A semiempirical formula for single-electron-capture cross sections of multiply charged ions colliding with H, H2 and He

A universal analytic formula is given for the total cross sections of single-electron capture by multiply-charged ions colliding with H, H2 or He. Values of constants in the formula have been determined by least-squares fit to ions of almost all atomic species with charge q greater than 4 (for the H and H2 targets) or 5 (for the He target) in the energy region from about 1 to 107 eV amu-1. The root-mean-square deviation of the data from the formula is 29%. The formula shows that the cross sections are proportional to q1.07 at low energies and to q2.86 at high energies. Other trends of the cross sections that can be derived from the formula are also discussed. (orig.)