Polarization of absorption lines as a diagnostics of circumstellar,   interstellar and intergalactic magnetic fields: Fine structure atoms
  The relative population of the fine structure sublevels of an atom's ground state is affected by radiative transitions induced by an anisotropic radiation flux. This causes the alignment of atomic angular momentum. In terms of observational consequences for the interstellar and intergalactic medium, this results in the polarization of the absorption lines. In the paper we consider the conditions necessary for this effect and provide calculations of polarization from a few astrophysically important atoms and ions with multiple upper and lower levels for an arbitrary orientation of magnetic fields to the a) source of optical pumping, b) direction of observation, c) absorbed source. We also consider an astrophysically important ``degenerate'' case when the source of optical pumping coincides with the source of the absorbed radiation. We present analytical expressions that relate the degree of linear polarization and the intensity of absorption to the 3D orientation of the magnetic field with respect to the pumping source, the source of the absorbed radiation, and the direction of observations. We discuss how all these parameters can be determined via simultaneous observations of several absorption lines and suggest graphical means that are helpful in practical data interpretation. We prove that studies of absorption line polarization provide a unique tool to study 3D magnetic field topology in various astrophysical conditions. 
Huirong Yan & A. Lazarian