Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system

Abstract

The problem of analytic continuation of the scattering data to the negative-energy region to obtain information on asymptotic normalization coefficients (ANCs) of bound states is discussed. It is shown that a recently suggested $\Delta$ method [O.L.Ram\'ırez Suárez and J.-M. Sparenberg, Phys. Rev. C {\bf 96}, 034601 (2017)] is not strictly correct in the mathematical sense since it is not an analytic continuation of a partial-wave scattering amplitude to the region of negative energies. However, it can be used for practical purposes for sufficiently large charges and masses of colliding particles. Both the $\Delta$ method and the standard method of continuing of the effective range function are applied to the $p{-}^{16}$O system which is of interest for nuclear astrophysics. The ANCs for the ground $5/2^{+}$ and excited $1/2^{+}$ states of ${}^{17}$F are determined.

References in corpus (4)

• Extrapolation of scattering data to the negative-energy region II
• Resonance-state properties from a phase shift analysis with the $S$-matrix pole method and the effective-range method
• Effective-range function methods for charged particle collisions
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function

Cited by in corpus (5)

• Low-energy bound states, resonances, and scattering of light ions
• New method of analytic continuation of elastic-scattering data to the negative-energy region and asymptotic normalization coefficients for ${}^{17}$O and ${}^{13}$C
• Cross sections at sub-Coulomb energies: full optical model vs.\ barrier transmission for ${}^{40}$Ca + $\alpha$
• Complex-energy analysis of proton-proton fusion
• Study of the direct ${}^{16}\mathrm{O}(p,\gamma {)}^{17}\mathrm{F}$ astrophysical capture reaction within a potential model approach