X-ray refractive-index measurement in silicon and lithium fluoride

The refractive indices $n$ of silicon and lithium fluoride were measured noninterferometrically with Mo $K\overline{\alpha }$ and Ag $K\overline{\alpha }$ x rays to a sub-part-per-billion accuracy. This high accuracy allows experimental determination of the real dispersion correction $f^{\prime }$ to ±2 millielectron accuracy. The $f^{\prime }$ values obtained are in excellent agreement with the best interferometric measurements, part of which are less accurate than the present results. The predictions of both the Cromer-Liberman and the modified Hönl theories are found to deviate significantly from the measured $f^{\prime }$ values, thus indicating the need for modification of the wave functions or, more likely, the exchange potential used.