Proton–proton chain

[3] In general, proton–proton fusion can occur only if the kinetic energy (temperature) of the protons is high enough to overcome their mutual electrostatic repulsion.

The theory that proton–proton reactions are the basic principle by which the Sun and other stars burn was advocated by Arthur Eddington in the 1920s.

After the development of quantum mechanics, it was discovered that tunneling of the wavefunctions of the protons through the repulsive barrier allows for fusion at a lower temperature than the classical prediction.

Starting with two protons combining to give a deuterium nucleus and a positron he found what we now call Branch II of the proton–proton chain.

[6] This was part of the body of work in stellar nucleosynthesis for which Bethe won the Nobel Prize in Physics in 1967.

As the protons fuse, one of them undergoes beta plus decay, converting into a neutron by emitting a positron and an electron neutrino[7] (though a small amount of deuterium nuclei is produced by the "pep" reaction, see below): The positron will annihilate with an electron from the environment into two gamma rays.

This is the rate-limiting reaction and is extremely slow due to it being initiated by the weak nuclear force.

[1] After it is formed, the deuteron produced in the first stage can fuse with another proton to produce the stable, light isotope of helium, 3He: This process, mediated by the strong nuclear force rather than the weak force, is extremely fast by comparison to the first step.

It is estimated that, under the conditions in the Sun's core, each newly created deuterium nucleus exists for only about one second before it is converted into helium-3.

The last three stages of this chain, plus the positron annihilation, contribute a total of 18.209 MeV, though much of this is lost to the neutrino.

In this reaction, helium-3 captures a proton directly to give helium-4, with an even higher possible neutrino energy (up to 18.8 MeV[citation needed]).

The mass–energy relationship gives 19.795 MeV for the energy released by this reaction plus the ensuing annihilation, some of which is lost to the neutrino.

Energy released as gamma rays will interact with electrons and protons and heat the interior of the Sun.

Neutrinos do not interact significantly with matter and therefore do not heat the interior and thereby help support the Sun against gravitational collapse.

Logarithm of the relative energy output (ε) of proton–proton (PP), CNO and Triple-α fusion processes at different temperatures (T). The dashed line shows the combined energy generation of the PP and CNO processes within a star. At the Sun's core temperature of 15.5 million K the PP process is dominant. The PP process and the CNO process are equal at around 20 MK. [ 1 ]
Scheme of the proton–proton branch I reaction
Proton–proton II chain
Proton–proton III chain
Proton–proton and electron-capture reactions in a star