Completely ℒ² Golden Rule method for resonance energies and widths

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.