The introduction of complex absorbing potentials as numerical tools to stabilize or increase the efficiency of calculations based on wave-packet propagation or on eigenvalue problems has the drawback of causing a modification of the Hamilton operator of the problem.In this work the consequences of such a modification are analyzed and the corrections required in order to properly describe the original physical process are derived.As an example,the decay of excited molecular states is considered: it is shown that the standard time-independent expression for the decay spectrum loses its validity when a complex absorbing potential is introduced in the nuclear Hamilton operator of the problem.To remedy the situation,a new,very stable formula is derived and tested on relevant model studies.Numerical examples are discussed.
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