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
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
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.
The triple-alpha process is not relevant in normal (main sequence) stars like the
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.