Calculation of Energies and Widths of Compound-State Resonances in Elastic Scattering: Stabilization Method

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Abstract
In a previous paper, the stabilization method of calculating resonance parameters was applied to a one-dimensional model problem of potential scattering. The method is here extended to compound-state resonances in elastic scattering, and its application to a model problem for a target with two bound states is examined. The resonance parameters are calculated by two methods which use information obtained in the diagonalization of the exact Hamiltonian in appropriately chosen sets of square-integrable basis functions: One is presented for the first time here; the other is similar to the procedure used in the potential-scattering problem. In addition to the stabilization method, we have applied to the model problem some other techniques, which have been previously proposed for the calculation of resonance parameters. The availability of the exact solutions enables us to make some preliminary assessments of the reliability and the difficulty that might be expected from these approximation methods.