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The pressure exerted by the ambient hot X-ray gas on cluster galaxies can lead to the presence of ram pressure stripped (RPS) galaxies, characterized by asymmetric shapes, and, in some cases, tails of blue stars and/or X-ray gas, with increased star formation. We searched for such galaxies in the cluster MS 0451.6-0305 at z~0.5, based on Hubble Space Telescope (HST) imaging covering a region of about 6x6 Mpc^2, an eight magnitude ground-based catalogue with photometric redshifts, and a spectroscopic redshift catalogue. We defined as cluster members a spectroscopic redshift sample of 359 galaxies within 4sigma_v of the mean cluster velocity, and a photometric redshift sample covering the [0.48,0.61] range. We searched for RPS galaxies and tested the error on their classification with a Zooniverse collaboration, and computed the phase space diagram for the spectroscopic sample. We ran the LePhare stellar population synthesis code to analyze and compare the properties of RPS and non-RPS galaxies. We find 56 and 273 RPS candidates in the spectroscopic and photometric redshift samples, respectively, distributed throughout the cluster and tending to avoid high density regions. The phase space diagram gives the percentages of virialized, backsplash, and infall galaxies. RPS galaxy candidates typically show rather high star formation rates, young ages, and relatively low masses. This study confirms that RPS galaxies host, on average, younger stellar populations and strongly form stars when compared with non-RPS counterparts. The fact that RPS candidates with spectroscopic and with photometric redshifts have comparable properties shows that large samples of such objects could be gathered based on multi-band photometry only, a promising result in view of future very large imaging surveys.