Left-right asymmetries in atomic transitions, depending upon the nuclear spin, could be a source of information on the neutral hadronic axial current. We show that the relevant electroweak parameter can be extracted from experiment by measuring hyperfine component ratios which do not involve the knowledge of the atomic wave function. In the standard electroweak model, the parity violating electron-nucleus interaction associated with the hadronic axial neutral current is accidently suppressed and, as a consequence, dominated by the electron interaction with the nuclear anapole moment, which describes the effect of the parity violating nuclear forces on the nucleus electromagnetic current. One of our objectives was to identify the various physical mechanisms which determine the size of the nuclear anapole moments. As an important step, we have established a simple relation between the anapole moment and the nuclear spin magnetization. From this relation it follows that the computation of the anapole moment can be reduced to that of one-body operators. The basic tool is a unitary transformation W which eliminates the one-body parity violating potential from the nuclear hamiltonian. It generalizes, to more realistic situations, a procedure used by F.C. Michel in the case of constant nuclear density. The fact that the transformation W does not commute with the residual spin-dependent nucleon-nucleon interaction can be accounted for - within some approximation - by a renormalization of the effective coupling constants which appear in the one-body reduction of the two-body parity violating nucleon-nucleon interaction induced by meson exchange. A particular attention was paid to nuclear correlation effects. They are treated semi-empirically in the independent pair approximation. The nuclear anapole moments of Rb-85, Cs-133, and Bi-209 have been evaluated for three sets of parity violating meson-nucleon coupling constants, taking into account configuration mixing effects in a semi-empirical way. We suggest a possible strategy to disentangle the axial neutral current from the anapole moment contribution. It requires experiments, accurate to few tenths of a percent, performed on several heavy nuclei. The results should be collected in a two-dimensional plot involving a suitably chosen set of variables (X,Y). In an ideal situation - small theoretical uncertainties - the points corresponding to various nuclei should fall on a straight line which crosses the line X = 0 at a point the ordinate of which is the sought for axial coupling constant.
