Abstract
State-to-state transition amplitudes are obtained from a variational functional for two colliding atomic systems whose states are self-consistently coupled. Specifying classical center-of-mass trajectories, this approach leads to an extension of the time-dependent self-consistent field approximation which requires iterative solutions of equations for forward and backward motions in time. The variational procedure is described for trial wave functions and trial transition densities. It is briefly illustrated with a model of two interacting two-state atoms.
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