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

This study applies Patterson function analysis to reconstruct the spatial distribution of the Δ(1232) magnetic dipole transition current directly from empirical form factors. By avoiding reliance on theoretical models, the method yields a density profile that is both strictly positive and sharply confined. The reconstruction reveals a pronounced central peak with a half‑maximum radius of 0.0877 fm, providing a stringent measure of spatial compactness. To our knowledge, this represents the first published reconstruction of a baryon transition current. Comparative evaluations with nucleons, mesons, and light nuclei show that the Δ(1232) distribution occupies an intermediate position between neutron and proton charge profiles. These results demonstrate that Patterson imaging offers a transparent and reproducible framework for probing hadronic and nuclear structure, now extended beyond charge, magnetic, and gravitational form factors to transition currents.