The threshold amplitude for Compton scattering is known to be proportional to the square of the total charge of the target. A naive application of the impulse approximation would give a result that would depend upon the sum of squares of the charges of the individual particles comprising the target. Resolution of these incompatible results depends upon careful treatment of the center‐of‐mass coordinate of the target. This treatment is presented in the context of nonrelativistic perturbation theory.