  This is the first of a series of papers devoted to a global study of the
photometric properties of the red stellar sequences in a complete sample of the
Large Magellanic Cloud clusters, by means of near infrared array photometry.
Deep J,H,Ks photometry and accurate Color Magnitude Diagrams down to K=18.5,
i.e. 1.5 mag below the red He-clump, for six intermediate age clusters (namely
NGC1987, NGC2108, NGC2190, NGC2209, NGC2231, NGC2249) are presented. A
quantitative estimate of the population ratios (by number and luminosity)
between Red Giant Branch and He-clump stars for each target cluster is provided
and discussed in the framework of probing the so-called Red Giant Branch phase
transition (RGB Ph-T). By using the Elson & Fall s-parameter as an age
indicator, the observed RGB population shows a sharp enhancement (both in
number and luminosity) at s=36. Obviously, the corresponding absolute age
strictly depends on the details of theoretical models adopted to calibrate the
s-parameter. Curiously, the currently available calibrations of the s-parameter
in term of age based on canonical (by Elson & Fall 1988) and overshooting
(Girardi et al. 1995) models provide ages that well agree within 10%,
suggesting that the full development of the Red Giant Branch occurs at t=700
Myr and be a relatively fast event (delta t=300 Myr). However, the RGB Ph-T
epoch derived from the overshooting calibration of the s-parameter turns out to
be significantly earlier than the epoch provided by the recent evolutionary
tracks by Girardi et al. (2000). A new calibration of the s-parameter based on
high quality Color Magnitude Diagrams and updated models is urged to address
the origin of this discrepancy and finally establish the epoch of the RGB Ph-T.
