carbon cycle (carbon-nitrogen (CN) cycle; carbon-nitrogen-oxygen (CNO) cycle; Bethe-Weizsäcker cycle)

A series of nuclear reactions, believed to take place in stars and to be one of the main sources of stellar energy, in which hydrogen is converted to helium. The six stages in the process are: 12C + 1H -> 13N + gamma-ray photon 13N -> 13C + positron + neutrino 1H + 13C -> 14N + gamma-ray photon 1H + 14N -> 15O + gamma-ray photon 15O -> 15N + positron + neutrino 1H + 15N -> 12C + 4He Thus, the 12C nucleus reappears at the end. The process cannot take place unless carbon is present, but relatively few 12C nuclei are required. The rate at which the carbon cycle occurs depends very sharply on temperature. A minimum temperature of 14 million K is needed for it to take place at all. Above 16 million K it dominates over the other main hydrogen-burning process, the proton-proton chain, and is believed to be the primary source of energy in relatively hot stars with masses greater than two or three times that of the Sun. Two longer variations on the sequence are also thought to occur, the CNO bi-cycle and the CNO tri-cycle, which result in the creation of 14N and 15N, respectively, rather than the reappearance of carbon. In the shorthand used to represent nuclear reactions, the CNO bi-cycle proceeds as: 15N(p,g) 16O(p,g) 17F(,b+ +n ) 17O(p,a) 14N. The CNO tri-cycle includes the additional stages: 17O(p,g) 18F(,b++n) 18O(p, a) 15N