Modeling of the Doppler Broadening Effect in the Reaction \({}^{{16}}\)O\({(n,\alpha\gamma)}^{{13}}\text{C}\) with Allowance for the Slowing Down of the \({}^{{13}}\text{C}^{{*}}\) Ion

Doppler broadening of \(\gamma\) lines of excited secondary \({}^{13}\) C \({}^{*}\) nuclei produced in the reaction \({}^{16}\) O \((n,\alpha\gamma)^{13}\) C induced by neutrons interacting with a beryllium-oxide target is calculated on the basis of the LSS model of the stopping power for low-energy ions. The cross sections for the reaction \({}^{16}\) O \((n,\alpha\gamma)^{13}\) C are determined within the quark-level CHIPS model of nuclear reactions. It is shown that, at not overly long and not overly short \(\gamma\) -line lifetimes, the slowing down of a radioactive ion determines the shape of detected \(\gamma\) lines.