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# annihilation

[uh-nahy-uh-ley-shuhn]

In physics, a reaction in which a particle and its antiparticle (see antimatter) collide and disappear. The annihilation releases energy equal to the original mass math.m multiplied by the square of the speed of light math.c, or math.E = math.mmath.c2, in accordance with Albert Einstein's special theory of relativity. The energy can appear directly as gamma rays or can convert back to particles and antiparticles (see pair production).

Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil (nothing). A literal translation is "to make into nothing". Annihilation is the opposite of exnihilation, which means "to create something out of nothing".

In physics, the word is used to denote the process that occurs when a subatomic particle collides with its respective antiparticle. Since energy and momentum must be conserved, the particles are not actually made into nothing, but rather into new particles. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.

During a low-energy annihilation, photon production is favored, since these particles have no mass. However, high-energy particle colliders produce annihilations where a wide variety of exotic heavy particles are created.

## Examples of annihilation

This is an example of renormalization in quantum field theory— the field theory being necessary because the number of particles changes from one to two and back again.

When a low-energy electron annihilates a low-energy positron (anti-electron), they can only produce two or more gamma ray photons, since the electron and positron do not carry enough mass-energy to produce heavier particles. However, if one or both particles carry a larger amount of kinetic energy, various other particle pairs can be produced. See electron-positron annihilation.

The annihilation (or decay) of an electron-positron pair into a single photon, e+ + e- → γ, cannot occur because energy and momentum would not be conserved in this process. The reverse reaction is also impossible for this reason, except in the presence of another particle that can carry away the excess energy and momentum. However, in quantum field theory this process is allowed as an intermediate quantum state. Some authors justify this by saying that the photon exists for a time which is short enough that the violation of energy conservation can be accommodated by the uncertainty principle. Others choose to assign the intermediate photon a non-zero mass. (The mathematics of the theory are unaffected by which view is taken.) This opens the way for virtual pair production or annihilation in which a one-particle quantum state may fluctuate into a two-particle state and back again (coherent superposition). These processes are important in the vacuum state and renormalization of a quantum field theory. It also allows neutral particle mixing through processes such as the one pictured here.

## References

### Notations

• Kragh, Helge (1999). Quantum Generations : A history of physics in the twentieth century. Princeton University Press. ISBN 0-691-01206-7.