The absorbing boundary method. III. Tunneling decay and scattering resonances

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Abstract
The recently developed absorbing boundary method (ABM) is applied to the calculation of tunneling decay rates and corresponding shape resonances in the scattering cross section. The analysis is carried out in terms of the contribution to the density of states from the resonant region of the spatial domain. One‐dimensional test calculations have been carried out using the ABM and several related continuum state methods. While the ABM produces practically useful predictions for the location and shape of the resonance lines, it cannot in its present forms match the accuracy of the best continuum state methods. We have compared results obtained by the ABM (SMA and ISMA), the R‐matrix method, the recently developed CGFEM and Bloch corrected R‐matrix method, the stabilization method of Hazi and Taylor, and a simple pseudo bound state method.