Particle Physics: Positronium and Pair Annihilation

Pair Production and Annihilation

• The collision of a positron with an electron produces a hydrogen-like atom called positronium, with a mean lifetime of about 10^(-10) s.
• Positronium is similar to a hydrogen atom, where the proton is replaced by a positron.

Pair Production

• Pair production occurs when a high-energy photon passes through a foil, resulting in the creation of an electron-positron pair.
• The process requires the interaction of the photon with an external field, such as the Coulomb field of an atomic nucleus, to conserve momentum.
• The energy of the incident photon (h) must be greater than the sum of the rest masses of the electron and positron (2m_ec^2) to conserve energy.

Minimum Energy for Pair Production

• The minimum energy of a photon required for pair production can be calculated using the equation: h = 2m_ec^2.

Relativistic Quantum Mechanics

• Dirac's relativistic quantum mechanics predicts the existence of the positron, the antiparticle of the electron, with the same mass and opposite charge.
• The positron was discovered by Anderson in 1932, four years after its prediction by Dirac's theory.

Pair Annihilation

• The inverse of pair production is pair annihilation, where an electron and a positron collide and annihilate each other, producing electromagnetic radiation.
• This process explains why positrons do not last long in nature, as they eventually get annihilated after colliding with an electron.

Conditions for Pair Production and Annihilation

• Charge, momentum, and energy conservation are required for pair production and annihilation to occur.
• A massive object, such as a nucleus, must participate in the process to take away some of the photon's momentum.