How do we convert absorption spectra to charge-fluctuation forces

For the real answer to this question, read past this Prelude. Here, to keep to familiar notation, write energies in terms of a Hamaker coefficient (but never Hamaker constant). In this language the interaction energy per unit area between parallel, infinitely thick walls A and B across a medium m of thickness l looks like -[AHam/(12jr/2)]. 

The coefficient AHam itself varies with separation /. It takes the form of a sum over all frequencies at which fluctuations can occur wherein each term depends on the frequency-dependent responses of materials A, B, and m to electromagnetic fields. These responses are written in terms of dielectric functions sA, b, and em that are extracted from absorption spectra. It is the differences in these dielectric responses that create interactions. To first approximation, 

For a vacuum, e = 1 for all materials the e s as used here are 1. In this schematic expression, Rel(/) 1 gives the effects of relativistic retardation, i.e., the suppression of interactions because of the finite velocity of light  

Van der Waals forces result from charge and electromagnetic-field fluctuations at all possible rates. We can frequency analyze these fluctuations over the entire frequency spectrum and integrate their force consequences over the frequency continuum. Alternatively, the modern theory shows a practical way to reduce integration over all frequencies into summation by the gathering of spectral information into a set of discrete sampling frequencies or eigenfrequencies. The nature and choice of the frequencies at which dielectric functions are evaluated reveal how the modern theory combines material properties with quantum mechanics and thermodynamics. 

Most intriguing to newcomers, these sampling frequencies are not expressed as ordinary sinusoidal ( real-frequency ) oscillations. Instead they are crafted in the language of exponential (horribly designated as imaginary-frequency ) variations pertaining to the ways in which spontaneous charge fluctuations die away. Different kinds of fluctuations die at different rates  

---

PR.2. How do we convert absorption spectra to charge-fluctuation forces 24... 

---