We develop a calculation method for describing the direct and pre-equilibrium processes in neutron-induced reactions based on the framework of noniterative finite amplitude method (FAM) and distorted-wave Born approximation (DWBA). The noniterative FAM is used to derive equations of quasiparticle random-phase approximation for neutron-induced inelastic scatterings to both the discrete and continuum states in a consistent manner. The Skyrme force is employed as an interaction between the projectile neutron with nucleons inside the target nucleus. We apply this method to the neutron-induced reaction on ${}^{208}\mathrm{Pb}$. We demonstrate that the calculated differential inelastic scattering cross-sections to low-lying states reproduce available experimental data without any phenomenological parameters that are often introduced in conventional DWBA calculations. The calculated double differential cross-section to the continuum state also agrees with the experimental data in the energy region relevant to the direct and pre-equilibrium processes. These results are used to investigate the spin distribution of the populated states in the residual nucleus.

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• Direct reactions
• Inelastic scattering reactions
• Nucleon induced nuclear reactions
• Random phase approximation