Refractive Indices and Anomalous Dispersion of Soft X-Rays in Platinum, Silver, Calcite and Glass

With a large x-ray vacuum spectrograph x-ray beams of nearly homogeneous wave-length were secured by reflection from a gypsum crystal. The indices of refraction of a number of substances for these rays were measured by the total reflection method in the wave-length range from 0.80 to 9.15A. Curves are obtained relating the values of $1-\mu =\delta$ ($\mu$ being the index of refraction) with the corresponding wave-length $\lambda$. The effects of anomalous dispersion are shown in lowered values of $\delta$ on both sides of an absorption limit wave-length. In the case of calcite this depression in the curve extends over the region from 2.5 to 3.4A, i.e. from frequencies 12 percent greater to frequencies 10 percent less than that of the $K$ limit of calcium at 3.06A, the minimum value of $\delta$ occurring precisely at 3.06A. The dispersion curves for platinum and silver show that in cases where the percent frequency difference between adjacent absorption limits is small the depressions due to the separate limits are not resolved. The relative frequency separation of the $L_{\mathrm{II}}$ and $L_{\mathrm{III}}$ limits of silver is less than that of the $L_I$ and $L_{\mathrm{II}}$ limits hence two minima or points of inflection appear in the dispersion curve, one at a mean of the $L_{\mathrm{II}}$ and $L_{\mathrm{III}}$ wave-lengths and the other at the $L_I$ limit. This is reversed in the case of platinum where the relative frequency separation is least between $L_I$ and $L_{\mathrm{II}}$ in which case these are not resolved although $L_{\mathrm{III}}$ appears as a separate depression in the curve. Similar results are found in the $M$ series of platinum, a depression appearing at a mean of the $M_I$ and $M_{\mathrm{II}}$ wave-lengths and also at a mean of the $M_{\mathrm{IV}}$ and $M_V$ wave-lengths while $M_{\mathrm{III}}$ having a greater frequency separation from other levels is clearly resolved. The dispersion curve for glass passes through minima at the $K$ limits of silicon and aluminum showing that the sample contained the latter element as well as the former but its composition was otherwise unknown. These results fully reveal for the first time the type of anomalous dispersion occurring in the region of the $K$, $L$ and $M$ absorption discontinuities. In general the values of $\delta$ are in fair but not excellent agreement with those computed from the Drude-Lorentz dispersion formula for regions not too close to an absorption limit. The form of curve obtained was found to be the same regardless of the particular sample used but the actual values found for $\delta$ appear to vary considerably with thickness of film and surface conditions.