Proton–proton chain

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. At the time, the temperature of the Sun was considered to be too low to overcome the Coulomb barrier. 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. In 1938, Hans Bethe and C.L. Critchfield proposed two protons combining to give a deuterium nucleus and a positron was the primary igniting reaction of pp chain nuclear reactions of the Sun, known today to be Branch II of the proton–proton chain. The reaction of two nuclei (Branch I) was not known at that time. This was part of the body of work in stellar nucleosynthesis for which Bethe won the Nobel Prize in Physics in 1967. ==The proton–proton chain==

The first step in all the branches is the fusion of two protons into a deuteron. As the protons fuse, one of them undergoes beta plus decay, converting into a neutron by emitting a positron and an electron neutrino (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. Including this annihilation and the energy of the neutrino, the net reaction has a Q value (released energy) of 1.442 MeV: but it can be calculated from theory. Once the helium-3 has been produced, there are four possible paths to generate . In , helium-4 is produced by fusing two helium-3 nuclei into beryllium-6, which immediately emits two protons to become helium-4. The and branches fuse with pre-existing to form beryllium-7, which undergoes further reactions to produce two helium-4 nuclei. About 99% of the energy output of the sun comes from the various chains, with the other 1% coming from the CNO cycle. According to one model of the sun, 83.3 percent of the produced by the various branches is produced via branch I while produces 16.68 percent and 0.02 percent. Since half the neutrinos produced in branches II and III are produced in the first step (synthesis of a deuteron), only about 8.35 percent of neutrinos come from the later steps (see below), and about 91.65 percent are from deuteron synthesis. However, another solar model from around the same time gives only 7.14 percent of neutrinos from the later steps and 92.86 percent from the synthesis of deuterium nuclei. The difference is apparently due to slightly different assumptions about the composition and metallicity of the sun. There is also the extremely rare branch. Other even rarer reactions may occur. The rate of these reactions is very low due to very small cross-sections, or because the number of reacting particles is so low that any reactions that might happen are statistically insignificant. The overall reaction is: releasing 26.73 MeV of energy, some of which is lost to the neutrinos. The branch The fusion of two nuclei produces a nucleus, which promptly ejects two protons. The complete chain releases a net energy of but 2.2 percent of this energy (0.59 MeV) is lost to the neutrinos that are produced. The branch is dominant at temperatures of 10 to . Below , the chain proceeds at slow rate, resulting in a low production of . The branch The branch is dominant at temperatures of 18 to . The following table calculates the amount of energy lost to neutrinos and the amount of "solar luminosity" coming from the three branches. "Luminosity" here means the amount of energy given off by the Sun as electromagnetic radiation rather than as neutrinos. The starting figures used are the ones mentioned higher in this article. The table concerns only the 99% of the power and neutrinos that come from the reactions, not the 1% coming from the CNO cycle. ==The PEP reaction==

A deuteron can also be produced by the rare pep (proton–electron–proton) reaction (electron capture): D + ve --> In the Sun, the frequency ratio of the pep reaction versus the reaction is 1:400. However, the neutrinos released by the pep reaction are far more energetic: while neutrinos produced in the first step of the reaction range in energy up to , the pep reaction produces sharp-energy-line neutrinos of . Detection of solar neutrinos from this reaction were reported by the Borexino collaboration in 2012. Both the pep and reactions can be seen as two different Feynman representations of the same basic interaction, where the electron passes to the right side of the reaction as a positron. This is represented in the figure of proton–proton and electron-capture reactions in a star, available at the NDM'06 web site. ==See also==