According to (4.8.15) in Section 4.8, the scattering rate for fermions is proportional to 1/2 (U D

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According to (4.8.15) in Section 4.8, the scattering rate for fermions is proportional to 1/2 (UD − UE)2, where UD is the direct interaction vertex and UE is the exchange vertex. In the diagram shown in Figure 8.32, only the direct term proportional to U2D occurs. Show that if you account for exchange (how many additional diagrams are needed?), you get agreement of the Matusbara imaginary self energy with the out-scattering rate of (4.8.15).

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