Pair Production Threshold & σ(E_γ)

This interactive simulator explores Pair Production Threshold & σ(E_γ) in Астрономия и небо. 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.

Для кого: For learners comfortable with heavier math or second-level detail. Typical context: Астрономия и небо.

Ключевые понятия

pair
production
threshold
pair production threshold
astronomy

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.

Измеренные величины

Threshold1.022e+0 MeV

σ at slider6.580e-2 b

E_γ slider5.000e+0 MeV

Как это работает

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).

Другие симуляторы в этой категории — или все 51.

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НовоеУниверситет / научные

CMB Power Spectrum (Acoustic Peaks)

Cosmic Microwave Background temperature D_ℓ vs ℓ with Sakharov peaks: tune Ω_b h², Ω_c h², n_s, A_s, τ, h and watch the parity flip between odd / even peaks, the Silk damping tail, and the Sachs–Wolfe plateau move. Pedagogical parametric ΛCDM model.

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НовоеУниверситет / научные

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.

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НовоеУниверситет / научные

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.

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НовоеУниверситет / научные

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.

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НовоеШкольные