00 Foundations
Pair production threshold
Kinetic energy shared by e⁻ e⁺ after the 1.022 MeV rest-mass cost.
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Simulation
Pair production threshold — Change the numbers; the scene follows.
Where it works
Linear accelerator
Isocenter
At isocenter, on the central axis through the patient (or a phantom in the same place).
Open this machineFormula
Variables
Results
E_k
Total kinetic energy
4.978MeV
E_k/2
Per particle if equal
2.489MeV
Curve
Explanation
What it means
Pair production converts a photon into an electron–positron pair in the Coulomb field of a nucleus. At least 2×511 keV = 1.022 MeV is consumed as rest mass; any surplus is kinetic energy of the pair (and a tiny nuclear recoil). The positron later annihilates, yielding two 511 keV photons. This is a working relation in Radiation physics.
Where it is used
Clinically it sits on the Linear accelerator — Isocenter. At isocenter, on the central axis through the patient (or a phantom in the same place). Radiation physics lives at the x-ray target, the linac head, and inside the patient: how a photon is born, how it scatters, and how it dies. Use these relations before you trust a spectrum, a wall, or a kV-versus-MV contrast argument.
Linear accelerator · Open this machineHow to use it
Enter photon energy in MeV. If hν < 1.022 MeV the pair channel is closed. Use it when discussing MV therapy spectra, PET annihilation, and shielding of high-energy linacs (where pair production dominates above ~10 MeV in high-Z). Change one input and watch the curve and the simulation follow.
Symbols
- hνPhoton energy6 MeV
Worked example
A typical case from the default values: hν = 6 MeV (Photon energy). Substituting into the relation gives E_k = 4.978 MeV; E_k/2 = 2.489 MeV. These are teaching numbers — align them with your machine.
Typical values give
- E_k = 4.978MeV
- E_k/2 = 2.489MeV
Where it comes from
The displayed formula is the working relation. Kinetic energy shared by e⁻ e⁺ after the 1.022 MeV rest-mass cost. Usual reference: Attix / Podgorsak. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Attix / Podgorsak
Assumptions & limits
Nuclear pair production threshold is 1.022 MeV; triplet production on an electron requires 2.044 MeV. Recoil kinetic energy of the nucleus is neglected. Angular distribution and screening are not modelled.
Pitfalls
Do not mix free-electron Compton kinematics with photoelectric-dominated kV imaging. Check keV versus MeV, and never treat a spectrum as one photon. Nuclear pair production threshold is 1.022 MeV; triplet production on an electron requires 2.044 MeV. Recoil kinetic energy of the nucleus is neglected. Angular distribution and screening are not modelled.
Keep this
Photons do not deposit dose; the electrons they set in motion do. Nuclear pair production threshold is 1.022 MeV; triplet production on an electron requires 2.044 MeV. Recoil kinetic energy of the nucleus is neglected. Angular distribution and screening are not modelled.
In this specialty