We have developed a many-electron model for multiple ionization of heavy atoms bombarded by bare ions. It is based on the transport equation for an ion in an inhomogeneous electronic density. Ionization probabilities are obtained by employing the shell-to-shell local plasma approximation with the Levine and Louie dielectric function to take into account the binding energy of each shell. Post-collisional contributions due to Auger-like processes are taken into account by employing recent photoemission data. Results for single-toquadruple ionization of Ne, Ar, Kr and Xe by protons are presented showing a very good agreement with experimental data.

We present an analytical continuous equation for the Tang and Leschhorn model [Phys. Rev. A 45, R8309 (1992)] derived from their microscopic rules using a regularization procedure. As well in this approach, the nonlinear term (nablah)(2) arises naturally from the microscopic dynamics even if the continuous equation is not the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)] with quenched noise (QKPZ). Our equation is similar to a QKPZ equation but with multiplicative quenched and thermal noise. The numerical integration of our equation reproduces all the scaling exponents of the directed percolation depinning model.

We present a theoretical study on proton energy loss in solid targets of atomic number greater than 54. Fully relativistic wave functions and binding energies are obtained by solving numerically the Dirac equation. Ab initio calculations are developed for the first ͑stopping͒ and second ͑straggling͒ moments of the energy transferred from the ion to the target electrons. The shellwise local plasma approximation is employed for the inner shells, and the Mermin dielectric function is employed for the valence electrons. The dielectric response of each subshell is calculated separately, including in this way the screening among the electrons of the same binding energy. Results for stopping and straggling cross sections of protons in Au, Pb, and Bi are compared with the available experimental data. The theoretical stopping results are very good in the case of Au, reproducing the experimental data in an extensive energy region ͑10 keV-100 MeV͒. For Pb and Bi, the stopping results agree with the measurements for energies above 300 keV, for which the inner shells play a major role. However, we found some difficulties around the stopping maximum. For the energy-loss straggling, we obtained reasonably good agreement with the experiments for the three targets studied.