Deducing physical properties of weakly bound states from low-energy scattering data. Application to 16O and 12C+α

Possibilities of deducing the asymptotic normalisation constant Cb of the 21+ subthreshold bound state of 16O from the low-energy 12C+α d-wave scattering phase shifts are studied. Within the potential model, it is shown that such a connection exists in principle, either by studying the range of potentials fitting the phase shifts, or by using the effective range expansion. However, present-day data do not seem sufficient to strongly constrain Cb, as values ranging from 20 to 180 × 103 fm−1/2 are obtained, depending on the order of the chosen effective-range expansion.