How to Use Compton Scattering Calculator
The Compton Scattering Calculator computes the wavelength shift and energy redistribution when an X-ray or gamma photon scatters from a free electron at an angle θ.
- Choose the input mode - Enter either the incident wavelength (in pm, nm, or Å) or the incident photon energy (in keV or MeV). The Compton Scattering Calculator converts internally to wavelength for the shift equation.
- Set the scattering angle - Enter θ in degrees from 0° (forward scatter, zero shift) to 180° (back-scatter, maximum shift). The Compton Scattering Calculator accepts any value in this range.
- Read the result - The panel reports the scattered photon wavelength λ’, its energy E’, and the kinetic energy ΔE transferred to the recoil electron.
- Sweep the angle to visualize the shift - Change θ from 0 to 180° in steps to see how the wavelength shift varies — it is zero at forward scatter and maximum (2λ_C) at exact back-scatter, confirming the textbook curve.
Formula & Theory - Compton Scattering Calculator
The Compton Scattering Calculator uses the original Compton equation:
λ' − λ = λ_C · (1 − cos θ)
λ_C = h / (m_e · c) ≈ 2.426e−12 m
E' = h c / λ'
ΔE = E − E' (energy to electron)| Symbol | Meaning |
|---|---|
| λ, λ’ | Incident and scattered wavelengths |
| θ | Scattering angle |
| λ_C | Electron Compton wavelength |
| E, E’ | Photon energies before and after |
| ΔE | Kinetic energy of the recoil electron |
The shift is independent of the incident wavelength and depends only on the geometry and the electron’s Compton wavelength.
Special Angles and the Compton Edge
| Angle θ | Δλ | Interpretation |
|---|---|---|
| 0° | 0 | Forward scatter — no energy transfer |
| 90° | λ_C ≈ 2.43 pm | Right-angle scatter |
| 180° | 2λ_C ≈ 4.85 pm | Back-scatter — maximum shift (Compton edge) |
In a gamma-ray spectrum the Compton edge appears as the maximum electron recoil energy, located at E_edge = E · 2α / (1 + 2α) where α = E / (m_e c²).
Assumptions and Limits
The calculator assumes a free electron at rest, ignoring binding energy, motion, and multiple scattering. In practice these corrections are small for X-rays at hundreds of keV but become important at very low photon energies or for electrons bound in heavy atoms.
Use Cases for Compton Scattering Calculator
The Compton Scattering Calculator is useful when you need a quick, transparent calculation for radiation interactions. Common uses include:
- Diagnostic radiology - Estimate scattered photon energies for X-ray image quality and dose planning; Compton scattering dominates in soft tissue at diagnostic energies.
- Gamma-ray detectors - Predict the Compton edge and plateau in a gamma spectrum to correctly interpret detector response and identify isotopes.
- Radiation shielding - Estimate how much energy each Compton interaction removes from the primary beam, which is the dominant attenuation mechanism at 0.5–10 MeV.
- Physics teaching - Plot λ’-λ vs θ to verify the textbook curve and confirm the ~2.43 pm back-scatter limit experimentally.
- Compton cameras - In medical and security imaging, two detector hits at known angles allow 3D source localization using the Compton kinematics this calculator models.
- Astrophysics - Estimate the photon energy after inverse Compton scattering off relativistic electrons in jets and coronae (boost factor replaces the shift formula).
For full radiation transport through matter or multiple-scattering corrections, run a Monte Carlo code. The Compton Scattering Calculator covers the exact single-event analytic case that underpins all radiation-physics training.