The Theory of Charge Exchange and Ionization by Heavy Particles

In the 1979 ASI on atomic processes of interest in fusion research, I surveyed the basic principles of the theory of charge exchange,1 concentrating on theoretical models in which the wave function of the system was expanded in some suitable set of functions.† At low to intermediate relative velocities of the colliding ions (v ≲ 1 a.u.) the expansion functions are frequently taken to be adiabatic, or diabatic, molecular orbitals, while over a region extending to somewhat higher velocities (0.1 ≲ v ≲ 3 a.u.), the expansion functions can be taken to be atomic orbitals, supplemented by pseudostate functions. Some higher order perturbation methods, like the continuum distorted wave approximation, which are useful at higher velocities (v ≳ 2.5 a.u.), were also discussed briefly in I. At this School, I shall not repeat this general material, but I shall concentrate on the special approximations which have been developed to describe charge exchange and ionization in the collision of fully stripped ions of charge Z (in atomic units) with atomic hydrogen in the ground state $$ {{\rm{A}}^{{\rm{Z + }}}}\,{\rm{ + }}\,{\rm{H(1s)}}\, \to \,{{\rm{A}}^{{\rm{(Z - 1) + }}}}\,{\rm{ + }}\,{{\rm{H}}^{\rm{ + }}} $$ (1) $$ {{\rm{A}}^{{\rm{Z + }}}}\,{\rm{ + }}\,{\rm{H(1s)}}\, \to {{\rm{A}}^{{\rm{(Z - 1) + }}}}\, + {{\rm{H}}^{\rm{ + }}}\,{\rm{ + }}\,{{\rm{e}}^{\rm{ - }}} $$ (2)