On the unphysical impact of complex absorbing potentials on the Hamiltonian and its remedy

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.