= Photon-induced triplet pair-production threshold
{title2=$E_{\gamma,\mathrm{thr}}=4m_ec^2$}
For a <photon> incident on a stationary <Electron>, producing an additional electron and positron leaves three massive particles in the final state. <Four-momentum conservation> gives $W^2=m_e^2c^4+2m_ec^2E_\gamma$ for the <centre-of-momentum energy>. Its minimum is $3m_ec^2$, so the incident threshold is $4m_ec^2$. At threshold all final particles are at rest in their centre-of-momentum frame, which moves at $4c/5$ relative to the target laboratory frame. This differs from a heavy-target threshold because the electron target's recoil cannot be neglected.
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