  We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the Ni
$K$ edge in an antiferromagnetic insulator NiO by applying the theory developed
by the present authors. It is based on the Keldysh Green's function formalism,
and treats the core-hole potential in the intermediate state within the Born
approximation. We calculate the single-particle energy bands within the
Hartree-Fock approximation on the basis of the multi-orbital tight-binding
model. Using these energy bands together with the $4p$ density of states from
an ab initio band structure calculation, we calculate the RIXS intensities as a
function of energy loss. By taking account of electron correlation within the
random phase approximation (RPA), we obtain quantitative agreement with the
experimental RIXS spectra, which consist of prominent two peaks around 5 eV and
8 eV, and the former shows considerable dispersion while the latter shows no
dispersion. We interpret the peaks as a result of a band-to-band transition
augmented by the RPA correlation.
