The Li-rich turn-off star in the globular cluster NGC 6397 could represent the smoking gun for some very rare episode of Li enrichment in globular clusters. We aim to understand the nature of the Li enrichment by performing a spectroscopic analysis of the star, in particular of its beryllium (Be) abundance, and by investigating its binary nature. We observe the near UV region where the Beii resonance doublet and the NH bands are located. We could not detect the Beii lines and derive an upper limit of log (Be/H)< -12.2, that is consistent with the Be observed in other stars of the cluster. We could detect a weak G-band, which implies a mild carbon enhancement [C/Fe]$+0.4pm0.2$. We could not detect the UV NH band, and we derive an upper limit [N/Fe]$< 0.0$. For oxygen we could notdetect any of the near UV OH lines, which implies that oxygen cannot be strongly enhanced in this star. This is consistent with the detection of the Oi triplet at 777nm, which is consistent with [O/Fe]~0.5. Combining the UVES and Mike data, we could not detect any variation in the radial velocity greater than 0.95 kms$^{-1}$ over 8 years. The chemical composition of the star strongly resembles that of `first generation NGC6397 stars, with the huge Li as the only deviating abundance. Not detecting Be rules out two possible explanations of the Li overabundance: capture of a substellar body and spallation caused by a nearby type II SNe. Discrepancies are also found with respect to other accretion scenarios,except for contamination by the ejecta of a star that has undergone the RGB Li-flash.
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