text: The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field.
  The interaction energy of a continuous charge distribution , confined within a finite volume , with an external electrostatic potential  is 
  This expression is valid classically and quantum-mechanically alike.
  If the potential varies weakly over the charge distribution, the multipole expansion converges fast, so only a few first terms give an accurate approximation. Namely, keeping only the zero- and first-order terms,
  where we introduced the electric field  and assumed the origin 0 to be somewhere within .
  Therefore, the interaction becomes
  where  and  are, respectively, the total charge (zero moment) and the dipole moment of the charge distribution.
  Classical macroscopic objects are usually neutral or quasi-neutral (), so the first, monopole, term in the expression above is identically zero. This is also the case for a neutral atom or molecule. However, for an ion this is no longer true. Nevertheless, it is often justified to omit it in this case, too. Indeed, the Stark effect is observed in spectral lines, which are emitted when an electron "jumps" between two bound states. Since such a transition only alters the internal degrees of freedom of the radiator but not its charge, the effects of the monopole interaction on the initial and final states exactly cancel each other.