Pair creation channels γ + nucleus → e⁺e⁻ (Bethe–Heitler, σ ∝ Z²), the higher-threshold triplet γ + e⁻ → e⁻e⁺e⁻, and Breit–Wheeler γγ → e⁺e⁻ that limits TeV photons against the cosmic background. Live threshold marker, log-σ curve, and material presets (H, C, Al, Cu, Pb) make the 1.022 MeV / 4 m_e c² thresholds intuitive.
About this model
This lab surveys photon pair-production channels and their thresholds. Nuclear Bethe–Heitler γ + nucleus → e⁺e⁻ has threshold 2m_e c² = 1.022 MeV in the nucleus rest frame and cross section scaling roughly σ ∝ Z². Triplet production γ + e⁻ → e⁻e⁺e⁻ needs a higher threshold (~4m_e c² kinematics). Breit–Wheeler γγ → e⁺e⁻ sets opacity for TeV photons on soft background light. A live threshold marker, log-σ(E_γ) curve, and material presets (H, C, Al, Cu, Pb) make Z dependence visible. Idealizations: schematic σ shapes, no full QED Monte Carlo, and no detailed atomic form factors. Vary photon energy and target material to see when pair creation opens and how σ rises above threshold.
Who it's for: Nuclear/particle physics and high-energy astrophysics courses covering photon interactions.
Key terms
pair production
Bethe-Heitler
Breit-Wheeler
threshold energy
triplet production
cross section
How it works
Pair-production cross-section σ(E_γ) for γ + nucleus → e⁺e⁻ (Bethe–Heitler, σ ∝ Z²), the higher-threshold triplet process γ + e⁻ → e⁺e⁻e⁻, and the Breit–Wheeler γγ → e⁺e⁻ channel that limits TeV photons against the cosmic background. Live threshold marker, log-σ curve, and material presets (H, C, Al, Cu, Pb).
Frequently asked questions
Why is the nuclear channel threshold 1.022 MeV?
Creating e⁺e⁻ requires at least twice the electron rest energy. A heavy nucleus can absorb recoil momentum, so the photon needs only ≈ 2m_e c² in the lab. A free photon in empty space cannot pair-produce alone — energy–momentum conservation forbids it; that is why a nucleus or second photon is required.
Why does triplet production need a higher threshold?
The target electron is light, so more of the photon’s energy goes into the final three-lepton kinematics and recoil. The effective threshold sits near 4m_e c² rather than 2m_e c². Students sometimes assume every channel opens at 1.022 MeV — only the nuclear Bethe–Heitler case does in the heavy-target limit.
How does Breit–Wheeler limit TeV photons?
A TeV gamma can collide with an infrared or CMB photon and still exceed 2m_e c² in the center-of-mass frame, producing pairs and attenuating the beam over cosmic distances. The simulator marks that channel alongside nuclear and triplet processes so you can compare thresholds, not replace a full cascade code.