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During type I X-ray bursts, the rapid-proton capture (rp-) process has to pass through the NiCu cycles and ZnGa cycles before reaching the region above germanium and selenium isotopes that hydrogen burning occurs in. According to the sensitivity study by Cyburt et al. (2016), the $^{57}$Cu(p,$\gamma$)$^{58}$Zn reaction located in the NiCu cycles is the fifth important rp-reaction influencing the burst light curves. Nevertheless, Langer et al. (2014) experimentally confirmed some low-lying energy levels of $^{58}$Zn, but the order of $1^+_1$ and $2^+_3$ resonance states that dominate at $0.2\leq T$(GK) $\leq 0.8$ is still not clear. The $1^+_2$ resonance state, which dominates at the XRB sensitive temperature regime $0.8\leq T$(GK) $\leq 2$ was also not detected. We use isobaric-multiplet-mass equation to propose the order of energy levels and resonance states that dominantly contribute to the total reaction rate but is outside the experimental range. Therefore, combine with calculations from large-scale shell model, we deduce the $^{57}$Cu(p,$\gamma$)$^{58}$Zn reaction rate. The new rate is up to a factor of five lower than the Forstner et al. (2001) rate recommended by JINA REACLIBv2.2. With new $^{57}$Cu(p,$\gamma$)$^{58}$Zn reaction rate in 1D implicit hydrodynamics KEPLER code to model the thermonuclear X-ray bursts of GS~1826$-$24 clocked burster, we find that the new rate redistributes the matter flow in the NiCu cycles and reduces the production of $^{58}$Zn, whereas the $^{59}$Cu(p,$\alpha$)$^{56}$Ni and $^{59}$Cu(p,$\gamma$)$^{60}$Zn reactions suppress the influence of the $^{57}$Cu(p,$\gamma$)$^{58}$Zn reaction and strongly diminish the impact of matter flow by-passing the important $^{56}$Ni waiting point induced by the $^{55}$Ni(p,$\gamma$)$^{56}$Cu reaction on burst light curve.
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