  We continue our studies of atomic alignment in diffuse media, in
particularly, in interstellar and circumstellar media, with the goal of
developing new diagnostics of magnetic fields in these environments. We
understand atomic alignment as alignment of atoms or ions in their ground
state. Such atoms are sensitive to weak magnetic fields. In particular, we
provide predictions of the polarization that arises from astrophysically
important aligned atoms (ions) with fine structure of the ground level, namely,
OI and SII and Ti II. Unlike our earlier papers which dealt with weak fields
only, a substantial part of our current paper is devoted to the studies of
atomic alignment when magnetic fields get strong enough to affect the emission
from the excited level, i.e. with the regime when the magnetic splitting is
comparable to the line-width. This is a regime of Hanle effect modified by the
atomic alignment. Using an example of emission and absorption lines of SII ion
we demonstrate how polarimetric studies can probe magnetic fields in
circumstellar regions and accretion disks. In addition, we show that atomic
alignment induced by anisotropic radiation can induce substantial variations of
magnetic dipole transitions within the ground state, thus affecting abundance
studies based on this emission. Moreover, the radio emission is polarized,
provides a new way to study magnetic fields, e.g. at the epoch of Universe
reionization.
