Context: Eruption of a coronal mass ejection (CME) drags and ``opens'' the coronal magnetic field, presumably leading to the formation of a large-scale current sheet and field relaxation by magnetic reconnection. Aims: We analyze the physical characteristics of ray-like coronal features formed in the aftermath of CMEs, to confirm whether interpreting this phenomenon in terms of a reconnecting current sheet is consistent with observations. Methods: The study focuses on measurements of the ray width, density excess, and coronal velocity field as a function of the radial distance. Results: The morphology of the rays implies that they are produced by Petschek-like reconnection in the large-scale current sheet formed in the wake of CME. The hypothesis is supported by the flow pattern, often showing outflows along the ray, and sometimes also inflows into the ray. The inferred inflow velocities range from 3 to 30 km s-1, and are consistent with the narrow opening-angle of rays, which add up to a few degrees. The density of rays is an order of magnitude higher than in the ambient corona. The density-excess measurements are compared with the results of the analytical model in which the Petschek-like reconnection geometry is applied to the vertical current sheet, taking into account the decrease in the external coronal density and magnetic field with height. Conclusions: The model results are consistent with the observations, revealing that the main cause of the density excess in rays is a transport of the dense plasma from lower to higher heights by the reconnection outflow.