On violation of the Bragg's additivity rule for single-electron capture by positive ions from H2 molecules

The ratio R=sigma(H-2)/sigma(H) of single-electron capture cross sections of positively charged ions colliding with H and H-2 targets was investigated at ion energies q= 2 keV/amu-200 MeV/amu and ion charges q=1-74 using the Brinkman-Kramers approximation with normalized capture probabilities. The dependence of the R ratio on the polar angle theta(rho) between H-2-molecule axis and the projectile-velocity direction was studied for angles 0(degrees)<= theta(rho) <= 90(degrees). It was shown that at certain angles theta(rho), the R ratio exhibits an oscillatory structure caused by interference of two waves scattered on two atomic centers of H-2 molecule. At scaled energies E-similar to =E(keV/amu)/q(4/7)approximate to 10(2)-10(3), the R ratios, obtained by averaging the corresponding sigma(H-2) cross sections over all orientations of H-2 target, also show an oscillatory structure, the shape of which depends on the ion charge q. At higher energies E-similar to approximate to 10(3)-10(5), the R ratio calculated for charges q = 1-74 is nearly independent on q and is equal to R approximate to 2.82, while the Bragg's rule gives R=2. In the present paper, the I approximate to 2.82 value is explained by modeling a H-2 molecule as a He atom with ionization energy I=15.43eV, equal to the binding energy of the H-2 molecule. Computed ratios are compared with available experimental data, semi-empirical formulae and other calculations.