Note how in both cases, 1/∆ i is recovered for ε = 0. The way in which the amplitudes are affected by the level shift technique is neatly captured by f (∆ i ; ε), which is plotted in Figure as a function of the energy denominator ∆ i . As can be seen, f (∆ i ; ε = 0.2) for the imaginary shift does not contain any pole, while the real one diverges at