Pair Production Threshold & σ(E_γ)
This interactive simulator explores Pair Production Threshold & σ(E_γ) in Astronomy & The Sky. 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. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Astronomy & The Sky.
Key terms
- pair
- production
- threshold
- pair production threshold
- astronomy
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).
More from Astronomy & The Sky
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Big Bang Nucleosynthesis (BBN)
Light-element abundance curves H, ⁴He, D, ³He, ⁷Li vs cosmic time / temperature. Weak freeze-out, neutron decay gap, deuterium bottleneck → Y_p ≈ 0.245. Slide η₁₀ and N_eff over the classic BBN curves; observed values overlaid.
EM Calorimeter Shower (Heitler / Rossi)
Toy electromagnetic cascade in a calorimeter: γ → e⁺e⁻, e⁻ → e⁻γ each X₀, with critical-energy cutoff E_c. Animate the branching tree, see N_max ≈ E₀/E_c, t_max ≈ log₂(E₀/E_c) live; presets for Pb, Cu, Si, air.
Bremsstrahlung & Synchrotron Radiation Pattern
Polar plot of dP/dΩ for an accelerating charge: a ∥ v (linear / brems) and a ⊥ v (circular / synchrotron). Pull β = v/c toward 1 — Larmor donut collapses into a forward beam of half-angle ≈ 1/γ; ω_g, ω_c shown for given B.
Venus Phases (Galileo)
Heliocentric geometry: full disk vs crescent at inferior conjunction; Earth-view inset.
Stellar Aberration
Bradley: telescope tilt v/c ~ 10⁻⁴ rad; annual ~20.5″ — not parallax.