Pion (π+) charge structure revisited: Insights from Patterson function analysis

Using Patterson function analysis, the pion’s charge distribution has been reconstructed directly from form factor data. The profile shows a sharply localized peak 43.96 fm⁻⁶ with a half-maximum radius of 0.142 fm, much smaller than the 0.659 fm charge radius reported by PDG. The density crosses zero at r = 0.364 fm, becomes negative with a minimum of −1.23 fm⁻⁶ at r = 0.431 fm, and returns to zero at r = 0.532 fm. These oscillatory features suggest a core–shell structure. When compared with nucleons and light nuclei (deuteron, tritium, ³He, ⁴He), the pion profile occupies an intermediate position: nucleons cluster together, followed by the pion, then the light nuclei group. These systematic similarities highlight the empirical power of Patterson reconstruction for probing the internal structure of fundamental particles.