Binary-encounter and Monte-Carlo methods in atomic collision theory physics.

Abstract

Collisions between various charged particles and excited hydrcgenic atoms and ions are described using the binary-encounter (classical-impulse) approximation and the exact-classical orbit-integration technique. In particular, emphasis is made on strong collisions such as rearrangement and ionization processes, rather than excitations. The classical methods have been justified rigorously by Abrines and Percival (1966b) for the cases in which all the initial and final quantum numbers of the target atom are large and all changes in the initial quantum numbers are also much greater than unity. In these regions quantal methods are particularly complicated and unpractical, whereas the classical approach can often be applied without having to make additional dynamical approximations. This approach is complementary to the standard quantal techniques, which are most useful for low initial and final quantum numbers, and the correspondence-principle methods of Percival and Richards (l970a,b, 1971a,b) which work best when the initial quantum numbers are large and all changes are small. Because the classical techniques, which have been used to calculate total cross sections, enable simple scaling laws to be applied, these cross sections can also be compared with quantal and experimental values for states with low initial quantum numbers including the ground state. Although there is no solid theoretical justification for applying classical theories in this region, a considerable amount of empirical evidence is presented, which suggests that accurate classical theories can be superior to quantal approximations for intermediate energies of the incident particle, provided that the changes in quantum number are large. Specific failures at low or high energies must, however, be expected since purely-quantal effects such as harrier penetration and interference are often dominant here. Many of the cross sections are of importance in the study of astrophysical and laboratory plasmas. The exact-classical results can also be used to test the validity of an existing dynamical approximation, or possibly to suggest a new simple model.