  We suggest to use the shape of the Red Giant Branch (RGB) Bump in metal-rich
globular clusters as a diagnostic of partial mixing processes between the base
of the convective envelope and the H-burning shell. The Bump located along the
differential luminosity function of cluster RGB stars is a key observable to
constrain the H-profile inside these structures. In fact, standard evolutionary
models that account for complete mixing in the convective unstable layers and
radiative equilibrium in the innermost regions do predict that the first
dredge-up lefts over a very sharp H-discontinuity at the bottom of the
convective region. Interestingly enough we found that both atomic diffusion and
a moderate convective overshooting at the base of the convective region
marginally affects the shape of the RGB Bump in the differential Luminosity
Function (LF). As a consequence, we performed several numerical experiments to
estimate whether plausible assumptions concerning the smoothing of the
H-discontinuity, due to the possible occurrence of extra-mixing below the
convective boundary, affects the shape of the RGB Bump. We found that the
difference between the shape of RGB Bump predicted by standard and by smoothed
models can be detected if the H-discontinuity is smoothed over an envelope
region whose thickness is equal or larger than 0.5 pressure scale heights.
Finally, we briefly discuss the comparison between theoretical predictions and
empirical data in metal-rich, reddening free Galactic Globular Clusters (GGCs)
to constrain the sharpness of the H-profile inside RGB stars.
