Baryon transition current structure (N(1440) Roper radial 1 excitation F1 form factor) revisited: Insights from Patterson function analysis

This study employs Patterson function analysis to reconstruct the spatial distribution of the N(1440) Roper radial excitation Dirac-type transition current based on empirical F1 form factors. By avoiding reliance on theoretical modeling, the method produces a sharply localized density profile containing both positive and negative components. The reconstruction reveals a dominant central peak with a half-maximum radius of 0.0374 fm, highlighting extreme compactness. Comparative evaluation against nucleons, mesons, and light nuclei demonstrates that the Roper excitation occupies the most confined position among baryon transition currents. These results confirm that Patterson imaging offers a transparent and reproducible framework for probing hadronic and nuclear structure, extending its scope beyond charge, magnetic, and gravitational form factors to transition currents.