Calculation of total inelastic-x-ray-scattering cross sections(dσdΩ)inel

A new method is proposed for the calculation of the total inelastic-scattering cross-section differential with respect to the solid angle for detection of scattered x rays from atomic or molecular targets within the Born approximation. The Born expression for the cross-section differential with respect to solid angle and energy loss is summed over energy loss for the cases of constant scattering angle and constant momentum transfer. The sums over final states required to derive the proposed formulas are carried out with an error of the order of the - 3.5 power of the maximum observable energy loss for both constant momentum transfer and scattering angle. The leading term in the expansion is the familiar Waller-Hartree result. All quantities involved can be calculated with a knowledge of the target ground-state electronic wave function. Problems encountered in the application of the theory to $\gamma$-ray scattering are discussed.