Nuclear Reactions in Stars. IV. Buildup from Carbon

Reaction leading to the formation of C, O, and Ne at temperatures T of about 10⁸ °K, in the core of red giant stars, had been studied previously. The nuclear reactions and resulting nucleo-genesis are now studied for a gas consisting of C¹², O¹⁶, and Ne²⁰ at 6×10⁸ to 10×10⁸ °K and densities around 10⁴ g/cc. The basic reaction rates are calculated and a set of simultaneous differential equations for various abundances as a function of time is solved numerically.

The C¹² is destroyed by compound nucleus formation from C+C collisions in about 10⁵ and 1 years, respectively, at 6×10⁸ and 8.5×10⁸ °K. The net result is the production of some additional amounts of O¹⁶ and Ne²⁰; appreciable amounts of Na²³ and the three stable magnesium isotopes (mainly Mg²⁴) and decreasing amounts of Al²⁷, Si, etc. The ratio of Na²³ to Mg²⁴ produced is almost ½, appreciably larger than the "cosmic" ratio.

During the carbon burning, protons and alphas are released. At temperatures below 7×10⁸ °K, neutrons are produced very copiously through the sequence C¹²(p, γ)N¹³; N¹³→C¹³; C¹³(α, n)O¹⁶. If small amounts of metals in the Fe-region (up to about one metal nucleus per 1000 C¹² nuclei) were present originally, each metal nucleus will absorb about 30 neutrons. At temperatures above 8×10⁸ °K, N¹³ is photodisintegrated and the neutron production is appreciably less.