Proton–proton chain reaction

The proton–proton chain reaction 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's, whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 times that of the Sun's. The proton–proton chain reaction 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's, whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 times that of the Sun's. In general, proton–proton fusion can occur only if the kinetic energy (i.e. temperature) of the protons is high enough to overcome their mutual electrostatic or Coulomb repulsion. In the Sun, deuterium-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 in the core of the Sun is calculated to take more than ten billion years. Although often called the 'proton-proton chain reaction', it is not a chain reaction in the normal sense of the word (at least not Branch I — in Branches II and III helium, which is the product, also serves as a catalyst). It does not produce particles that go on to induce the reaction to continue (such as neutrons given off during fission). In fact, the rate is self-limiting because the heat produced tends toward reducing the density. It is however a chain (like a decay chain) and a reaction, or more accurately a branched chain of reactions starting with two protons coming together and yielding deuterium. 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. Even so, it was unclear how proton–proton fusion might proceed, because the most obvious product, helium-2 (diproton), is unstable and almost instantly dissociates back into two protons. In 1939, Hans Bethe proposed that one of the protons could decay by beta emission into a neutron via the weak interaction during the brief moment of fusion, making deuterium a vital product in the chain. This idea was part of the body of work in stellar nucleosynthesis for which Bethe won the Nobel Prize in Physics in 1967. The first step in all the branches is the fusion of two protons into deuterium. As the protons fuse, one of them undergoes beta plus decay, converting into a neutron by emitting a positron and an electron neutrino. The positron will probably annihilate with an electron from the environment into two gamma rays. Including this annihilation the whole reaction has a Q-Value (released energy) of 1.442 MeV. This reaction 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 of these long time scales.