This is not really an example of fine-tuning. The energy level of the carbon nucleus only sets the temperature (T ~ 100 MK) at which helium and beryllium fusion will occur. If the energy had been different, carbon would have been produced at a different temperature, which means at a different stage of contraction of the star's helium core.
The triple alpha process is extremely temperature dependent though, is it not? And the lifetime of berylium -8 is short. I dunno, man; this looks pretty fine-tuned to me...
Alpha Fusion Chain
Once all of the hydrogen in a gas is converted into helium-4, fusion stops until the temperature rises to about 108K. At this temperature, helium-4 is converted into heavier elements, predominantly carbon-12 and oxygen.-16, both of which are multiples of helium-4 in their proton and neutron composition. To create these isotopes, beryllium-8 must first be created from two helium-4 nuclei, but this unstable isotope, with a lifetime of only 2.6 10-16 seconds, rapidly decays back into helium-4.
The short lifetime of beryllium-8 ensures that the creation and decay of beryllium-8 are in equilibrium. This means that the density of beryllium-8 is set by the thermodynamic properties of the gas, specifically the temperature and the density of the gas; the creation and decay rated drop out of the problem. As a practical matter, because the amount of energy required to create beryllium-8 is large, 92.1 keV, the density of berylium-8 to helium-4 is minuscule: for a temperature of 108 K and a helium-4 density of 105 gm cm-3, the ratio of beryllium-8 nuclei to helium-4 nuclei will be around 10-9. The density of beryllium-8 is proportional to T-3/2 e-40 keV/T. This temperature dependence imples that a small change in temperature produces a large change in the berylium-8 density; for a temperature of 108 K (9 keV), a 15% change in temperature produces a factor of 2 change in the berylium-8 density.
While berylium-8 is present, its creation is a small energy sink. To release energy, carbon-12 and heavier elements must be created. Carbon-12 is created when helium-4 combines with beryllium-8. In this interaction, carbon-12 nucleus is left in an energetic state from which it decays, releasing a gamma-ray. The conversion of beryllium-8 into carbon-12 releases 7.37 MeV.
The conversion of helium-4 into carbon-12 is therefore accomplished through the following two reactions:
He4 + He4 → Be8
Be8 + He4 → C12 +
The process of converting three helium-4 nuclei into a single carbon-12 nucleus releases a total of 7.27 MeV, all of which remains trapped within the star. This fusion chain can be treated as a single process; it is then called the triple-alpha process (an alpha particle is a helium-4 nucleus). The triple-alpha reaction rate is proportional to the cube of the helium-4 density. Because of the strong temperature dependence of the beryllium-8 density, the triple-alpha reaction rate is much more temperature dependent than any of the hydrogen fusion rates. Within a star, helium fusion provides sufficient energy to support a star when the core temperature rises to about 100 million degrees. The practical effect of this is that helium fusion within stars occurs over a very narrow range of temperatures.
For temperatures that enable the triple-alpha process to proceed, other nuclear reactions are possible involving helium that create elements with atomic masses that are multiples of 4. These processes are as follows:
C12 + He4 → O16 +
O16 + He4 → Ne20 +
Ne16 + He4 → Mg24 +
Each of these reactions release energy. The creation of oxygen-16 generates 7.16 MeV, while the generation of neon-20 generates 4.730 MeV. The next-two elements release even more energy, with 9.32 MeV from the creation of magnesium-24 and 9.98 from the creation of silicon-28. The creation of sulfur-32 and argon-26 generates 6.95 MeV and 6.65 MeV respectively. These large amounts of energy point to the stability of these isotopes.
Because the triple-alpha process switches on so rapidly with temperature, all stellar cores that are fusing helium have essentially the same temperature, so that the ratios of carbon-12 to oxygen-16 to neon-20 to magnesium-24 within a stellar core is essentially the same for all stellar cores.
In the universe, the third, fourth, fifth, and sixth most abundant elements are oxygen, neon, nitrogen, and carbon. The triple-alpha process and the CNO process of hydrogen fusion are responsible for this, with the triple-alpha process creating the carbon, oxygen, and neon, and the CNO process creating the nitrogen from the carbon and oxygen.
Source; The Astrophysics Spectator
read your own study done by your own "we" group.
