Theoretical treatment of the magnetoelectric Jones birefringence and dichroism is developed through the bilinear in static
electric and magnetic field dipole-forbidden corrections to the amplitude of Rayleigh scattering. In particular cases of
orientation of the static fields relative the polarization and wave vectors of monochromatic radiation, the amplitude determines
corrections to the refractive index of atomic gas responsible for (i) the Jones birefringence and dichroism, (ii) linear
birefringence and dichroism and (iii) directional anisotropy for the monochromatic wave. The analytical equations and
numerical data for the indicated corrections, calculated for alkali atoms, determine optimal conditions for observing the
effects in vapours. For resonance on D state essential enhancement is discovered in the frequency dependence for the ratio
of refractive index anisotropy of the Jones effect to the square-root product of corresponding anisotropy determining the
Kerr and Cotton-Mouton effects.
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