Elastic $\alpha$-$^{12}$C scattering at low energies with the bound states of $^{16}$O in effective field theory

TL;DR

This paper applies effective field theory to analyze low-energy elastic alpha-12C scattering, incorporating bound states of 16O, introduces a new renormalization method, and calculates key nuclear parameters relevant to stellar reactions.

Contribution

It presents a novel renormalization approach for EFT in Coulomb-dominated scattering and computes asymptotic normalization constants for excited states of 16O.

Findings

Effective range parameters fitted to phase shift data.

Calculated asymptotic normalization constants for 16O states.

Discussed uncertainties in stellar energy extrapolations.

Abstract

The elastic $\alpha$-$^{12}$C scattering for $l=0,1,2,3$ channels at low energies is studied, including the energies of excited bound states of $^{16}$O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ states of $^{16}$O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction.