Theoretical Approach to the Calculation of Energies and Widths of Resonant (Autoionizing) States in Many-Electron Atoms

Abstract

A theoretical approach, capable of providing quantitative results for $N$-electron nonrelativistic "nonstationary" states is presented. I treat inner-hole or doubly excited states, observed in various types of experiments, from a conceptually single point of view, as decaying states. First, the relevant important quantities already known, e.g., from Feshbach's theory, are derived and interpreted in a mathematically and physically meaningful way. Then I consider the exact square-integrable $N$-electron function describing the initial localized $N$-electron state and, from straightforward variation-perturbation-theory considerations, I derive a variational minimum principle which permits one to incorporate systematically the important correlation effects without the danger of a "variational collapse." This method requires projection onto known one-electron zeroth-order functions and it thus overcomes the difficulties of the well-known $P$, $Q$ methods which require projection onto exact wave functions. From preliminary $N$-body calculations I find the ${\mathrm{He}}^{-}$ ${}_{}{}^2{}_{}{}^{}P_{}^0{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}D$ resonances, previously observed experimentally, at about 57.3 and 58.4 eV. In addition, I predict the positions of various autoionizing states: in Li I at about 140.7 eV (a ${}_{}{}^2{}_{}{}^{}P_{}^0{}_{}{}^{}$ state), in C IV at about 306.7 eV (${}_{}{}^2{}_{}{}^{}D$), in N I at about 14.9 eV (${}_{}{}^2{}_{}{}^{}D$), and in F I at about 22.4 eV (${}_{}{}^2{}_{}{}^{}S$) above the ground state. These states, which are just samples of states treatable by this approach, may in principle cause observable structures, e.g., in photon-absorption experiments, in particle-atom scattering experiments, or in beamfoil experiments.