$S$ matrices of elastic $n$-$^{16}$O scattering at low energies in cluster effective field theory

Abstract

Elastic $n$-$^{16}$O scattering at low energies is studied in the framework of cluster effective field theory. An evaluated data set of the total cross section of elastic $n$-$^{16}$O scattering at neutron energy, $0\le E_n\le 4$~MeV, is adopted from Evaluated Nuclear Data File (ENDF/B-VIII.0). We derive an expression for the $S$ matrices of the elastic scattering for seven spin-partial wave channels, $lj=s_{1/2}$, $p_{1/2}$, $p_{3/2}$, $d_{3/2}$, $d_{5/2}$, $f_{5/2}$, $f_{7/2}$, including one excited state and nineteen resonant states of $^{17}$O. Thirty-four parameters of the theory are fitted to the ENDF data, and we find that a plotted line, by using the fitted parameters, reproduces the ENDF data well. We discuss the uncertainties that may appear in the present approach from the fitted parameters of the resonant states with widths, larger than $Γ= 90$~keV. We also discuss the implications of the fitted values of energies and widths of the resonant states in the estimate of the astrophysical $S$ factor of $^{13}$C($α$,$n$)$^{16}$O reaction at stellar energies.