A high-purity germanium detector was used to determine differential cross sections for the elastic scattering of 81-keV gamma rays by aluminum, nickel, tantalum, gold, and lead through angles of 60-degrees, 90-degrees, 120-degrees, and 133. The atomic Rayleigh scattering amplitudes were obtained in the independent-particle approximation by calculations of modified relativistic form factors (MF's), a combination of MF's and angle-independent ''anomalous'' scattering factors (ASF's), and the relativistic second-order S matrix. Most experimental cross sections for gold and lead are slightly smaller than the calculations in the S matrix or the MF-ASF approaches, the differences being larger in the latter case. The calculated cross sections based on MF's are enormously larger than these values. The tantalum data are in good agreement with S-matrix calculations. The data for Al show agreement with the different calculations, which differ by less than about 6%.
