# Pair Production

In pair production, the photon interacts with a Coulomb field and is absorbed, with its energy being converted to mass in the form of an electron and a positron. The remaining photon energy is transferred as kinetic energy to the two particles; in some cases kinetic energy is also transferred to a second electron, a process known as triplet production. Pair production occurs when the photon interacts with the nuclear Coulomb field, while triplet production occurs when the photon interacts with the Coulomb field of the atomic electrons.

To produce these two particles the photon must have at least enough energy as their combined rest mass:

E_{photon} \ge 2m_ec^2

E_{photon} \ge 1.022 \: MeV

Therefore pair production only occurs for higher-energy photons. Due to momentum conservation, triplet production actually requires E_{photon} \ge 4m_ec^2. As an approximation, the cross sections for pair and triplet production are proportional to Z^2 and Z, respectively:

\kappa_{pair} \propto Z^2

\kappa_{triplet} \propto Z

Although, pair production is much more likely to occur than triplet production. The pair production mass attenuation coefficient is the sum of pair and triplet interaction coefficients:

\frac{\kappa}{\rho} = \frac{\kappa_{pair}}{\rho} + \frac{\kappa_{triplet}}{\rho}

The energy transferred to matter is equal to the photon energy minus the mass-energy conversion, so the pair production mass-energy transfer coefficient can be calculated as:

\frac{\kappa_{tr}}{\rho} = \frac{\kappa}{\rho} \Big( \frac{E_{photon}-2m_ec^2}{E_{photon}} \Big)