CROSSING OF 2 BANDS OF POTENTIAL CURVES

Various problems in atomic physics can be formulated in terms of two bands of potential curves which cross each other. Each band consists of parallel (non-interacting) diabatic potential curves equally spaced on the energy axis. The bands with infinite number of states are considered under the assumption of 'translational' symmetry along the energy axis. The adiabatic potential curves are constructed explicitly. The system of avoided crossings appears not only in the weak coupling case (which is obvious), but also in the strong coupling limit. This feature also holds in the generalized model where the bands are finite and non-equidistant. In the case of an infinite number of states in each band the dynamic description (i.e. evolution in time) is reduced to the two-state problem which contains an additional continuous parameter (analogue of the quasimomentum). Some peculiarities of the time propagation are discussed. The present model generalizes the famous Landau-Zener two-state case and Demkov-Osherov model (one level interacting with a band of levels).