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Stars

Fusion of Helium

Alpha Fusion Chain

Once all of the hydrogen in a gas is converted into helium-4, fusion stops until the temperature rises to about 108°K. At this temperature, helium-4 is converted into heavier elements, predominantly carbon-12 and oxygen.-16, both of which are multiples of helium-4 in their proton and neutron composition. To create these isotopes, beryllium-8 must first be created from two helium-4 nuclei, but this unstable isotope, with a lifetime of only 2.6 × 10-16 seconds, rapidly decays back into helium-4.

The short lifetime of beryllium-8 ensures that the creation and decay of beryllium-8 are in equilibrium. This means that the density of beryllium-8 is set by the thermodynamic properties of the gas, specifically the temperature and the density of the gas; the creation and decay rated drop out of the problem. As a practical matter, because the amount of energy required to create beryllium-8 is large, 92.1 keV, the density of berylium-8 to helium-4 is minuscule: for a temperature of 108° K and a helium-4 density of 105 gm cm-3, the ratio of beryllium-8 nuclei to helium-4 nuclei will be around 10-9. The density of beryllium-8 is proportional to T-3/2 e-40 keV/T. This temperature dependence imples that a small change in temperature produces a large change in the berylium-8 density; for a temperature of 108° K (9 keV), a 15% change in temperature produces a factor of 2 change in the berylium-8 density.

While berylium-8 is present, its creation is a small energy sink. To release energy, carbon-12 and heavier elements must be created. Carbon-12 is created when helium-4 combines with beryllium-8. In this interaction, carbon-12 nucleus is left in an energetic state from which it decays, releasing a gamma-ray. The conversion of beryllium-8 into carbon-12 releases 7.37 MeV.

The conversion of helium-4 into carbon-12 is therefore accomplished through the following two reactions:

He4 + He4 Be8
Be8 + He4 C12 + γ

The process of converting three helium-4 nuclei into a single carbon-12 nucleus releases a total of 7.27 MeV, all of which remains trapped within the star. This fusion chain can be treated as a single process; it is then called the triple-alpha process (an alpha particle is a helium-4 nucleus). The triple-alpha reaction rate is proportional to the cube of the helium-4 density. Because of the strong temperature dependence of the beryllium-8 density, the triple-alpha reaction rate is much more temperature dependent than any of the hydrogen fusion rates. Within a star, helium fusion provides sufficient energy to support a star when the core temperature rises to about 100 million degrees. The practical effect of this is that helium fusion within stars occurs over a very narrow range of temperatures.

For temperatures that enable the triple-alpha process to proceed, other nuclear reactions are possible involving helium that create elements with atomic masses that are multiples of 4. These processes are as follows:

C12 + He4 O16 + γ
O16 + He4 Ne20 + γ
Ne16 + He4 Mg24 + γ

Each of these reactions release energy. The creation of oxygen-16 generates 7.16 MeV, while the generation of neon-20 generates 4.730 MeV. The next-two elements release even more energy, with 9.32 MeV from the creation of magnesium-24 and 9.98 from the creation of silicon-28. The creation of sulfur-32 and argon-26 generates 6.95 MeV and 6.65 MeV respectively. These large amounts of energy point to the stability of these isotopes.

Because the triple-alpha process switches on so rapidly with temperature, all stellar cores that are fusing helium have essentially the same temperature, so that the ratios of carbon-12 to oxygen-16 to neon-20 to magnesium-24 within a stellar core is essentially the same for all stellar cores.

In the universe, the third, fourth, fifth, and sixth most abundant elements are oxygen, neon, nitrogen, and carbon. The triple-alpha process and the CNO process of hydrogen fusion are responsible for this, with the triple-alpha process creating the carbon, oxygen, and neon, and the CNO process creating the nitrogen from the carbon and oxygen.

Secondary Helium Fusion Processes

The CNO hydrogen fusion process converts carbon-12 and the oxygen-16 into four other isotopes as hydrogen is converted into helium-4. These isotopes are carbon-13, nitrogen-14, nitrogen-15, and oxygen-15. Two of these isotopes, carbon-13 and nitrogen-14, can be destroyed by combining with helium-4 during the helium fusion stage. During these reactions, neutrons are released that either combine with other isotopes to form heavier elements or decay to a proton and an electron. Because the CNO isotopes are present in only small quantities in a star, the amount of energy release through their fusion with helium-4 is generally negligible; the importance of these fusion processes is in their effect on the isotopes found in the universe. The absorption of a neutron by a nucleus can produce isotopes away from the C12 → O1620 → Mg24 path.

The destruction of carbon-13 proceeds through the following reaction with helium-4:

C13 + He4 O16 + n

In this reaction, the carbon absorbs a helium nucleus and releases a neutron to become oxygen-16, releasing 2.21 MeV of energy.

The destruction of nitrogen-14 through the absorption of helium-4 creates the unstable nucleus fluorine-18, which decays to oxygen-18. These reactions are as follows:

N14 + He4 F18 + γ
F18 O18 + e+ + νe

The energy released in these processes is 4.42 MeV.

The oxygen-18 created from nitrogen-14 can be destroyed by absorbing a helium-4 nucleus. This interaction has two branches, one that creates neon-21, and a second that creates neon-22. The first of these reactions is as follows:

O18 + He4 Ne21 + n

This reaction is endothermic, absorbing a total of 0.699 MeV of energy from the gas.

The second reaction is as follows:

O18 + He4 Ne22 + γ
Ne22 + He4 Mg25 + n

The first of these reactions is exothermic, generating 9.67 MeV of energy. The reaction producing the magnesium-25 in endothermic, swallowing 0.48 MeV of energy.

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