quote the result. It is a question of a certain sequence of formulae, which may be stated here, as follows:
(1) 6C12 + 1H1 → 7N13
(2) 7N13 → 6C13 + 1e0
(3) 6C13 + 1H1 → 7N14
(4) 7N14 + 1H1 → 8O15
(5) 8O15 → 7N15 + 1e0
(6) 7N15 + 1H1 → 6C12 + 2He4
This series consists partly of proton-induced reactions (1H1 is t
he symbol of the proton), partly of transmutations by the emission of a positron (1e0). The initial substances are carbon of mass number 12, and hydrogen. It is a known fact that the stars consist to a large extent of hydrogen, and that carbon also is present in them in small quantities. The hydrogen is already in the form of protons, since as a result of the enormous velocities due to the high temperatures (10–20 million degrees C.) prevalent in the interiors of stars, practically all the hydrogen atoms have been stripped of their single planetary electrons. This enormous velocity enables the protons to penetrate the other nuclei.
So, first, a nitrogen nucleus is formed from an ordinary carbon nucleus and one proton (1). This nitrogen nucleus is unstable and changes by the emission of a positron, into a carbon nucleus (2). This newly produced carbon nucleus is a heavy isotope of that which started the process. (The entire process is well known from laboratory experiments, too.) Now, another bombardment by a proton changes this carbon nucleus into an ordinary nitrogen nucleus (3). The latter changes, by the absorption of another proton, into an unstable oxygen nucleus (4), which immediately emits a positron and thus becomes a heavy isotope of the first nitrogen nucleus (5). Finally, the entire process is concluded by another absorption of a proton, and the emission of a helium nucleus (in other words, an alpha particle) results once again in an ordinary carbon nucleus.
