Extrapolation of scattering data to the negative-energy region. II. Applicability of effective range functions within an exactly solvable model

A problem of analytical continuation of scattering data to the negative-energy region to obtain information about bound states is discussed within an exactly solvable potential model. This work is continuation of the previous one by the same authors [L. D. Blokhintsev et al., Phys. Rev. C 95, 044618 (2017)]. The goal of this paper is to determine the most effective way of analytic continuation for different systems. The $d+\ensuremath{\alpha}$ and $\ensuremath{\alpha}+^{12}\mathrm{C}$ systems are considered and, for comparison, an effective-range function approach and a recently suggested $\mathrm{\ensuremath{\Delta}}$ method [O. L. Ram\'{\i}rez Su\'arez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017).] are applied. We conclude that the $\mathrm{\ensuremath{\Delta}}$ method is more effective for heavier systems with large values of the Coulomb parameter, whereas for light systems with small values of the Coulomb parameter the effective-range function method might be preferable.