Real-time wavelength shift Δλ = λ_C(1 − cos θ) for photon-electron scattering. See the scattered-photon energy, recoil-electron kinetic energy, scattering angle, and detector hit/miss with a geometry diagram and Δλ(θ) curve.
Parameters
Incident photon energy E_in
keV
Scattering angle θ
deg
Target mass ratio m/m_e
×m_e
Detector threshold E_detect
keV
Electron Compton wavelength λ_C = h/(m_e c) ≈ 2.426 pm. Setting the target mass to a proton (~1836 m_e) collapses Δλ toward zero, recovering elastic Thomson scattering. Photons below the detector threshold are not counted.
Results
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Scattered photon energy E_f
—
Wavelength shift Δλ
—
Electron kinetic energy
—
Electron angle φ_e
Detector status: —
Scattering geometry
Yellow incoming photon with wavelength λ_in hits the electron at the centre; the scattered photon (blue) leaves at angle θ and the recoil electron (red) at φ_e. Wavefront spacing reflects λ_in vs λ_f.
Wavelength shift Δλ(θ)
x = scattering angle θ (deg), y = Δλ (pm). Δλ = λ_C(1 − cos θ) reaches its maximum 2λ_C at θ = 180°. The yellow vertical line marks the current θ.
Theory & Key Formulas
Compton scattering follows from photon-electron energy and momentum conservation, giving the wavelength shift below.
Wavelength shift ($\lambda_C = h/(m_e c) \approx 2.426$ pm is the electron Compton wavelength):
$m_e c^2 = 511$ keV. For a heavier target of mass $m$, $\lambda_C \to h/(m c)$ so Δλ shrinks inversely with the target mass.
What is the Compton scattering simulator?
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Compton scattering — that's where an X-ray bounces off an electron and comes out at a longer wavelength, right? Why does the wavelength get longer at all?
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Exactly. Arthur Compton found it in 1923 by hitting carbon with X-rays. If light were purely a wave, the scattered frequency should match the incident one. Instead, the wavelength grew with the scattering angle — and matched perfectly an elastic collision between a photon (carrying energy and momentum) and a free electron. The relation is Δλ = λ_C(1 − cos θ), where λ_C = h/(m_e c) ≈ 2.426 pm is the electron's Compton wavelength.
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For the default values (E_in = 100 keV, θ = 90°) the scattered photon is 83.6 keV, Δλ = 2.43 pm, and the electron picks up 16.4 keV at 39.9°. Less goes to the electron than I'd expect — why?
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Because at 100 keV the parameter α = E_in/(m_e c²) = 100/511 ≈ 0.196 is still much smaller than 1. The wavelength change scales like λ_C, so the relative energy loss stays around 16 %. Push E_in to 1 MeV and α ≈ 2; the same 90° scattering then transfers more than 60 % of the energy. Try sliding E_in to 200, 500, 1000 keV and watch how E_f keeps falling.
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When I raise the target mass ratio, Δλ shrinks until the photon hardly loses any energy. What's that telling me?
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Good catch. Δλ scales as 1/m. For an electron the shift at 90° is 2.43 pm, but for a proton (m ≈ 1836 m_e) it drops to 1.3 fm — utterly negligible. In real materials Compton scattering on "free" electrons only happens when the photon energy (X-ray, gamma) is much larger than the electron's binding energy (a few eV to a few keV). Visible light just sees Rayleigh / Mie elastic scattering — wavelength preserved.
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Sweeping the angle pushes Δλ up to 2λ_C ≈ 4.85 pm at θ = 180°. So back-scattering loses the most?
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Right. cos 180° = −1, so Δλ = 2λ_C is the absolute maximum. That's the back-scatter limit, important for CT/PET scatter correction and for the Compton edge in gamma-ray spectrometers — the kink in the spectrum at the maximum electron kinetic energy. For Cs-137's 662 keV gamma, the Compton edge sits near 477 keV, exactly the recoil-electron energy you get here at θ = 180°.
FAQ
Visible photons carry only 1.6–3.1 eV, comparable to or smaller than electron binding energies in atoms (several eV to tens of eV in valence shells). The electron is firmly attached to its atom, so the relevant elastic process is Rayleigh scattering off the atom as a whole, with no wavelength shift. Once the photon energy is well above the binding energy — tens of keV X-rays or hundreds of keV gamma-rays — the electron behaves as effectively free, and the Compton formula applies.
In the photoelectric effect the photon is fully absorbed: the electron carries away the photon energy minus its binding energy. In Compton scattering the photon survives with reduced energy and longer wavelength while the electron recoils. At low keV the photoelectric cross-section dominates; from a few hundred keV upward Compton scattering takes over; above 1.022 MeV electron-positron pair production also enters the picture.
In diagnostic CT (80–140 kVp) and clinical PET (511 keV) Compton scattering dominates inside the body, degrading contrast and contributing to dose. CT reconstruction relies on scatter-correction algorithms (Monte Carlo, kernel-based, or Single Scatter Simulation) to remove the scattered component. PET uses an energy window (typically 350–650 keV) to reject the lowest-energy scatter and applies model-based correction for the rest, since the scatter fraction can reach 30–40 % of total counts.
When a monoenergetic gamma is detected by a scintillator or HPGe, Compton scattering produces a continuous spectrum of recoil electrons (the Compton continuum) with a sharp upper cut-off where θ = 180°. That cut-off is the Compton edge — about 477 keV for Cs-137's 662 keV line and 1.12 MeV for Co-60's 1.33 MeV. Together with the photopeak it defines the detector response and is often used as an energy-calibration landmark.
Real-world applications
Medical imaging (CT, PET, SPECT): Compton scattering is the dominant interaction in soft tissue throughout diagnostic CT (80–140 kVp) and PET (511 keV). Scatter-correction algorithms — Monte Carlo, Single Scatter Simulation, kernel-based — are now standard in reconstruction pipelines. Plug E_in = 511 keV and θ = 180° into this simulator and you can read off the most scattered photon energy in PET (~170 keV), exactly the regime that energy windows must reject.
Gamma-ray spectroscopy and environmental monitoring: HPGe and NaI(Tl) spectra always show a Compton continuum and a Compton edge below each photopeak. The edge positions for Cs-137 (477 keV) and Co-60 (1.12 MeV) help confirm nuclide identification and serve as energy-calibration landmarks. Shielding designs (lead, tungsten) similarly use Compton angular distributions (Klein-Nishina) to estimate scattered-photon leakage paths.
X-ray astronomy and Compton telescopes: In the 10 keV–10 MeV cosmic gamma window, Compton telescopes such as NASA's COMPTEL (1991–2000) and the upcoming COSI mission reconstruct the source direction by recording the scattering angle and the scattered-photon trajectory. Understanding the angular dependence covered by this tool makes the instrument response of those missions much more intuitive.
Radiation therapy: 6–25 MV linac beams undergo mostly Compton scattering inside the patient. Pencil-beam, convolution/superposition, and Monte Carlo dose engines all incorporate Compton angular and energy distributions explicitly so that scattered dose around the target volume is predicted accurately, helping spare organs at risk.
Common misconceptions and caveats
The most common misconception is to assume Δλ depends on the incident photon energy. The formula Δλ = λ_C(1 − cos θ) clearly does not — it depends only on the scattering angle. A 100 eV UV photon and a 10 MeV gamma both yield Δλ = 2.43 pm at 90°. What does change with energy is the relative shift Δλ/λ_in or the energy loss KE_e/E_in, both of which grow with E_in. Compare them in the simulator by sliding E_in while watching Δλ stay fixed.
A second pitfall is to think Compton scattering only happens in X-rays. Even visible or infrared light can scatter from very weakly bound electrons (free electrons in metals, plasma electrons). Laser Thomson scattering — the low-energy limit of Compton scattering — is routinely used to diagnose electron temperature and density in fusion plasmas. With this tool, lowering E_in toward 0.001 keV (~1 eV) shows that Δλ stays at 2.43 pm but the relative shift becomes vanishingly small (10⁻⁹).
Finally, do not treat the recoil electron angle φ_e as an independent variable. Momentum conservation locks φ_e to θ and to the incident energy: φ_e is bounded above by 90° (in the limit θ → 0°) and falls to 0° at back-scattering (θ → 180°). Compton coincidence experiments exploit exactly this correlation between photon and electron directions to suppress background; sweep θ here and watch the φ_e value to feel the constraint directly.