Kinetic equation and transport properties of large, heavy ions in a gas in any regime in external fields

The general problem of the formulation of a complete kinetic and transport theory for large, heavy (l.h.) ions in a gas in any regime is considered. It is shown that the problem can be satisfactorily solved observing that the appropriate Langevin equation for a l.h. ion in a gas of any density has the same form and the same properties of the Langevin equation customarily assumed for a Brownian particle in a dense fluid. So, also for l.h. ions in a gas an appropriate Fokker-Planck equation can immediately be written. From it, not only the previously derived mobility formula can easily be recovered, but, as shown in this paper, also the appropriate diffusion coefficient satisfying the Einstein relation can naturally be found, and the formula for the l.h.-ion mean energy in external fields can quickly be obtained. A related discussion on the l.h.-ion conduction in gases in electrostatic fields is also given. Finally, the limits of validity of the theory are examined, and its usefulness in the interpretation of possible future experiments is put in evidence.