00 Foundations

Compton wavelength shift

Δλ = λ_C (1 − cos θ) with λ_C = 2.426 pm, independent of E.

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Simulation

Compton wavelength shift — 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

\Delta\lambda = \lambda_C(1-\cos\theta),\quad \lambda_C=h/(m_ec)=2.426\,\mathrm{pm}

Variables

θ · Angle°

Results

Δλ
Shift
0.002426nm
Δλ
Shift
2.4263pm

Curve

Explanation

\Delta\lambda = \lambda_C(1-\cos\theta),\quad \lambda_C=h/(m_ec)=2.426\,\mathrm{pm}

What it means

The Compton wavelength shift depends only on scatter angle, not on incident energy. λ_C = h/(m_e c) = 2.426 pm. At 90°, Δλ = λ_C; at 180°, Δλ = 2λ_C. Energy change is large when λ is comparable to λ_C (hard x-rays and γ-rays) and tiny for optical photons. 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.

Linear accelerator · Open this machine

How to use it

Enter θ. Combine with the energy calculator when you also need E′. Useful to remember that backscatter of 511 keV is 170 keV because Δλ = 2λ_C on a 2.43 pm photon. Change one input and watch the curve and the simulation follow.

Symbols

θAngle90 °

Worked example

A typical case from the default values: θ = 90 ° (Angle). Substituting into the relation gives Δλ = 0.002426 nm; Δλ = 2.4263 pm. These are teaching numbers — align them with your machine.

Typical values give

Δλ = 0.002426nm
Δλ = 2.4263pm

Where it comes from

The displayed formula is the working relation. Δλ = λ_C (1 − cos θ) with λ_C = 2.426 pm, independent of E. Usual reference: Attix. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Attix

Assumptions & limits

Free-electron Compton kinematics only. Bound-electron Compton (incoherent scatter with binding) has a small extra shift and Doppler width.

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. Free-electron Compton kinematics only. Bound-electron Compton (incoherent scatter with binding) has a small extra shift and Doppler width.

Keep this

Photons do not deposit dose; the electrons they set in motion do. Free-electron Compton kinematics only. Bound-electron Compton (incoherent scatter with binding) has a small extra shift and Doppler width.

In this specialty

Radiation physics