Older stars start to accumulate helium produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle in their cores. The products of further nuclear fusion reactions of helium with hydrogen or another helium nucleus produce lithium-5 and beryllium-8 respectively, both of which are highly unstable and decay almost instantly back into smaller nuclei. When the star starts to run out of hydrogen to fuse, the core of the star begins to collapse until the central temperature rises to 108 K (8.6 keV). At this point helium nuclei are fusing together at a rate high enough to exceed the rate at which their product, beryllium-8, decays back into two helium nuclei. This means that there are always a few beryllium-8 nuclei in the core, which can fuse with yet another helium nucleus to form carbon-12, which is stable:
The net energy release of the process is 1.166 pJ.
Because the triple-alpha process is unlikely, it requires a long period of time to produce much carbon. One consequence of this is that no significant amount of carbon was produced in the Big Bang because within minutes after the Big Bang, the temperature fell below that necessary for nuclear fusion.
Ordinarily, the probability of the triple alpha process would be extremely small. However, the beryllium-8 ground state has almost exactly the energy of two alpha particles. In the second step, 8Be + 4He has almost exactly the energy of an excited state of 12C. These resonances greatly increase the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted by Fred Hoyle before its actual observation, based on the physical necessity for it to exist, in order for carbon to be formed in stars. In turn, prediction and then discovery of this energy resonance and process gave very significant support to Hoyle's hypothesis of stellar nucleosynthesis, which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance.
As a side effect of the process, some carbon nuclei can fuse with additional helium to produce a stable isotope of oxygen and release energy:
See alpha process for more details about this reaction and further steps in the chain of stellar nucleosynthesis.
This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen but only a small fraction of these elements is converted into neon and heavier elements. Both oxygen and carbon make up the 'ash' of helium-4 burning. The anthropic principle has been controversially cited to explain the fact that nuclear resonances are sensitively arranged to create large amounts of carbon and oxygen in the Universe.
Fusion processes produce elements only up to nickel (which decays later to iron); heavier elements (those beyond Ni) are created mainly by neutron capture. The slow capture of neutrons, the s-process, produces about half of these heavy elements. The other half are produced by rapid neutron capture, the r-process, which probably occurs in a core-collapse supernova.
Reaction rate and stellar evolution 
The triple-alpha steps are strongly dependent on the temperature and density of the stellar material. The power released by the reaction is approximately proportional to the temperature to the 40th power, and the density squared. Contrast this to the PP chain which produces energy at a rate proportional to the fourth power of temperature and directly with density.
This strong temperature dependence has consequences for the late stage of stellar evolution, the red giant stage.
For lower mass stars, the helium accumulating in the core is prevented from further collapse only by electron degeneracy pressure. The pressure in the core is thus nearly independent of temperature. A consequence of this is that once a smaller star begins burning using the triple-alpha process, the core does not expand and cool in response; the temperature can only increase, which results in the reaction rate increasing further still and becoming a runaway reaction. This process, known as the helium flash, lasts a matter of seconds but burns 60–80% of the helium in the core. In the core flash prodigious quantities of energy are produced, allowing the star to reach approximately 1011 solar luminosities which is comparable to a whole galaxy, although no effects will be immediately visible at the star's surface.
For higher mass stars, the helium burning occurs in a shell surrounding a degenerate carbon core. Since the helium shell is not degenerate, the increased thermal pressure due to energy released by helium burning causes the star to expand. The expansion cools the helium layer and shuts off the reaction, and the star contracts again. This cyclical process causes the star to become strongly variable, and results in it blowing off material from its outer layers.
The triple alpha process is highly dependent on carbon-12 and beryllium-8 having resonances with the same energy as helium-4, and before 1952 no such energy level was known. Astrophysicist Fred Hoyle used the fact that carbon-12 is abundant in the universe as evidence for the existence of the carbon-12 resonance, in what is an example of the application of the Anthropic Principle: we are here, and we are made of carbon, so carbon must have originated somehow and the only physically conceivable way is through triple alpha processes that requires the existence of a resonance in a given very specific location in the spectra of carbon-12 nuclei. Hoyle suggested the idea to nuclear physicist William (Willy) A. Fowler, who conceded that it was possible that this energy level had been missed in previous work. By 1952, Fowler had already discovered the beryllium-8 resonance, and Edwin Salpeter calculated the reaction rate taking this resonance into account. This helped to explain the rate of the process, but the rate calculated by Salpeter was still somewhat too low. A few years later, after an undertaking by his research group at the Kellogg Radiation Laboratory at the California Institute of Technology, Fowler discovered a carbon-12 resonance near 7.65 MeV, which has eliminated the final discrepancy between the nuclear theory and the theory of stellar evolution.
The final reaction product lies in a 0+ state. Since the Hoyle State was predicted to be either a 0+ or a 2+ state, electron-positron pairs or gamma rays were expected to be seen. However, when experiments were carried out, the gamma emission reaction channel was not observed, and this meant the state must be a 0+ state. This state completely suppresses single gamma emission, since single gamma emission must carry away at least 1 unit of angular momentum. Production of an electron–positron pair from an excited 0+ state is possible because their combined spins (0) can couple to a reaction that has a change in angular momentum of 0.
See also 
- Editors Appenzeller, Harwit, Kippenhahn, Strittmatter, & Trimble (3rd Edition). Astrophysics Library. Springer, New York. ISBN.
- Ostlie, D.A. & Carroll, B.W. (2007). An Introduction to Modern Stellar Astrophysics. Addison Wesley, San Francisco. ISBN 0-8053-0348-0.
- G. Audia,§, O. Bersillonb, J. Blachotb and A.H. Wapstrac, http://www.nndc.bnl.gov/amdc/nubase/Nubase2003.pdf/ The NUBASE evaluation of nuclear and decay properties, (2001)
- Carroll, Bradley W. & Ostlie, Dale A. (2nd Edition). An Introduction to Modern Astrophysics. Addison-Wesley, San Francisco. pp. 312–313. ISBN 0-8053-0402-9.
- Carroll, Bradley W. & Ostlie, Dale A. (2nd Edition). An Introduction to Modern Astrophysics. Addison-Wesley, San Francisco. pp. 461–462. ISBN 0-8053-0402-9.
- Salpeter, E. E. (1952). "Nuclear Reactions in Stars Without Hydrogen". The Astrophysical Journal 115: 326–328. Bibcode:1952ApJ...115..326S. doi:10.1086/145546.
- Salpeter, E. E. (2002). "A GENERALIST LOOKS BACK". Annu. Rev. Astron. Astrophys. 40: 1–25. Bibcode:2002ARA&A..40....1S. doi:10.1146/annurev.astro.40.060401.093901.
- Cook, CW; Fowler, W.; Lauritsen, C.; Lauritsen, T. (1957). "12B, 12C, and the Red Giants". Physical Review 107 (2): 508–515. Bibcode:1957PhRv..107..508C. doi:10.1103/PhysRev.107.508.