FIG. 7: (color online) (a) Imaginary part of χ$_{0}$ ( q , ω ) (eV), for undoped LaOFeAs, as a function of q and ω . Results are plotted along Γ − X − Γ − M − Γ directions. (b) Plot of the real and imaginary parts of χ$_{0}$ as a function of ω for q corresponding to the X and M points of the BZ. Black and red refer to x = 0 and x = 0 . 14 respectively. The inset of (b) shows the low frequency part of χ$_{0}$ at M for x = 0 and x = 0 . 14 (black and red dashed respectively), and at one q -point point close to M corresponding to the edge of the volcano-like structure of Re χ$_{0}$ (thin red line). the Im χ$_{0}$ ( q , ω ). Interestingly, if we move slightly away from M (on the edges of the volcano structure discussed above), we recover a linear trend starting at ω = 0. The band decomposition of Im χ$_{0}$ ( q , ω ), reported in Fig. 8 along the Γ − M − Γ line, shows that the inter-band ( e − h ) contributions dominate the high frequency part, and are also responsible for the low frequency peak around M . The two dispersive peaks at low frequency discussed above originate from the intra-band transitions ( e − e and h − h ); in particular, the relatively high frequency branch comes mainly from electronic bands, while the low frequency one from hole bands. Fig. 8 clearly shows that the h − h and e − e contributions are quite asymmetric; this asymmetry is clearly a consequence of the richness of the electronic structure of LaOFeAs near E$_{F}$ . 11