Detailed Study of the ⁵⁹Cu(p,α)⁵⁶Ni Reaction and Constraints on Its Astrophysical Reaction Rate

The $^{59}$Cu$(p,\alpha)^{56}$Ni reaction plays an important role in explosive astrophysical scenarios such as Type I X-ray bursts and the $\nu p$-process in neutrino-driven winds following a core-collapse supernova, where it regulates the flow of nucleosynthesis through the NiCu cycle and the synthesis of heavier nuclei. We present a direct measurement of the $^{59}\mathrm{Cu}(p,\alpha)^{56}\mathrm{Ni}$ excitation function from 2.43--5.88~MeV in the center-of-mass frame, performed in inverse kinematics with the high-efficiency MUSIC active-target detector at FRIB. The angle- and energy-integrated cross sections extend direct measurements to lower energies than previously reported and remove the angular-integration model dependence of earlier work. To extrapolate the rate to astrophysical energies, we constrain the statistical-model description through a systematic optimization of the DEM-3 $\alpha$-optical model potential geometry, and quantify the model-selection uncertainty with a Bayesian model averaging analysis over 96 TALYS combinations. The resulting stellar rate carries a temperature-dependent uncertainty factor of 1.26--1.63 over $T_9 = 0.2$--10 and is systematically lower than the REACLIB evaluation, remaining below the competing $(p,\gamma)$ rate for $T_9 \lesssim 3.94$. These results substantially weaken the inferred NiCu cycle strength and establish the $^{59}$Cu$(p,\gamma)^{60}$Zn rate as the dominant remaining uncertainty.