We have searched for unresolved X-ray sources in the vicinity of two rich clusters of galaxies: Abell 1995 (A1995) and MS 0451.6-0305 (MS0451), using the Chandra X-ray observatory. We detected significantly more unresolved sources around A1995 than expected based on the number of X-ray sources to the same flux limit detected in deep CHANDRA observations of blank fields. Previous studies have also found excess X-ray sources in the vicinity of several nearby clusters of galaxies using ROSAT$ $, and recently in more distant ($z ~ 0.5$) clusters (RXJ0030 and 3C295) using Chandra. In contrast, we detect only 14 unresolved X-ray sources near MS0451, which is consistent with the number expected from a cluster-free background. We determine the luminosity functions of the extra sources under the assumption that they are at the distance of their respective clusters. The characteristic luminosity of the extra sources around A1995 must be an order of magnitude fainter than that of the extra sources around RXJ0030 and 3C295. The apparent lack of extra sources around MS0451 is consistent with its greater distance and the same characteristic luminosity as the A1995 sources. Hardness ratios suggest that, on average, the extra sources in A1995 may have harder spectra than those of RXJ0030 and 3C295. These results indicate that different classes of objects may dominate in different clusters, perhaps depending on the formation history and/or dynamical state of the accompanying cluster.
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