Note on the Scattering of X-Rays from Fluids Containing Polyatomic Molecules

The intensity of the (unmodified) scattered radiation from a fluid containing one kind of molecules is given by: S=(1ΣnZₙ)[F₁²+F₂²∫P(R)dR(sinkR)kR], where F₁²=Σn^Σm^fₙfₘ(sinkrₙₘ)krₙₘ, while F₂² depends both upon the molecular structure and upon the relative orientation of the molecules. It is shown that the radial distribution function PR may be obtained directly from the observed scattering curve if the molecular structure is known: ${P}(R)=4{π}{R}²{{ρ}}₀+{2R}{{π}}{∫}{0}^{{∞}}k[{S{Σ}{}{n}{Z}ₙ}{{{F}₁}²}{-}1]{{{F}₁}²}{{{F}₂}²}sin(kR)dk,$ where ${{ρ}}₀$ is the density of the fluid in molecules per unit volume.