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Incoherent scattering is one of the major processes by which gamma rays interact with matter in the energy range from 100 KeV to I MeV. The effect was simultaneously but separately observed by Compton (1923) and Debye (1923) based on Einstein's light quantum hypothesis. Debye suggested that the effect should bear Compton's name alone and hence it was named "Compton effect". Tabulations are presented of the atomic form factor, F ( , Z), and the incoherent scattering function, S (x, Z), for values of x (=sin /2)/ ) from 0.005 Å-1 to 109 Å-1, for all elements A=1 to 100. These tables are constructed from available state-of-the-art theoretical data, including the Pirenne formulas for Z=1, configuration-into action results by Brown using Brown-Fontana and Weiss correlated wave functions for Z=2 to 6 non-relativistic Hartree-Fock results by Cromer for Z=7 to 100 and a relativistic K-shell analytic expression for F(x, Z) by Bethe Levinger for x 10 Å-1 for all elements Z=2 to 100. These tabulated values are graphically compared with available photon scattering angular distribution measurements.