The diagonal 2ph-TDA and quasiparticle decouplings of the dilated electron propagator (based on an underlying bi-variational SCF) are utilized to calculate energy and width of the Be+(1s−1)2S Auger resonance for the first time. Comparison with experimental and other theoretical results reveals that the renormalized infinite order diagonal 2ph-TDA decoupling seems to offer a less balanced approach to the treatment of resonances than the second-order decoupling. The diagonal quasiparticle approximation to the self energy is seen to offer an effective and economic alternative to the non-diagonal propagator calculations.
