Linking the exotic structure of ¹⁷C to its unbound mirror ¹⁷Na

The structure of ¹⁷C is used to define a nuclear interaction that, when used in a multichannel algebraic scattering theory for the n+C16 system, gives a credible definition of the (compound) excitation spectra. When couplings to the low-lying collective excitations of the ¹⁶C-core are taken into account, both sub-threshold and resonant states about the n+C16 threshold are found. Adding Coulomb potentials to that nuclear interaction, the method is used for the mirror system of p+Ne16 to specify the low excitation spectrum of the particle unstable ¹⁷Na. We compare the results with those of a microscopic cluster model. A spectrum of low excitation resonant states in ¹⁷Na is found with some differences to that given by the microscopic cluster model. The calculated resonance half-widths (for proton emission) range from ~2 to ~672 keV.