The nucleosynthesis of light elements

Key points: The light elements were formed by nuclear reactions in stars formed from primeval hydro gen and helium; total mass number and overall charge are conserved in nuclear reactions; a large bind ing energy signifies a stable nucleus. The earliest stars resulted from the gravitational condensation of clouds of H and He at oms. The compression of these clouds under the influence of gravity gave rise to high temperatures and densities within them, and fusion reactions began as nuclei merged together. The earliest nuclear reactions are closely related to those now being studied in connection with the development of controlled nuclear fusion. Energy is released when light nuclei fuse together to give elements of higher atomic number. For example, the nuclear reaction in which an particle (a 4He nucleus with two protons and two neutrons) fuses with a carbon-12 nucleus to give an oxygen-16 nucleus and a -ray photon (y) is 16O This reaction releases 7.2 MeV of energy.1 Nuclear reactions are very much more ener getic than normal chemical reactions because the strong force is much stronger than the electromagnetic force that binds electrons to nuclei. Whereas a typical chemical reaction might release about 103 kJ mol 1, a nuclear reaction typically releases a million times more energy, about 109 kJ mol 1. In this nuclear equation, the nuclide, a nucleus of specific atomic number Z and mass number A, is designated Z AE , where E is the chemical symbol of the element. Note that, in a balanced nuclear equation, the sum of the mass numbers of the reactants is equal to the sum of the mass numbers of the products (12 16). The 8) provided an electron, e , when it appears as a particle, is denoted 1 0e and a positron, e , is denoted 1 0e. A positron is a positively charged 4 atomic numbers sum similarly (6 2 version of an electron: it has zero mass number (but not zero mass) and a single positive charge. When it is emitted, the mass number of the nuclide is unchanged but the atomic number decreases by 1 because the nucleus has lost one positive charge. Its emission is equivalent to the conversion of a proton in the nucleus into a neutron: 1 1p ➝ 0 1n e ν. A neutrino, (nu), is electrically neutral and has a very small (possibly zero) mass. Elements up to Z=26 were formed inside stars. Such elements are the products of the nuclear fusion reactions referred to as ‘nuclear burning’. The burning reactions, which should not be confused with chemical combustion, involved H and He nuclei and a com plicated fusion cycle catalysed by C nuclei. (The stars that formed in the earliest stages of the evolution of the cosmos lacked C nuclei and used noncatalysed H-burning reactions.) Some of the most important nuclear reactions in the cycle are

The net result of this sequence of nuclear reactions is the conversion of four protons (four ¹H nuclei) into an particle (a ⁴He nucleus):

¹An electronvolt (1 eV) is the energy required to move an electron through a potential difference of 1 V. It follows that 1 eV=1.602 10^-19 J, which is equivalent to 96.48 kJ mol^-1; 1 MeV= 10⁶ eV.

The reactions in the sequence are rapid at temperatures between 5 and 10 MK (where 1 MK=10⁶ K). Here we have another contrast between chemical and nuclear reactions, because chemical reactions take place at temperatures a hundred thousand times lower. Moderately energetic collisions between species can result in chemical change, but only highly vigorous collisions can provide the energy required to bring about most nuclear processes. Heavier elements are produced in significant quantities when hydrogen burning is complete and the collapse of the star’s core raises the density there to 108 kg m3 (about 105 times the density of water) and the temperature to 100 MK. Under these extreme conditions, helium burning becomes viable. The low abundance of beryllium in the present-day universe is consistent with the observation that 4 8Be formed by collisions 2 C: between particles goes on to react with more particles to produce the more stable carbon nuclide ₆²C:

Thus, the helium-burning stage of stellar evolution does not result in the formation of Be as a stable end product; for similar reasons, low concentrations of Li and B are also formed. The nuclear reactions leading to these three elements are still uncertain, but they may result from the fragmentation of C, N, and O nuclei by collisions with high-energy particles. Elements can also be produced by nuclear reactions such as neutron (n) capture accompanied by proton emission:

This reaction still continues in our atmosphere as a result of the impact of cosmic rays and contributes to the steady-state concentration of radioactive carbon-14 on Earth. The high abundance of iron and nickel in the universe is consistent with these elements having the most stable of all nuclei. This stability is expressed in terms of the binding energy, which represents the difference in energy between the nucleus itself and the same numbers of individual protons and neutrons. This binding energy is often presented in terms of a difference in mass between the nucleus and its individual protons and neu trons because, according to Einstein’s theory of relativity, mass and energy are related by E=mc², where c is the speed of light. Therefore, if the mass of a nucleus differs from the total mass of its components by ∆m=mn_ucleons =m_nucleus, then its binding energy is E_bind= (∆m)c². The binding energy of 56Fe, for example, is the difference in energy between the ⁵⁶Fe nucleus and 26 protons and 30 neutrons. A positive binding energy corresponds to a nucleus that has a lower, more favourable, energy (and lower mass) than its constituent nucleons (Box 1.1).

Figure 1.2 shows the binding energy per nucleon, E_bind /A (obtained by dividing the total binding energy by the number of nucleons), for all the elements. Iron and nickel occur at the maximum of the curve, showing that their nucleons are bound more strongly than in any other nuclide. Harder to see from the graph is an alternation of binding energies as the atomic number varies from even to odd, with even-Z nuclides slightly more stable than their odd-Z neighbours. There is a corresponding alternation in cosmic abundances, with nuclides of even atomic number being marginally more abundant than those of odd atomic number. This stability of even-Z nuclides is attributed to the lowering of energy by pairing nucleons in the nucleus.

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