Context : Homogeneous investigations of red giant stars in open clusters contribute to studies of internal evolutionary mixing processes inside stars , which are reflected in abundances of mixing-sensitive chemical elements like carbon , nitrogen , and sodium , while \alpha - and neutron-capture element abundances are useful in tracing the Galactic chemical evolution .

Aims : The main aim of this study is a comprehensive chemical analysis of red giant stars in the open cluster IC 4756 , including determinations of ^ { 12 } C / ^ { 13 } C and C/N abundance ratios , and comparisons of the results with theoretical models of stellar and Galactic chemical evolution .

Methods : We used a classical differential model atmosphere method to analyse high-resolution spectra obtained with the FEROS spectrograph on the 2.2 m MPG/ESO Telescope .
The carbon , nitrogen , and oxygen abundances , ^ { 12 } C / ^ { 13 } C ratios , and neutron-capture element abundances were determined using synthetic spectra , and the main atmospheric parameters and abundances of other chemical elements were determined from equivalent widths of spectral lines .

Results : We have determined abundances of 23 chemical elements for 13 evolved stars and ^ { 12 } C / ^ { 13 } C ratios for six stars of IC 4756 .
The mean metallicity of this cluster , as determined from nine definite member stars , is very close to solar – [ Fe/H ] = -0.02 \pm 0.01 .
Abundances of carbon , nitrogen , and sodium exhibit alterations caused by extra-mixing : the mean ^ { 12 } C / ^ { 13 } C ratio is lowered to 19 \pm 1.4 , the C/N ratio is lowered to 0.79 \pm 0.05 , and the mean [ Na/Fe ] value , corrected for deviations from the local thermodynamical equilibrium encountered , is enhanced by 0.14 \pm 0.05 dex .
We compared our results to those by other authors with theoretical models .

Conclusions : Comparison of the \alpha -element results with the theoretical models shows that they follow the thin disc \alpha -element trends .
Being relatively young ( \sim 800 Myr ) , the open cluster IC 4756 displays a moderate enrichment of s -process-dominated chemical elements compared to the Galactic thin disc model and confirms the enrichment of s -process-dominated elements in young open clusters compared to the older ones .
The r -process-dominated element europium abundance agrees with the thin disc abundance .
From the comparison of our results for mixing-sensitive chemical elements and the theoretical models , we can see that the mean values of ^ { 12 } { C } / ^ { 13 } { C } , C/N , and [ Na/Fe ] ratios lie between the model with only the thermohaline extra-mixing included and the model which also includes the rotation-induced mixing .
The rotation was most probably smaller in the investigated IC 4756 stars than 30 % of the critical rotation velocity when they were on the main sequence .