Electron-induced pair-production threshold
= Electron-induced pair-production threshold
{title2=$E_{\mathrm{incident,th}}=7m_ec^2$}
For a free target <electron> at rest, $e^-e^-\to e^-e^-e^-e^+$ has threshold <invariant mass> $4m_e$. In <natural units>, $s=2m_e^2+2m_eE_{\rm incident}$ gives incident total <energy> $7m_e$, or incident <kinetic energy> $6m_e$. Atomic binding and recoil of the rest of an atom are excluded by this free-target model. This threshold differs from photon-induced pair production.