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We performed a detailed study of the evolution of the luminosity ofHe-ignition stage and of the red giant branch bump luminosity during the redgiant branch phase transition for various metallicities. To this purpose wecalculated a grid of stellar models that sample the mass range of thetransition with a fine mass step equal to ${\rm 0.01M_\odot}$. We find that fora stellar population with a given initial chemical composition, there is acritical age (of 1.1-1.2~Gyr) around which a decrease in age of just 20-30million years causes a drastic drop in the red giant branch tip brightness. Wealso find a narrow age range (a few $10^7$ yr) around the transition,characterized by the luminosity of the red giant branch bump being brighterthan the luminosity of He ignition. We discuss a possible link between thisoccurrence and observations of Li-rich core He-burning stars.

The red giant branch phase transition: Implications for the RGB luminosity function bump and detections of Li-rich red clump stars