Electron-positron annihilation is the process that occurs when an electron and a positron (the electron's anti-particle) collide. The result of the collision is the destruction of the electron and positron (which are often formed as the result of a beta decay), and the creation of a gamma ray photon pair. Due to conservation laws the following conditions must be met:

• Charge must be conserved.
• Momentum (both linear and angular) must be conserved.
• Energy must be conserved (both potential energy and kinetic energy).

Charge is conserved, as the electron and positron have equal and opposite charges (±1.6022 × 10−19 C) and the photons have zero charge. Conservation of (linear) momentum dictates that two photons must be created.

If both electron and positron are approximately at rest (which happens in an exotic but not uncommon form of matter called positronium) both gamma ray photons will have energy approximately equal to the rest energy of the electron or positron (511 keV). In order to conserve momentum the photons are emitted roughly in opposite directions (in practice, except in the case of a head-on collision, the momentum will be more than 0). If electron and/or positron have appreciable kinetic energies, the energies (and therefore frequencies) of the photons emitted will be higher. Also, if the particles do not collide head-on, the angle between the photons' velocities will be more noticeable as significant momentum has to be conserved. Note that at low energies classical momentum can be used, but if the electron and positron have appreciable energies (velocities nearing c) then 4-momentum should be used in calculations.

The equation below summarises the energies involved in this process:

$2m\_0\; c^2\; +\; K\_\{e-\}\; +\; K\_\{e+\}\; =\; 2hf\; \backslash !$

where $m\_0\; \backslash !$ is the mass of the electron and positron, $c\; \backslash !$ is the speed of light, $K\_\{e-\}\; \backslash !$ and $K\_\{e+\}\; \backslash !$ are the kinetic energies of the electron and positron respectively, $h\; \backslash !$ is planck's Constant, and $f\; \backslash !$ is the frequency of the photons.

Creation of other pairs

At higher relative velocities, other particle-antiparticle pairs can also be produced (e.g. D⁺ and D^- mesons), since there is enough kinetic energy in the relative velocities to provide for the rest energies of those particles. At much higher relative velocities, there may be enough energy to produce a single neutral Z boson.

Practical uses

The process is the physical phenomena relied on as the basis of PET imaging.

See also

• Positron emission tomography
• Annihilation
• Electromagnetic spectrum (shows that the photons are in the high-energy range)

Particle physics | Nuclear medicine

إبادة إلكترون-بوزيترون | Aniquilación positrón-electrón | 쌍소멸 | Annichilazione elettrone-positrone | Anihilacija para