Atomic Diffusion and Mixing in Old Stars. III. Analysis of NGC 6397
  Stars under New Constraints
  We have previously reported on chemical abundance trends with evolutionary
state in the globular cluster NGC 6397 discovered in analyses of spectra taken
with FLAMES at the VLT. Here, we reinvestigate the FLAMES-UVES sample of 18
stars, ranging from just above the turnoff point (TOP) to the red giant branch
below the bump. Inspired by new calibrations of the infrared flux method, we
adopt a set of hotter temperature scales. Chemical abundances are determined
for six elements (Li, Mg, Ca, Ti, Cr, and Fe). Signatures of cluster-internal
pollution are identified and corrected for in the analysis of Mg.
  On the modified temperature scales, evolutionary trends in the abundances of
Mg and Fe are found to be significant at the 2{\sigma} and 3{\sigma} levels,
respectively. The detailed evolution of abundances for all six elements agrees
with theoretical isochrones, calculated with effects of atomic diffusion and a
weak to moderately strong efficiency of turbulent mixing. The age of these
models is compatible with the external determination from the white dwarf
cooling sequence. We find that the abundance analysis cannot be reconciled with
the strong turbulent-mixing efficiency inferred elsewhere for halo field stars.
A weak mixing efficiency reproduces observations best, indicating a
diffusion-corrected primordial lithium abundance of log {\epsilon}(Li) = 2.57
+- 0.10. At 1.2{\sigma}, this value agrees well with WMAP-calibrated Big-Bang
nucleosynthesis predictions.
