Use of the time-dependent variational method for polarization and energy loss in ion-atom collisions

The collision-induced polarization and momentum transfer are treated as the two components of a time-dependent complex variational parameter p(t). The equation of motion derived from the Schrödinger Hamiltonian is investigated. Within the linear approximation the energy transfer to a bound electron is shown to be E=|p|22m. The harmonic oscillator and the hydrogen atom are studied. To be consistent with the results of Bohr, Bethe, and Bloch, for fast collisions, the impulse approximation must be incorporated into the variational approach. Higher-order Z corrections to electronic stopping are worked out. The problem of joining together distant and close collisions is avoided.