Proton-proton chain reaction

The proton-proton reaction--the first step in the proton-proton chain. Two protons fuse to form a deuterium nucleus. The reaction results in the emission of a positron and a neutrino.

In the second step of the chain, a single proton fuses with a deuterium nucleus, resulting in 3He and a gamma ray

The proton-proton chain reaction 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 10⁹ years to complete. Because of the slowness of this reaction the Sun is still shining; if it were faster, the Sun would have exhausted its hydrogen long ago.

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.

The pp chain reaction

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⁺ + ν_e

with the neutrinos released in this step carrying energies up to 0.42 MeV.

This first step is extremely slow, because it depends on the weak interaction to convert one proton into a neutron. In fact this is the limiting step, with a proton waiting an average of 10⁹ years before fusing into deuterium.

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

From here three different main branches arise to generate helium isotope ⁴He. In pp1 helium-4 comes from fusing two of the helium-3 nuclei produced; the other two branches, pp2 and pp3 require the helium-4 produced in pp1, both branches arising from the different paths that Beryllium-7 can follow. In the Sun, branch pp1 takes place with a frequency of 91%, pp2 with 9% and pp3 with 0.1%.

The pp I branch

³He +³He → ⁴He + ¹H + ¹H + 12.86 MeV

The complete pp I chain reaction releases a net energy of 26.7 MeV. The pp I branch is dominant in temperatures of 10 to 14 megakelvins (MK). Below 10 MK, the PP chain does not produce much ⁴He.

The pp II branch

The pp II branch is dominant in temperatures of 14 to 23 MK.

90% of the neutrinos produced in the reaction ⁷Be(e⁻,ν_e)⁷Li* carry an energy of 0.861 MeV, while the remaining 10% carry 0.383 MeV (depending on whether lithium-7 is excited or in the ground state).

The pp III branch

The pp III chain is dominant if the temperatures exceeds 23 MK.

The pp III chain is not a major source of energy in the Sun (as the Sun's core temperature is not high enough), but was very important in the solar neutrino problem because it generates the highest energy neutrinos (≤14.06 MeV).

The pp IV or Hep

In this case Helium-3 reacts directly with a proton to give helium-4

³He + ¹H → ⁴He + ν_e + e⁺

The pep reaction

The socalled pep (proton-electron-proton) reaction is a pretty rare one, that can take place instead of the pp reaction:

¹H + e⁻ + ¹H → ²H + ν_e

In the Sun, the frequency of pep reaction versus pp reaction is 1:400. However the neutrinos released are far more energetic: while neutrinos produced in the first step of the pp reaction range in energy up to 0.42 MeV, the neutrinos from the pep reaction produce sharp-energy-line neutrinos of 1.44 MeV.

See also

• Triple-alpha process
• CNO cycle

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