  The influence of finite relaxation times on Thomson scattering from
warm-dense plasmas is examined within the framework of the average-atom
approximation. Presently most calculations use the collision-free Lindhard
dielectric function to evaluate the free-electron contribution to the Thomson
cross section. In this work, we use the Mermin dielectric function, which
includes relaxation time explicitly. The relaxation time is evaluated by
treating the average atom as an impurity in a uniform electron gas and depends
critically on the transport cross section. The calculated relaxation rates
agree well with values inferred from the Ziman formula for the static
conductivity and also with rates inferred from a fit to the frequency-dependent
conductivity. Transport cross sections determined by the phase-shift analysis
in the average-atom potential are compared with those evaluated in the commonly
used Born approximation. The Born approximation converges to the exact cross
sections at high energies; however, differences that occur at low energies lead
to corresponding differences in relaxation rates. The relative importance of
including relaxation time when modeling X-ray Thomson scattering spectra is
examined by comparing calculations of the free-electron dynamic structure
function for Thomson scattering using Lindhard and Mermin dielectric functions.
Applications are given to warm-dense Be plasmas, with temperatures ranging from
2 to 32~eV and densities ranging from 2 to 64~g/cc.
