We present coupled-channel Gamow shell model (GSM-CC) calculations of the ${}^{13}\mathrm{O}$($p,p$) and ${}^{14}\mathrm{O}$($p,p$) elastic-scattering reactions in the $\mathrm{core}+\mathrm{valence}$ nucleon picture. Within this unified framework, we investigate the structural and scattering properties of the proton-unbound nuclei ${}^{14}\mathrm{F}$ and ${}^{15}\mathrm{F}$. GSM-CC reproduces the ground-state separation energies and describes the low-lying spectra and decay widths of ${}^{14}\mathrm{F}$ ($2_1^{-}, 1^{-}, 3^{-}, 2_2^{-}, 4^{-}$) and ${}^{15}\mathrm{F}$ ($1/2^{+}, 5/2^{+}$) nuclear states. For ${}^{15}\mathrm{F}$, phase shifts and spectroscopic factors in the $1/2^{+}$ and $5/2^{+}$ channels are analyzed to identify the dominant configurations. The calculated ${}^{14}\mathrm{O}$($p,p$) excitation functions at several ${\theta }_{\mathrm{c}.\mathrm{m}.}$ angles agree with available experimental data, thereby providing a benchmark for the reaction framework. We then provide GSM-CC calculations and predictions related to the ${}^{13}\mathrm{O}$($p,p$) elastic scattering reaction and characterize the five lowest resonances in ${}^{14}\mathrm{F}$ in terms of their energies, widths, and spectroscopic factors. Notably, and consistently with other theoretical studies, GSM-CC predicts an excited $2_2^{-}$ resonance contributing to the ${}^{13}\mathrm{O}$($p,p$) excitation function at higher energy, which was not identified in the previous experimental measurement. Comparison with the GSM structure calculations reflects the enhanced coupling provided by the configuration mixing present in the GSM-CC framework.

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• Elastic scattering reactions
• H & He induced nuclear reactions
• Nuclear structure & decays
• 6 ≤ A ≤ 19
• Shell model