Reconstructed pion (π⁺) charge structure via selective flattening: Insights from Patterson function analysis

We present the first empirical reconstruction of the pion’s internal charge distribution using a selective flattening procedure applied to Patterson function analysis. By constraining the minima of the radial Patterson charge density, the method achieves closer agreement with experimental data and yields a spatially resolved profile. The reconstruction reveals a compact positive core with a peak density of 68,400 fm⁻³ and a half‑maximum radius of 0.134 fm, surrounded by a diffuse negative shell reaching −2,740 fm⁻³ at r=0.431 fm. The charge density crosses zero at 0.357 fm and 0.563 fm. Grid integration produces a net charge of 1,080 (885 within r = 0.563 fm), far exceeding the pion’s unit charge, underscoring the non‑uniqueness of this reconstruction. This model‑independent approach establishes a reproducible framework for visualizing charge distributions of elementary particles and situates the pion within the broader systematics of nucleons and light nuclei.