Resonant in situ photoemission from Mn 3d states in Ga_{1-x}Mn_{x}As is reported for Mn concentrations down to very dilute limit of 0.1 at %. The properties of the peak at the valence-band maximum reveal an effective interaction between Mn 3d states
for concentration as low as 2.5 %. Concentration-dependent spectral features are analyzed on the basis of first-principles calculations for systems with selected impurity positions as well as for random alloys.
The emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident
in the case of the hydrogen atom. When applied to the hydrogen atom, the emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.
