A Closed-Form Detection Threshold for Muon Absorption Tomography of Concrete Voids

We derive a closed-form expression for the minimum exposure time required to detect a void of diameter d in concrete of thickness T using cosmic ray muon absorption tomography: t_min = σ² × 2R / ΔR², where R is the transmitted muon rate computed from the PDG sea-level spectrum and Groom et al. (2001) energy loss parameterization, and ΔR is the rate excess through the void. The formula replaces case-specific Geant4 Monte Carlo simulation with a one-equation feasibility screening tool. Validated against the measured sea-level muon rate and published tunnel imaging data. Practical lookup tables and open-source Python code are provided for overburden thicknesses of 0.5–15 m and void diameters of 2–100 cm. A safety factor of 10–100× converts the statistical floor to practical design estimates.