Muon Tomography: Cosmic-Ray Scattering Imaging

Hidden Object Material

Beam & Detector

Muon flux 60 /s

Mean muon momentum p 4.0 GeV/c

Reconstruction

Muons recorded

θ₀ for this material (typical path)

0 mrad

Avg. muons / image pixel

0.0

How it works

Cosmic-ray muons are produced when high-energy protons hit the upper atmosphere; roughly one passes through every square centimetre of ground per minute, with enough energy (GeV-scale) to punch through metres of rock or steel. As a muon crosses matter it repeatedly scatters off atomic nuclei — multiple Coulomb scattering — and the more nuclear charge (higher density × atomic number) it crosses, the more its trajectory bends. Measuring the bend angle of many muons and mapping where the largest deflections occur reconstructs an image of hidden material, exactly as real muon tomography scanners do at ports, reactor sites, volcanoes and pyramids.

Highland formula (RMS scattering angle):
θ₀ = (13.6 MeV / βcp) · √(x/X₀) · [1 + 0.038·ln(x/X₀)]

p = muon momentum, x = path length through the material
X₀ = radiation length (material property: Water 36 cm,
     Concrete 27 cm, Iron 1.8 cm, Lead 0.56 cm, Uranium 0.32 cm)

Material buttons — set the hidden block's radiation length X₀; denser/higher-Z materials give a much larger θ₀ for the same thickness.
New Hidden Object — randomises the block's size and position; try to spot it in the reconstructed image before revealing it.
Flux — how many muons per second are simulated; a real detector needs minutes to hours of exposure because muon flux is low — this sped-up version shows the statistical build-up.
Momentum — higher-momentum muons scatter less (θ₀ ∝ 1/p), which is why real scanners must estimate each muon's momentum to correct the image.
Each muon's measured deflection angle is squared and averaged into the pixel where it crossed the object's mid-plane — the image is a live estimate of local scattering density, the same quantity real cosmic-ray tomography reconstructs.

Muon track (scattered) Muon track (straight)

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