Nuclear reactions of interest for astrophysics and applications often rely on statistical model calculations for nuclear reaction rates, particularly for nuclei far from $beta$-stability. However, statistical model parameters are often poorly constrained, where experimental constraints are particularly sparse for exotic nuclides. For example, our understanding of the breakout from the NiCu cycle in the astrophysical rp-process is currently limited by uncertainties in the statistical properties of the proton-rich nucleus $^{60}$Zn. We have determined the nuclear level density of $^{60}$Zn using neutron evaporation spectra from $^{58}$Ni($^3$He, n) measured at the Edwards Accelerator Laboratory. We compare our results to a number of theoretical predictions, including phenomenological, microscopic, and shell model based approaches. Notably, we find the $^{60}$Zn level density is somewhat lower than expected for excitation energies populated in the $^{59}$Cu(p,$gamma$)$^{60}$Zn reaction under rp-process conditions. This includes a level density plateau from roughly 5-6 MeV excitation energy, which is counter to the usual expectation of exponential growth and all theoretical predictions that we explore. A determination of the spin-distribution at the relevant excitation energies in $^{60}$Zn is needed to confirm that the Hauser-Feshbach formalism is appropriate for the $^{59}$Cu(p,$gamma$)$^{60}$Zn reaction rate at X-ray burst temperatures.
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