Resonance scattering formalism for the hydrogen lines in the presence of magnetic and electric fields

We derive a formalism for the computation of resonance-scattering polarization of hydrogen lines in the presence of simultaneous magnetic and electric fields, within a framework of the quantum theory of polarized line formation in the limit of complete frequency redistribution and of collisionless regime. Quantum interferences between fine-structure levels are included in this formalism. In the presence of a magnetic field, these interferences affect, together with the magnetic Hanle effect, the polarization of the atomic levels. In the presence of an electric field, interferences between distinct orbital configurations are also induced, further affecting the polarization of the hydrogen levels. In turn, the electric field is expected to affect the polarization of the atomic levels (electric Hanle effect), in a way analogous to the magnetic Hanle effect. We find that the simultaneous action of electric and magnetic fields give rise to complicated patterns of polarization and depolarization regimes, for varying geometries and field strengths.