The low-energy amplitude of Compton scattering on the bound state of two charged particles of arbitrary masses, charges and spins is calculated. A case in which the bound state exists due to electromagnetic interaction (QED) is considered. The term, proportional to $omega^2$, is obtained taking into account the first relativistic correction. It is shown that the complete result for this correction differs essentially from the commonly used term $Deltaalpha$, proportional to the r.m.s. charge radius of the system. We propose that the same situation can take place in the more complicated case of hadrons.
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