We report high resolution angle-resolved photoemission spectroscopy (ARPES) studies of the electronic structure of BaFe$_2$As$_2$, which is one of the parent compounds of the Fe-pnictide superconductors. ARPES measurements have been performed at 20 K and 300 K, corresponding to the orthorhombic antiferromagnetic phase and the tetragonal paramagnetic phase, respectively. Photon energies between 30 and 175 eV and polarizations parallel and perpendicular to the scattering plane have been used. Measurements of the Fermi surface yield two hole pockets at the $Gamma$-point and an electron pocket at each of the X-points. The topology of the pockets has been concluded from the dispersion of the spectral weight as a function of binding energy. Changes in the spectral weight at the Fermi level upon variation of the polarization of the incident photons yield important information on the orbital character of the states near the Fermi level. No differences in the electronic structure between 20 and 300 K could be resolved. The results are compared with density functional theory band structure calculations for the tetragonal paramagnetic phase.
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