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The synthesis of heavy elements in supernovae is affected by low-energy $(n,p)$and $(p,n)$reactions on unstable nuclei, yet experimental data on such reaction rates are scarce. The SECAR (SEparator for CApture Reactions) recoil separator at FRIB (Facility for Rare Isotope Beams) was originally designed to measure astrophysical reactions that change the mass of a nucleus significantly. We used a novel approach that integrates machine learning with ion-optical simulations to find an ion-optical solution for the separator that enables the measurement of $(p,n)$reactions, despite the reaction leaving the mass of the nucleus nearly unchanged. A new measurement of the ${}^{58}\mathrm{Fe}(p,n){}^{58}\mathrm{Co}$reaction in inverse kinematics with a $3.66\pm 0.12$MeV/nucleon ${}^{58}\mathrm{Fe}$beam (corresponding to $3.69\pm 0.12$MeV proton energy in normal kinematics) yielded a cross-section of $20.3\pm 6.3$ mb and served as a proof of principle experiment for the new technique demonstrating its effectiveness in achieving the required performance criteria. This novel approach paves the way for studying astrophysically important $(p,n)$reactions on unstable nuclei produced at FRIB. Published by the American Physical Society2025