Pair production

Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron–positron pair near a nucleus. For pair production to occur, the incoming energy of the interaction must be above a threshold of at least the total rest mass energy of the two particles, and the situation must conserve both energy and momentum. However, all other conserved quantum numbers (angular momentum, electric charge, lepton number) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1. Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron–positron pair near a nucleus. For pair production to occur, the incoming energy of the interaction must be above a threshold of at least the total rest mass energy of the two particles, and the situation must conserve both energy and momentum. However, all other conserved quantum numbers (angular momentum, electric charge, lepton number) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1. The probability of pair production in photon–matter interactions increases with photon energy and also increases approximately as the square of atomic number of the nearby atom. For photons with high photon energy (MeV scale and higher), pair production is the dominant mode of photon interaction with matter. These interactions were first observed in Patrick Blackett's counter-controlled cloud chamber, leading to the 1948 Nobel Prize in Physics. If the photon is near an atomic nucleus, the energy of a photon can be converted into an electron–positron pair: γ → e− + e+ The photon's energy is converted to particle mass in accordance with Einstein’s equation, E=mc2; where E is energy, m is mass and c is the speed of light. The photon must have higher energy than the sum of the rest mass energies of an electron and positron (2 × 0.511 MeV = 1.022 MeV) for the production to occur. The photon must be near a nucleus in order to satisfy conservation of momentum, as an electron–positron pair produced in free space cannot both satisfy conservation of energy and momentum. Because of this, when pair production occurs, the atomic nucleus receives some recoil. The reverse of this process is electron positron annihilation. These properties can be derived through the kinematics of the interaction. Using four vector notation, the conservation of energy-momentum before and after the interaction gives: p γ = p e − + p e + + p R {displaystyle p_{gamma }=p_{e^{-}}+p_{e^{+}}+p_{R}} where p R {displaystyle p_{R}} is the recoil of the nuclei. Note the modulus of the four vector A = ( A 0 , A ) {displaystyle A=(A^{0},mathbf {A} )} is: A 2 = A μ A μ = − ( A 0 ) 2 + A ⋅ A {displaystyle A^{2}=A^{mu }A_{mu }=-(A^{0})^{2}+mathbf {A} cdot mathbf {A} }