Proton–proton chain

The proton–proton chain, also commonly referred to as the p–p chain, is one of two known sets of nuclear fusion reactions by which stars convert hydrogen to helium. It dominates in stars with masses less than or equal to that of the Sun, whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 solar masses. 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. In the Sun, deuteron-producing events are rare. Diprotons are the much more common result of proton–proton reactions within the star, and diprotons almost immediately decay back into two protons. Since the conversion of hydrogen to helium is slow, the complete conversion of the hydrogen initially in the core of the Sun is calculated to take more than ten billion years. Although sometimes called the "proton–proton chain reaction", it is not a chain reaction in the normal sense. In most nuclear reactions, a chain reaction designates a reaction that produces a product, such as neutrons given off during fission, that quickly induces another such reaction. The proton–proton chain is, like a decay chain, a series of reactions. The product of one reaction is the starting material of the next reaction. There are two main chains leading from hydrogen to helium in the Sun. One chain has five reactions, the other chain has six.

History of the theory 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 3He 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. In 2014, the Borexino collaboration conducted the first direct real time measurement of pp neutrinos, reporting a neutrino flux of (6.6 ± 0.7)×1010 cm-2⋅s-1. This measurement is consistent with predictions from the standard solar model, (5.98 ± 0.04)×1010 cm-2⋅s-1.

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: The relative amounts of energy going to the neutrino and to the other products is variable. This is the rate-limiting reaction and is extremely slow due to it being initiated by the weak nuclear force. The average proton in the core of the Sun waits 9 billion years before it successfully fuses with another proton. It has not been possible to measure the cross-section of this reaction experimentally because it is so low but it can be calculated from theory. 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. In the Sun, each helium-3 nucleus produced in these reactions exists for only about 400 years before it is converted into helium-4. Once the helium-3 has been produced, there are four possible paths to generate 4He. In p–p I, helium-4 is produced by fusing two helium-3 nuclei into beryllium-6, which immediately emits two protons to become helium-4. The p–p II and p–p III branches fuse 3He with pre-existing 4He 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 p–p chains, with the other 1% coming from the CNO cycle. According to one model of the sun, 83.3 percent of the 4He produced by the various p–p branches is produced via branch I while p–p II produces 16.68 percent and p–p III 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 p–p IV 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 p–p I branch

The fusion of two 32He nuclei produces a 64Be nucleus, which promptly ejects two protons. The complete chain releases a net energy of 26.732 MeV but 2.2 percent of this energy (0.59 MeV) is lost to the neutrinos that are produced. The p–p I branch is dominant at temperatures of 10 to 18 MK. Below 10 MK, the p–p chain proceeds at slow rate, resulting in a low production of 4He.

The p–p II branch

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