by Isaac Asimov
Among the magic-number nuclei are helium 4 (2 protons and 2 neutrons), oxygen 16 (8 protons and 8 neutrons), and calcium 40 (20 protons and 20 neutrons), all especially stable and more abundant in the universe than other nuclei of similar size.
As for the higher magic numbers, tin has ten stable isotopes, each with 50 protons, and lead has four, each with 82 protons. There are five stable isotopes (each of a different element) with 50 neutrons each, and seven stable isotopes with 82 neutrons each. In general, the detailed predictions of the nuclear-shell theory work best near the magic numbers. Midway between (as in the case of the lanthanides and actinides), the fit is poor. But just in the midway regions, nuclei are farthest removed from the spherical (and shell theory assumes spherical shape) and are most markedly ellipsoidal. The 1963 Nobel Prize for physics was awarded to Goeppert Mayer and to two others: Wigner, and the German physicist Johannes Hans Daniel Jensen, who also contributed to the theory.
In general, as nuclei grow more complex, they become rarer in the universe, or less stable, or both. The most complex stable isotopes are lead 208 and bismuth 209, each with the magic number of 126 neutrons, and lead, with the magic number of 82 protons in addition. Beyond that, all nuclides are unstable and, in general, grow more unstable as the size of the nucleus increases. A consideration of magic numbers, however, explains the fact that thorium and uranium possess isotopes that are much more nearly stable than other nuclides of similar size. The theory also predicts that some isotopes of elements 110 and 114 (as I mentioned earlier) might be considerably less unstable than other nuclides of that size. For this last, we must wait and see.
Leptons
The electron and the positron are notable for their small masses—only 1/1,836 that of the proton, the neutron, the antiproton, or the antineutron—and hence are lumped together as leptons (from the Greek leptos, meaning “thin”).
Although the electron was first discovered nearly a century ago, no particle has yet been discovered that is less massive than the electron (or positron) and yet carries an electric charge. Nor is any such discovery expected. It may be that the electric charge, whatever it is (we know what it does and how to measure its properties, but we do not know what it is), has associated with itself a minimum mass, and that that is what shows up in the electron. In fact, there may be nothing to the electron but the charge; and when the electron behaves as a particle, the electric charge on that particle seems to have no extension but occupies a mere point.
To be sure, some particles have no mass associated with them at all (actually, no rest-mass, which I shall explain in the next chapter), but these have no electric charge. For instance, waves of light and other forms of electromagnetic radiation can behave as particles (see the next chapter). This particle manifestation of what we ordinarily think of as a wave is called photon from the Greek word for “light.”
The photon has a mass of 0, and an electric charge of 0, but it has a spin of 1, so that it is a boson. How can one tell what the spin is? Photons take part in nuclear reactions, being absorbed in some cases, given off in others. In such nuclear reactions, the total spin of the particles involved before and after the reaction must remain unchanged (conservation of spin). The only way for this to happen in nuclear reactions involving photons is to suppose that the photon has a spin of 1. The photon is not considered a lepton, that term being reserved for fermions.
There are theoretical reasons for supposing that, when masses undergo acceleration (as when they move in elliptical orbits about another mass or undergo gravitational collapse), they give off energy in the form of gravitational waves. These waves, too, can possess a particle aspect, and such a gravitational particle is called a graviton.
The gravitational force is much, much weaker than the electromagnetic force. A proton and an electron attract each other gravitationally with only about 1/1039 as much force as they attract each other electromagnetically. The graviton must be correspondingly less energetic than the photon and must therefore be unimaginably difficult to detect.
Nevertheless, the American physicist Joseph Weber began the formidable task of trying to detect the graviton in 1957. Eventually he made use of a pair of aluminum cylinders 153 centimeters long and 66 centimeters wide, suspended by a wire in a vacuum chamber. The gravitons (which would be detected in wave form) would displace those cylinders slightly, and a measuring system for detecting a displacement of a hundred-trillionth of a centimeter is used. The feeble waves of the gravitons, coming from deep in space, ought to wash over the entire planet, and cylinders separated by great distances ought to be affected simultaneously. In 1969, Weber announced he had detected the effects of gravitational waves. This produced enormous excitement, for it lent support to a particularly important theory (Einstein’s theory of general relativity). Unfortunately, not all scientific tales have happy endings. Other scientists could not duplicate Weber’s results no matter how they tried, and the general feeling is that gravitons are still undetected. Nevertheless, physicists are confident enough of the theory to be sure they exist. They are particles with a mass of 0, a charge of 0, and a spin of 2 and are also bosons. The gravitons, too, are not listed among the leptons.
Photons and gravitons do not have antiparticles; or, rather, each is its own antiparticle. One way of visualizing this is to imagine a paper folded lengthwise, then opened, so that there is a crease running down its center. If you put a little circle to the left of the crease, and another an equal distance to the right, they would represent an electron and a positron. The photon and the graviton would be right on the crease.
NEUTRINOS AND ANTINEUTRINOS
So far, then, it would seem there are two leptons: the electron and the positron. Physicists would have been content with that; there seemed to be no overwhelming need for any more—except that there was such a need. There were complications that had to do with the emission of beta particles by radioactive nuclei.
The particle emitted by a radioactive nucleus generally carries a considerable amount of energy. Where does the energy come from? It is created by conversion into energy of a little of the nucleus’s mass; in other words, the nucleus always loses a little mass in the act of expelling the particle. Now physicists had long been troubled by the fact that often the beta particle emitted in a nucleus’s decay did not carry enough energy to account for the THE PARTICLES 317 amount of mass lost by the nucleus. In fact, the electrons were not all equally deficient. They emerged with a wide spectrum of energies, the maximum (attained by very few electrons) being almost right, but all the others falling short to a smaller or greater degree. Nor was this a necessary concomitant of subatomic particle-emission. Alpha particles emitted by a particular nuclide possessed equal energies in expected quantities. What, then, was wrong with beta-particle emission? What had happened to the missing energy?
Lise Meitner, in 1922, was the first to ask this question with suitable urgency; and by 1930, Niels Bohr, for one, was ready to abandon the great principle of conservation of energy, at least as far as it applied to subatomic particles. In 1931, however, Wolfgang Pauli, in order to save conservation of energy (see chapter 8), suggested a solution to the riddle of the missing energy. His solution was very simple: another particle carrying the missing energy comes out of the nucleus along with the beta particle. This mysterious second particle has rather strange properties: it has no charge and no mass; .all it has, as it speeds along at the velocity of light, is a certain amount of energy. This particle looked, in fact, like a fictional item created justto balance the energy books.
And yet, no sooner had it been proposed than physicists were sure that the particle existed. When the neutron was discovered and found to break down into a proton, releasing an electron which, as in beta decay, also carried a deficiency of energy, they were still surer. Enrico Fermi in Italy gave the putative particle a name—neutrino, Italian for “little neutral one.”
The neutron furnished physicists with another piece of evidence for the existence of the
neutrino. As I have mentioned, almost every particle has a spin. The amount of spin is expressed in multiples of one-half, plus or minus, depending on the direction of the spin. Now the proton, the neutron, and the electron have each a spin of ½. If, then, the neutron, with spin of ½, gives rise to a proton and an electron, each with spin of ½, what happens to the law of conservation of spin? There is something wrong here. The proton and the electron may total their spins to 1 (if both spin in the same direction) or to 0 (if their spins are opposite); but any way you slice it, their spins cannot add up to ½. Again, however, the neutrino comes to the rescue. Let the spin of the neutron be +½. Let the proton’s spin be +½ and the electron’s –½, for a net of 0. Now give the neutrino the spin +½, so that it, too, is a fermion (and therefore a lepton)—and the books are neatly balanced.
+½(n) = +½(p) – ½(e) + ½(neutrino).
There is still more balancing to do. A single particle (the neutron) has formed two particles (the proton and the electron) and, if we include the neutrino, actually three particles. It seems more reasonable to suppose that the neutron is converted into two particles and an antiparticle, or a net of one particle. In other words, what we really need to balance is not a neutrino out an antineutrino.
The neutrino itself would arise from the conversion of a proton into a neutron. There the products would be a neutron (particle), a positron (antiparticle), and a neutrino (particle). This, too, balances the books.
In other words, the existence of neutrinos and antineutrinos would save not one, but three, important conservation laws: the conservation of energy, the conservation of spin, and the conservation of particle/antiparticles. It is important to save these laws for they seem to hold in all sorts of nuclear reactions that do not involve electrons or positrons, and it would be very useful if they hold in reactions that did involve those particles, too.
The most important proton-to-neutron conversions are those involved in the nuclear reactions that go on in the sun and other stars. Stars therefore emit fast floods of neutrinos, and it is estimated that perhaps 6 percent to 8 percent of their energy is carried off in this way. This, however, is only true for such stars as our sun. In 1961, the American physicist Hong Yee Chiu suggested that, as the central temperatures of a star rise, additional neutrino-producing reactions become important. As a star progresses in its evolutionary course toward a hotter core (see chapter 2), an ever larger proportion of its energy is carried off by neutrinos.
There is crucial importance in this notion. The ordinary method of transmitting energy, by photons, is slow. Photons interact with matter, and they make their way out from the sun’s core to its surface only after uncounted myriads of absorptions and re-emissions. Consequently, although the sun’s central temperature is 15,000,000° C, its surface is only 6,000° C. The substance of the sun is a good heat insulator.
Neutrinos, however, virtually do not interact with matter. It has been calculated that the average neutrino could pass through 100 light-years of solid lead with only a 50 percent chance of being absorbed. Hence, any neutrinos formed in the sun’s core leave at once and at the speed of light, reaching the sun’s surface, without interference, in less than 3 seconds and speeding off. (Any neutrinos that move in our direction pass through without affecting us in any way either by day or by night; for at night, when the bulk of the earth is between ourselves and the sun, the neutrinos can pass through the earth and ourselves as easily as through ourselves alone.)
By the time a central temperature of 6,000,000,000° K is reached, Chiu calculates, most of a star’s energy is being pumped into neutrinos. The neutrinos leave at once, carrying the energy with them, and the sun’s center cools drastically. It is this, perhaps, which leads to the catastrophic contraction that then makes itself evident as a supernova.
TRACKING DOWN THE NEUTRINO
Antineutrinos are produced in any neutron-to-proton conversion, but these do not go on (as far as is known) on the vast scale that leads to such floods of neutrinos from every star. The most important sources of antineutrinos are from natural radioactivity and uranium fission (which I shall discuss in more detail in chapter 10).
Naturally physicists could not rest content until they had actually tracked THE PARTICLES 319 down the neutrino; scientists are never happy to accept phenomena or laws of nature entirely on faith. But how to detect an entity as nebulous as the neutrino—an object with no mass, no charge, and practically no propensity to interact with ordinary matter?
Still, there was some slight hope. Although the probability of a neutrino reacting with any particle is exceedingly small, it is not quite zero. To be unaffected in passing through one hundred light-years of lead is just a measure of the average; but some neutrinos will react with a particle before they go that far, and a few—an almost unimaginably small proportion of the total number—will be stopped within the equivalent of 1/10 inch of lead.
In 1953, a group of physicists, led by Clyde Lorrain Cowan and Frederick Reines of the Los Alamos Scientific Laboratory, set out to try the next-to-impossible. They erected their apparatus for detecting neutrinos next to a large fission reactor of the Atomic Energy Commission on the Savannah River in Georgia. The reactor would furnish streams of neutrons, which, hopefully, would release floods of antineutrinos. To catch them, the experimenter used large tanks of water. The plan was to let the antineutrinos bombard the protons (hydrogen nuclei) in the water and detect the results of the capture of an antineutrino by a proton.
What would happen? When a neutron breaks down, it yields a proton, an electron, and an antineutrino. Now a proton’s absorption of an antineutrino should produce essentially the reverse. That is to say, the proton should be converted to a neutron, emitting a positron in the process. So there were two things to be looked for: (I) the creation of neutrons, and (2) the creation of positrons. The neutrons could be detected by dissolving a cadmium compound in the water, for when cadmium absorbs neutrons, it emits gamma rays of a certain characteristic energy. And the positrons could be identified by their annihilating interaction with electrons, which would yield certain other gamma rays. If the experimenters’ instruments detected gamma rays of exactly these two telltale energies and separated by the proper time interval, they could be certain that they had caught antineutrinos.
The experimenters arranged their ingenious detection devices, waited patiently; and, in 1956, exactly a quarter-century after Pauli’s invention of the particle, they finally trapped the antineutrino. The newspapers and even some learned journals called it simply the neutrino.
To get the real neutrino, we need some source that is rich in neutrinos. The obvious one is the sun. What system can be used to detect the neutrino as opposed to the antineutrino? One possibility (following a suggestion of the Italian physicist Bruno Pontecorvo) begins with chlorine 37, which makes up about one-fourth of all chlorine atoms. Its nucleus contains 17 protons and 20 neutrons. If one of those neutrons absorbs a neutrino, it becomes a proton (and emits an electron). The nucleus will then have 18 protons and 19 neutrons and will be argon 37.
To form a sizable target of chlorine neutrons, one might use liquid chlorine, but it is a very corrosive and toxic substance, and keeping it liquid presents a problem in refrigeration. Instead, chlorine-containing organic compounds can be used; one called tetrachloroethylene is a good one for the purpose;
The American physicist Raymond R. Davis made use of such a neutrino trap in 1956 to show that there really was a difference between the neutrino and the anti neutrino. Assuming the two particles were different, the trap would detect only neutrinos and not antineutrinos. When it was set up near a fission reactor in 1956 under conditions where it would certainly detect antineutrinos (if antineutrinos were identical to neutrinos), it did not detect them.
The next step was to try to detect neutrinos from the sun. A huge tank containing 100,000 gallons of tetrachloroethylene was used for the purpose. It was set up in a deep mine in South Dakota. There was enough earth above
it to absorb any particles, except neutrinos, emerging from the sun. (Consequently, we have the odd situation that in order to study the sun, we must burrow deep, deep into the bowels of the earth.) The tank was then exposed to the solar neutrinos for several months to allow enough argon 37 to accumulate to be detectable. The tank was then flushed with helium for twenty-two hours, and the tiny quantity of argon 37 in the helium gas determined. By 1968, solar neutrinos were detected, but in not more than one-third the amounts expected from current theories about what is going on inside the sun. This finding proved very disturbing and I will get back to it later in the chapter.
NUCLEAR INTERACTION
Our list of subatomic particles now stands at ten: four massive particles (or baryons, from a Greek word for “heavy”)—the proton, the neutron, the antiproton, and the antineutron; four leptons—the electron, the positron, the neutrino, and the anti neutrino; and two bosons—the photon and the graviton. And yet these are not enough, as physicists decided by the following considerations.
Ordinary attractions between isolated protons and electrons, or repulsions between two protons or two electrons, can easily be explained as the result of electromagnetic interactions. The manner in which two atoms hold together, or two molecules, can also be explained by electromagnetic interactions—the attraction of positively charged nuclei for the outer electrons.
As long as the atomic nucleus was thought to be made up of protons and electrons, it seemed reasonable to assume that the electromagnetic interaction—the overall attraction between protons and electrons—would suffice to explain how nuclei held together as well. Once, however, the proton-neutron theory of nuclear structure came to be accepted in 1930, there was an appalled realization that there was no explanation for what holds the nucleus in being.
