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Influence of Integral Instability of Kramers–Kronig Transformation on Photoabsorption Cross Sections

The photoabsorption cross sections of condensed atoms and molecules have proven to be dependent not only on the imaginary parts but also on the real parts of the polarizabilities due to the strong interatomic interactions in condensed environment. The real parts of the polarizabilities calculated usually by using the famous Kramers–Kronig transformation (KKT) from the photoabsorption cross sections of the isolated atoms are very sensitive to the accuracy of the implementation method of the infinite integral in the KKT. The influence of the integral instability of the KKT and the real part of the polarizability on the variation of the photoabsorption cross sections with the number density and the structure of the condensed matter has been studied in the present work for the first time. The conclusion is that the integration method with interpolation has given more reasonable results than the direct truncation method if some appropriate interpolation functions have been used. Some notes and conclusions have also been given for the applications of the alternative coupled expressions of photoabsorption cross sections.