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Equation of motion for a bound system of charged particles

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of polarizabilities. Due to the lack of separation of the total momentum from the internal degrees of freedom, the notion of polarizability of the bound state immersed in the continuum spectrum of the global motion is nontrivial. We introduce a bound-continuum perturbation theory and obtain a complete formula for the equation of motion for a polarizable bound system, such as atom, ion, or the nucleus. This formula may find applications when high precision is sought and small effects due polarizabilities are important.