In atoms charges are neatly separated. Instead of pairing which seems natural they all stick together with their peers.
What drives this peer behaviour? Why is it stable?
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The nuclear forces are much stronger than the electromagnetic forces, but their range is much shorter. So nucleons very close together are pulled together by the nuclear forces, and less strongly pushed apart by the Coulomb force.
The electrons, on the other hand, are attracted by the oppositely charged nucleus, here, the Coulomb force of the core is stronger than the Coulomb force of the other electrons. But the electron interaction is strong enough to keep them on different levels, so to say.
Fusion usually occurs under very high temperatures, where everything is in a plasma state, so naturally electrons are "standing aside", only the reaction cross-sections of the cores matter for the fusion process. When the temperature is high enough, the cores have enough kinetic energy to overcome the Coulomb barrier on a direct hit. The cores pass their barrier and a sort of friction occurs, which causes internal excitation. The system is heating up. As long as the reaction partners are "mixed", i.e. within each others boundary region, mass transfer can occur from one to the other. Depending on the reaction time, more or less mass is transferred/exchanged. During the process the system is rotating. Eventually the two partners will split up again. During this reaction, their kinetic energy was mainly transformed into internal excitation and they exchanged mass.