During the X-ray bursts of GS 1826$-$24, "clocked burster", the nuclear reaction flow that surges through the rapid-proton capture process path has to pass through the NiCu cycles before reaching the ZnGa cycles that moderate the further extent of hydrogen burning in the region above germanium and selenium isotopes. The $^{57}$Cu(p,$γ$)$^{58}$Zn reaction located in the NiCu cycles plays an important role in influencing the burst light curves as found by Cyburt et al. (2016). We deduce the $^{57}$Cu(p,$γ$)$^{58}$Zn reaction rate based on the experimentally determined important nuclear structure information, isobaric-multiplet-mass equation, and large-scale shell model calculations. Based on the isobaric-multiplet-mass equation, we propose a possible order of $1^+_1$ and $2^+_3$ dominant resonance states and constrain the resonance energy of the $1^+_2$ state. The latter reduces the contribution of the $1^+_2$ dominant resonance state. The new reaction rate is up to a factor of four lower than the Forstner et al. (2001) rate recommended by JINA REACLIB v2.2 at the temperature regime sensitive to clocked bursts of GS 1826$-$24. Using the simulation from the one-dimensional implicit hydrodynamic code, KEPLER, to model the thermonuclear X-ray bursts of GS 1826$-$24 clocked burster, we find that the new $^{57}$Cu(p,$γ$)$^{58}$Zn coupled with the latest $^{56}$Ni(p,$γ$)$^{57}$Cu and $^{55}$Ni(p,$γ$)$^{56}$Cu reaction rates redistributes the reaction flow in the NiCu cycles and strongly influences the burst ash composition, whereas the $^{59}$Cu(p,$α$)$^{56}$Ni and $^{59}$Cu(p,$γ$)$^{60}$Zn reactions suppress the influence of the $^{57}$Cu(p,$γ$)$^{58}$Zn reaction and diminish the impact of nuclear reaction flow that by-passes the important $^{56}$Ni waiting point induced by the $^{55}$Ni(p,$γ$)$^{56}$Cu reaction on burst light curve.
The Regulated GeAs Cycles with the New $^{63}$Ga(p,$γ$)$^{64}$Ge and $^{64}$Ge(p,$γ$)$^{65}$As Reaction Rates and Their Impact on the GS 1826$-$24 Clocked Bursts and SAX J1808.4$-$3658 Photospheric Radius Expansion Bursts
The Impact of the New $^{65\!}$As(p,$γ$)$^{66\!}$Se Reaction Rate on the Two-Proton Sequential Capture of $^{64}\!$Ge, Weak GeAs Cycles, and Type-I X-Ray Bursts such as the Clocked Burster GS 1826$-$24
Advancement of Photospheric Radius Expansion and Clocked Type-I X-Ray Burst Models with the New $^{22}$Mg$(α,p)^{25}$Al Reaction Rate Determined at Gamow Energy
Return of the Clocked Burster: Exceptionally Short Recurrence Time in GS 1826-238
Hiroshima University（广岛大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先导研究院）；RIKEN Nishina Center（理化学研究所西成中心）；Tokyo University of Science（东京科学大学）；Kyoto University（京都大学）；RIKEN Center for Advanced Photonics (RAP)（理化学研究所先进光子学中心）；Chiba University（千叶大学）；National Changhua University of Education (NCUE)（国立彰化师范大学）；Rikkyo University（立教大学）；Kogakuin University（工学园大学）；The University of Tokyo（东京大学）
Direct measurement of $^{59}$Cu($p$,$α$)$^{56}$Ni precludes a strong NiCu cycle in Type-I X-ray bursts
Astronomy and Physics Department, Saint Mary’s University（圣玛丽大学天文与物理系）；TRIUMF（特里厄姆夫实验室）；Department of Physics and Astronomy, Mississippi State University（密西西比州立大学物理与天文学系）；Department of Physics, University of Notre Dame（圣母大学物理系）；Department of Chemistry, Simon Fraser University（西蒙弗雷泽大学化学系）；Department of Physics, Simon Fraser University（西蒙弗雷泽大学物理系）
