Electrodynamics of finite-size particles with arbitrary spin

We construct the most general Hamiltonian for the electromagnetic interaction of the finite-size particle-like nucleus with arbitrary spin, magnetic dipole, and electric quadrupole moments. It includes all the terms, which are important for obtaining atomic energy levels up to the order ${\alpha }^6$. The result is verified against spin $s=0$, $1/2$, and $1$ cases, where the Foldy-Wouthuysen transformation is performed of the corresponding relativistic equation.