Nuclear Reactions in Stars. Buildup from Helium

The rates are calculated for thermonuclear reactions involving alpha particles, at temperature T of the order of 10⁸ ^∘{}K. In particular, the conversion of three alpha particles into a C¹² nucleus and (α, γ) reactions on C¹², O¹⁶, and Ne²⁰ are considered, as well as C¹³(α, n)O¹⁶. Rough estimates are also given for alpha reactions on the other isotopes of N, O, F, and Ne.The reaction rates are used to re-evaluate some characteristic central temperatures Tc for Hoyle and Schwarzschild's model for the evolution of a population II red giant: for stars "at the tip of the red-giant branch," where helium burning first becomes important, Tc≈1.0×10⁸^∘K; for stars at the beginning of the "horizontal branch," where helium burning contributes appreciably to the energy production, Tc≈1.3×10⁸^∘K. At these temperatures the rates of formation of C¹², O¹⁶, and Ne²⁰ are roughly comparable (if the spin and parity of a certain resonance level in Ne²⁰ is suitable), but the production rate of Mg²⁴ and heavier nuclei is negligible. Of the alpha reactions on the rarer isotopes, by far the fastest is C¹³(α, n) and most of the C¹³ is used up near Tc=0.8×10⁸^∘K.