Multiple vacancy production by high energy heavy ions

The theory of atomic collisions has two ingredients: collision theory and atomic structure theory. The collision theories differ with respect to (A) the collision dynamics and (B) the treatment of the relative motion of the projectile and target nuclei. With regard to the dynamics multiple vacancy production is of fundamental interest because it is a signature for and probe of strong interactions between the projectile and the target electrons. For projectiles of large nuclear charge, Z/sub p/, especially for those which are highly stripped so as to have a large ionic charge, q, the interaction becomes strong enough to give a high probability of multiple vacancy production and a breakdown of perturbation theory. The familiar first and second Born approximations and their off-shoots cease to be adequate. Not even the recent strong-potential Born approximation (see Taulbjerg 1984) is sufficient, because the weaker of the potentials generated by the projectile and the target nuclei, respectively, is treated in first order. One needs a unitary, non-perturbative collision theory. At present this is generally available for multiple vacancy production only in the form of the highly numerical coupled channels theory (Becker et al. 1983, 1984b). For special problems analytically tractable models have been devised. For example, a simple, unitary, geometrical encounter probability model for the calculation of p/sub L/(0), the inclusive L-shell vacancy probability per electron in collisions with impact parameter B = 0, has been introduced by Sulik et al. (1984) and further developed by Sulik and Hock (1984). Along with earlier coupled-channels calculations (Becker et al. 1984ab) and first Magnus calculations (Becker et al. 1984b), this model is able to describe the saturation of p/sub L/(0) with Z/sub p/ at fixed impact speed, v, whereas all the first-order theories predict p/sub L/ proportional to Z/sub p//sup 2/, which eventually exceeds unity.