(Abridged) The chemical content of the planetary nebula NGC 3918 is investigated through deep, high-resolution UVES at VLT spectrophotometric data. We identify and measure more than 750 emission lines, making ours one of the deepest spectra ever taken for a planetary nebula. Among these lines we detect very faint lines of several neutron-capture elements (Se, Kr, Rb, and Xe), which enable us to compute their chemical abundances with unprecedented accuracy, thus constraining the efficiency of the s-process and convective dredge-up in the progenitor star of NGC 3918. We find that Kr is strongly enriched in NGC 3918 and that Se is less enriched than Kr, in agreement with the results of previous papers and with predicted s-process nucleosynthesis. We also find that Xe is not as enriched by the s-process in NGC 3918 as is Kr and, therefore, that neutron exposure is typical of modestly sub-solar metallicity AGB stars. A clear correlation is found when representing [Kr/O] vs. log(C/O) for NGC 3918 and other objects with detection of multiple ions of Kr in optical data, confirming that carbon is brought to the surface of AGB stars along with s-processed material during third dredge-up episodes, as predicted by nucleosynthesis models. We also detect numerous refractory element lines (Ca, K, Cr, Mn, Fe, Co, Ni, and Cu). We compute physical conditions from a large number of diagnostics. Thanks to the high ionization of NGC 3918 we detect a large number of recombination lines of multiple ionization stages of C, N, O and Ne. The abundances obtained for these elements by using recently-determined state-of-the-art ICF schemes or simply adding ionic abundances are in very good agreement, demonstrating the quality of the recent ICF scheme for high ionization planetary nebulae.
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