We propose a new method to solve the multistate coupled equation. It overcomes the fatal defect of divergence which conventional perturbation theory has when the interaction is not small. We apply it successfully to laser-induced transition processes and obtain a total-cross-section formula.
We formulate a perturbative approach for studying a class of multilevel time-dependent quantum systems with constant off-diagonal couplings and diabatic energies being odd functions of time. Applying this approach to a general multistate Landau-Zener (MLZ) model with all diabatic levels crossing at one point (named the one-crossing MLZ model), we derive analytical formulas of all its transition probabilities up to fourth order in the couplings. For one-crossing MLZ models it is difficult to obtain such analytical results by other kinds of approximation methods; thus, these perturbative results can serve as reliable benchmarks for future studies of any one-crossing MLZ models that have not been exactly solved.
Experimental studies of two laser-induced charge-transfer reactions in Ca and Sr are presented. In both reactions, a Ca ion collides with an Sr neutral in the presence of a laser field to produce a Ca neutral and an excited Sr ion. The two reactions differ in the final level of the Sr+ species. The collision cross sections associated with these reactions are studied as functions of applied laser frequency and power density. The largest cross section induced is equal to ${10}^{\ensuremath{-}16}$ cm2, obtained at a power density of 2\ifmmode\times\else\texttimes\fi{}109 W/cm2. Differences in experimental results associated with the two reactions are explained qualitatively by an examination of the potential curves of the CaSr+ quasimolecule.