  AIMS: After the first dredge-up, low-mass Red Giant Branch (RGB) stars
experience an extra-mixing episode that strongly affects the chemical
abundances on their surface. This mixing occurs at the bump in the luminosity
function. In this Letter we describe the efficiency of the extra-mixing in RGB
stars found in very metal-poor globular clusters (GC) METHODS: The VLT/ISAAC
spectra of twenty stars located between the bump and the tip of the RGB in four
GCs with metallicities between [Fe/H]=-1.2 and -2.5dex were collected. The
carbon isotopic ratios on their surface were derived from the second overtone
bands of the CO molecule at 2.3mic with the spectral synthesis method. RESULTS:
It is found that the carbon isotopic ratios of very metal-poor GC stars always
reach the equilibrium value of the CNO cycle almost immediately above the bump
in the luminosity function. No additional mixing episode at brighter
luminosities and no variations with the clusters' metallicity were detected.
The extra-mixing is therefore found to be very efficient in metal-poor low-mass
RGB stars, in very good agreement with theoretical expectations.
