Pion-nucleus scattering and absorption as a solution of the Boltzmann equation

We calculate inelastic pion-nucleus collisions and pion absorption from the Boltzmann equation. The pion-nucleus optical potential and the elementary pion-nucleon cross section are the dynamical input. We describe the construction of a scattering solution and propose an approximation scheme based on a straight line trajectory (allowing for backward scattering). The total reaction cross sections, the one for absorption and for double charge exchange, are calculated as a function of the pion energy (from 50 to 300 MeV). Doubly differential cross sections $\frac{d^3\sigma }{d\Omega \mathrm{dE}}$ are computed for inelastic (${\pi }^{+}$,${\pi }^{+}$) and (${\pi }^{+}$,${\pi }^0$) reactions. Without adjusting any parameter, the absolute magnitude and the shape of the experimental data are fairly well reproduced. Pion absorption and single quasifree scattering are the two dominant channels in pion-nucleus interactions.