恆星中的能量產生

The paper sets a sharp problem: which nuclear reactions can supply the energy that ordinary stars radiate, given central temperatures of order ten to twenty million degrees and material that is mostly hydrogen? Gravitational contraction alone could power the Sun for only tens of millions of years — far too short — so the source must be nuclear.

Bethe surveys the reactions of protons with the light nuclei and asks which proceed fast enough at stellar temperatures, where particles must tunnel through the electrical repulsion of the nucleus. A key conclusion: building nuclei heavier than helium this way is blocked, because no stable nucleus exists at mass 5 or mass 8 — so proton capture self-limits at helium, and the energy comes from turning hydrogen into helium.

Two processes dominate the main sequence. In the lightest, coolest stars, hydrogen burns by the direct proton–proton chain (worked out by Bethe with Critchfield). In stars as hot as the Sun and hotter, the leading process is a catalytic cycle running on carbon and nitrogen.

Bethe's reaction scheme for the cycle is: ¹²C + H → ¹³N + γ ; ¹³N → ¹³C + ε⁺ + ν ; ¹³C + H → ¹⁴N + γ ; ¹⁴N + H → ¹⁵O + γ ; ¹⁵O → ¹⁵N + ε⁺ + ν ; ¹⁵N + H → ¹²C + ⁴He. The original ¹²C reappears unchanged at the end, so carbon and nitrogen serve only as catalysts; the net effect is to combine four protons (and two electrons) into one ⁴He nucleus.

Because the reaction rate climbs very steeply with temperature, a star's energy output is governed chiefly by its central temperature and its content of carbon and nitrogen. Bethe concludes that the carbon–nitrogen cycle is the principal source of energy in the Sun and in brighter main-sequence stars. (Later work, with better opacities and a lower solar central temperature, reassigned most of the Sun's output to the proton–proton chain — see the introduction.)