Higher-order decoupling of the electron propagator

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Abstract
The decoupling of the electron propagator in the superoperator formalism is extended to include a description of processes corresponding to simultaneous electron ionization (or electron attachment) and double excitation, observed in electron spectrometry, by including products of five spin–orbital field operators in the inner projection basis. Although the terms thus introduced are fourth order in the electron interaction, an argument based on the self‐consistent solution of the second‐order equations suggests that these fourth‐order terms are more important than the third‐order terms. The argument is substantiated by numerical applications to the neon atom. A calculation using third‐order shifts is compared with a calculation using the suggested fourth‐order terms, but without third‐order terms.