Finely Tuned Carbon?

Eventually a star exhausts its supply of hydrogen in its core, gravitational contraction occurs, the temperature reaches about 108 K, and helium burning can occur via the reaction 3He-4 → C-12 + 2 photons. In fact, the nucleosynthesis of all the heavier elements essential for life relies on this reaction. However, the chance that three helium nuclei get together fast enough to form the carbon nucleus is negligible. So this critical reaction actually proceeds via an intermediate beryllium step given by 2He-4 + (99 ± 6) keV → Be-8 followed by

Be-8 + He-4 → C-12 + 2 photons. Since the Be-8 lifetime of about 10–17 second is much longer than the He-4 + He-4 collision time in a star, the beryllium will be around long enough for the reaction to occur.

The total energy of the Be-8 nucleus and a He-4 nucleus at rest is 7.4 MeV above the energy of the normal state of the C-12 nucleus. The radioactive state of the C-12 is 7.65 MeV above the normal state. If the energy of the radioactive state were more than 7.7 MeV above the normal state, the formation of C-12 via Be-8 plus He-4 would require the reactants to have at least 0.3 MeV of total kinetic energy, which is extremely unlikely at the temperatures found in most stars.

The importance of this process is emphasized by physicists who inject the Anthropic Principle, that certain constants of nature have values that seem to have been mysteriously fine-tuned to just the values that allow for the possibility of life. Recently, others have introduced a further extension that claims that this carbon nucleus coincidence can be explained only by the intervention of a designer with some special concern for life. Both groups cite the closeness of the required energy to the actual limit, 7.7 MeV – 7.65 MeV = 0.05 MeV, a quantity less than 1% of 7.65 MeV, as their evidence for the fine-tuning. Why is their reasoning suspect with regard to this carbon formation process?

Answer

The crucial energy comparison to make is not simply the radioactive state energy of 7.65 MeV to the practical limit value of 7.7 MeV, but one must include the comparison of the radioactive state energy 7.65 MeV to the energy 7.4 MeV of the reactants at rest. This energy of 0.25 MeV misses being too high for the production of carbon by the fractional amount of 0.05 MeV/0.25 MeV, or 20 percent, which is not so critical after all.