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

Abstract

We study the single ionization of hydrogen and helium by the impact of a highly charged Coulomb projectile. To interpret the cross section we introduce a diagonal Padé approximant. We find that the use of a Padé [4, 4] describes the continuum distorted wave eikonal initial state theory within its range of validity very well. The nodes of the denominator of the Padé approximant give rise to four poles in the velocity complex plane: two in the upper plane and their conjugates 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 in a scaling very near to that of Janev and Presnyakov. The experiments available were described very well in its entire velocity range with the use of a Padé [8, 8], with four poles in the upper plane and their conjugates in the lower plane. We conclude that the poles of the Padé approximant seem to have all the information of the total ionization cross section.