  We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the K
edge of Mn in the antiferromagnetic insulating manganite LaMnO3. We make use of
the Keldysh-type Green-function formalism, in which the RIXS intensity is
described by a product of an incident-photon-dependent factor and a
density-density correlation function in the 3d states. We calculate the former
factor using the 4p density of states given by an ab initio band structure
calculation and the latter using a multi-orbital tight-binding model. The
ground state of the model Hamiltonian is evaluated within the Hartree-Fock
approximation. Correlation effects are treated within the random phase
approximation (RPA). We obtain the RIXS intensity in a wide range of
energy-loss 2-15 eV. The spectral shape is strongly modified by the RPA
correlation, showing good agreement with the experiments. The
incident-photon-energy dependence also agrees well with the experiments. The
present mechanism that the RIXS spectra arise from band-to-band transitions to
screen the core-hole potential is quite different from the orbiton picture
previously proposed, enabling a comprehensive understanding of the RIXS
spectra.
