Viktor Khmara
Department of Theoretical Physics and Astrophysics
P. J. Šafárik University in Košice

The interest to the study of localised states in atomic physics is, on the one hand, evoked by the fact, that in the numerous cases their analysis can be carried out analytically. Such method belongs to not much approaches, which allow investigating the system with nonfactorised variables without the use of perturbation theory or cumbersome numerical methods. On the other hand, the aforementioned states often occur and in numerous cases play a crucial role. Thus, the idea of the localisation of the vicinity of the most probable tunneling path allows one to develop the asymptotic theory of processes with redistribution of particles and, in particular, the one-electron charge exchange reaction in slow collisions of atoms with multiply charged ions. This method, combined with the quasiclassical approximation, makes it possible to obtain an explicit form of wave functions concentrated in the vicinity of classical trajectories and represents an approach adapted for the calculation of the exchange interaction of an atom with a multiply charged ion.