Influence of low-energy scattering on loosely bound states

Compact algebraic equations are derived that connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations are established for positively charged and neutral particles, using the analytic continuation of the scattering (S) matrix in the complex wave-number plane. Their accuracy is checked on simple local potential models for the $^{16}\mathrm{O}+n$, $^{16}\mathrm{O}+p$, and $^{12}\mathrm{C}+\ensuremath{\alpha}$ nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind.

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