  We present exact analytical solutions for charge transfer reactions between
two arbitrarily charged hard dielectric spheres. These solutions, and the
corresponding exact ones for sphere-sphere interaction energies, include sums
that describe polarization effects to infinite orders in the inverse of the
distance between the sphere centers. In addition, we show that these exact
solutions may be approximated by much simpler analytical expressions that are
useful for many practical applications. This is exemplified through
calculations of Langevin type cross sections for forming a compound system of
two colliding spheres and through calculations of electron transfer cross
sections. We find that it is important to account for dielectric properties and
finite sphere sizes in such calculations, which for example may be useful for
describing the evolution, growth, and dynamics of nanometer sized dielectric
objects such as molecular clusters or dust grains in different environments
including astrophysical ones.
