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In nuclear fusion, the particles require enough energy to overcome the Coulomb barrier. The Coulomb barrier is caused by the Coulomb force, which is created by the protons repelling each other because all protons (and therefore nuclei) are positively charged. But my question is: does fusion occur when electrons are present i.e. with atoms and not ions? It would make sense that it doesn’t since electrons are negatively charged and should push each other away as well, but I don’t know.

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  • $\begingroup$ You mean "electrons are negatively charged". $\endgroup$ – anna v Oct 14 '19 at 12:30
  • $\begingroup$ @annav ah yes that’s right $\endgroup$ – Melvin Oct 14 '19 at 12:33
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    $\begingroup$ The energies binding electrons to the atom are of the order of KeV. The energies that bind a nucleus together are of order of MeV. That is why atoms are easily stripped of their electrons at the plasma temperatures,of order of 100.000.000 Celsius which are needed for fusion, at ITER for example iter.org $\endgroup$ – anna v Oct 14 '19 at 12:48
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Electrons are always present when fusion is taking place, but they are usually not "attached" to the ions.

The typical Coulomb barrier that needs to be overcome (or tunneled through) in order for two protons to fuse is of order $q^2/4\pi \epsilon_0 r$, where $q$ is the (positive) ion charge (assuming the fusion of two similar ions) and $r$ is around $10^{-15}$ m, where the strong nuclear force dominates over Coulomb repulsion. The minimum value for this is around 1.4 MeV in the case of two protons.

This has to be compared with the binding energy of electrons in an atom, which are of order a few to tens of eV.

In stars and in nuclear fusion reactors, the fusing particles are given sufficient energy to overcome the Coulomb barrier by making them hot (typically $10^{7}$ to $10^{8}$ K). Such high temperatures will inevitably mean that the atoms are completely ionised. The electrons do not play any significant role in the energetics of the fusion reactions and effectively form a pseudo-uniformly distributed background of negative charge.

Fusion can also take place in cold, dense, crystalline material. The idea here is that although "cold", the zeropoint quantum mechanical oscillator energy can be sufficient to initiate fusion. However, in these case, the material is so dense that the electrons are degenerate and have energies of several MeV or more and so the fusion is again between completely ionised ions.

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Fusion can happen with atoms, but the size of the atoms is very large compared to the distances at which fusion rate is high enough. At these small distances the positive charge of the nucleus is not screened by the negative charge of the electrons, so the electrons do not help much. However, if electrons are replaced with muons in atoms, the size of the atoms is much smaller because of the large mass of the muons, so atoms can come much closer to each other, and efficient fusion is possible without high temperature. However, this approach to fusion has its own share of problems (https://en.wikipedia.org/wiki/Muon-catalyzed_fusion).

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