Electron-positron annihilation

The annihilation of an electron and a positron conserves total energy, momentum, and charge. In the center-of-mass frame, the two particles approach with equal and opposite momenta, and the final state typically consists of two photons emitted back-to-back, each carrying an energy of 511 keV (the rest energy of the electron). The two-photon final state is the most common because it conserves momentum while minimizing the number of particles; single-photon emission is forbidden by momentum conservation in free space, and three-photon annihilation occurs with a probability of about 1/372 relative to two-photon emission, arising from a higher-order quantum electrodynamics process.¹

When the electron and positron are not at rest, the emitted photons are Doppler-shifted and the opening angle between them deviates from 180°, providing a sensitive probe of the electron momentum in the material. This principle underlies the technique of angular correlation of annihilation radiation (ACAR), used to study the electronic structure of solids.²

Positron emission tomography (PET) relies on the back-to-back emission of 511 keV photons from electron-positron annihilation to locate positron-emitting radiotracers within the body. The coincident detection of the two photons allows the reconstruction of a three-dimensional image of metabolic activity, making PET a cornerstone of oncology, neurology, and cardiology.³

In materials science, positron annihilation spectroscopy is used to detect and characterize defects such as vacancies, dislocations, and voids in metals and semiconductors. The lifetime of positrons in a material is sensitive to the local electron density; longer lifetimes indicate larger open-volume defects. This technique has been applied to study radiation damage in reactor steels and to monitor the quality of semiconductor wafers.⁴

Electron-positron annihilation is a major source of gamma-ray emission in astrophysical environments. The observation of a characteristic 511 keV line from the Galactic Center indicates the presence of a large population of positrons annihilating with electrons in the interstellar medium. The origin of these positrons remains an open question, with candidate sources including supernovae, pulsars, and annihilation of dark matter particles.⁵

In the early universe, electron-positron annihilation occurred when the temperature dropped below about 1 MeV, roughly one second after the Big Bang. This process heated the photon gas and slightly altered the ratio of neutrinos to photons, leaving an imprint on the cosmic microwave background and on the primordial abundance of light elements such as helium-4.⁶

Beyond the standard two-photon channel, electron-positron annihilation can produce other final states. In the presence of a nearby nucleus, annihilation can occur with the emission of a single photon, a process known as one-photon annihilation, which is important in high-energy astrophysical plasmas. Additionally, annihilation into a neutrino-antineutrino pair is possible but extremely rare, with a branching ratio of about 10⁻¹⁰ relative to the two-photon channel, making it a sensitive probe of physics beyond the Standard Model.⁷

Positronium, a bound state of an electron and a positron, can exist in two forms: para-positronium (singlet state) decays primarily into two photons with a lifetime of about 125 picoseconds, while ortho-positronium (triplet state) decays into three photons with a lifetime of about 142 nanoseconds. The precise measurement of these lifetimes provides stringent tests of quantum electrodynamics and has been used to search for new forces.⁸

Positron

The antimatter counterpart of the electron, with the same mass but opposite charge.

Annihilation

The process in which a particle and its antiparticle collide and convert their mass into energy.

Positronium

A short-lived bound state consisting of an electron and a positron.

PET

Positron emission tomography, a medical imaging technique that uses positron annihilation to produce images.