Corrections to the usual x-ray scattering factors in rare gases: Experiment and theory

The ratio of the total x-ray scattering from Ne to that from He has been determined for photon energies in the range 4–15 keV at scattering angles of 45 and 90 degrees (corresponding to momentum transfers ranging from 0.90 to 5.69 a.u.). An arrangement of two gas cells in series was employed, allowing simultaneous measurements on both gases at the same scattering angle, which eliminates possible errors due to fluctuating beam intensity. Pairs of measurements corresponding to the same momentum transfer (at momentum transfers of 1.67 and 3.08 a.u.) but to different energies, provide a direct test of the corrections to the (momentum-transfer-dependent) form-factor incoherent-scattering-factor theory. These corrections include the anomalous p⋅A contributions, which are found to be important. We also consider corrections to the usual approximations made within the inelastic $A^2$ theory (the incoherent-scattering factor, using closure approximation, and the impulse approximation, assuming free-particle kinematics with a given momentum distribution). In these cases an incoherent-scattering-factor treatment is generally adequate, while anomalous scattering factor corrections to form factors are needed for elastic scattering.