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I know that fusion and fission can be esothermic processes if they happen between the "right" elements (meaning, indicatively, lighter/heavier than iron respectively). I always thought I got this until this moment, but now I need to figure out this: in what form is the mass excess released in fusion? In Fission may well be kinetic energy of the new nuclei, but in fusion must be something else. Is radiation the only possibility?

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As a general rule you can't fuse two nuclei by colliding them unless some third body present to carry away the excess energy.

The problem is that you have to give the two incoming nuclei a lot of energy to get past the electrostatic repulsion. That energy can't just disappear, so when the two nuclei fuse they form the new nucleus in such a higher energy state that it quickly falls apart again. There has to be some mechanism to carry away the excess energy.

The mechanism could be the ejection of a particle. For example when deuterium and tritium fuse this forms a helium-4 nucleus and the spare neutron is ejected. The excess energy can be carried away as the kinetic energy of the ejected neutron. Likewise in stellar fusion the energy is carried away by the positron and neutrino formed when one of the protons becomes a neutron.

Alternatively the excited state formed by the initial fusion could collide with some third body and the excess energy be shed in the collision. I'd guess this would only be common in very dense materials such as in stars. Finally I guess it's also possible the excited state could lose energy by emitting a photon,

So the basic principle is that the energy is produced as kinetic energy, just as happens in fission.

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