Extraction of the Electron Self-Energy from Angle Resolved Photoemission Data: Application to Bi2212

The self-energy $\mathrm{\Sigma }(\mathbf{k},\omega )$, the fundamental function which describes the effects of many-body interactions on an electron in a solid, is usually difficult to obtain directly from experimental data. In this paper, we show that by making certain reasonable assumptions, the self-energy can be directly determined from angle resolved photoemission data. We demonstrate this method on data for the high temperature superconductor $B{i}_{2}S{r}_{2}CaC{u}_2{O}_{8+x}$ (Bi2212) in the normal, superconducting, and pseudogap phases.