The Impact of the New $^{65\!}$As(p,$\gamma$)$^{66\!}$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.

We deduce $^{65}$As(p,$\gamma$)$^{66}$Se reaction rates based on a set of proton thresholds of $^{66}$Se, $S_\mathrm{p}$($^{66}$Se), estimated from the experimental mirror nuclear masses, theoretical mirror displacement energies, and full $pf$-model space shell-model calculation. The self-consistent relativistic Hartree-Bogoliubov theory is employed to obtain the mirror displacement energies with much reduced uncertainty, and thus reducing the proton-threshold uncertainty up to 161 keV compared to the AME2020 evaluation. The influence of this set of $S_\mathrm{p}$($^{66}$Se) on the $^{65}$As(p,$\gamma$)$^{66}$Se forward and reverse reaction rates is presented. Using the one-dimensional multi-zone implicit hydrodynamic code, KEPLER, that closely reproduces the observed GS 1826$-$24 clocked bursts, the present $^{65}$As(p,$\gamma$)$^{66}$Se forward and reverse reaction rates based on a selected $S_\mathrm{p}$($^{66}$Se) = 2.469$\pm$0.054 MeV, and the latest $^{22}$Mg($\alpha$,p)$^{25}$Al, $^{56}$Ni(p,$\gamma$)$^{57}$Cu(p,$\gamma$)$^{58}$Zn, $^{55}$Ni(p,$\gamma$)$^{56}$Cu, and $^{64}$Ge(p,$\gamma$)$^{65}$As reaction rates, we find that though the GeAs cycles is weakly established in the rapid-proton capture process path during the clocked X-ray bursts of GS 1826$-$24 burster, the $^{65}$As(p,$\gamma$)$^{66}$Se reaction still strongly characterizes the burst tail end due to the two-proton sequential capture on $^{64}$Ge, not found by Cyburt et al. (2016) sensitivity study. The $^{65}$As(p,$\gamma$)$^{66}$Se reaction influences the abundances of nuclei $A$ = 64, 68, 72, 76, and 80 up to a factor of 1.4. The inclusion of the updated $^{22}$Mg($\alpha$,p)$^{25}$Al reaction rate influences the production of $^{12}$C up to a factor of 4.5 that could be the main fuel for Type-I X-ray superburst. The status of $^{64}$Ge waiting point and the influence of other $^{66}$Se are also discussed.