The Origin of the Elements

There are just under a hundred naturally occurring elements, and about 300 isotopes in the solar system (Fig. 11.13). In Sect. 11.4, we have seen how the elements up to iron are produced when hydrogen burns to helium and helium further to carbon, oxygen and heavier elements.

Almost all nuclei heavier than helium were produced in nuclear reactions in stellar interiors. In the oldest stars, the mass fraction of heavy elements is only about 0.02%, whereas in the youngest stars it is a few per cent. Nevertheless, most of the stellar material is hydrogen and helium. According to the standard cosmological model, those were formed in the early stages of the Universe, when the temperature and density were suitable for nuclear reactions. (This will be discussed in Chap. 19.) Although helium is produced during the main sequence stellar evolution, very little of it is actually returned into space to be incorporated into later stellar generations. Most of it is either transformed into heavier elements by further reactions, or else remains locked up inside white dwarf remnants. Therefore the helium abundance does not increase by much due to stellar processes.

The most important nuclear reactions leading to the build-up of the heavy nuclei up to iron were presented in Sect. 10.3. The probabilities of the various reactions are determined either by experiments or by theoretical calculations. When they are known, the rel

Fig. 11.13. Element abundances in the solar system as a function of the nuclear mass number. The abundance of Si has been normalized as 106

Fig. 11.13. Element abundances in the solar system as a function of the nuclear mass number. The abundance of Si has been normalized as 106

ative abundances of the various nuclei produced can be calculated.

The formation of elements heavier than iron requires an input of energy, and thus they cannot be explained in the same manner. Still heavy nuclei are continually produced. In 1952 technetium was discovered in the atmosphere of a red giant. The half-life of the most longlived isotope 98Tc is about 1.5 x 106 years, so that the observed technetium must have been produced in the star.

Most of the nuclei more massive than iron are formed by neutron capture. Since the neutron does not have an electric charge, it can easily penetrate into the nucleus. The probability for neutron capture depends both on the kinetic energy of the incoming neutron and on the mass number of the nucleus. For example, in the solar system the abundances of isotopes show maxima at the mass numbers A = 70-90, 130, 138, 195 and 208. These mass numbers correspond to nuclei with closed neutron shells at the neutron numbers N = 50, 82, and 126. The neutron capture probability for these nuclei is very small. The closed shell nuclei thus react more slowly and are accumulated in greater abundances.

In a neutron capture, a nucleus with mass number A is transformed into a more massive nucleus:

The newly formed nucleus may be unstable to P decay, where one neutron is transformed into a proton:

Two kinds of neutron capture processes are encountered, depending on the value of the neutron flux. In the slow s-process, the neutron flux is so small that any P decays have had time to occur before the next neutron capture reaction takes place. The most stable nuclei up to mass number 210 are formed by the s-process. These nuclei are said to correspond to the P stability valley. The s-process explains the abundance peaks at the mass numbers 88, 138 and 208.

When the neutron flux is large, P decays do not have time to happen before the next neutron capture. One then speaks of the rapid r-process, which gives rise to more neutron-rich isotopes. The abundance maxima produced by the r-process lie at mass numbers about ten units smaller than those of the s-process.

A neutron flux sufficient for the s-process is obtained in the course of normal stellar evolution. For example, some of the carbon and oxygen burning reactions produce free neutrons. If there is convection between the hydrogen and helium burning shells, free protons may be carried into the carbon-rich layers. Then the following neutron-producing reaction chain becomes important:

The convection can also carry the reaction products nearer to the surface.

The neutron flux required for the r-process is about 1022 cm-3, which is too large to be produced during normal stellar evolution. The only presently known site where a large enough neutron flux is expected is near a neutron star forming in a supernova explosion. In this case, the rapid neutron capture leads to nuclei that cannot capture more neutrons without becoming strongly unstable. After one or more rapid P decays, the process continues.

The r-process stops when the neutron flux decreases. The nuclei produced then gradually decay by the P-

process towards more stable isotopes. Since the path of the r-process goes about ten mass units below the stability valley, the abundance peaks produced will fall about ten units below those of the s-process. This is shown in Fig. 11.14. The most massive naturally occurring elements, such as uranium, thorium and plutonium, are formed by the r-process.

There are about 40 isotopes on the proton-rich side of the P stability valley that cannot be produced by neutron capture processes. Their abundances are very small, relative to the neighbouring isotopes. They are formed in supernova explosions at temperatures higher than 109 K by reactions known as the p-process. At this temperature, pair formation can take place:

The positron may either be annihilated immediately or be consumed in the reaction e+ + (Z, A) ^ (Z +1, A) + Ve. Another reaction in the p-process is (Z, A) + p ^ (Z +1, A +1) + y . Finally, the fission of some heavier isotopes may give rise to p-process nuclei. Examples of this are the isotopes 184W, 190Pt and 196Hg formed by the fission of lead.

All the preceding reaction products are ejected into the interstellar medium in the supernova explosion. Collisions between cosmic rays and heavy nuclei then finally give rise to the light elements lithium, beryllium and boron. Thus the abundances of essentially all naturally occurring isotopes can be explained.

During succeeding generations of stars the relative abundance of heavy elements increases in the interstellar medium. They can then be incorporated into new stars, planets - and living beings.

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