We have investigated the relevant trend of the bolometric correction (BC) at the cool-temperature regime of red giant stars and its possible dependence on stellar metallicity. Our analysis relies on a wide sample of optical-infrared spectroscopic observations, along the 3500A-2.5micron wavelength range, for a grid of 92 red giant stars in five (3 globular + 2 open) Galactic clusters, along the -2.2<[Fe/H]<+0.4 metallicity range. Bolometric magnitudes have been found within an internal accuracy of a few percent. Making use of our new database, we provide a set of fitting functions for the V and K BC vs. Teff and broad-band colors, valid over the interval 3300K<Teff<5000K, especially suited for Red Giants. No evident drift of both BC(V) and BC(K) with [Fe/H] is found. Things may be different, however, for the B-band correction, given a clear (B-V) vs. [Fe/H] correlation in place for our data, with metal-poor stars displaying a bluer (B-V) with respect to the metal-rich sample, for fixed Teff. Our empirical bolometric scale supports the conclusion that (a) BC(K) from the most recent studies are reliable within <0.1 mag over the whole color/temperature range considered in this paper, and (b) the same conclusion apply to BC(V) only for stars warmer than ~3800K. At cooler temperatures the agreement is less general, and MARCS models are the only ones providing a satisfactory match to observations.
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