The Triple-Alpha

The fusion of hydrogen to helium by either the PP chain or the CNO cycle requires temperatures of the order of 10,000,000 K or higher, since only at those temperatures will there be enough hydrogen ions in the plasma with high enough velocities to tunnel through the Coulomb barrier at sufficient rates.

The Mass-5 and Mass-8 Bottlenecks

The helium that is produced as the "ash" in this thermonuclear "burning" cannot undergo fusion reactions at these temperatures or even substantially above because of a basic fact of nuclear physics in our Universe: there are no stable isotopes (of any element) having atomic masses 5 or 8. This means that the two most likely initial steps for the fusion of helium-4 (the next most abundant isotope in stars after hydrogen-1) involve combining the He-4 with H-1 to form a mass-5 isotope, or combining two He-4 nuclei to form a mass-8 isotope. But both are unstable, and so immediately fly apart before they can undergo any further reactions. This produces a bottleneck to further fusion at mass 5 and at mass 8.

High Temperatures and Helium Fusion

Only at extremely high temperatures, of order 100 million K, can this bottleneck be circumvented by a highly improbable reaction. At those temperatures, the fusion of two He-4 nuclei forms highly unstable Beryllium-8 at a fast enough rate that there is always a very small equilibrium concentration of Be-8 at any one instant.

The situation is somewhat like running water through a sieve. Normally the sieve holds no water because it drains out as fast as it is added. However, if the flow of water into the sieve is made fast enough, a small equilibrium amount of water will be in the sieve at any instant because even the sieve cannot empty the water fast enough to keep up with the incoming water.

This small concentration of Be-8 can begin to undergo reactions with other He-4 nuclei to produce an excited state of the mass-12 isotope of Carbon. This excited state is unstable, but a few of these excited Carbon nuclei emit a gamma-ray quickly enough to become stable before they disintegrate. This extremely improbable sequence is called the triple-alpha process because the net effect is to combine 3 alpha particles (that is, 3 He-4 nuclei) to form a C-12 nucleus.

Red Giants

The triple-alpha process is not relevant in normal (main sequence) stars like the Sun because their central temperatures are too low. However, in the red giant phase after many main sequence stars (like the Sun) have consumed their core hydrogen fuel the central temperatures rise high enough to initiate the triple-alpha process and to fuse Helium into Carbon. Further reactions can then convert some of this Carbon to Oxygen. Thus, much of the energy for red giants will come from the fusion of Helium to Carbon and Oxygen in their cores.

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