RAD-03

Klein–Nishina total snapshot

σ/σ_T ≈ (3/4)[ (1+k)/k³ ((2+2k)/(1+2k) − ln(1+2k)/k) + ln(1+2k)/(2k) − (1+3k)/(1+2k)² ].

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AttenuationKlein–Nishina

Governing equation

\sigma_{KN}=\sigma_T\,f_{KN}(k),\quad k=E/m_ec^2

where

E: Photon energy (keV)
k: E/mc² (—)
\sigma: KN total (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-03 — Klein–Nishina total snapshot) is the form associated with Klein–Nishina. Working symbols: $E$ $\rightarrow$ $k$ , $\sigma$ . σ_T = 0.665 b. The cross section falls as ~ (ln k)/k at high energy.

Purpose

Purpose: compute

k

\sigma

from

E

in Radiation physics via

\sigma_{KN}=\sigma_T\,f_{KN}(k),\quad k=E/m_ec^2

σ/σ_T ≈ (3/4)[ (1+k)/k³ ((2+2k)/(1+2k) − ln(1+2k)/k) + ln(1+2k)/(2k) − (1+3k)/(1+2k)² ]. 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

E = 511.000\,\mathrm{keV}

, the governing relation

\sigma_{KN}=\sigma_T\,f_{KN}(k),\quad k=E/m_ec^2

yields

k = 1.000\,\mathrm{—}

\sigma = 0.2865\,\mathrm{b}

. A σ(E) that falls from Thomson. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Photon energy E511 keV

Outputs

E/mc² k1.000 —
KN total \sigma0.2865 b

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Narration of this film

A σ(E) that falls from Thomson.

σ_T = 0.665 b. The cross section falls as ~ (ln k)/k at high energy.

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