Pair Production Threshold Calculator

Pair production is the creation of a particle-antiparticle pair, most commonly an electron and a positron, from pure energy. In the photon-photon process (γγ→e⁺e⁻) calculated here, two photons collide and convert their energy directly into the rest mass and kinetic energy of the new electron-positron pair.

E₁E₂(1−cosθ) ≥ 2(m_ec²)², where E₁ and E₂ are the two photon energies, θ is the angle between their directions of travel, and m_ec² is the electron rest energy (0.511 MeV). This calculator solves for the minimum E₁ given E₂ and θ.

1.022 MeV is exactly twice the electron rest energy (2 × 0.511 MeV), and it is the minimum TOTAL photon energy needed for pair production in the special, most efficient case: two photons of equal energy colliding exactly head-on (θ=180°). This is one of the most quoted numbers in particle physics.

A single photon cannot simultaneously conserve both energy and momentum while converting into two massive particles in a vacuum, there is always a reference frame where the photon's energy is insufficient, or momentum fails to balance. A second photon (or a nearby nucleus to absorb recoil momentum) is required.

The (1−cosθ) term is maximized (equal to 2) exactly at θ=180° (head-on), meaning the same product E₁E₂ is most 'efficient' at producing pairs in this geometry. At smaller angles, (1−cosθ) shrinks, so a larger E₁E₂ product (and therefore more total energy) is needed to reach the same threshold.

Very-high-energy gamma rays traveling across cosmological distances can pair-produce against the diffuse extragalactic background light (starlight and infrared light filling the universe), effectively absorbing the gamma ray. This creates a 'horizon' beyond which the highest-energy gamma rays from distant sources cannot reach us, a major consideration in gamma-ray astronomy.

As written, this calculator uses the electron rest energy specifically, since electron-positron pair production is by far the most common and lowest-threshold case (electrons being the lightest charged particle). The same formula structure applies to heavier pairs (like muon-antimuon) by substituting the appropriate rest energy, though that isn't what this specific calculator computes.

As θ approaches 0° (photons traveling in nearly the same direction), (1−cosθ) approaches zero, driving the required threshold energy toward infinity, physically meaning two photons traveling almost parallel essentially never pair-produce, matching the intuition that they need to genuinely collide, not just travel alongside each other.

Yes, exactly, electron-positron annihilation (e⁺e⁻→γγ) converts a particle-antiparticle pair into two photons, while pair production (γγ→e⁺e⁻) runs this process in reverse, converting photon energy back into a particle-antiparticle pair. Both processes obey the same underlying conservation laws.

Photons carry zero net electric charge, and since charge must be conserved, they can only produce a particle-antiparticle pair (equal and opposite charge, summing to zero) rather than any arbitrary pair of massive particles. This is why the process specifically produces electron-positron pairs, not, say, two electrons.