Lithium in the intermediate age cluster NGC 3680: Following Li evolution along the C-M diagram

We present an analysis of high resolution spectroscopic observations (R similar to 30 000, S/N = 60-150) of 24 members of the intermediate age (similar to1.5 Gyr) open cluster NGC 3680, covering all regions of the cluster colour-magnitude (C-M) diagram where cluster members are known to exist. These observations represent in many aspects challenges to our understanding of stellar interior and mixing. Four main sequence G stars have, within the errors, the same Li abundance, 0.3 dex lower than similar stars in the similar to1 Gyr younger Hyades but comparable with those observed in the coeval cluster IC 4651. The cluster shows a clear Li-dip located around the turn-off; two stars on the upper part of the turn-off are out of the dip and reach solar system meteoritic Li abundances. Just above the turn-off, in a very small range of magnitudes (similar to0.2 in V), a factor of similar to5 Li depletion occurs. This sudden decrease explains puzzling results recently obtained on field subgiants but it is not at all reproduced by standard (e.g. no rotation, no diffusion) models, whereas it is in somewhat better agreement with the predictions of recent models which include rotational mixing and atomic diffusion. Out of the six cluster giants, one is probably a binary; of the remaining five single cluster members, three have a Li abundance log n(Li) similar to 1.1 while two have Li abundances from a factor 6 to more than a factor 30 lower than the other three. The star with no detected Li is the coolest and most luminous object in the sample and is most likely an AGB star; the other has instead a similar magnitude and effective temperature as the three more Li rich giants. The reasons for this difference in Li abundance among otherwise similar stars can be ascribed either to differential depletion during main-sequence or post-main sequence evolution, possibly induced by rotation, or to differences in the evolutionary status of these evolved stars. By comparing our results with those found for clusters of similar age and for field stars, we find that none of the possible scenarios gives a fully satisfactory explanation if the present population of NGC 3680 giants re ect the expected ratio of clump vs. first-ascent RGB stars. If the more abundant Li-rich giants in NGC 3680 are indeed clump giants, their relatively high Li content requires that Li is produced, or brought to the surface, between the tip of the RGB and the clump, which is not consistent with observations of the similar age cluster NGC 752, where the more abundant, presumably clump giants have low Li abundances. Finally, we have used our spectra to determine the metallicity of the cluster giants, finding [Fe/H] = 0.17 +/- 0.12. This value is in very good agreement with that derived from spectral indexes analysis, but substantially lower than the value inferred from Stromgren photometry.