Binary stars can inflate the observed velocity dispersion of stars in dark matter dominated systems such as ultra-faint dwarf galaxies (UFDs). However, the population of binaries in UFDs is poorly constrained by observations, with preferred binary fractions for individual galaxies ranging from a few percent to nearly unity. Searching for wide binaries through nearest neighbor (NN) statistics (or the two-point correlation function) has been suggested in the literature, and we apply this method for the first time to detect wide binaries in a UFD. By analyzing the positions of stars in Reticulum~II (Ret~II) from Hubble Space Telescope images, we search for angularly resolved wide binaries in Ret~II. We find that the distribution of their NN distances shows an enhancement at projected separations of $lesssim8$ arc seconds relative to a model containing no binaries. We show that such an enhancement can be explained by a binary fraction of $f_bapprox0.07^{+0.04}_{-0.03}$, with modest evidence for a smaller mean separation than is seen in the solar neighborhood. We also use the observed magnitude distribution of stars in Ret~II to constrain the initial mass function over the mass range $0.34-0.78~M_{odot}$, finding that a shallow power-law slope of $alpha = 1.10^{+0.30}_{-0.09}$ matches the data.
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