Properties of particle-unstable nuclei lying beyond the proton drip line can be ascertained by considering the (usually known) properties of its mirror neutron-rich system. We have used a multichannel algebraic scattering theory to map the known properties of the neutron-${}^{14}\mathrm{C}$ system to those of the proton-${}^{14}\mathrm{O}$ one from which we deduce that the particle-unstable ${}^{15}\mathrm{F}$ will have a spectrum of two low-lying broad resonances of positive parity and, at higher excitation, three narrow negative-parity ones. A key feature is to use coupling to Pauli-hindered states in the target.

• Received 20 October 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.072502