We describe bound states, resonances and elastic scattering of light ions using a $delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients, effective-range parameters, and phase shifts, we adjust the two parameters of the potential to some of these observables and make predictions for the nuclear systems $d+alpha$, $mbox{$^3$He}+alpha$, $mbox{$^3$He}+alpha$, $alpha+alpha$, and $p+mbox{$^{16}$O}$. We identify relevant momentum scales for Coulomb halo nuclei and propose how to apply systematic corrections to the potentials. This allows us to quantify statistical and systematic uncertainties. We present a constructive criticism of Coulomb halo effective field theory and compute the unknown charge radius of $^{17}$F.
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