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.

Pair Production Threshold & σ(E_γ)

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.

Process

Pair-production channel

Target nucleus

Photon energy E_γ (MeV, log)0.6989700043360189 log₁₀ MeV

Log y-axis (σ)

Pair production turns a high-energy photon into an electron–positron pair. In the field of a nucleus the threshold is 2 m_e c² (1 + m_e/M_N) ≈ 1.022 MeV with the σ ∝ Z² Bethe–Heitler scaling. The triplet process γ + e⁻ requires ≈ 4 m_e c². Two-photon Breit–Wheeler annihilation γγ → e⁺e⁻ underpins the cosmic gamma-ray horizon: a TeV photon attenuates against EBL/CMB photons satisfying E₁ E₂ ≥ (m_e c²)². Curves are pedagogical Bethe–Heitler shapes, not fits to NIST tables.

Measured values

Threshold1.022e+0 MeV

σ at slider6.580e-2 b

E_γ slider5.000e+0 MeV

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.

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How it works

Frequently asked questions