# Search procedure for multichannel resonances in electron-atom scattering

## Abstract

A general computational procedure is described for locating electron-atom scattering resonances and for computing accurate values of the resonance parameters (eigenchannel vector, energy, width, and background eigenphase). The procedure makes use of the anomaly-free multichannel variational method and of the hierarchical continuum Bethe-Goldstone formalism published previously. Eigenvalues of the electronic Hamiltonian in a variational Hilbert space are located by an accurate procedure that takes advantage of analytic properties of the matrices constructed in a variational phase shift calculation. Without computing the Hilbert space eigenvector, effective bound-free matrix elements for a resonance are computed from residues of matrix elements that have poles at the Hilbert space eigenvalues. Each eigenvalue associated with a resonance defines an initial approximation to the resonance parameters, which are then refined by an iterative process that uses variational calculations of the eigen-phases. The proposed method combines the ability of stabilization methods to locate narrow resonances with an accurate computation of phase shifts in the resonant region. Calculations of electron-hydrogen resonances are given as examples of the method. © 1971 The American Physical Society.