  Recent experiments by Larson et al. demonstrate the feasibility of measuring
local $dd$ excitations using nonresonant inelastic X-ray scattering (IXS). We
establish a general framework for the interpretation where the $dd$ transitions
created in the scattering process are expressed in effective one-particle
operators that follow a simple selection rule. The different operators can be
selectively probed by employing their different dependence on the direction and
magnitude of the transferred momentum. We use the operators to explain the
presence of nodal directions and the nonresonant IXS in specific directions and
planes. We demonstrate how nonresonant IXS can be used to extract valuable
ground state information for orbiton excitations in manganite.
