The splitting of atomic spectral lines as a result of an externally applied electric field was discovered by Stark, and is called the Stark effect. As the splitting of a line of the helium spectrum shows, the splitting is not symmetric like that of the Zeeman effect.
The splitting of the energy levels by an electric field first requires that the field polarize the atom and then interact with the resulting electric dipole moment. That dipole moment depends upon the magnitude of Mj, but not its sign, so that the energy levels are split into J+1 or J+1/2 levels, for integer and half-integer spins respectively.
The Stark effect has been of marginal benefit in the analysis of atomic spectra, but has been a major tool for molecular rotational spectra.