Completely ℒ2 Golden Rule method for resonance energies and widths

Abstract

We have calculated the resonance energies and widths for both one-dimensional scattering resonances and a two-dimensional model of van der Waals molecule predissociation by a general method involving only Hamiltonian and overlap integrals in a single square-integrable basis set containing a scale parameter. We use a stabilization method with a compactness criterion to find the resonance energies and a generalization of the Golden Rule formalism of Macías and Riera to calculate the widths. The results are compared to accurate resonance energies and widths obtained by Breit–Wigner fits. For the final method, as applied to four cases, the errors in the resonance energies are 10−3%, 0.8%, 0.5%, and 0.03%, and the errors in the widths are 2%, 3%, 6%, and 11%, respectively. The new method has particular advantages over the analytic continuation of stabilization graphs when the density of states is high.