The carbon challenge

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1. Helium burning

Figure 1: Synthesis of carbon in a burning star. Two alpha particles react to form beryllium-8. Beryllium-8 and an alpha particle react to form carbon-12, proceeding via the Hoyle state. This state in carbon-12 is a “resonance” in the beryllium-8 plus alpha-particle system. Once the resonant state is formed, it tends to decay by breaking up into beryllium-8 and an alpha particle. However, approximately four out of ten thousand decays bring the excited carbon-12 nucleus to its stable ground state.

“…In the first-generation stars the ash resulting from hydrogen burning via the p-p chain is entirely helium-4, the creation of heavier elements having been blocked by the instabilities at A=5 and A=8. These are referred to as the mass gaps.
Since carbon-12, the fourth most abundant nuclear species observed in the universe, could not synthesized in its observed abundances in the early universe, the site for its creation has to be in stars. Thus, a major question in the early studies of nucleosynthesis was how the stability gaps were bridged to create carbon-12 using only helium. While the simultaneous interaction of three α-particles to form carbon-12 is energetically possible, the probability for this direct process is much to small to account for the observed carbon-12 abundances.
The solution of this problem was provided in principle by Salpeter and Opik, who proposed that carbon-12 was created via a two-step process. In the first step, two a-particles combine to form beryllium-8 in its ground state.
The ground state of beryllium-8 is known to be unstable against decay into two α-particles with a lifetime of 10-16 s, which is the reason for the mass-8 stability gap. However, as Salpeter pointed out, this lifetime is long compared with the 10-19 s transit time of two α-particles with kinetic energies corresponding to Q.
As a result, a small concentration of beryllium-8 nuclei builds up in equilibrium with the decay products, two α-particles.
The actual equilibrium concentration of beryllium-8 in a helium environment can be calculated using the Saha equation.
For typical values, the Saha equation leads to one beryllium-8 nucleus for every 109 helium-4 nuclei.
In the second step, Salpeter suggested that, since the first step provides an appreciable concentration of beryllium-8 nuclei, these nuclei capture an additional α-particle, thus completing the carbon-12 creation process.
Since the combined effect of these two steps is to transform three α-particles into a carbon-12 nucleus, this set of reactions is referred to as the triple-α process:

3α —> 12C

Assuming the triple-α process to be the correct mechanism for synthesis of 12C, Hoyle showed that the amount of 12C produced in this way is insufficient to expalin the obseved abundance.
To surmount this difficulty, Hoyle suggested that sufficient 12C nuclei could be synthesized if the 8Be(α,γ)12C reaction took place through an s-wave resonance near the 8Be + α threshold, since the existence of such a resonance would greatly accelerate the rate of triple-α process….. Read the rest of this entry »

Written by physicsgg

May 9, 2011 at 10:44 pm