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Proton-proton chain

The proton-proton chain reaction (also known as the PP chain) is one of two fusion reactions by which stars convert hydrogen to helium, the other being the CNO cycle. The proton-proton chain is more important in stars the size of the Sun or less.

To overcome the electromagnetic repulsion between two hydrogen nuclei requires a large amount of energy, and this reaction takes an average of 10 billion years to complete. Because of the slowness of this reaction the Sun is still shining; if it where faster, the Sun would have exhausted its hydrogen long ago.

The first step involves the fusion of two hydrogen nuclei 1H (protons) into deuterium 2H, releasing a positron as one proton changes into a neutron, and a neutrino.

1H + 1H → 2H + e+ + νe + 0.42 MeV

The positron immediately annihilates with one of the hydrogen's electrons, and their mass energy is carried off by two gamma ray photons.

e+ + e- → 2γ + 1.02 MeV

After this the deuterium produced in the first stage can fuse with another hydrogen to produce a light isotope of helium, 3He:

2H + 1H → 3He + γ + 5.49 MeV

Finally, after millions of years, two of the helium nuclei 3He produced can fuse together to make the common helium isotope 4He, releasing two hydrogen nuclei to start the reaction again through three different paths called PP1, PP2 and PP3:

PP1:

3He +3He → 4He + 1H + 1H + 12.86 MeV

The complete PP1 chain reaction releases a net energy of 26.7 MeV. The PP1 chain is dominant in temperatures of 10-14 million Kelvin. Below 10 million Kelvin, the PP chain does not produce much 4He.
PP2:

3He + 4He → 7Be + γ
7Be + e- → 7Li + νe
7Li + 1H → 4He + 4He

The PP2 chain is dominant in temperatures of 14-23 million Kelvin.

PP3:
3He + 4He → 7Be + γ
7Be + 1H → 8B + γ
8B → 8Be + e+ + νe
8Be ↔ 4He + 4He

The PP3 chain is dominant if the temperatures exceeds 23 million Kelvin.

The PP3 chain is not a major source of energy in the Sun (as the Sun's core temperature is not high enough), but is very important in the solar neutrino problem because it generates the highest energy neutrinos.

The neutrinos detected from the Sun are significantly below what the proton-proton calculations predict, resulting in what is known as the solar neutrino problem. Observations of pressure waves in the Sun, known as helioseismology, have indicated that the pressures and temperatures in the Sun are very close to the pressures and temperatures predicted, assuming our understanding the proton-proton chain is correct. This has led astrophysicists to believe that the resolution of the solar neutrino problem lies in unexpected behavior of the neutrinos after they are produced.

In general, proton-proton fusion can occur only if the temperature (i.e., kinetic energy) of the protons is high enough that they can overcome the mutual Coulomb force repulsion. The theory that proton-proton reactions were the basic principle by which the Sun and other stars burn was advocated by Arthur Eddington in the 1920s. At the time, the temperature of the Sun was considered too low to overcome the Coulomb-force barrier. After the development of quantum mechanics, it was discovered that the tunneling of the wave functions of the protons through the repulsive barrier allowed for fusion at a lower temperature than the classical prediction.


Triple-alpha process

The triple alpha process is the process by which three helium nuclei (alpha particles) are transformed into carbon.

This nuclear fusion reaction can only ocurr rapidly at temperatures above 100,000,000 degrees and in stellar interior 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. Because the helium initially does not produce energy, the star 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 2.6×10-6 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 the temperature rapidly fell below the temperature necessary for nuclear fusion.

Ordinarily, the probability of this occurring 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 probablility that an incoming alpha particle will combine with beryllium-8 to form carbon. The fact that the existence of carbon depends on an energy level being exactly the right place, has been controversially cited by Fred Hoyle as evidence for the anthropic principle.

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 change in which oxygen combines with an alpha particle to form neon turns out to be more difficult because of nuclear spin rules. 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. Fusion produces energy only up to Fe. Heavier elementes are created in supernova explosion with absorption of energy. Hoyle has cited this as additional evidence for the anthropic principle. Both oxygen and carbon make up the ash of helium burning.


CNO cycle

The CNO (carbon-nitrogen-oxygen) cycle is one of two fusion reactions by which stars convert hydrogen to helium, the other being the proton-proton chain. While the proton-proton chain is more important in stars the size of the sun or less, theoretical models show that the CNO cycle is the dominant source of energy in heavier stars.

The CNO cycle may also be the dominant cause of nitrogen and oxygen production.

In actuality there is not only CNO cycle but three possible cycles which are astrophysically important. The main CNO cycle looks like this:

12C + 1H → 13N + γ
13N → 13C + e+ + νe
13C + 1H → 14N + γ
14N + 1H → 15O + γ
15O → 15N + e+ + νe
15N + 1H → 12C + 4He

The cycle results in the fusion of four hydrogen nuclei (1H, protons) into a single helium nucleus (4He, alpha particle), which supplies energy to the star in accordance with Einstein's equation. Ordinary carbon serves as a catalyst in this set of reactions and is regenerated.