Static over-the-barrier model for electron transfer between metallic spherical objects

We present a static classical over-the-barrier model (OBM) for electron transfer between two isolated, infinitely conducting spheres with arbitrary and different electrical charges. This model is shown to be very useful for first estimates of single- and multiple-electron transfer cross sections in cluster-cluster collisions when the collision velocities are significantly lower than the typical target electron velocities. For faster collisions, more advanced models such as the dynamical OBM, or the time-dependent local density approximation (TDLDA) or the solutions of their semiclassical counterparts---the Vlasov equations have to be used. The latter two methods clearly provide the most detailed information on the electronic response, but they are also computationally very demanding and have, so far, only been used for collisions involving one cluster (and an atomic ion). We compare our static OBM results (in the limit in which one of the sphere radii approaches zero) with TDLDA and Vlasov calculations of cluster charging in Ar⁸⁺-Na₄₀ collisions at different velocities to demonstrate that the present static OBM is valid at sufficiently low velocities. The static OBM is then used in a comparison with experimental target charge state distributions in C₆₀q+-C₆₀ and Cq+-C₆₀ collisions at 0.01√q and 0.06√qv₀, respectively. Calculated electronic excitation of the projectile after two-electron transfer in C₆₀⁴⁺-C₆₀ collisions readily explains the recently observed suppression of the transfer ionization channel in this reaction. Finally, we model the total projectile electron loss and dissociation cross section in highly protonated Lysozyme-oxygen (Lys-H₉⁹⁺-O₂) collisions and make comparisons with recent experimental results at 0.01v₀.