Quantifying Non-Gaussian Scattering Tails in Micro-Heterogeneous Phantoms for Proton Therapy Applications

Multiple Coulomb scattering (MCS) in heterogeneous media governs the lateral penumbra in proton therapy. Molière theory predicts Gaussian cores with rare large-angle non-Gaussian tails, but internal microstructure influence remains unquantified. We performed Geant4 simulations of 1 GeV/c protons traversing four targets of matched total radiation length: homogeneous PMMA, layered PMMA-Al, PMMA with air-void lattices, and PMMA with tungsten inclusions. For each, 5×10⁵ primary protons were tracked. Trajectories were reconstructed and analyzed using the ROOT framework. The Gaussian core width, estimated via the Highland approximation, stayed within 2% across all targets. However, heterogeneous phantoms exhibited significantly enhanced non-Gaussian tails. The probability P(|Δθ|>3σ) increased by factors of 2.1 (layered), 2.8 (voids), and 3.3 (W inclusions) relative to PMMA. The 99th-percentile scattering angle rose up to 43%, and excess kurtosis reached 1.9–4.6. Q-Q plots confirmed systematic heavy-tail behavior. These results demonstrate that internal density interfaces amplify rare large-angle scattering at constant macroscopic scattering strength, impacting tissue dose-calculation algorithms.