Efficiency of convection and Pre-Main Sequence lithium depletion

We show by detailed model computation how much the Pre-Main Sequence (PMS) lithium depletion depends on the treatment of over-adiabaticity, by taking advantage of the results of new models by Montalbán et al., which apply different treatments of convection to non-grey PMS models. In order to reproduce both the PMS lithium depletion (inferred from the lithium depletion patterns in young open clusters), and the location of PMS tracks in the HR diagram (inferred from the study of young PMS stars), convection both in the atmosphere and in a good fraction of the stellar envelope must be highly inefficient: e.g., in the Mixing Length Theory approximation, it must have a very low alpha =l/H_p. Unfortunately, the radii of these models are at variance with the solar radius, possibly indicating that there is some additional physical input, generally not taken into account in the stellar models, which affects the efficiency of convection in PMS stars, but probably not in the main sequence stars nor in evolved red giants. We stress the importance of determining precisely masses and lithium abundance in PMS binaries such as the important spectroscopic and eclipsing binary RXJ 0529.4+0041.