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

$E \in \left[1, 10000\right]$

where

E: Photon energy (keV)
k: E/mc² (—)
\sigma: KN total (b)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

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

$E \in \left[1, 10000\right]$

$E = 1$ $k = 338.6$

Along the curve

②

Domain of the variable — blue

E_{\min} = 1,\quad E_{\max} = 10000

$E \in \left[1, 10000\right]$

$E = 1$ $E = 1$

Along the curve

③

Response curve — green

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

$E \in \left[1, 10000\right]$

$E = 1$ $k = 338.6$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}k}{\mathrm{d}E}

$E \in \left[1, 10000\right]$

$E = 63.89$ $k^{\prime} = -2.678$

Along the curve

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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