We measure redshifts for 67 galaxies in the field of six cluster candidates from the ESO Imaging Survey (EIS). The cluster candidates are selected in the EIS patches C and D among those with estimated mean redshifts 0.5 <= z <= 0.7. The observations were made with EFOSC2 at the 3.6m ESO telescope. In the six candidate cluster fields, we identify 19 possible sets of 2 to 7 galaxies in redshift space. In order to establish which of the 19 sets are likely to correspond to real dense systems we compare our counts with those expected from a uniform distribution of galaxies with given luminosity function. In order to take into account the effect of the Large Scale Structure, we modulate the probability computed from the luminosity function with random samplings of the Canada-France Redshift Survey. We find that four out of six candidate EIS clusters are likely to correspond to real systems in redshift space (> 95% confidence level). Two of these systems have mean redshift in agreement with the redshift estimate given by the matched filter algorithm (Δz = ± 0.1). The other two systems have significantly lower redshifts. We discuss the implications of our results in the context of our ongoing research projects aimed at defining high-redshift optically-selected cluster samples. Based on observations collected at the European Southern Observatory (La Silla, Chile), Proposal ID: 62.O-0601
