A proper motions study of the globular cluster NGC 3201

With a high value of heliocentric radial velocity, a retrograde orbit, and being suspected to have an extragalactic origin, NGC 3201 is an interesting globular cluster for kinematical studies. Our purpose is to calculate the relative proper motions (PMs) and membership probability for the stars in the wide region of globular cluster NGC 3201. Proper motion based membership probabilities are used to isolate the cluster sample from the field stars. The membership catalogue will help address the question of chemical inhomogeneity in the cluster. Archive CCD data taken with a wide-field imager (WFI) mounted on the ESO 2.2m telescope are reduced using the high-precision astrometric software developed by Anderson et al. for the WFI images. The epoch gap between the two observational runs is $\sim$14.3 years. To standardize the $BVI$ photometry, Stetson's secondary standard stars are used. The CCD data with an epoch gap of $\sim$14.3 years enables us to decontaminate the cluster stars from field stars efficiently. The median precision of PMs is better than $\sim$0.8 mas~yr$^{-1}$ for stars having $V<$18 mag that increases up to $\sim$1.5 mas~yr$^{-1}$ for stars with $18<V<20$ mag. Kinematic membership probabilities are calculated using proper motions for stars brighter than $V\sim$20 mag. An electronic catalogue of positions, relative PMs, $BVI$ magnitudes and membership probabilities in $\sim$19.7$\times$17 arcmin$^2$ region of NGC 3201 is presented. We use our membership catalogue to identify probable cluster members among the known variables and $X$-ray sources in the direction of NGC 3201.