We describe the two dimensional angular correlation of positron annihi
lation radiation (2D-ACAR) method and show that it can be advantageous
ly used to study the electronic structure of defects, in addition to s
tandard positron lifetime and Doppler broadening measurements. Using a
nnihilation fractions determined by lifetime measurements, we separate
2D-ACAR distributions for negatively charged and neutral arsenic vaca
ncies in n-type GaAs. In electron-irradiated semi-insulating GaAs, we
present 2D-ACAR results for the negatively charged gallium vacancy and
for positron Rydberg states induced by gallium antisites. The 2D-ACAR
for delocalized positrons, needed in the separation process, has been
obtained from measurements on as-grown semi-insulating GaAs. Our resu
lts outline the capabilities of the 2D-ACAR technique when it is appli
ed to the study of defects: the electronic structure in the vacancies
are found to be well described by recent molecular dynamics calculatio
ns. The method also provides information about atomic relaxations arou
nd the vacancy sites, they are in agreement with the calculated relaxa
tions. We conclude that the 2D-ACAR method is a promising tool to inve
stigate defects in semiconductors.