Muon Scanner Resolution Calculator
A Muon-based scanner measures the deflection of a muon as it passes through a material. The higher the density of the material or atomic number, the larger the deflection. This calculator determines the mimimum detectable quantity of a material based on properties of the material, distance from the material and the resolution of the detector. As always, use at your own risk, not warranted for any purpose. Do not depend on any results without independent verification.
| Material | Density (g/cm³) | Radiation Length X₀ (cm) | Dominant Atomic Z | Minimum Detectable Volume |
|---|
Formulas Used:
1. RMS Scattering Angle:
$$ \theta_{rms} \approx \frac{13.6\,\text{MeV}}{\beta p} Z \sqrt{\frac{t}{X_0}} $$
This estimates the typical angle that a muon is deflected when it passes through a material. The greater the atomic number \(Z\), or the thickness \(t\), the larger the deflection. A material with a lower radiation length \(X_0\) causes more scattering.
2. Positional Deflection at Detector:
$$ \Delta x = Z \cdot \theta_{rms} $$
The change in position of the muon at the detector (located a distance \(Z\) from the material) increases linearly with distance. This means that more separation between the material and the detector helps resolve smaller deflections.
3. Minimum Detectable Volume:
$$ \text{Volume}_{min} \propto \frac{g_x \cdot g_y}{(Z \cdot \theta_{rms})^2} $$
The smallest volume of a material that the muon scanner can detect is proportional to the product of detector granularity in X and Y, divided by the square of the muon's deflection at the detector. A finer granularity and a greater Z (distance) both lead to improved resolution.
The result is then converted into the appropriate unit selected on the Y-axis (volume in cm³/m³ or mass in g/kg) using the material density.