  We describes a new approach for performing quantitative structure-factor
analysis and density measurements of liquids using x-ray diffraction with a
pink-spectrum x-ray source. The methodology corrects for the pink beam effect
by performing a Taylor series expansion of the diffraction signal. The mean
density, background scale factor, peak x-ray energy about which the expansion
is performed, and the cutoff radius for density measurement are estimated using
the derivative-free optimization scheme. The formalism is demonstrated for a
simulated radial distribution function for tin. Finally, the proposed
methodology is applied to experimental data on shock compressed tin recorded at
the Dynamic Compression Sector at the Advanced Photon Source, with derived
densities comparing favorably to other experimental results and the equations
of state of tin.
