Semiclassical distorted wave model of nucleon inelastic scattering to continuum

A semiclassical distorted wave model is presented for one-step nucleon inelastic-scattering process leading to the continuous states of residual nucleus. The model is based on semiclassical approximations for the distorted waves and the Thomas-Fermi model of the nuclear states. The squared modulus of the matrix elements of nucleon-nucleon (N-N) interaction is substituted by the corresponding N-N scattering cross section in the free space. The model gives a closed-form expression with no adjustable free parameter for the double-differential cross section. We apply the model to the proton inelastic scattering from ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ at 62 MeV, and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ at 100 and 164 MeV. Experimental data are reproduced very well at high emission energies except in small- and large-angle regions. The cross sections of the neutron inelastic scattering from ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ ${,}^{120}$Sn, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at 60 and 160 MeV, for which no experimental data are available, are predicted to be quite similar to the cross sections of the proton inelastic scattering. Calculations are also compared with the exciton model and the multistep direct reaction theory.