On the phase-shift parameterization and ANC extraction from elastic-scattering data

We develop a method to parameterize elastic-scattering phase-shifts for charged nuclei, based on Pad\'e expansions of a simplified effective-range function. The method is potential independent and the input is reduced to experimental phase shifts and bound-state energies. It allows a simple calculation of resonance properties and of asymptotic normalization constants (ANCs) of subthreshold bound states. We analyze the $1^-$ and $2^+$ phase shifts of the $^{12}$C$+\alpha$ system and extract the ANCs of the corresponding bound states. For the $1^-$ state, a factor-3 improvement with respect to the best value available today is obtained, with a factor-10 improvement in reach. For the $2^+$ state, no improvement is obtained due to relatively larger error bars on the experimental phase shifts.