00 Foundations

Compton scattered photon energy

Scattered photon energy versus scatter angle for a free electron.

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Simulation

Compton scattered photon energy — Change the numbers; the scene follows.

Where it works

Linear accelerator

Isocenter

At isocenter, on the central axis through the patient (or a phantom in the same place).

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Formula

E' = \frac{E}{1+(E/m_ec^2)(1-\cos\theta)},\quad m_ec^2=511\,\mathrm{keV}

Variables

E · Incident photon energykeVθ · Scatter angle°

Results

E′
Scattered energy
83.6334keV
ΔE
Energy transfer
16.3666keV
Δλ
Wavelength shift
0.002426nm

Curve

Explanation

E' = \frac{E}{1+(E/m_ec^2)(1-\cos\theta)},\quad m_ec^2=511\,\mathrm{keV}

What it means

In Compton scatter the photon transfers part of its energy to a loosely bound electron. The outgoing photon energy E′ falls as the scatter angle θ rises. At 180° (backscatter) E′ = E / (1 + 2E/511 keV). For 511 keV annihilation photons, backscatter is 170 keV — the origin of the 180 keV backscatter peak. This is a working relation in Radiation physics.

Where it is used

Clinically it sits on the Linear accelerator — Isocenter. At isocenter, on the central axis through the patient (or a phantom in the same place). Radiation physics lives at the x-ray target, the linac head, and inside the patient: how a photon is born, how it scatters, and how it dies. Use these relations before you trust a spectrum, a wall, or a kV-versus-MV contrast argument.

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How to use it

Enter incident energy E in keV and θ in degrees. Read E′, the energy transfer ΔE, and the Compton wavelength shift. Use it in scatter rejection, SPECT windowing, and shielding of scattered radiation. Change one input and watch the curve and the simulation follow.

Symbols

EIncident photon energy100 keV
θScatter angle90 °

Worked example

A typical case from the default values: E = 100 keV (Incident photon energy); θ = 90 ° (Scatter angle). Substituting into the relation gives E′ = 83.6334 keV; ΔE = 16.3666 keV; Δλ = 0.002426 nm. These are teaching numbers — align them with your machine.

Typical values give

E′ = 83.6334keV
ΔE = 16.3666keV
Δλ = 0.002426nm

Where it comes from

The displayed formula is the working relation. Scattered photon energy versus scatter angle for a free electron. Usual reference: Klein–Nishina / Attix. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Klein–Nishina / Attix

Assumptions & limits

Assumes a free electron at rest (binding energy ≪ E). Coherent scatter and Doppler broadening from bound electrons are omitted. Klein–Nishina cross section is not computed here — only kinematics.

Pitfalls

Do not mix free-electron Compton kinematics with photoelectric-dominated kV imaging. Check keV versus MeV, and never treat a spectrum as one photon. Assumes a free electron at rest (binding energy ≪ E). Coherent scatter and Doppler broadening from bound electrons are omitted. Klein–Nishina cross section is not computed here — only kinematics.

Keep this

Photons do not deposit dose; the electrons they set in motion do. Assumes a free electron at rest (binding energy ≪ E). Coherent scatter and Doppler broadening from bound electrons are omitted. Klein–Nishina cross section is not computed here — only kinematics.

In this specialty

Radiation physics