The ACS and NICMOS have been used to obtain new HST images of NGC 4038/4039 (The Antennae). These new observations allow us to better differentiate compact star clusters from individual stars, based on both size and color. We use this ability to extend the cluster luminosity function by approximately two magnitudes over our previous WFPC2 results, and find that it continues as a single power law, dN/dL propto L^alpha with alpha=-2.13+/-0.07, down to the observational limit of Mv~-7. Similarly, the mass function is a single power law dN/dM propto M^beta with beta=-2.10+/-0.20 for clusters with ages t<3x10^8 yr, corresponding to lower mass limits that range from 10^4 to 10^5 Msun, depending on the age range of the subsample. Hence the power law indices for the luminosity and mass functions are essentially the same. The luminosity function for intermediate-age clusters (i.e., ~100-300 Myr old objects found in the loops, tails, and outer areas) shows no bend or turnover down to Mv~-6, consistent with relaxation-driven cluster disruption models which predict the turnover should not be observed until Mv~-4. An analysis of individual ~0.5-kpc sized areas over diverse environments shows good agreement between values of alpha and beta, similar to the results for the total population of clusters in the system. Several of the areas studied show evidence for age gradients, with somewhat older clusters appearing to have triggered the formation of younger clusters. The area around Knot B is a particularly interesting example, with an ~10-50 Myr old cluster of estimated mass ~10^6 Msun having apparently triggered the formation of several younger, more massive (up to 5x10^6 Msun) clusters along a dust lane.
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