On the basis of the kinetic approach, the self-consistent problem of the gas discharge ion distribution function in the sheath near a surface at a negative potential with respect to the plasma is solved. For the first time, the solution takes into account the dependence of the ion charge exchange cross section from the atom on the ion energy, as well as the real ion distribution function in the unperturbed plasma. It is shown that the dependence of the charge exchange cross section on the ion energy significantly affects the shape of the ion distribution function. It is found that the mean energy of the ions near the wall depends on the electron mean energy in the unperturbed plasma. It was also found that, at the same electron mean energy, the form of the distribution function has practically no effect on the ion distribution function in the wall sheath. The calculations are in good agreement with the known mass spectrometric measurements of the ion distribution function. The obtained results give an opportunity to develop a self-consistent solution of the wall layer structure problem including the quasi-neutral presheath.