On possibility of calculating Siegert eigenvalues for autoionizing electronic states

The energy and lifetimes of metastable states (equivalently, the positions and widths of scattering resonances) are determined by the complex poles of the S -matrix, the Siegert eigenvalues. A variational, basis set method proposed by Bardsley and Junker for calculating these complex eigenvalues has been applied to several examples — a one-dimensional potential resonance and several autoionizing states of He and H − — with encouraging results. The method is seen to converge to the correct results as the basis set is increased, and the convergence is seen to be well-behaved. It is also significant that results of useful accuracy (e.g., lifetimes to ≈ 10% accuracy) can be obtained with reasonably modest basis sets (≈ 10 configurations for He, H − , of a quality that is attainable for systems with more than two electrons.