For very slow collisions, the ionization cross section depends on the
projectile kinematics in the combined field of the nucleus and atomic
electrons, on the time evolution of the electron wave function, and on
the recoil of the nucleus. First-order semiclassical cross sections i
n the united-atom limit were calculated for the Thomas-Fermi and Hartr
ee-Fock screening potentials. The time evolution of the wave function
was considered by the model of a perturbed harmonic oscillator and by
a simplified atomic model involving only a few lowest states. Theoreti
cal K-shell ionization cross sections were compared with the mean expe
rimental data calculated for groups of atoms with neighboring atomic n
umbers. It was pointed out that the averaging process, also employing
theoretical data, depends essentially on the projectile kinematics in
the screened atomic field. Taking this into account, good agreement be
tween mean experimental and theoretical cross sections was obtained.