  Multistate generalizations of Landau-Zener model are studied by summing
entire series of perturbation theory. A new technique for analysis of the
series is developed. Analytical expressions for probabilities of survival at
the diabatic potential curves with extreme slope are proved. Degenerate
situations are considered when there are several potential curves with extreme
slope. New expressions for some state-to-state transition probabilities are
derived in degenerate cases.
