Simple discretization method for autoionization widths. I. Theory

A description of the theoretical basis is presented for a new method to calculate widths of two-electron Feshbach resonances, which employs discretization techniques for the continuum projection of the wave function. New features of our approach are the finite-difference expressions used to evaluate the density of states and the inverse interpolation procedure needed to achieve the required discrete-continuum degeneracy. Two following papers illustrate the use of our method to calculate resonance widths for atomic and molecular systems, respectively.