Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon (or another neutral boson). For example an electron and its antiparticle the positron may be created. This is allowed, provided there is enough energy available to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved (though not necessarily on shell). Other pairs produced could be a muon and antimuon or a tau and antitau. However all other conserved quantum numbers (angular momentum, electric charge, lepton number (whether the particle is an electron, muon or tau)) of the produced particles must sum to zero — thus the created particles shall have opposite values of each (for instance, if one particle has electric charge of +1 the other must have electric charge −1, or if one particle has strangeness +1 then another one must have strangeness −1).
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Examples
Electronpositron pair production
In nuclear physics, this occurs when a highenergy photon interacts in the vicinity of a nucleus. The energy this (massless) photon has can be converted into mass through Einstein's equation E=mc² where E is energy, m is mass and c is the speed of light. Thus if the energy of the photon is high enough so that it can make the mass of an electron plus the mass of a positron (basically twice the mass of an electron which is 9.11 × 10^{−31} kg) then an electronpositron pair may be created.
If there is more energy in the photon than just enough to create the mass of the electronpositron pair then the electron and positron will have some kinetic energy  meaning they will be moving. The electron and positron can move in opposite directions (at an angle of 180 degrees) meaning they have a total momentum of zero or they can move at an angle of less than 180 degrees resulting in a combined momentum which is very small (since momentum is a vector quantity). However, if the photon only just had enough energy to create the mass of the electronpositron pair then the electron and positron will be at rest. This could violate the conservation of momentum since the photon has momentum and the two resulting electrons have none if they are stationary (since momentum = mass x velocity). This means that the pair production must take place near another photon or the nucleus of at atom since they can absorb the momentum of the original photon i.e since the momentum of the initial photon must be absorbed by something, pair production cannot occur in empty space out of a single photon; the nucleus (or another photon) is needed to conserve both momentum and energy (consider the time reversal of Electronpositron annihilation).^{[1]}
Energy
Photonnucleus pair production can only occur if the photons have an energy exceeding twice the rest energy (m_{e}c^{2}) of an electron (1.022 MeV), photonphoton pair production may occur at 511 keV; the same conservation laws apply for the generation of other higher energy leptons such as the muon and tauon (for two photons each should have the oneparticle energy in the center of momentum frame, for one photon and a heavy nucleus, the photon needs the entire pair rest energy). These interactions were first observed in Patrick Blackett's countercontrolled cloud chamber, leading to the 1948 Nobel Prize in Physics.
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