The complex momentum representation approach and its application to low-lying resonances in ${^{17}}$O and ${^{29,31}}$F
Approaches for predicting low-lying resonances, uniformly treating bound, and resonant levels have been a long-standing goal in nuclear theory. Accordingly, we explored the viability of the complex momentum representation (CMR) approach coupled with new potentials. We focus on predicting the energy of the low-lying 2p 3/2 resonance in 17 O, which is critical for s-process nucleosynthesis and missing in previous theoretical research. Here, using a Woods-Saxon potential based on the Koning-Delaroche optical model and constrained by the experimental one-neutron separation energy, we successfully predicted the resonant energy of this level for the first time. Our predictions of the bound levels and 1d 3/2 resonance agree well with the measurement results. Additionally, we utilize this approach to study the near-threshold resonances that play a role when forming a two-neutron halo in 29,31 F. We found that the CMR-based predictions of the bound-level energies and unbound 1f 7/2 level agree well with the results obtained using the scattering phase shift method. Subsequently, we successfully found a solution for the 2p 3/2 resonance with energy just above the threshold, which is decisive for halo formation.