The recently developed absorbing boundary method is implemented by the use of a weak coupling approximation. The derivation then results in a generalized Golden Rule which in the limit of vanishing coupling reproduces the usual simple exponential decay for elastic processes. The same arguments are then applied to inelastic decay processes driven by a monochromatic external perturbation. It is shown that the usual single step Golden Rule mechanism can be decomposed into a twohyphen;step mechanism with one vertical (inelastic) step followed by a horizontal (elastic) step. This form of the absorbing boundary method applies, e.g., to photoionization and photodissociation and allows the calculation of cross sections and decay rates without the use of continuum energy eigenstates.
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