1 Introduction

The accretion of planets or planetary material onto stars have been considered as a possible explanation of the high metallicity frequently found in planet host stars (Laughlin & Adams 1997; Gonzalez 1997, 1998, 2001; Sandquist et al. 1998; Laughlin 2000; Santos et al. 2000; Murray et al. 2001; Pinsonneault et al. 2001). The very recent detection of the $^6{\rm Li}$ isotope in the atmosphere of the solar-type star HD 82943 (Israelian et al. 2001), which hosts a planetary system (Mayor et al. 2001), has also been interpreted as evidence for accretion of planets. Jupiter-like planets are expected to preserve their original content of the lithium isotopes, while stars like HD 82943 with a mass $\sim$1.1  ${M}_{\odot }$ destroy, via nuclear reactions with protons, all its $^6{\rm Li}$ (and a small fraction of the more robust ⁷Li) during the pre-main sequence (PMS) evolution (see e.g. Proffitt & Michaud 1989). It has been argued that ingestion and dilution of planetary material in HD 82943 after its superficial convective zone receded to the main-sequence location allowed long-term preservation of the newly acquired abundances of lithium isotopes. In fact, according to standard models for this type of stars, the base of the convective zone does not reach the temperatures needed for $^6{\rm Li}$ and $^7{\rm Li}$ burning ( $T \geq 2.2 \times 10^6$ K and $T \geq 2.6 \times 10^6$ K, respectively). The rate of destruction of $^6{\rm Li}$ by protons has a temperature dependence similar to that of ⁷Li, but on much shorter time scale (i.e. 100 times shorter at 1  ${M}_{\odot }$ in the standard model).

In this paper, we examine in quantitative terms the possibility that the dilution of one or several Jupiter-like planets in the convective envelope of a main sequence star could appreciably change the observed abundance of $^6{\rm Li}$ and $^7{\rm Li}$. In the framework of the standard model we predict the evolution of these isotopic abundances in stars with masses ranging from 1.3 to 0.6  ${M}_{\odot }$. We also discuss the effect due to some transport processes which cause extra-mixing below the convective zone (see for review Michaud & Charbonneau 1991). We will show that there is a narrow range of mass (or $T_{\rm eff}$) where the accretion of planetary material could produce an observable increase of ^6,7Li abundance during a significant fraction of the lifetime of the star.