Up to now we have studied nuclear reactions mainly for their role in stellar energy generation. Now let's consider them again, but this time as the processes responsible for creating much of the world in which we live. The evolution of the elements, combining nuclear physics with astronomy, is a very complex subject and a very important problem in modern astronomy.
We currently know of 112 different elements, ranging from the simplest—hydrogen, containing 1 proton—to the most complex, discovered in 1996, with 112 protons in its nucleus. (See Appendix Table 2.) All elements exist in several different isotopic forms, each isotope having the same number of protons but a different number of neutrons. We often think of the most common or stable isotope as being the "normal" form of an element. Some elements, and many isotopes, are radioactively unstable, meaning that they eventually decay into other, more stable, nuclei.
| TABLE 21.1 Cosmic Abundances of the Elements | ||||||||||||||||||
*The total does not equal 100 percent because of uncertainties in the helium abundance. |
The 81 stable elements found on Earth make up the overwhelming bulk of matter in the universe. In addition, 10 radioactive elements—including radon and uranium—also occur naturally on our planet. Even though their half-lives (the time required for half the nuclei to decay into something else) of these elements are very long (millions or even billions of years, typically), their steady decay means that they are scarce on Earth, in meteorites, and in lunar samples. (More Precisely 7-2) They are not observed in stars—there is just too little of them to produce detectable spectral lines.
Besides these 10 naturally occurring radioactive elements, 19 more radioactive elements have been artificially produced under special conditions in nuclear laboratories on Earth. The debris collected after nuclear weapons tests also contains traces of some of these elements. Unlike the naturally occurring radioactive elements, these artificial ones decay into other elements quite quickly (in much less than a million years). Consequently, they too are extremely rare in nature. Two other elements round out our list. Promethium is a stable element that is found on our planet only as a by-product of nuclear laboratory experiments. Technetium is an unstable element that is found in stars but does not occur naturally on Earth.
How and where did all these elements form? Were they always present in the universe, or were they created after the universe formed? Since the 1950s, astronomers have come to realize that the hydrogen and most of the helium in the universe are primordial—that is, these elements date from the very earliest times. All other elements in our universe result from stellar nucleosynthesis—that is, they were formed by nuclear fusion in the hearts of stars.
To test this idea we must consider not just the list of different kinds of elements and isotopes but also their observed abundances, shown in Figure 21.12. This curve is derived largely from spectroscopic studies of stars, including the Sun. The essence of the figure is summarized in Table 21.1, which combines all the known elements into eight distinct groups based on the number of nuclear particles (protons and neutrons) that they contain. (All isotopes of all elements are included in both Table 21.1 and Figure 21.12, although only a few elements are marked by dots and labeled in the figure.) Any theory proposed for the creation of the elements must reproduce these observed abundances. The most obvious feature is that the heavy elements are much less abundant than most light elements. However, the many peaks and troughs evident in Figure 21.12 also represent important constraints.
Figure 21.12 A summary of the cosmic abundances of the elements and their isotopes, expressed relative to the abundance of hydrogen. The horizontal axis shows atomic number—the number of protons in the nucleus. Notice how many common terrestrial elements are found on "peaks" of the distribution, surrounded by elements that are tens or hundreds of times less abundant. Notice especially the large peak around the element iron.
Let's begin by reviewing the reactions leading to heavy-element production at various stages of stellar evolution. Stellar nucleosynthesis begins with the proton—proton chain studied in Chapter 16. 
(Sec. 16.5) Provided that the temperature is high enough—at least 107 K—a series of nuclear reactions occur, ultimately forming a nucleus of ordinary helium (4He) from four protons (1H):
Recall that the positrons immediately interact with nearby free electrons, producing high-energy gamma rays through matter—antimatter annihilation. The neutrinos rapidly escape, carrying energy with them but playing no direct role in nucleosynthesis. The validity of these reactions has been directly confirmed in nuclear experiments conducted in laboratories around the world during recent decades. In massive stars, the CNO cycle (Interlude 20-1) may greatly accelerate the hydrogen-burning process, but the basic 4-protons-to-1-helium-nucleus reaction, illustrated in Figure 21.13, is unchanged.
Figure 21.13 Diagram of the basic proton—proton hydrogen-burning reaction. Four protons combine to form a nucleus of helium-4, releasing energy in the process.
As helium builds up in the core of a star, the burning ceases, and the core contracts and heats up. When the temperature exceeds about 108 K, helium can overcome their mutual electrical repulsion, leading to the triple-alpha reaction, which we discussed in Chapter 20: (Sec. 20.2)
The net result of this reaction is that three helium-4 nuclei are combined into one carbon-12 nucleus (Figure 21.14), releasing energy in the process.
Figure 21.14 Diagram of the basic triple-alpha helium-burning reaction occurring in post—main-sequence stars. Three helium-4 nuclei combine to form carbon-12.
At higher and higher temperatures, heavier and heavier nuclei can gain enough energy to overcome the electrical repulsion between them. At about 6 
108 K (reached only in the cores of stars much more massive than the Sun), carbon nuclei can fuse to form magnesium, as depicted in Figure 21.15(a):
However, because of the rapidly mounting nuclear charges—that is, the increasing number of protons in the nuclei—fusion reactions between any nuclei larger than carbon require such high temperatures that they are actually quite uncommon in stars. The formation of most heavier elements occurs by way of an easier path. For example, the repulsive force between two carbon nuclei is three times greater than the force between a nucleus of carbon and one of helium. Thus, carbon—helium fusion occurs at a lower temperature than that at which carbon—carbon fusion occurs. As we saw in Section 20.3, at temperatures above 2 108 K, a carbon-12 nucleus colliding with a helium-4 nucleus can produce oxygen-16:
If any helium-4 is present, this reaction, shown in Figure 21.15(b), is much more likely to occur than the carbon—carbon reaction.
Figure 21.15 Carbon can form heavier elements (a) by fusion with other carbon nuclei or, more commonly, (b) by fusion with a helium nucleus.
Similarly, the oxygen-16 thus produced may fuse with other oxygen-16 nuclei at a temperature of about 109 K to form sulfur-32,
but it is much more probable that an oxygen-16 nucleus will capture a helium-4 nucleus (if one is available) to form neon-20:
The second reaction is more likely because it requires a lower temperature than that necessary for oxygen—oxygen fusion.
Thus, as the star evolves, heavier elements tend to form through helium-capture rather than by fusion of like nuclei. Because these helium-capture reactions are so much more common, elements with nuclear masses of 4 units (that is, helium itself), 12 units (carbon), 16 units (oxygen), 20 units (neon), 24 units (magnesium), and 28 units (silicon) stand out as prominent peaks in Figure 21.12, our chart of cosmic abundances. Each element is built by combining the preceding element and a helium-4 nucleus as the star evolves.
Helium capture is by no means the only type of nuclear reaction occurring in evolved stars. As nuclei of many different kinds accumulate, a great variety of reactions become possible. In some, protons and neutrons are freed from their parent nuclei and are absorbed by others, resulting in new nuclei with masses intermediate between those formed by helium capture. Laboratory studies confirm that common nuclei, such as fluorine-19, sodium-23, phosphorus-31, and many others, are created in this way. Their abundances, however, are not so great as those produced directly by helium capture, simply because the helium-capture reactions are much more common in stars. For this reason many of these elements (those with masses not divisible by 4, the mass of a helium nucleus) are found in the troughs of Figure 21.12.
Around the time silicon-28 appears in the core of a star, a competitive struggle begins between the continued capture of helium to produce even heavier nuclei and the tendency of more complex nuclei to break down into simpler ones. The cause of this breakdown is heat. By now the star's core temperature has reached the unimaginably large value of 3 billion K, and the gamma rays associated with that temperature have enough energy to break a nucleus apart, as illustrated in Figure 21.16(a). This is the same process of photodisintegration that will ultimately accelerate the star's iron core in its final collapse toward a Type II supernova.
Figure 21.16 (a) At high temperatures heavy nuclei (such as silicon, shown here) can be broken apart into helium nuclei by high-energy photons. (b) Other nuclei can capture the helium nuclei—or alpha particles—thus produced, forming heavier elements by the so-called alpha process. This process continues all the way to the formation of iron.
Under the intense heat, some silicon-28 nuclei break apart into seven helium-4 nuclei. Other nearby nuclei that have not yet photodisintegrated may capture some or all of these helium-4 nuclei, leading to the formation of still heavier elements (Figure 21.1b). The process of photodisintegration provides raw material that allows the helium-capture process to proceed to greater masses. The process continues, with some heavy nuclei being destroyed and others increasing in mass. In succession the star forms sulfur-32, argon-36, calcium-40, titanium-44, chromium-48, iron-52, and nickel-56. The chain of reactions building from silicon-28 up to nickel-56 is
This two-step process—photodisintegration followed by the direct capture of some or all of the resulting helium-4 nuclei (or alpha particles)—is often called the alpha process.
Nickel-56 is unstable. It decays rapidly, first into cobalt-56, then into a stable iron-56 nucleus. Any unstable nucleus will continue to decay until stability is achieved, and iron-56 is the stablest of all nuclei. Thus, the alpha process leads inevitably to the buildup of iron in the stellar core.
Iron's 26 protons and 30 neutrons are bound together more strongly than the particles in any other nucleus. Iron is said to have the greatest nuclear binding energy of any element. Any nucleus with more or fewer protons or neutrons has less nuclear binding energy and is not quite so stable as the iron-56 nucleus. This enhanced stability of iron explains why some of the heavier nuclei in the iron group are more abundant than many lighter nuclei (see Table 21.1 and Figure 21.12)—nuclei tend to "accumulate" near iron as stars evolve.
If the alpha process stops at iron, how did heavier elements, such as copper, zinc, and gold, form? To form them, some nuclear process other than helium capture must have been involved. That other process is neutron capture—the formation of heavier nuclei by the absorption of neutrons.
Deep in the interiors of highly evolved stars, conditions are ripe for neutron capture to occur. Neutrons are produced as "by-products" of many nuclear reactions, so there are many of them present to interact with iron and other nuclei. Neutrons have no charge, so there is no repulsive barrier for them to overcome in combining with positively charged nuclei. As more and more neutrons join an iron nucleus its mass continues to grow.
Adding neutrons to a nucleus—iron, for example—does not change the element. Rather, a more massive isotope is produced. Eventually, however, so many neutrons are added to the nucleus that it becomes unstable and then decays radioactively to form a stable nucleus of some other element. The neutron-capture process then continues. For example, an iron-56 nucleus can capture a single neutron (n) to form a relatively stable isotope, iron-57:
This reaction may be followed by another neutron capture:
producing another relatively stable isotope, iron-58. Iron-58 can capture yet another neutron to produce an even heavier isotope of iron:
Iron-59 is known from laboratory experiments to be radioactively unstable. It decays in about a month into cobalt-59, which is stable. The neutron-capture process then resumes: cobalt-59 captures a neutron to form the unstable cobalt-60, which in turn decays to nickel-60, and so on.
Each successive capture of a neutron by a nucleus typically takes about a year, so most unstable nuclei have plenty of time to decay before the next neutron comes along. Researchers usually refer to this "slow" neutron-capture mechanism as the s-process. It is the origin of the copper and silver in the coins in our pockets, the lead in our car batteries, the gold (and the zirconium) in the rings on our fingers.
The s-process explains the synthesis of stable nuclei up to and including bismuth-209, the heaviest known nonradioactive nucleus, but it cannot account for the heaviest nuclei, such as thorium-232, uranium-238, or plutonium-242. Any attempt to form elements heavier than bismuth-209 by slow neutron capture fails because the new nuclei decay back to bismuth as fast as they form. There must be yet another nuclear mechanism that produces the very heaviest nuclei. This process is called the r-process (where r stands for "rapid," in contrast to the "slow" s-process we just described). The r-process operates very quickly, occurring (we think) literally during the supernova explosion that signals the death of a massive star.
During the first 15 minutes of the supernova blast, the number of free neutrons increases dramatically as heavy nuclei are broken apart by the violence of the explosion. Unlike the s-process, which stops when it runs out of stable nuclei, the neutron-capture rate during the supernova is so great that even unstable nuclei can capture many neutrons before they have time to decay. Jamming neutrons into light- and middle-weight nuclei, the r-process is responsible for the creation of the heaviest known elements. The heaviest of the heavy elements, then, are actually born after their parent stars have died. However, because the time available for synthesizing these heaviest nuclei is so brief, they never become very abundant. Elements heavier than iron (see Table 21.1) are a billion times less abundant than hydrogen and helium.
The modern picture of element formation involves many different types of nuclear reactions occurring at many different stages of stellar evolution, from main-sequence stars all the way to supernovae. Light elements—from hydrogen to iron—are built first by fusion, then by alpha capture, with proton and neutron capture filling in the gaps. Elements beyond iron form by neutron capture and radioactive decay. We are reassured of the basic soundness of our theories by three convincing pieces of evidence.
First, the rate at which various nuclei are captured and the rate at which they decay are known from laboratory experiments. When these rates are incorporated into detailed computer models of the nuclear processes occurring in stars and supernovae, the resulting elemental abundances agree extremely well, point by point, with the observational data presented in Figure 21.12 and Table 21.1. The match is remarkably good for elements up through iron and is still fairly close for heavier nuclei. Although the reasoning is indirect, the agreement between theory and observation is so striking that most astronomers regard it as very strong evidence in support of the entire theory of stellar evolution and nucleosynthesis.
Second, the presence of one particular nucleus—technetium-99—provides direct evidence that heavy-element formation really does occur in the cores of stars. Laboratory measurements show that the technetium nucleus has a radioactive half-life of about 200,000 years. This is a very short time astronomically speaking. No one has ever found even traces of naturally occurring technetium on Earth because it all decayed long ago. The observed presence of technetium in the spectra of many red-giant stars implies that it must have been synthesized through neutron capture—the only known way that technetium can form—within the past few hundred thousand years. Otherwise, we would not observe it. Many astronomers consider the spectroscopic evidence for technetium as proof that the s-process really does operate in evolved stars.
Third, the study of typical light curves from Type I supernovae indicates that radioactive nuclei form as a result of the explosion. Figure 21.17(a) (see also Figure 21.7) displays the dramatic rise in luminosity at the moment of explosion and the characteristic slower decrease in brightness. Depending on the initial mass of the exploded star, the luminosity takes from several months to many years to decrease to its original value, but the shape of the decay curve is nearly the same for all exploded stars. These curves have two distinct features. After the initial peak, the luminosity first declines rapidly, then decreases at a slower rate. This change in the luminosity decay invariably occurs about 2 months after the explosion, regardless of the intensity of the outburst.
Figure 21.17 (a) The light curve of a Type I supernova, showing not only the dramatic increase and slow decrease in luminosity but also the characteristic change in the rate of decay about 2 months after the explosion (after the time indicated by the arrow). This particular supernova occurred in the faraway galaxy IC4182 in 1938. The crosses are the actual observations of the supernova's light. (b) Theoretical calculations of the light emitted by the radioactive decay of nickel-56 and cobalt-56 produce a light curve very similar to those actually observed in real supernova explosions, lending strong support to the theory of stellar nucleosynthesis.
We can explain the two-stage decline of the luminosity curve in Figure 21.17(a) in terms of the radioactive decay of unstable nuclei, notably nickel-56 and cobalt-56, produced in abundance during the early moments of the supernova explosion. From theoretical models of the explosion we can calculate the amounts of these elements expected to form, and we know their half-lives from laboratory experiments. Because each radioactive decay produces a known amount of visible light, we can then determine how the light emitted by these unstable elements should vary in time. The result is in very good agreement with the observed light curve in Figure 21.17(b)—the luminosity of a Type I supernova is entirely consistent with the decay of about 0.6 solar masses of nickel-56. More direct evidence for the presence of these unstable nuclei was first obtained in the 1970s, when a gamma-ray spectral feature of decaying cobalt-56 was identified in a supernova observed in a distant galaxy.
