Triple-alpha process

The triple alpha process is the process by which three helium nuclei (alpha particles) are transformed into carbon.^[1][2]

This nuclear fusion reaction can occur rapidly only at temperatures above 100,000,000 Kelvin and in stellar interiors having a high helium abundance. As such, it occurs in older stars, where helium produced by the proton-proton chain and the carbon-nitrogen-oxygen cycle has accumulated in the center of the star. After the completion of hydrogen burning in the stellar core, the core will collapse until the central temperature rises to the point where helium burning occurs.

⁴He + ⁴He ↔ ⁸Be

⁸Be + ⁴He ↔ ¹²C + γ + 7.367 MeV

The net energy release of the process is 7.275 MeV.

The ⁸Be produced in the first step is unstable and decays back into two helium nuclei in 2.6×10^-16 seconds. However, under the conditions of helium burning a small equilibrium abundance of ⁸Be is formed; capture of another alpha particle then leads to ¹²C. This conversion of three alpha particles to ¹²C is called the triple-alpha process.

Because the triple-alpha process is unlikely, it requires a long period of time to produce carbon. One consequence of this is that no 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:

¹²C + ⁴He → ¹⁶O + γ

The next step of the chain in which oxygen combines with an alpha particle to form neon turns out to be more difficult because of nuclear spin rules, and as a result heavier elements cannot easily be formed in 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 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 iron; heavier elements (those beyond Fe) 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.

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Reaction Rate and Stellar Evolution

The triple-alpha process is strongly dependent on the temperature and density of the stellar material. The energy released by the reaction is approximately proportional to the temperature to the 30th 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 only for minutes but burns 60-80% of the helium in the core and produces prodigious quantities of energy.^{[citation needed]}

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.

Discovery

The triple alpha process is highly dependent on carbon-12 having a resonance with the same energy as helium-4 and beryllium-8, 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. Hoyle suggested the idea to nuclear physicist Willy Fowler, who conceded that it was possible that this energy level had been missed in previous work. After a brief undertaking by his research group at the Kellogg Radiation Laboratory at the California Institute of Technology, they discovered a carbon-12 resonance near 7.65 Mev.

See also

• Proton-proton chain
• CNO cycle

References

1. ^ Editors Appenzeller, Harwit, Kippenhahn, Strittmatter, & Trimble (3rd Edition). Astrophysics Library. Springer, New York. ISBN. 
2. ^ Ostlie, D.A. & Carroll, B.W. (2007). An Introduction to Modern Stellar Astrophysics. Addison Wesley, San Francisco. ISBN 0-8053-0348-0.