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