Anomalous dispersion and absorption of X-rays

The general nature of the anomalous dispersion of X-rays, and its relation to absorption, was considered by Kallmann and Mark in 1927. The purpose of this paper is first to make more detailed calculations of the dispersion for certain special cases; secondly, to consider the theroretical reasons foe the observed value of the oscillator strength, particularly the equivalence of the 2K electrons to about 1.3 classical electrons. By virtue of the general applicability of the electromagnetic theory of radiation an atom in quantum mechanics is in many respects equivalent to an multitude of classical oscillator. The dispersion and absorption of radiation by the atom depend upon the frequency and strength of these virtual oscillators. In calculating the dispersion of X-rays there are two courses open. We can either use approximate estimates of the theoretical quantum-mechanical strength of the oscillators concerned, or use the theoretical relation which exists between the oscillator strength and the intensity of absorption of radiation, and assume the experimental values of the latter. The second procedure is possible since the necessary experimental data are available, and we adopt accuracy with which the theoretical oscillator strength can be evaluated. Kallmann and Mark, in their treatment of dispersion, also adopt the same procedure so far as they assume that the variation of the oscillator strength with frequency corresponds to the λ3-law of photoelectric absorption. The dispersion calculated in this way is only partially dependent on theory.