RAD-02

Compton scattered energy

E′ = E / (1 + (E/m_e c²)(1−cosθ)). Photon energy after Compton scatter.

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AttenuationCompton

Governing equation

E'=E\bigl(1+(E/m_ec^2)(1-\cos\theta)\bigr)^{-1}

$\theta \in \left[0, 180\right]$

where

E: Incident energy (keV)
\theta: Angle (°)
E': Scattered energy (keV)

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

E'=E\bigl(1+(E/m_ec^2)(1-\cos\theta)\bigr)^{-1}

$\theta \in \left[0, 180\right]$

$\theta = 0$ $E' = 511$

Along the curve

②

Domain of the variable — blue

\theta_{\min} = 0,\quad \theta_{\max} = 180

$\theta \in \left[0, 180\right]$

$\theta = 0$ $\theta = 0$

Along the curve

③

Response curve — green

E'=E\bigl(1+(E/m_ec^2)(1-\cos\theta)\bigr)^{-1}

$\theta \in \left[0, 180\right]$

$\theta = 0$ $E' = 511$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E'}{\mathrm{d}\theta}

$\theta \in \left[0, 180\right]$

$\theta = 1.132$ $E'^{\prime} = -0.176$

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-02 — Compton scattered energy) is the form associated with Compton. Working symbols: $E$ , $\theta$ $\rightarrow$ $E'$ . Backscatter of a high-energy photon saturates at m_e c² / 2 = 255 keV.

Purpose

Purpose: compute

E'

from

E

\theta

in Radiation physics via

E'=E\bigl(1+(E/m_ec^2)(1-\cos\theta)\bigr)^{-1}

E′ = E / (1 + (E/m_e c²)(1−cosθ)). Photon energy after Compton scatter. 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}

\theta = 90.000\,\mathrm{^{\circ}}

, the governing relation

E'=E\bigl(1+(E/m_ec^2)(1-\cos\theta)\bigr)^{-1}

yields

E' = 255.50\,\mathrm{keV}

. A photon, an electron, a lower E′. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Incident energy E511 keVAngle \theta90 °

Outputs

Scattered energy E'255.50 keV

Reading speed

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Narration of this film

A photon, an electron, a lower E′.

Backscatter of a high-energy photon saturates at m_e c² / 2 = 255 keV.

Reading speed

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