On the Atomic Polarization of the Ground Level of Na I

In a recent letter (Trujillo Bueno et al. 2002), we showed the remarkable result that the atomic alignment of the levels P$_{1/2}$ and S$_{1/2}$ of the D$_1$ line of Na I is practically destroyed in the presence of magnetic fields sensibly larger than 10 G, irrespectively of the field direction. In this paper, we demonstrate analytically that this property is a consequence of the decoupling of the electronic and nuclear angular momenta, J and I, in the excited state P$_{3/2}$, which is achieved when the Zeeman splitting from the local magnetic field becomes much larger than the typical hyperfine separation for that level.