  In order to shed light on the electronic structure of Na_xCoO_2, and
motivated by recent Co L-edge X-ray absorption spectra (XAS) experiments with
polarized light, we calculate the electronic spectrum of a CoO_6 cluster
including all interactions between 3d orbitals. We obtain the ground state for
two electronic occupations in the cluster that correspond nominally to all O in
the O^{-2} oxidation state, and Co^{+3} or Co^{+4}. Then, all excited states
obtained by promotion of a Co 2p electron to a 3d electron, and the
corresponding matrix elements are calculated. A fit of the observed
experimental spectra is good and points out a large Co-O covalency and cubic
crystal field effects, that result in low spin Co 3d configurations. Our
results indicate that the effective hopping between different Co atoms plays a
major role in determining the symmetry of the ground state in the lattice.
Remaining quantitative discrepancies with the XAS experiments are expected to
come from composition effects of itineracy in the ground and excited states.
