Liquid X‐ray scattering with a pink‐spectrum undulator

X‐ray scattering from a liquid using the spectrum from the undulator fundamental is examined as a function of the bandwidth of the spectrum. The synchrotron‐generated X‐ray spectrum from an undulator is `pink', i.e. quasi‐monochromatic but having a saw‐tooth‐shaped spectrum with a bandwidth from 1 to 15%. It is shown that features in S(q) are slightly shifted and dampened compared with strictly monochromatic data. In return, the gain in intensity is 250–500 which makes pink beams very important for time‐resolved experiments. The undulator spectrum is described by a single exponential with a low‐energy tail. The tail shifts features in the scattering function towards high angles and generates a small reduction in amplitude. The theoretical conclusions are compared with experiments. The r‐resolved Fourier transformed signals are discussed next. Passing from q‐ to r‐space requires a sin‐Fourier transform. The Warren convergence factor is introduced in this calculation to suppress oscillatory artifacts from the finite q_M in the data. It is shown that the deformation of r‐resolved signals from the pink spectrum is small compared with that due to the Warren factor. The q‐resolved and the r‐resolved pink signals thus behave very differently.