# Why does lithium fuse at lower temperatures than hydrogen?

This is a basic question, but it's been bugging me. In the Wikipedia article for lithium burning, it states that:

Stars, which by definition must achieve the high temperature (2.5 × 10^6 K) necessary for fusing hydrogen, rapidly deplete their lithium. This occurs by a collision of lithium-7 and a proton producing two helium-4 nuclei. The temperature necessary for this reaction is just below the temperature necessary for hydrogen fusion.

I would imagine that with lithium having more protons, it would have a stronger Coulomb repulsion and require higher temperatures to fuse with hydrogen. Now, this article is pretty sketchy since it cites no sources, and I would normally dismiss this. But according to here, lithium burning occurs in protostars, before hydrogen fusion even takes place. How could lithium fuse with hydrogen at temperatures that low?

## 1 Answer

The slowest reaction rate in the pp chain determines how quickly hydrogen can "burn" in the core of a sun-like star. That rate-determining step is actually the fusion of two protons to form deuterium via the diproton and a weak interaction decay.

The fusion of lithium, whereby it fuses with a proton and then splits into two Helium nuclei is actually part of the PPII series of reactions that convert helium 3 into helium 4. It does not involve weak interactions and therefore the cross-section at a given temperature is much higher than the first step in the pp chain, regardless of the stronger coulomb repulsion between the reactants. It is therefore initiated at lower temperatures - as you say, Li "burning" occurs in low-mass pre main sequence stars well before hydrogen "burning" commences (but after deuterium burning).

• Hmm...so if a star's core is hot enough for lithium burning, but not for hydrogen burning, could it still be considered a protostar? – Sir Cumference Jun 5 '16 at 12:53
• @SirCumference A star doesn't know it is a star until it starts hydrogen burning. There is little physics that distinguishes between a 0.1 solar mass "star", that will eventually burn H after contracting for about 200 million years, and a 0.02 solar mass brown dwarf, when both are 10 million years old. I suppose pedantically you could distinguish a protostar from a brown dwarf based on its mass. – ProfRob Jun 5 '16 at 13:26
• So why does helium require such high temperatures to fuse, even when it has a lower Coulomb repulsion than lithium? It doesn't require $\beta^+$ decay. – Sir Cumference Jun 13 '16 at 5:10
• @SirCumference (a) Coulomb repulsion between two He nuclei is larger than between Li and a proton. (b) You have to get THREE in the same place at once - it's the "triple alpha reaction". – ProfRob Jun 13 '16 at 7:40
• Why is that? It's two protons vs three protons. – Sir Cumference Jun 13 '16 at 11:38