Real stabilization of resonance states employing two parameters: basis-set size and coordinate scaling

Abstract

The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, Er, and widths, , are calculated using the density of states and an L2 golden rule-like formula. We present a recipe to select adequately some solutions of the variational problem. The set of approximate energies obtained shows a very regular behaviour with the basis-set size, N. Indeed, these particular variational eigenvalues show a quite simple scaling behaviour and convergence when N → ∞. Following the same prescription to choose particular solutions of the variational problem we obtain a set of approximate widths. Using the scaling function that characterizes the behaviour of the approximate energies as a guide, it is possible to find a very good approximation to the actual value of the resonance width.igharrow infty$. Following the same prescription tochoose particular solutions of the variational problem we obtain a set of approximatewidths. Using the scaling function that characterizes the behaviour of theapproximate energies as a guide, it is possible to find a very good approximationto the actual value of the resonance width.