Fig. 2: Scattering boundary conditions.
From: Tutorial: theoretical methods for attosecond molecular ionization and dynamics
The S-matrix element \({S}_{\beta \alpha }^{* }\) describes the probability amplitude for transition of the system from the channel β into the channel α induced by the non-spherical field of the molecule in the absence of an external field. The equipotential surface of a highly non-spherical molecule is shown in the middle. Probabilities associated with the channel α must sum up to 1. In weak fields, the external field (represented as a wave packet) is accounted for perturbatively by a dipole matrix element between the field-free scattering state and the initial bound state.
