# Does nuclear fusion of light nuclei occur in fire or boiling water?

At the temperature range of ordinary fire or maybe even ordinary boiling water, is the Coulomb potential between light atomic nuclei occasionally overcome to give way to fusion?

Basically, how are the nuclear fusion cross sections calculated and are they a function of temperature?

• The temperature of boiling water is 370K, the temperature of fire in the range of around 1000-3000K. Fusion reactions won't occur until temperatures reach millions of K. While one can calculate fusion cross sections, the most reliable way is to measure them in an accelerator experiment. The energy of the beam can then be converted into a temperature which would produce collisions of the same energy. – CuriousOne Apr 21 '16 at 6:40

• This is technically correct but misleading, because you don't have enough "very"s in "very low probability." I haven't done the computation, but my instinct is that if you could keep a mole of water ($10^{24}$ atoms) at its boiling point ($kT =35\rm\,meV$) for a billion years, you'd get only a handful of tails-induced fusion events (energy required $\sim1\rm\,MeV$). – rob Apr 21 '16 at 14:36
• @rob that is a gross over-exaggeration! The exponent (1MeV/35meV) is about -28,000,000. $e^{-28}$ is 7E-13. Call it 1E-12 for simplicity, so $e^{-28000000}$ is 1E-12000000. You could have the whole universe boiling for the lifetime of the universe and not get any fusions. – Jon Custer Apr 21 '16 at 15:04