Proton-proton chain

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

In the second step of the chain, a single proton fusion with a deuterium nucleus, resulting in He³ and a gamma ray

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⁺ + ν_e + 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^- → 2&gamma + 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 + &gamma + 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 + &gamma

       ⁷Be + e^- → ⁷Li + ν_e

       ⁷Li + ¹H → ⁴He + ⁴He

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

PP3:

³He + ⁴He	→	⁷Be + &gamma
⁷Be + ¹H	→	⁸B + γ
⁸B	→	⁸Be + e⁺ + ν_e
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.

See also:

³He + ⁴He	→	⁷Be + &gamma
⁷Be + e^-	→	⁷Li + ν_e
⁷Li + ¹H	→	⁴He + ⁴He