Carbon-12 and carbon-13 abundances have been measured in eleven bright giant members of the globular cluster \omega Centauri via observations of the first-overtone CO bands near 2.3 \mu m. The stars in this sample were selected to span a substantial fraction of the range of iron abundances found in this cluster .
In addition , the sample covers a range of [ O/Fe ] , [ Na/Fe ] and [ Al/Fe ] abundance ratios derived in previous studies .
In all \omega Cen giants the ^ { 12 } { C } / ^ { 13 } { C } abundance ratio is found to be quite low , indicating deep mixing in these red giants .
The mean value for the entire sample is \langle ^ { 12 } { C } / ^ { 13 } { C } \rangle = 4.3 \pm 0.4 ( \sigma = 1.3 ) , with nine stars equal , within the errors , to the equilibrium ratio ^ { 12 } { C } / ^ { 13 } { C } = 3.5 and two stars having slightly higher values .
There is no correlation between the ^ { 12 } { C } / ^ { 13 } { C } and the abundance of iron .
In addition , no correlation of ^ { 12 } { C } / ^ { 13 } { C } with [ ^ { 12 } C/Fe ] is found ( all giants are deeply mixed ) , although the derived abundances of [ ^ { 12 } C/Fe ] show a positive correlation with [ O/Fe ] , and an anticorrelation with [ Na/Fe ] ( with the oxygen and sodium abundances taken from previous studies in the literature ) .
A comparison of the isotopic carbon ratios in \omega Cen with those from other globular clusters ( M4 , M71 , NGC6752 , and 47 Tuc ) , and with literature oxygen abundances , may reveal a slight trend of decreasing ^ { 12 } { C } / ^ { 13 } { C } ratios with decreasing [ O/Fe ] in the entire globular cluster sample of red giants .
A comparison between ^ { 12 } C/ ^ { 13 } C and both [ Na/Fe ] and [ Al/Fe ] , however , reveals no trend .