By exploiting the exceptional high-resolution capabilities of the near-IR camera GSAOI combined with the multi-conjugate adaptive optics system GeMS at the GEMINI South Telescope, we investigated the structural and physical properties of the heavily obscured globular cluster Liller 1 in the Galactic bulge. We have obtained the deepest and most accurate color-magnitude diagram published so far for this cluster, reaching Ks ~ 19 (below the main sequence turn-off level). We used these data to re-determine the center of gravity of the system, finding that it is located about 2.2 south-east from the literature value. We also built new star density and surface brightness profiles for the cluster, and re-derived its main structural and physical parameters (scale radii, concentration parameter, central mass density, total mass). We find that Liller 1 is significantly less concentrated (concentration parameter c=1.74) and less extended (tidal radius r_t=298 and core radius r_c=5.39) than previously thought. By using these newly determined structural parameters we estimated the mass of Liller 1 M_tot = 2.3 x 10^6 Msun (Mtot = 1.5 x 10^6 Msun for a Kroupa IMF), which is comparable to that of the most massive clusters in the Galaxy (omega Centauri and Terzan 5). Also Liller 1 has the second highest collision rate (after Terzan 5) among all star clusters in the Galaxy, thus confirming that it is an ideal environment for the formation of collisional objects (such as millisecond pulsars).
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