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.

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

References in corpus (2)

• Resonance-state properties from a phase shift analysis with the $S$-matrix pole method and the effective-range method
• Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method

Cited by in corpus (12)

• Connection formulas between Coulomb wave functions
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• Extrapolation of scattering data to the negative-energy region II
• Extrapolation of scattering data to the negative-energy region
• Low-energy bound states, resonances, and scattering of light ions
• Effective-range function methods for charged particle collisions
• Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system
• Cluster effective field theory and nuclear reactions
• Determination of asymptotic normalization coefficients for the channel ${}^{16}$O$\to \alpha {+}^{12}$C. Excited state ${}^{16}$O($0^{+};6.05$ MeV)
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
• Complex-energy analysis of proton-proton fusion
• The energies and ANCs for 5Li resonances deduced from experimental p-$\alpha$ scattering phase shifts using the effective-range and $\Delta$ methods