Baryon transition current structure (Δ(1232) electric quadrupole) revisited: Insights from Patterson function analysis

This study employs Patterson function analysis to reconstruct the spatial distribution of the Δ(1232) electric quadrupole transition current directly from empirical form factors. By avoiding reliance on theoretical models, the method produces a density profile that is both positive and sharply localized. The reconstruction reveals a dominant central peak with a half‑maximum radius of 0.0933 fm, offering a stringent measure of spatial compactness. Comparative evaluations with nucleons, mesons, and light nuclei place the Δ(1232) distribution in an intermediate position between nucleon and meson profiles. These findings confirm that Patterson imaging provides a transparent and reproducible framework for probing hadronic and nuclear structure, now extended beyond charge, magnetic, and gravitational form factors to transition currents.