A new mechanism for the FIP fractionation in the solar wind in the form of a stationary diffusion model is proposed. It is based on a weakly stratified chromospheric layer of constant density and temperature, permeated everywhere by ionizing photons and a homogeneous magnetic field. Our model does not invoke any particular geometry or special set up of the system and is founded solely on robust and well understood atomic collisional physics. Technically, a boundary value problem of four coupled differential equations is solved for each chemical element, i. e. a continuity equation and a momentum equation for both atoms and singly ionized particles. For the main gas (hydrogen), an analytical solution can be found. This then serves as a background for the numerical integration of each trace gas system (several elements from He to Fe). We find that, after a few hydrogen diffusion lengths, each minor species asymptotically approaches a constant density. The ratios of these density values to some reference element reproduce the observed FIP fractionation pattern remarkably well.