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RAD-11

Pair-production cross-section sketch

σ_pair ∝ Z² ln(E / 2 m c²) above 1.022 MeV. High-energy photon channel.

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AttenuationPair production

Governing equation

σκ∝Z2ln⁡(E/2mec2)\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2)

E∈[1.022,40]E \in \left[1.022, 40\right]

where

Z
Atomic number (—)
E
Photon energy (MeV)
\sigma_0
Prefactor (b)
\sigma_\kappa
Pair cross section (b)

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RAD-11 · spectrum
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①

Governing law — red

σκ∝Z2ln⁡(E/2mec2)\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2)

E∈[1.022,40]E \in \left[1.022, 40\right]

E=1.022E = 1.022σκ=6.72×10−4\sigma_\kappa = 6.72\times 10^{-4}

②

Domain of the variable — blue

Emin⁡=1.022,Emax⁡=40E_{\min} = 1.022,\quad E_{\max} = 40

E∈[1.022,40]E \in \left[1.022, 40\right]

E=1.022E = 1.022E=1.022E = 1.022

③

Response curve — green

σκ∝Z2ln⁡(E/2mec2)\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2)

E∈[1.022,40]E \in \left[1.022, 40\right]

E=1.022E = 1.022σκ=6.72×10−4\sigma_\kappa = 6.72\times 10^{-4}

④

Rate of change — amber

dσκdE\frac{\mathrm{d}\sigma_\kappa}{\mathrm{d}E}

E∈[1.022,40]E \in \left[1.022, 40\right]

E=1.267E = 1.267σκ′=5.373\sigma_\kappa^{\prime} = 5.373

Lecture brief

Historical brief

Beer attenuation, Compton (1923), Klein–Nishina, Bragg–Gray cavity and KERMA are the transport of photons and charged particles in matter. The sheets compute fluence, kerma and stopping. This sheet (RAD-11 — Pair-production cross-section sketch) is the form associated with Pair production. Working symbols: ZZ, EE, σ0\sigma_0 →\rightarrow σκ\sigma_\kappa. Dominates above a few MeV in high-Z. The nucleus recoils; triplet production is on electrons.

Purpose

Purpose: compute σκ\sigma_\kappa from ZZ, EE, σ0\sigma_0 in Radiation physics via σκ∝Z2ln⁡(E/2mec2)\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2) σ_pair ∝ Z² ln(E / 2 m c²) above 1.022 MeV. High-energy photon channel. Use it when a real radiation physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given Z=82.000 —Z = 82.000\,\mathrm{—}, E=5.000 MeVE = 5.000\,\mathrm{MeV}, σ0=0.001 b\sigma_0 = 0.001\,\mathrm{b}, the governing relation σκ∝Z2ln⁡(E/2mec2)\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2) yields σκ=10.6755 b\sigma_\kappa = 10.6755\,\mathrm{b}. A photon, a nucleus, an e⁺e⁻ pair. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Pair cross section \sigma_\kappa10.6755 b
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RAD-11 · spectrum
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Narration of this film

A photon, a nucleus, an e⁺e⁻ pair.

Dominates above a few MeV in high-Z. The nucleus recoils; triplet production is on electrons.

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