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 sim ilar to 30 000, S/N = 60-150) of 24 members of the intermediate age (simila r to1.5 Gyr) open cluster NGC 3680, covering all regions of the cluster col our-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 er rors, the same Li abundance, 0.3 dex lower than similar stars in the simila r to1 Gyr younger Hyades but comparable with those observed in the coeval c luster IC 4651. The cluster shows a clear Li-dip located around the turn-of f; 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 o btained 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 agree ment with the predictions of recent models which include rotational mixing and atomic diffusion. Out of the six cluster giants, one is probably a bina ry; 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 m ore 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 tempe rature as the three more Li rich giants. The reasons for this difference in Li abundance among otherwise similar stars can be ascribed either to diffe rential depletion during main-sequence or post-main sequence evolution, pos sibly 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 scen arios gives a fully satisfactory explanation if the present population of N GC 3680 giants re ect the expected ratio of clump vs. first-ascent RGB star s. 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 cons istent 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, findi ng [Fe/H] = 0.17 +/- 0.12. This value is in very good agreement with that d erived from spectral indexes analysis, but substantially lower than the val ue inferred from Stromgren photometry.