Influence of low energy scattering on loosely bound states

Abstract

Compact algebraic equations are derived, which 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 16O+n, 16O+p and 12C+alpha nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind.