Atomic ionization by multicharged ions interpreted in terms of poles in the velocity complex space

We study the single ionization of hydrogen and helium by the impact of a highly-charged Coulomb projectile. To interpretate the cross section we introduce a diagonal Pad'{e} approximant. We find that the use of Pad'{e}% [4,4] describes very well the Continnum Distorted Wave Eikonal Initial State theory within its range of validity. The nodes of the denominator of the Pad% '{e} approximant give rise to four poles in the velocity complex plane: two in the upper plane and their conjugate in the lower plane. The dependence of these poles with the projectile charge can be reasonably fitted to give a closed-form for the ionization cross section, resulting a scaling very near to the one of Janev and Presnyakov. The experiments available were described very well in its entire velocity range with the use of a Pad'{e}[8,8], having four poles in the upper plane and their conjugate in the lower plane. We conclude that the poles of the Pad'{e} approximant seem to have all the information of the total ionization cross section