The lithium plateau observed in halo stars has long appeared as a paradox in the general context of the lithium abundance behavior in stellar outer layers. First, the plateau is at, second, the lithium abundance dispersion is extremely small. This seems in contradiction with the large lithium variations observed in younger stars. It is also difficult to understand theoretically: as lithium nuclei are destroyed by nuclear reactions at a relatively low temperature ( congruent to2.5 million degrees), the occurrence of macroscopic motions in the stellar outer layers easily lead to lithium depletion at the surface. On the other hand, if no macroscopic motions occur in the stellar gas, lithium is subject to microscopic diffusion which, in the case of halo stars, should also lead to depletion. Several ideas have been proposed to account for the lithium behavior in halo stars. The most promising possibilities were rotational-induced mixing, which could reduce lithium in the same way for all the stars (Vauclair 1988; Pinsonneault et al. 1992 and 1999) and mass-loss, which could oppose the lithium settling (Vauclair & Charbonnel 1995, 1998). In both cases however, the parameters should be tightly adjusted to prevent any dispersion in the final results. Vauclair (1999) (Paper I) looked for a physical process which could occur in slowly rotating stars and explain why the dispersion of the lithium abundances in the halo stars' plateau is so small. She pointed out that the mu -gradient terms which appear in the computations of the meridional circulation velocity (e.g. Mestel 1953) were not introduced in previous computations of rotationally-induced mixing. This can lead to a self-regulating process which reduces the efficiency of the meridional circulation as well as the microscopic diffusion. Here we present numerical computations of this process and its influence on the lithium abundance variations in halo stars. We show that in slowly rotating stars, under some conditions, lithium can be depleted by a factor of up to two with a dispersion smaller than 0.1 dex in the middle part of the lithium plateau. We derive a primordial lithium abundance of 2.5 +/-0.1, consistent with the recent determinations of D/H and He-4/H.
