The presence of the interference effect easily reconciles the hypothesis of a σ -band for- mation with the data. First of all, it explains the fact that the peak shape is similar for all emission directions. For emission near ¯ K the peak is narrow because of the degeneracy of the bands at ¯ K . At the ¯ Γ points the peak is also narrow, in contrast to naive expectation, because it does not show both the bonding and the anti-bonding bands but rather only one of them at every given ¯ Γ point. The interference effect is also responsible for the apparently incorrect periodicity of the band dispersion in reciprocal space. The situation is not such that all ¯ Γ points are equivalent, because one either observes emission from the bonding or from the anti-bonding band. Note that the sign of the observed modulation is consistent with this interpretation, too. The binding energy of the peak observed at normal emission is close to the global maximum of the entire data set, consistent with emission from the bonding σ -band. In fact, the calculated emission from the bonding band shown in Fig. 3(d) can be compared directly to the plot of the apparent binding energy in Fig. 2, which is also scaled such that high binding energies are bright. 

The size of the bonding / anti-bonding splitting in graphene can be inferred from the difference of observed binding energies at inequivalent ¯ Γ points. Combing all the available data from ¯ Γ points showing either the bonding or the anti-bonding band, we evaluate the $^{size of the splitting to be 60}$±10 meV. We can compare this value to the size of the bonding / anti-bonding splitting in small carbon-containing molecules such as C$_{2}$H$_{2}$ (C-C distance of 1.2 ˚ A, splitting of 105 meV [1]) and C$_{2}$H$_{4}$ (C-C distance of 1.34 ˚ A expected splitting of 20-30 meV [6]) if we assume that the matrix element for hopping between the core electrons on the two carbon atoms depends exponentially on the C-C distance and that the size of the splitting scales linearly with the number of nearest neighbors. Assuming a splitting of 105 meV and 25 meV for C$_{2}$H$_{2}$ and C$_{2}$H$_{4}$, respectively, we would expect a total bandwidth of ≈ 30 meV for graphene. The observed magnitude of the dispersion is somewhat larger but in the right order of magnitude. 

Apart from the fundamental importance of our results for the bonding in solids, a de- pendence of the core level binding energy on the emission angle can have implications for the interpretation of high-resolution core level data from graphene, graphite and related materials. The absolute magnitude of the binding energy variation observed here is appre- ciable compared with usual chemical shifts and could easily be interpreted incorrectly. In a limited data set, for instance, an apparent shift of the C 1 s peak as a function of polar 

