Pair production

A gamma-ray photon passing close to a nucleus can transform into an electron–positron pair, provided its energy is at least the combined rest energy of the two particles: 2 × 0.511 MeV = 1.022 MeV. Set the photon energy, fire, and watch the energy budget.

Energy budget (0–10 MeV scale)

e− rest energy e+ rest energy e− kinetic e+ kinetic threshold 1.022 MeV

Photon energy

Ephoton2.500 MeV
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Photon

Frequency f
Wavelength λ

Pair produced

Rest energy (pair)
1.022 MeV
Total kinetic energy
KE each (equal share)
Lorentz factor γ
Speed of each particle

Assumes the kinetic energy is shared equally and nuclear recoil energy is negligible (the nucleus is thousands of times more massive than an electron).

The physics

Mass–energy equivalence. Pair production is a direct demonstration of E = mc²: the photon's energy is converted into the mass of two particles. Each electron or positron has rest energy mec² = 0.511 MeV, so the photon must supply at least

Emin = 2mec² = 1.022 MeV   (λ ≤ 1.21 pm)

Any energy above the threshold appears as kinetic energy of the pair:

Ephoton = 2mec² + KEe− + KEe+

Why the nucleus is needed. A photon in empty space cannot become a pair, even above 1.022 MeV: energy and momentum cannot both be conserved. The photon carries momentum p = E/c, and a pair created from it alone could never account for all of that momentum while also conserving energy. A nearby nucleus takes up the excess momentum. Because it is so massive, it recoils with almost no kinetic energy, so effectively all the photon's energy goes to the pair. (Watch the nucleus twitch in the animation.)

Conservation of charge. The photon is uncharged, so the pair must have zero net charge: one negative electron and one positive positron (the electron's antiparticle) are always created together. Lepton number is also conserved (+1 for the electron, −1 for the positron).

Opposite curvature in a magnetic field. Switch on the magnetic field (directed into the page) and the two tracks curve in opposite senses because the charges are opposite, with radius r = p/(qB). Faster pairs (higher photon energy) make straighter tracks. This is exactly how pairs appear in bubble-chamber photographs, and how the positron was discovered (Anderson, 1932).

The reverse process. Annihilation is pair production run backwards: an electron and positron meet and become (at least) two 0.511 MeV photons emitted in opposite directions, the principle behind PET scanning.