We present Johnson BV, and Kron-Cousins I-band time series data collected over three consecutive nights in a region of 13 arcmin^2 centered on the Galactic Globular Cluster (GGC) NGC3201. The time sampling of current CCD data allowed us to derive accurate light curves, and in turn mean magnitudes and colors for a sample of 53 RR Lyrae. To overcome the thorny problem of differential reddening affecting this cluster, we derived new empirical relations connecting the intrinsic (B-V) and (V-I) colors of fundamental ($RR_{ab}$) RR Lyrae to the luminosity amplitude, the metallicity, and the pulsation period. The key features of these relations are the following: i) they rely on stellar parameters which are not affected by reddening; ii) they supply accurate estimates of intrinsic colors across the fundamental instability strip and cover a wide metallicity range; iii) they were derived by neglecting the RR Lyrae that are affected by amplitude modulation. Moreover, the zero-point of the E(B-V) reddening scale was empirically checked using the large sample of RR Lyrae in M3 (Corwin & Carney 2001), a GGC affected by a vanishing reddening. According to these relations we estimated individual reddenings for RR Lyrae in our sample and the main results we found are the following: i) the mean cluster reddening based on E(B-V) color excesses is <E(B-V)>=0.30pm0.03. iii) According to current individual E(B-V) and E(V-I) reddenings and theoretical predictions for Horizontal-Branch stars, we found that the true distance modulus for this cluster is 13.32pm0.06 mag. iv) The comparison between present luminosity amplitudes and estimates available in the literature discloses that approximately 30% of fundamental RR Lyrae are affected by amplitude modulation (Blazhko effect).
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