Charge-Exchange Reactions Accompanied by a Single $\pi^+$ Production in Medium-Energy Heavy-Ion Collisions
Heavy-ion charge-exchange (CE) reactions provide a sensitive probe of isospin dynamics in nuclear collisions. We investigate the reaction $^{12}\mathrm{C}(^{12}\mathrm{C},\,^{12}\mathrm{N}\,\pi^{+})\,^{12}\mathrm{Be}$ at 400--600 A MeV within the ultra-relativistic quantum molecular dynamics model combined with a phase-space coalescence approach. This reaction represents a nontrivial CE channel accompanied by a single $\pi^+$ production in heavy-ion collisions, extending previous studies from lepton-induced to hadronic systems. The $^{12}\mathrm{N}$ fragment is formed via nucleon and meson exchange, whereas $\pi^+$ production is primarily governed by $\Delta$ resonance excitation and decay, enabling simultaneous investigations of CE processes and $\Delta$-induced pion production within the same reaction system. We calculate the reaction cross section and analyze the four-momentum distributions of $^{12}\mathrm{N}$ and $\pi^+$. Characteristic phase-space features reflect different production mechanisms and provide guidance for future experimental designs. Additionally, this reaction may serve as a potential pathway for rare-isotope production.