Elastic $\alpha$-$^{12}$C scattering at low energies with the resonant $2_2^+$ and $2_3^+$ states of $^{16}$O

TL;DR

This study models low-energy elastic alpha-12C scattering by explicitly including resonant states of 16O, fitting phase shift data, and calculating asymptotic normalization coefficients with significant uncertainties.

Contribution

It introduces an effective Lagrangian approach that explicitly incorporates resonant states in alpha-12C scattering analysis, providing a new method to estimate asymptotic normalization coefficients.

Findings

Reproduces small and large ANC values depending on conditions.

Large error bars found for the large ANC values from alpha transfer reactions.

Fitted phase shift data at low energies with explicit resonant states.

Abstract

The elastic $\alpha$-$^{12}$C scattering for $l=2$ at low energies is studied in an effective Lagrangian approach. We explicitly include two resonant $2_2^+$ and $2_3^+$ states of $^{16}$O in the scattering amplitudes and construct an $S$ matrix assuming that three amplitudes, the non-resonant part of the amplitude which has the sub-threshold $2_1^+$ state of $^{16}$O and those of the two resonant states, are represented by the summation of corresponding parts of the phase shift. Then, we fit the parameters in the $S$ matrix to the phase shift data by imposing three conditions at very low energies where the phase shift data are not available. By using the fitted parameters, we calculate the asymptotic normalization coefficients (ANC) of the $2_1^+$ state of $^{16}$O and find that the previously reported small and large values of the ANC can be reproduced depending on the imposed conditions, but we obtain large error bars for the large ANC values which are reported from the $\alpha$ transfer reactions.