A non-LTE analysis of K i resonance lines at 7664.91 and 7698.97 \AA was carried out for 15 red giants belonging to three globular clusters of different metallicity ( M 4 , M 13 , and M 15 ) along with two reference early-K giants ( \rho Boo and \alpha Boo ) , in order to check whether the K abundances are uniform within a cluster and to investigate the behavior of [ K/Fe ] ratio at the relevant metallicity range of -2.5 \ltsim [ Fe/H ] \ltsim - 1 .
We confirmed that [ K/H ] ( as well as [ Fe/H ] ) is almost homogeneous within each cluster to a precision of \ltsim 0.1 dex , though dubiously large deviations are exceptionally seen for two peculiar stars showing signs of considerably increased turbulence in the upper atmosphere .
The resulting [ K/Fe ] ratios are mildly supersolar by a few tenths of dex for three clusters , tending to gradually increase from \sim +0.1–0.2 at [ Fe/H ] \sim - 1 to \sim + 0.3 at [ Fe/H ] \sim - 2.5 .
This result connects reasonably well with the [ K/Fe ] trend of disk stars ( -1 \ltsim [ Fe/H ] ) and that of extremely metal-poor stars ( -4 \ltsim [ Fe/H ] \ltsim - 2.5 ) .
That is , [ K/Fe ] appears to continue a gradual increase from [ Fe/H ] \sim 0 toward a lower metallicity regime down to [ Fe/H ] \sim - 3 , where a broad maximum of [ K/Fe ] \sim +0.3–0.4 is attained , possibly followed by a slight downturn at [ Fe/H ] \ltsim - 3 .