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: $S=\left(\frac{1}{\Sigma \stackrel{}{n}{Z}_n}\right)\left[{F_1}^2+{F_2}^2\int \frac{P_{\mathrm{}\left(R\right)\mathrm{}}dR\left(sinkR\right)}{\mathrm{kR}}\right],$ where ${F_1}^2=\Sigma n^{}\Sigma m^{}\frac{f_n{f}_m\left(sink{r}_{\mathrm{nm}}\right)}{k{r}_{\mathrm{nm}}}$, while ${F_2}^2$ depends both upon the molecular structure and upon the relative orientation of the molecules. It is shown that the radial distribution function $P_R$ may be obtained directly from the observed scattering curve if the molecular structure is known: $P_{\mathrm{}\left(R\right)\mathrm{}}=4\mathrm{}\pi R^2{\rho }_0+\frac{2R}{\pi }\int 0^{\infty }k\left[\frac{S\Sigma \stackrel{}{n}{Z}_n}{{F_1}^2}-1\mathrm{}\right]\frac{{F_1}^2}{{F_2}^2}sin\mathrm{}\left(\mathrm{kR}\right)dk,$ where ${\rho }_0$ is the density of the fluid in molecules per unit volume.