Semiclassical distorted wave model with Wigner transform of one-body density matrix

Abstract

A semiclassical distorted wave (SCDW) model with realistic single particle wave functions in a finite range single particle potential is presented for multistep direct processes in nucleon inelastic scattering and charge exchange reactions to the continuum, making use of the Wigner transform of a one-body density matrix. The higher momentum components of target nucleons are properly taken into account in comparison with the previous SCDW model with a local density Fermi gas model. The new SCDW model still gives a simple closed-form expression for the cross section with no free adjustable parameter which allows a simple intuitive interpretation, just as in the previous SCDW model. This model is applied to the analyses of multistep direct processes of ${}^{90}\mathrm{Zr}{(p,p}^{\ensuremath{'}}x)$ reactions at incident energies of 80 and 160 MeV. The calculated double differential cross sections including up to three-step processes are compared with experimental data. The calculated cross sections at backward angles are larger than those given by the previous calculations, and the agreement with experimental data is much improved. Discussions on the mechanism of this improvement are given in terms of the momentum distribution of target nucleons.