  Resonant inelastic x-ray scattering (RIXS) is a spectroscopic technique which
has been widely used to study various elementary excitations in correlated and
other condensed matter systems. For strongly correlated materials, besides
boosting the overall signal the dependence of the resonant profile on incident
photon energy is still not fully understood. Previous endeavors in connecting
indirect RIXS, such as Cu K-edge for example where scattering takes place only
via the core-hole created as an intermediate state, with the charge dynamical
structure factor S(q,\omega) neglected complicated dependence on the
intermediate state configuration. To resolve this issue, we performed an exact
diagonalization study of the RIXS cross-section using the single-band Hubbard
model by fully addressing the intermediate state contribution. Our results are
relevant to indirect RIXS in correlated materials, such as high Tc cuprates. We
demonstrate that RIXS spectra can be reduced to S(q,\omega) when there is no
screening channel for the core-hole potential in the intermediate state. We
also show that two-magnon excitations are highlighted at the resonant photon
energy when the core-hole potential in the corresponding intermediate state is
poorly screened. Our results demonstrate that different elementary excitations
can be emphasized at different intermediate states, such that selecting the
exact incident energy is critical when trying to capture a particular
elementary excitation.
