Red Giant stars in the Large Magellanic Cloud clusters

We present deep J,H,Ks photometry and accurate Color Magnitude Diagrams down to $rm Kapprox 18.5$, for a sample of 13 globular clusters in the Large Magellanic Cloud. This data set combined with the previous sample of 6 clusters published by our group gives the opportunity to study the properties of giant stars in clusters with different ages (ranging from $sim 80~Myr$ up to $3.5~Gyr$). Quantitative estimates of star population ratios (by number and luminosity) in the Asymptotic Giant Branch, the Red Giant Branch and the He-clump, have been obtained and compared with theoretical models in the framework of probing the so-called phase transitions. The AGB contribution to the total luminosity starts to be significant at $approx 200~Myr$ and reaches its maximum at $5-600~Myr$, when the RGB Phase Transition is starting. At $approx 900~Myr$ the full developing of an extended and well populated RGB has been completed. Both the occurrence of the AGB and RGB Phase Transitions are sharp events, lasting a few hundreds $Myr$ only. These empirical results agree very well with the theoretical predictions of simple stellar population models based on canonical tracks and the fuel-consumption approach.