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

TL;DR

This paper introduces a potential-independent method using Padé expansions to parameterize elastic-scattering phase-shifts, enabling improved extraction of resonance properties and ANCs from experimental data for charged nuclei.

Contribution

The authors develop a novel, potential-independent phase-shift parameterization method based on Padé expansions, simplifying ANC extraction from experimental data.

Findings

Achieved a threefold improvement in ANC accuracy for the 1^- state.

Demonstrated the method's effectiveness on the 12C+α system.

Identified limitations due to experimental error bars for the 2^+ state.

Abstract

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.