An approximate, analytical solution to the collisional problem of atmospheric particles is presented. It is based on the potential flow theory and takes into account the effects of the non-frictional flow outside the boundary layer. In combination with a previous solution from the boundary layer theory this new approach leads to accurate solutions in some cases where the boundary layer approach alone was erroneous: The combined theories are in fair agreement with measurements and numerical results on coalescence, on the riming of various planar shapes and of columns and on the impaction on drops of aerosols down to a critical size of the latter, at which the collision efficiency sharply drops to zero.