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===X-ray and extreme UV=== For [[X-ray]] and [[extreme ultraviolet]] radiation the complex refractive index deviates only slightly from unity and usually has a real part smaller than 1. It is therefore normally written as {{math|{{uu|''n''}} {{=}} 1 β ''Ξ΄'' + ''iΞ²''}} (or {{math|{{uu|''n''}} {{=}} 1 β ''Ξ΄'' β ''iΞ²''}} with the alternative convention mentioned above).<ref name=Attwood/> Far above the atomic resonance frequency delta can be given by <math display="block"> \delta = \frac{r_0 \lambda^2 n_\mathrm{e}}{2 \pi} </math> where {{math|''r''{{sub|0}}}} is the [[classical electron radius]], {{mvar|Ξ»}} is the X-ray wavelength, and {{math|''n''{{sub|e}}}} is the electron density. One may assume the electron density is simply the number of electrons per atom {{mvar|Z}} multiplied by the atomic density, but more accurate calculation of the refractive index requires replacing {{mvar|Z}} with the complex [[atomic form factor]] {{nowrap|<math> f = Z + f' + i f'' </math>.}} It follows that <math display="block">\begin{align} \delta &= \frac{r_0 \lambda^2}{2 \pi} (Z + f') n_\text{atom} \\ \beta &= \frac{r_0 \lambda^2}{2 \pi} f'' n_\text{atom} \end{align}</math> with {{mvar|Ξ΄}} and {{mvar|Ξ²}} typically of the order of {{val|e=β5}} and {{val|e=β6}}.
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