Generalization of the stabilization method for Green functions and quantum resonances

The stabilization method provides an efficient approach to many problems in atomic and molecular dynamics. Real avoided crossings and smoothing techniques provide relevant information to compute the real density of states. An extension of the stabilization method is presented, allowing for a direct determination of full Green functions and resonance energies. The method is based on the use of optical potentials and perturbation theory. Real avoided crossings of the original stabilization method become complex, and resonance energies appear to stabilize in the complex-energy plane. A numerical illustration is presented for a simple model of shape resonance. Accurate results are obtained with a small number of real square-integrable functions as in the original stabilization method. The computational efficiency of the approach and its generality are emphasized. (author)