(ABRIDGED) The ACS camera on board the Hubble Space Telescope has been used to obtain deep images of the giant elliptical galaxy NGC 3610, a well-established dissipative galaxy merger remnant. These observations supersede previous WFPC2 images which revealed the presence of a population of metal-rich globular clusters (GCs) of intermediate age (~1.5-4 Gyr). We detect a total of 580 GC candidates, 46% more than from the previous WFPC2 images. The new photometry strengthens the significance of the previously found bimodality of the color distribution of GCs. Peak colors in V-I are 0.93 +/-0.01 and 1.09 +/- 0.01 for the blue and red subpopulations, respectively. The luminosity function (LF) of the inner 50% of the metal-rich (`red) population of GCs differs markedly from that of the outer 50%. In particular, the LF of the inner 50% of the red GCs shows a flattening consistent with a turnover that is about 1.0 mag fainter than the turnover of the blue GC LF. This is consistent with predictions of recent models of GC disruption for the age range mentioned above and for metallicities that are consistent with the peak color of the red GCs as predicted by population synthesis models. We determine the specific frequency of GCs in NGC 3610 and find a present-day value of S_N = 1.4 +/- 0.6. We estimate that this value will increase to S_N = 3.8 +/- 1.7 at an age of 10 Gyr, which is consistent with typical S_N values for `normal ellipticals. Our findings constitute further evidence in support of the notion that metal-rich GC populations formed during major mergers involving gas-rich galaxies can evolve dynamically (through disruption processes) into the red, metal-rich GC populations that are ubiquitous in `normal giant ellipticals.
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