1.022
MeV
1
(1=Yes, 0=No)
3.978
MeV
1.989
MeV
1,213.150685
pm
1.022
MeV
1
(1=Yes, 0=No)
3.978
MeV
1.989
MeV
1,213.150685
pm
The Pair Production Calculator determines whether a photon has enough energy to create a particle-antiparticle pair, and if so, how much kinetic energy the created particles receive. Pair production is one of the most dramatic demonstrations of Einstein's \(E = mc^2\)—pure electromagnetic energy (a photon) is converted into matter (a particle and its antiparticle).
The minimum photon energy required for pair production is \(E_{\gamma} \geq 2m_e c^2\), where \(m_e c^2\) is the rest mass energy of the particle being created. For electron-positron pair production, this threshold is \(2 \times 0.511 = 1.022\) MeV. Any energy above the threshold becomes kinetic energy of the created pair.
Pair production cannot occur in free space—it requires a nearby nucleus or electron to conserve both energy and momentum simultaneously. A photon has momentum \(p = E/c\) but the pair has more rest mass than the photon's energy can account for at the same momentum. The recoiling nucleus absorbs the excess momentum, allowing energy-momentum conservation to be satisfied.
This process is the dominant photon interaction mechanism at high energies (above ~5 MeV in most materials) and is the basis of electromagnetic cascades in calorimeters, cosmic ray air showers, and high-energy astrophysical phenomena. The reverse process—electron-positron annihilation producing photons—is the basis of PET (Positron Emission Tomography) medical imaging.
While electron-positron pair production is most common, the same principle applies to heavier particles. Muon-antimuon pair production requires \(E_{\gamma} \geq 2 \times 105.66 = 211.32\) MeV, and proton-antiproton production requires \(E_{\gamma} \geq 2 \times 938.27 = 1876.54\) MeV. This calculator accepts any particle mass, making it versatile for all pair production processes.
The threshold wavelength corresponds to the photon wavelength at minimum production energy, connecting the wave and particle descriptions of the phenomenon. For e⁺e⁻ pair production, the threshold wavelength is about 1.21 pm—deep in the gamma ray regime.
Threshold energy:
$$E_{threshold} = 2 m c^2$$
For electron-positron production: \(E_{th} = 2 \times 0.511 = 1.022\) MeV.
Excess kinetic energy:
$$KE_{total} = E_{\gamma} - 2mc^2$$
This energy is shared between the particle and antiparticle (and a small recoil of the nucleus).
Maximum KE per particle (equal sharing):
$$KE_{each} = \frac{E_{\gamma} - 2mc^2}{2}$$
Threshold wavelength:
$$\lambda_{th} = \frac{hc}{E_{th}} = \frac{1.23984 \times 10^{-6} \text{ eV·m}}{E_{th}}$$
If the photon energy exceeds the threshold, pair production is energetically allowed (though it still requires a nearby nucleus). The excess energy appears as kinetic energy of the pair. At exactly threshold, the particles are created at rest. At much higher energies, the particles are produced with large kinetic energies and travel nearly in the forward direction. A result of 'Production Possible = 0' means the photon is below threshold.
Inputs
Results
A 5 MeV gamma ray exceeds the 1.022 MeV threshold by 3.978 MeV. Each particle (electron and positron) receives up to 1.989 MeV of kinetic energy.
Inputs
Results
A 0.5 MeV photon cannot produce an electron-positron pair because it is below the 1.022 MeV threshold. It may undergo Compton scattering or photoelectric absorption instead.
In empty space, a single photon cannot simultaneously conserve both energy and momentum when creating a massive pair. The photon has momentum E/c, but a pair at rest has zero momentum. A nearby nucleus (or electron) is needed to absorb the recoil momentum, acting as a third body. This is why pair production occurs in matter, not in vacuum.
The threshold is 2 × m_e c² = 2 × 0.511 MeV = 1.022 MeV. This is the minimum photon energy needed to create the rest mass of one electron and one positron. Any additional energy goes into kinetic energy of the pair.
PET scans use the reverse process: a positron (from β⁺ decay of a tracer isotope) annihilates with an electron, producing two 511 keV gamma rays emitted in opposite directions. Detectors register these coincident gamma rays to reconstruct the location of the tracer. Pair production creates e⁺e⁻; annihilation destroys them.
Yes, any particle-antiparticle pair can be produced if the photon energy exceeds 2mc². Muon pairs require Eγ ≥ 211.3 MeV, tau pairs require ≥ 3554 MeV, and proton-antiproton pairs require ≥ 1876.5 MeV. In practice, these are produced in high-energy collider experiments.
The positron loses kinetic energy through ionization and eventually annihilates with an electron in the medium, producing two 511 keV photons (or rarely, three photons via positronium). The positron's average lifetime in matter is typically nanoseconds to microseconds, depending on the material density.
The three main photon interactions are: photoelectric effect (dominant at low energies, < 0.5 MeV), Compton scattering (dominant at medium energies, 0.5–5 MeV), and pair production (dominant at high energies, > 5 MeV in high-Z materials). The crossover energies depend on the atomic number of the material. Pair production becomes increasingly dominant as photon energy increases.
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