Updated Toulouse solar models including the diffusion-circulation coupling and the effect of μ-gradients

New solar models are presented, which have been computed with the most recent physical inputs (nuclear reaction rates, equation of state, opacities, microscopic diffusion). Rotation-induced mixing has been introduced in a way which includes the feed-back effect of the $\mu$-gradient induced by helium settling. A parametrization of the tachocline region below the convective zone has also been added in the computations. The sound velocities have been computed in the models and compared to the seismic sun. Our best model is described in some detail. Besides the new physical inputs, the most important improvement concerns the computations of $\mu$-gradients during the solar evolution and their influence in slowing down rotation-induced mixing. This process can explain why lithium is depleted in the present Sun while beryllium is not, and meanwhile why $^3$He has not increased at the solar surface for at least 3 Gyrs.