Collinear laser spectroscopy on a monoenergetic neutral Na beam is used to study charge exchange collisions between a fast Na+ beam and Na vapour at different densities. Analysis of the 3s-3p optical resonances monitored by laser-induced fluorescence shows that, at low vapour density and at 5 keV beam energy, mainly two processes produce fast neutral Na atoms: a resonant channel, which is the more efficient, and a non-resonant one. At high vapour density, multiple inelastic collisions occur, with energy defect corresponding to the 3s-3p energy difference. The probability of an atom undergoing several successive collisions of this type is well represented by Poisson's law.