Criterion of maximum stability for the calculation of resonance energies. Application to the Stark effect

The authors analyse the relationship between two stabilisation methods: the minimum variance and the Rayleigh-Ritz methods. Stark resonances are considered explicitly but most of the conclusions are general. The case where a stable and an unstable eigenvalue of the variational method pseudocross as functions of a non-linear parameter is studied in detail. By using information as to the interaction of the stabilised wavefunctions with the background continuum, the variance method does not yield these unphysical avoided crossings. Both outside the avoided crossing regions and when the avoided crossing is a physical one, the two methods yield virtually identical results. A simple example is presented to illustrate how the variance method works. The inverse of the variance sigma -1 may be defined as the stability of the energy calculated with any stabilisation method (e.g. the variational method).