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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 

Abstract The observation of X-rays during quiescence from transiently accreting neutron stars provides unique clues about the nature of dense matter. This, however, requires extensive modeling of the crusts and matching the results to observations. The pycnonuclear fusion reaction rates implemented in these models are theoretically calculated by extending phenomenological expressions and have large uncertainties spanning many orders of magnitude. We present the first sensitivity studies of these pycnonuclear fusion reactions in realistic network calculations. We also couple the reaction network with the thermal evolution codedStarto further study their impact on the neutron star cooling curves in quiescence. Varying the pycnonuclear fusion reaction rates alters the depth at which nuclear heat is deposited although the total heating remains constant. The enhancement of the pycnonuclear fusion reaction rates leads to an overall shallower deposition of nuclear heat. The impurity factors are also altered depending on the type of ashes deposited on the crust. These total changes correspond to a variation of up to 9 eV in the modeled cooling curves. While this is not sufficient to explain the shallow heat source, it is comparable to the observational uncertainties and can still be important for modeling the neutron star crust.