Single and Double Ionization

Collision physics provides fundamental knowledge of ionization process. The differential spectra of ionized electrons provide detailed information about the dynamics of the ionization process. The characteristic structure in the species can be associated with different collision mechanism. Ionization of atoms and molecules is one of the basic processes in atomic physics. Single and multiple ionization of atoms by ions is one of the fundamental processes in atomic physics with important applications in Plasma physics, Fusion, Upper atmospheric studies, Astrophysics, Nuclear astrophysics and many others technological areas. Due to this broad range of application there have been great efforts, both in experimental and theoretical, to improve our understanding of the ionization processes resulting from ion impact with atoms.

The description of multiple ionization is very tedious mainly due to the complexity of the many possible path ways leading to it. For an example, double ionization of atoms by fast ions is usually understood in terms of three mechanisms (McGuire, 1982). First the shake off process, in which a fast electron is ejected in the direct ionization with the projectile, while the second electron is ionized by the final state rearrangement, secondly a two-step process, in which both electrons are simultaneously ejected by the direct interaction with the projectile and thirdly the ionization of the inner shell electron with a post collision Auger decay. The shake off process and inner shell ionization yields double ionization cross sections and are essentially proportional to the single ionization.

The two step mechanism is based on the action of the projectile over the two active electrons. Multiple ionizations depend on projectile energy and its charge state which is significantly different from those of single ionization. In case of different multiple ionization processes the double ionization is the most important as the main contributions to the total ionization of the target is given by single and double ionization processes. Theoretical calculations of double ionization cross sections are considered to be of much significance because contribution from different physical processes e.g. simultaneous ejection of two electrons, inner shell ionization followed by Auger emission, resonance excitation double auto ionization process etc. can be separately estimated at various impact energies.

The independent particle model is widely-used approach for the multiple ionization process. In this approach it is assumed that the ionization of one electron is independent of the other and the related probabilities are given by the binomial distribution (Sant-Anna et al., 1998; Kirchner et al.,1999). This method depends strongly on the quality of the calculation of the single electron ionization probability. Although some general qualitative estimates can be obtained through simple semi-classical calculations using hydrogenic wave function (Sant-Anna et al., 1998). An alternatively theoretical approach to the IPM is the statistical energy distribution model. It was formulated by Russek and Thomas (1958) and further developed by Cocke (1979) and Kabachnik et al.(1997). The hypothesis is based on the fact that the probability of multiple ionizations is directly related to the energy deposited by the projectile on the target. The energy deposited is then distributed statistically among all atomic electrons and finally one or more electrons auto ionizes to the final state.

The direct double ionization cross section becomes extremely difficult as it is related to a four body Coulomb potential in the final channel (Berakdar, 1996). Among different experimental investigations on metals, Mc Cartney et al.(1999) of the Belfast group have used a cross beam technique incorporating time–of- flight analysis and coincidence counting of the collision products. The group to carry out an interesting work on processes involving electron capture and multiple ionization in collisions of fast H+ and He2+ ions with ground state Pb atoms in the limited energy ranges. They have also carried out calculations in an independent electron model for the processes experimentally investigated. Unfortunately, agreement of the theoretical results with the experimental data is not satisfactory.