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

\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2)

where

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

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: $Z$ , $E$ , $\sigma_0$ $\rightarrow$ $\sigma_\kappa$ . Dominates above a few MeV in high-Z. The nucleus recoils; triplet production is on electrons.

Purpose

Purpose: compute

\sigma_\kappa

from

Z

E

\sigma_0

in Radiation physics via

\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\,\mathrm{—}

E = 5.000\,\mathrm{MeV}

\sigma_0 = 0.001\,\mathrm{b}

, the governing relation

\sigma_{\kappa}\propto Z^2\ln(E/2m_ec^2)

yields

\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.

Calculator

Inputs

Atomic number Z82 —Photon energy E5 MeVPrefactor \sigma_00.001 b

Outputs

Pair cross section \sigma_\kappa10.6755 b

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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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