Pair production creates a particle and its antiparticle while conserving energy, momentum and relevant charges. For an electron–Positron pair, the available invariant energy must at least supply their combined rest mass, with additional kinetic energy and other final-state requirements included.
A single free photon in empty flat spacetime cannot produce just that pair: its four-momentum has zero invariant mass, while the massive pair has a positive invariant mass. A second photon or another participant, such as a nucleus taking recoil, can satisfy the full kinematics. The pair's charges cancel globally, but each outgoing particle can leave its own detector track. A laboratory-frame photon energy threshold therefore depends on the complete reaction, not only on writing twice the electron rest energy.
For a free target electron at rest, has threshold invariant mass . In natural units, gives incident total energy , or incident kinetic energy . 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.
Two photons meeting at angle can produce an electron and a Positron when their combined four-momentum has sufficient invariant mass. For a head-on collision the threshold is . Threshold means zero relative momentum in the centre-of-momentum frame, not necessarily in the laboratory.
Two head-on photons can create an electron-positron pair at the limiting product . A target at the peak of the frequency-density blackbody spectrum has , whereas the wavelength-density peak corresponds to . At these conventions give incident thresholds approximately and respectively. A real blackbody has a continuum of target energies and angles, so an absorption calculation integrates the spectrum and cross section rather than imposing a sharp peak-photon opacity boundary.
