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

Abstract

We develop a method to parameterize elastic-scattering phase-shifts for charged nuclei, based on Padé 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.

Comments: 6 pages, 5 figures; v2: 4 references added, 2 figures modified, better comparison made with existing methods