Modeling direct and pre-equilibrium processes of neutron-induced reactions with the noniterative finite amplitude method and with the distorted-wave Born approximation

This work develops a fully microscopic framework for neutron-induced reactions to describe direct and one-step pre-equilibrium processes. The authors combine the noniterative finite-amplitude method (FAM) with the distorted-wave Born approximation (DWBA). The resulting FAM-QRPA+DWBA formalism employs the Skyrme effective interaction to derive quasiparticle random-phase approximation (QRPA) equations, which leads to a consistent and parameter-free treatment of neutron inelastic scattering to both discrete and continuum states. Applied to the ${}^{208}$Pb($n$,$n\ensuremath{'}$) reaction, the method accurately reproduces measured differential and double-differential cross sections across 7--25 MeV without empirical adjustments. The calculated spin distributions of residual nuclei agree with combinatorial 1p--1h systematics, demonstrating that the noniterative FAM-QRPA+DWBA approach provides an efficient and predictive tool for modeling neutron-induced reactions within a unified microscopic framework.